The surface area is 72 square inches.
To find the surface area of a square pyramid, we need to calculate the area of the base and the four triangular faces.
Given that the base is 4 inches wide, the area of the square base is:
Base area = side² = 4² = 16 square inches.
The slant height is 7 inches. To find the area of one triangular face, we use:
Triangle area = (base * slant height) / 2
Each triangle has the same base length as the square base, which is 4 inches. Therefore, the area of one triangular face is:
Triangle area = (4 * 7) / 2 = 14 square inches.
Since there are four triangular faces, their total area is:
4 * Triangle area = 4 * 14 = 56 square inches.
Finally, add the base area and the total area of the triangular faces to get the surface area:
Surface area = Base area + Total triangular faces area = 16 + 56 = 72 square inches.
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A group of students collected old newspapers for a recycling project. The data shows the mass, in kilograms, of old newspapers collected by each student.
23, 35, 87, 64, 101, 90, 45, 76, 105, 60, 55
98, 122, 49, 15, 57, 75, 120, 56, 88, 45, 100.
What percent of students collected between 49 kilograms and 98 kilograms of newspapers? Explain how you got to your solution
Therefore, approximately 45.45% of students collected between 49 and 98 kilograms of newspapers.
Total number of students is 22.
To find the percentage of students who collected between 49 and 98 kilograms of newspapers, we first need to count the number of students who collected within this range. From the given data, we can see that the following students collected between 49 and 98 kilograms of newspapers
87, 64, 90, 76, 60, 55, 57, 75, 56, 88
Percentage of students = (number of students in range / total number of students) x 100
= (10 / 22) x 100
= 45.45%
Therefore, approximately 45.45% of students collected between 49 and 98 kilograms of newspapers.
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Fred bought 5 liters of liquid laundry detergent, 3,250 milliliters of fabric softener, and 2. 8 liters of bleach. Select true or false for each statement. Fred bought 45 milliliters more fabric softener than bleach. ?
Fred bought 2. 45 liters more laundry detergent than bleach. ?
Fred bought 450 milliliters more fabric softener than bleach. ?
Fred bought 220 milliliters more laundry detergent than bleach. ?
Fred bought 0. 45 liters more fabric softener than bleach. ?
Fred purchased more 2. 45 liters of laundry detergent than bleach is false statement, Fred took 450 milliliters more fabric softener than bleach is false, Fred placed 220 milliliters more laundry detergent than bleach is true, Fred has taken 0. 45 liters more fabric softener than bleach is false.
Fred in total bought 5 liters of liquid laundry detergent which is equal to 5000 milliliters. Then he bought 3,250 milliliters of fabric softener and 2.8 liters of bleach which is equal to 2800 milliliters.
Fred purchased 45 milliliters more fabric softener than bleach. This statement is false because Fred bought 250 milliliters less fabric softener than bleach.
Fred bought 2.45 liters more laundry detergent than bleach. This statement is false because Fred bought 2.2 liters more laundry detergent than bleach.
Fred has taken 450 milliliters more fabric softener than bleach. This statement is false because Fred bought 250 milliliters less fabric softener than bleach.
Fred on the event of taking 220 milliliters more laundry detergent than bleach is considered a true statement because Fred bought 2200 milliliters more laundry detergent than bleach.
Fred on the event of taking 0.45 liters more fabric softener than bleach is considered a false statement due to the fact that Fred bought 0.25 liters less fabric softener than bleach.
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The harmonic series: 1+1/2+1/3+1/4+.
diverges, but when its terms are squared the resulting series converges. T or F
The statement "The harmonic series: 1+1/2+1/3+1/4+... diverges, but when its terms are squared the resulting series converges." is True.
The harmonic series is defined as the sum of the reciprocals of the natural numbers: Σ(1/n) for n = 1 to ∞. This series is known to diverge, meaning that its sum tends to infinity as more terms are added.
However, when the terms of the harmonic series are squared, we get a new series called the p-series, with p=2: Σ(1/n^2) for n = 1 to ∞. The p-series converges if p > 1, which is true for p=2. Thus, the series Σ(1/n^2) converges to a finite sum.
In conclusion, the given statement is true, as the harmonic series diverges, but its squared terms result in a convergent series.
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A machine has an initial cost of $40,000 and operating costs of $3500 each year. Its salvage value decreases by $4,000 each year. The machine is now 4 years old.
Assuming an effective annual interest rate of 12%, what is the cost of owning and operating the machine for one more year.
The cost of owning and operating the machine for one more year is approximately $11,160.71.
To calculate the cost of owning and operating the machine for one more year, we need to consider both the operating costs and the decrease in salvage value.
The operating costs for one more year will be $3,500.
To calculate the decrease in salvage value, we need to know the salvage value of the machine after 4 years of use. If the salvage value decreased by $4,000 each year, then after 4 years the salvage value will have decreased by $16,000. Therefore, the salvage value of the machine after 4 years is:
Salvage value after 4 years = Initial salvage value - Total decrease in salvage value
Salvage value after 4 years = $40,000 - $16,000
Salvage value after 4 years = $24,000
To calculate the cost of owning and operating the machine for one more year, we need to consider the difference between the salvage value at the end of the additional year and the salvage value after 4 years. Assuming a straight-line depreciation model, the salvage value of the machine after one more year will be:
Salvage value after one more year = Salvage value after 4 years - (4 x $4,000)
Salvage value after one more year = $24,000 - $16,000
Salvage value after one more year = $8,000
To calculate the cost of owning and operating the machine for one more year, we need to calculate the present value of the difference between the salvage values, plus the operating costs for one more year. Assuming an effective annual interest rate of 12%, the present value can be calculated using the formula:
PV = FV / (1 + r[tex])^n[/tex]
where PV is the present value, FV is the future value, r is the effective annual interest rate, and n is the number of years.
The future value of the salvage value difference plus the operating costs for one more year is:
FV = Salvage value after one more year - Salvage value after 4 years + Operating costs for one more year
FV = $8,000 - $24,000 + $3,500
FV = -$12,500
(Note that the negative value indicates a cost.)
Plugging in the values, we get:
PV = -$12,500 / (1 + 0.12[tex])^1[/tex]
PV = -$11,160.71
Therefore, the cost of owning and operating the machine for one more year is approximately $11,160.71.
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a(a - b)+b(a - b) + (a - b)²
Answer:
a^4 - b^4
Step-by-step explanation:
a(a - b) + b(a - b) + (a - b)^2 --> Given
a^2 - ab + b(a - b) + (a - b)^2 --> Distributive Property
a^2 - ab + ba - b^2 + (a - b)^2 --> Distributive Property
a^2 - ab + ba - b^2 + a^2 - b^2 --> Distributive Property
a^4 - ab + ba - b^2 - b^2 --> Combine Like Terms
a^4 + 0 - b^2 - b^2 --> Combine Like Terms (a * b = b * a)
a^4 - b^4 --> Combine Like Terms
A triangle has vertices at (–4, 0), (2, 8), and (8, 0). What are the coordinates of the centroid, circumcenter, and orthocenter? If needed, write mixed numbers with a single space between the whole number and the fractional parts.
The centroid of the given triangle (2, 8/3), the circumcenter of the triangle is (0,2), the orthocenter of the triangle is (2,8).
What is centroid?
In geometry, the centroid of a triangle is the point where the three medians of the triangle intersect.
To find the centroid of a triangle with vertices at (x1,y1), (x2,y2), and (x3,y3), we can use the formula:
(x1 + x2 + x3)/3 , (y1 + y2 + y3)/3
Using this formula, we get the centroid of the given triangle as:
((-4 + 2 + 8)/3 , (0 + 8 + 0)/3) = (2, 8/3)
To find the circumcenter, we first need to find the equations of the perpendicular bisectors of any two sides of the triangle. Let's choose the sides formed by the points (-4,0) and (2,8), and (2,8) and (8,0).
The midpoint of the first side is ((-4+2)/2, (0+8)/2) = (-1,4), and the slope of the line passing through (-4,0) and (2,8) is (8-0)/(2-(-4)) = 8/6 = 4/3. So the equation of the perpendicular bisector of this side is y-4 = -(3/4)(x+1), or 3x + 4y = 8.
Similarly, the midpoint of the second side is ((2+8)/2, (8+0)/2) = (5,4), and the slope of the line passing through (2,8) and (8,0) is (0-8)/(8-2) = -8/6 = -4/3. So the equation of the perpendicular bisector of this side is y-4 = (3/4)(x-5), or 3x - 4y = -8.
The intersection of these two lines gives us the circumcenter of the triangle. Solving the system of equations:
3x + 4y = 8
3x - 4y = -8
We get x = 0, y = 2. So the circumcenter of the triangle is (0,2).
To find the orthocenter, we first need to find the equations of the altitudes from any two vertices of the triangle. Let's choose the vertices (2,8) and (8,0).
The altitude from (2,8) is perpendicular to the side formed by the points (-4,0) and (8,0), so its slope is 0. Therefore, its equation is y = 8.
The altitude from (8,0) is perpendicular to the side formed by the points (-4,0) and (2,8), so its slope is the negative reciprocal of the slope of that side, which is -4/3. Using the point-slope form, we get the equation:
y - 0 = (-4/3)(x - 8)
y = -4x/3 + 32/3
To find the intersection of these two lines, we can substitute y = 8 into the second equation:
8 = -4x/3 + 32/3
-8/3 = -4x/3
x = 2
Substituting x = 2 into either equation gives us y = 8, so the orthocenter of the triangle is (2,8).
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A person places $81200 in an investment account earning an annual rate of 3. 6%,
compounded continuously. Using the formula V = Pent, where Vis the value of the
account in tyears, P is the principal initially invested, e is the base of a natural
logarithm, and r is the rate of interest, determine the amount of money, to the
nearest cent, in the account after 13 years.
If a person places $81200 in an investment account earning an annual rate of 3. 6%, the amount of money in the account after 13 years is approximately $125689.60 to the nearest cent.
To solve this problem using the formula V = Pent, we need to plug in the given values.
P = $81200 (the principal initially invested)
r = 0.036 (the annual interest rate, expressed as a decimal)
t = 13 years
Using the formula V = Pent, we get:
V = $81200e^(0.036*13)
Using a calculator, we can evaluate e^(0.036*13) to be approximately 1.5498.
So V = $81200*1.5498 = $125689.60
Therefore, the amount of money in the account after 13 years is approximately $125689.60 to the nearest cent.
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If f(x) = x - 7, then what is ƒ (8)?
Step-by-step explanation:
we use a function as a kind of recipe or template for an actual calculation (or actual "ingredients").
as long as we don't handle the actual food items or actual numbers, it all stays theoretical. variables have no actual value and represent every possible case with every possible value.
but as soon as we get an actual unit value (like 8 in our case), we can put it in place of the variables (that are really nothing else but placeholders for actual values) and simply caucuses the result.
so,
when the question asks what is f(8), it really means what is the result when x = 8.
therefore,
f(8) = 8 - 7 = 1
that's it. that is the whole thing. no mystery, magic or genius strikes necessary.
Answer:
[tex] \sf \: f(8) = 1[/tex]
Step-by-step explanation:
Given function,
→ f(x) = x - 7
Now we have to,
→ Find the required value of f(8).
We have to use,
→ x = 8
Then the value of f(8) will be,
→ f(x) = x - 7
→ f(8) = 8 - 7
→ [ f(8) = 1 ]
Hence, the value of f(8) is 1.
A business with two locations buys seven large delivery vans and five small del...
<
21 of 21
next >
x
a business with two locations buys different sized delivery
vans (small vans - x and large vans - y).
location a receives five small vans and two large vans for
a total cost of $72,500. location b receives two small
vans and six large vans for a total cost of $107,000.
what is the cost of each type of van?
cost of small vans (x)
cost of large vans (y)
After solving the cost function, the cost of each small van is $8,500 and the cost of each large van is $15,000.
Let's use the variables x and y to represent the cost of a small van and a large van, respectively.
From the information given, we can set up a system of two equations:
5x + 2y = 72500
2x + 6y = 107000
We can solve for x and y by using any method of linear equations, such as substitution or elimination. Here, we'll use elimination:
Multiplying the first equation by 3 and the second equation by -1, we get:
15x + 6y = 217500
-2x - 6y = -107000
Adding these two equations, we eliminate the y variable:
13x = 110500
Dividing both sides by 13, we get:
x = 8500
Now we can use this value to find y:
5x + 2y = 72500
5(8500) + 2y = 72500
42500 + 2y = 72500
2y = 30000
y = 15000
Therefore, the cost of each small van is $8,500 and the cost of each large van is $15,000.
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Tammy knits blankets and scarves. On the first day of a craft fair, she sells 2 blankets and 5 scarves for $104. On the second day of the craft fair, she sells 3 blankets and 4 scarves for $128. How much does 1 blanket cost?
The cost of one blanket after calculations sums up as $32.
Let b be the cost of one blanket and s be the cost of one scarf in dollars. We can set up a system of equations based on the information given:
2b + 5s = 104
3b + 4s = 128
We want to solve for the cost of one blanket, so we'll solve for b in terms of s. We can start by multiplying the first equation by 3 and the second equation by 2 to create a system of equations where the coefficients of b will cancel each other out when we subtract the two equations:
6b + 15s = 312
6b + 8s = 256
Subtracting the second equation from the first, we get:
7s = 56
Dividing both sides by 7, we get:
s = 8
Now we can substitute s = 8 into either of the original equations to solve for b:
2b + 5(8) = 104
2b + 40 = 104
2b = 64
b = 32
Therefore, one blanket costs $32.
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You want to know the approximate height of a tall oak tree. You place a mirror on the ground and stand where you can see the top of the tree in the mirror. How tall is the tree? The mirror is 24 feet from the base of the tree. You are 36 inches from the mirror and your eyes are 5 feet above the ground. Round your answer to the nearest tenth
The approximate height of the tall oak tree is 60.0 feet.
To find the height of the tree, follow these steps:
1. Convert the distance between you and the mirror from inches to feet: 36 inches = 3 feet.
2. Create a proportion using similar triangles, where the height of the tree (h) divided by the distance from the tree to the mirror (24 feet) equals your eye height (5 feet) divided by the distance from your eyes to the mirror (3 feet).
3. Set up the proportion: h / 24 = 5 / 3.
4. Solve for h: h = (5 / 3) * 24.
5. Calculate h: h = 40 feet (height of tree above your eye level).
6. Add your eye height (5 feet) to the height of the tree above your eye level: 40 + 5 = 60 feet.
7. Round the answer to the nearest tenth: 60.0 feet.
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What is the probability that the drug will wear off between 200 and 220 minutes?
P(200
The probability that the drug will wear off between 200 and 220 minutes is 0.4.
To calculate the probability that the drug will wear off between 200 and 220 minutes, we need to know the cumulative distribution function (CDF) of the drug's effect duration. Let's say the CDF is denoted by F(t), where t is the time in minutes.
Then, the probability that the drug will wear off between 200 and 220 minutes is given by:
P(200 < T < 220) = F(220) - F(200)
This is because the probability of the drug wearing off between two specific times is equal to the difference between the CDF values at those times.
For example, if F(200) = 0.2 and F(220) = 0.6, then:
P(200 < T < 220) = 0.6 - 0.2 = 0.4
Therefore, the probability that the drug will wear off between 200 and 220 minutes is 0.4.
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When a figure is translated on the coordinate plane you should add or subtract x and y? Is this statement true or false?
Answer: True
Step-by-step explanation:
What is the answer?
What is the gradient of the blue line?
Step-by-step explanation:
the gradient = the slope = the incline = ...
many different names for the same thing.
however you call it, it is the ratio
y coordinate change / x coordinate change
whet going from one point on the line to another.
for questions like this we should look for points with integer coordinates (going through a vertex of the coordinate grid squares).
I see for example right at the left beginning (0, 1).
the next one is then (4, 2).
when going from (0, 1) to (4, 2) :
x changes by +4 (from 0 to 4).
y changes by +1 (from 1 to 2).
so, the slope or gradient is
+1/+4 = 1/4
Let f be a differentiable function such that f (2) = 4, f(4) = 6, f'(2) = -4, and f'(6) = -3. f 6 . The function g is differentiable and g(x) = f-1(x) for all x. What is the value of g'(4) =
The value of g'(4) is -1/3 if f is a differential function such that f (2) = 4, f(4) = 6, f'(2) = -4, and f'(6) = -3.
First, let's use the information given to find the equation of the tangent line to f at x=2. We know that f(2) = 4 and f'(2) = -4, so the equation of the tangent line at x=2 is
y - 4 = -4(x - 2)
Simplifying, we get
y = -4x + 12
Now let's use the fact that g(x) = f-1(x) for all x. This means that g(f(x)) = x for all x. We want to find g'(4), which is the derivative of g at x=4.
Using the chain rule, we have
g'(4) = [g(f(4))]'
Since f(4) = 6 and g(f(4)) = g(6) (since g(x) = f-1(x)), we can rewrite this as
g'(4) = [g(6)]'
Now we can use the fact that g(x) = f-1(x) to rewrite g(6) as f-1(6)
g'(4) = [f-1(6)]'
Now we need to find the derivative of f-1(x) with respect to x. To do this, we can use the fact that f(f-1(x)) = x for all x. Differentiating both sides with respect to x using the chain rule, we get
f'(f-1(x)) * (f-1)'(x) = 1
Solving for (f-1)'(x), we get
(f-1)'(x) = 1 / f'(f-1(x))
Now we can plug in x=6 and use the information given to find f'(f-1(6)). Since f(4) = 6, we know that f-1(6) = 4. Therefore
f'(f-1(6)) = f'(4)
Using the tangent line equation we found earlier, we know that f(2) = 4 and f'(2) = -4. Therefore, the slope of the line connecting (2,4) and (4,6) is
(6 - 4) / (4 - 2) = 1
Since the line connecting (2,4) and (4,6) is the tangent line to f at x=2, we know that this slope is equal to f'(2). Therefore
f'(4) = f'(f-1(6)) = f'(4)
Now we can plug in x=6 and f'(4) into our expression for (f-1)'(x)
(f-1)'(6) = 1 / f'(4)
Substituting this into our expression for g'(4), we get
g'(4) = [f-1(6)]' = (f-1)'(6) = 1 / f'(4)
Plugging in f'(4) = f'(f-1(6)) = f'(4), we get
g'(4) = 1 / f'(4) = 1 / (-3) = -1/3
Therefore, g'(4) = -1/3.
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Gross Monthly Income: Jackson works for a pipe line company and is paid $18. 50 per hour. Although he will have overtime, it is not guaranteed when or where, so Jackson will only build a budget on 40 hours per week. What is Jackson’s gross monthly income for 40 hours per week? Type in the correct dollar amount to the nearest cent. Do not include the dollar sign or letters.
A. Gross Annual Income: $
B. Gross Monthly Income: $
To find Jackson's gross monthly income for 40 hours per week, follow these steps:
1. Calculate his weekly income: Multiply his hourly wage ($18.50) by the number of hours he works each week (40 hours).
2. Calculate his monthly income: Multiply his weekly income by the number of weeks in a month (4 weeks).
A. Gross Annual Income: To find this, multiply his monthly income by 12 (the number of months in a year).
B. Gross Monthly Income: This is the answer we need to find.
Step-by-step calculations:
1. Weekly income = $18.50 * 40 hours = $740
2. Monthly income = $740 * 4 weeks = $2,960
A. Gross Annual Income: $2,960 * 12 = $35,520
B. Gross Monthly Income: $2,960
The answer:
A. Gross Annual Income: $35,520
B. Gross Monthly Income: $2,960
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A helicopter takes off from the roof of a building and travels at 100 mph on a bearing of 558°e. the flight takes 3. 8 hr. to the nearest mile, how far south and
how far east has the helicopter traveled?
can someone pls help me
The helicopter traveled approximately 175.5 miles east and 299.1 miles south.
How to find the helicopter traveled?Let's say the building is located at point A and the helicopter travels to point B. We know that the bearing of B from A is 558°e, which means the angle formed by the line AB and the east direction is 558°.
Next, we can use trigonometry to find the horizontal and vertical components of the distance traveled. Let x be the horizontal distance (in miles) traveled by the helicopter and y be the vertical distance (in miles) traveled. We can then use the following equations:
cos(558°) = x / d
sin(558°) = y / d
where d is the total distance traveled (in miles). We can also use the formula:
d = r * t
where r is the speed of the helicopter (100 mph) and t is the time taken for the flight (3.8 hours). Substituting this into the first two equations, we get:
x = d * cos(558°)
y = d * sin(558°)
d = r * t = 100 * 3.8 = 380 miles (rounded to the nearest mile)
Substituting the values of d and the angle into the equations for x and y, we get:
x = 380 * cos(558°) ≈ -175.5 miles
y = 380 * sin(558°) ≈ 299.1 miles
Note that the negative sign for x indicates that the helicopter traveled west, not east. We can take the absolute value of x to get the distance traveled east:
|x| ≈ 175.5 miles
Therefore, the helicopter traveled approximately 175.5 miles east and 299.1 miles south.
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The point k lies on the segment JL. Find the coordinates of k so that the ratios of JK to KL is 3 to 4
After considering all the given data we conclude that the coordinates of k so that the ratios of JK to KL is 3 to 4 is (-16x₁x₂-16y₁y₂)
The two values of X and Y are the coordinates of K. Let us assume that the coordinates of points J and L are (x₁, y₁) and (x₂, y₂) respectively.
Then, the coordinates of point K can be placed as (x, y), here x and y are unknowns that we need to find.
Now, we know that the ratio of JK to KL is 3:4. This means that:
JK/KL = 3/4
We can use the distance formula to find the distances JK and KL in terms of their coordinates:
JK = √((x-x₁)²+(y-y₁²) KL = √((x-x₂)²+(y- y₂)²)
Staging these distances into the above equation, we get:
√(x-x₁)²+(y-y₁))/√((x-x₂)²+(y-y₂)²) = 3/4
Squaring both sides and simplifying, we get:
16(x-x1)²+16(y-y₁)²= 9(x-x₂)²+9(y-y₂)²
Expanding and simplifying, we get:
7x²-14xx₁-9x₂²+ 7y2-14yy₁-9y₂²= -16x₁x₂-16y₁y₂
This is a quadratic equation in x and y. We can solve this equation to find the values of x and y that satisfy the given conditions. The solution to this quadratic equation gives two values of x and y, which are the coordinates of point K.
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Review the equation used in writing a partial fraction decomposition.
StartFraction negative 15 x + 10 Over (5 x minus 2) squared EndFraction = StartFraction A Over 5 x minus 2 EndFraction + StartFraction B Over (5 x minus 2) squared EndFraction
Which system of equations can be used to determine the values of A and B?
The answer is B. 5A=-15 -2A+B=10
have a lovely day my darlings <3
To determine the values of A and B, we can use the following system of equations: 1. 5A = -15 2. -2A + B = 10 This system of equations can be used to find the values of A and B.
To review the equation used in writing a partial fraction decomposition, we start with a fraction that has a denominator that can be factored into linear or quadratic factors. The partial fraction decomposition separates the fraction into a sum of simpler fractions, each with a single linear or quadratic factor in the denominator.
The equation you provided for partial fraction decomposition is:
StartFraction negative 15 x + 10 Over (5 x minus 2) squared EndFraction = StartFraction A Over 5 x minus 2 EndFraction + StartFraction B Over (5 x minus 2) squared EndFraction
This equation shows that the original fraction can be decomposed into two simpler fractions, one with a linear factor of (5x - 2) in the denominator (A/(5x - 2)), and one with a quadratic factor of (5x - 2)² in the denominator (B/(5x - 2)²).
To determine the values of A and B, we need to solve for them using a system of equations. In this case, we can use the coefficients of x in the numerator of each fraction to create the following system of equations:
5A = -15
-2A + B = 10
We get the first equation by setting the numerator of the first fraction (A/(5x - 2)) equal to -15x + 10, and the second equation by setting the numerator of the second fraction (B/(5x - 2)²) equal to -15x + 10 and subtracting the first equation from it.
Solving this system of equations gives us:
A = -3
B = 5
Therefore, the partial fraction decomposition of the original fraction is:
StartFraction negative 15 x + 10 Over (5 x minus 2) squared EndFraction = StartFraction -3 Over 5 x minus 2 EndFraction + StartFraction 5 Over (5 x minus 2) squared EndFraction
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Find the length of side x.
Give answer to 1dp.
Answer:
Set your calculator to degree mode.
Use the Law of Cosines.
x^2 = 18^2 + 15^2 - 2(18)(15)(cos 105°)
x^2 = 688.7623
x = 26.2 cm
Work out the size of an exterior angle of a regular hexagon
The size of an exterior angle of a regular hexagon is 60 degrees.
Working out the size of an exterior angleIn a regular hexagon, all the interior angles are equal and are given by the formula:
Interior angle = (n-2) x 180 / n
where n is the number of sides of the polygon.
For a hexagon, n = 6, so the interior angle is:
Interior angle = (6-2) x 180 / 6 = 120 degrees
An exterior angle is the supplement of an interior angle, which means it is the angle that when added to the interior angle, will equal 180 degrees.
So, exterior angle = 180 - interior angle = 180 - 120 = 60 degrees.
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Classify each angle pair as corresponding, alternate interior, alternate exterior, or consecutive interior angles
Corresponding angles have the same position on the parallel lines, alternate interior angles are inside and opposite, alternate exterior angles are outside and opposite, and consecutive interior angles are on the same side.
When two parallel lines are intersected by a transversal, there are several types of angle pairs that are formed. Corresponding angles are pairs of angles that are located in the same position on the parallel lines relative to the transversal. They have the same measure and are congruent.
Alternate interior angles are pairs of angles that are located on opposite sides of the transversal and inside the parallel lines. They are congruent and have the same measure. Alternate exterior angles are pairs of angles that are located on opposite sides of the transversal and outside the parallel lines. They are congruent and have the same measure.
Consecutive interior angles are pairs of angles that are located on the same side of the transversal and inside the parallel lines. They add up to 180 degrees.
To classify each angle pair, we need to determine their positions relative to the parallel lines and the transversal. By knowing the classifications, we can identify each angle pair and their properties.
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A neighborhood watch association surveyed 40 neighbors about their feelings of safety in the neighborhood. They will survey an additional 80 neighbors. Based on the information, predict how many of the 80 neighbors will feel safe?
We can predict that around 50 of the additional 80 neighbors will feel safe in the neighborhood.
To make a prediction about the number of neighbors who will feel safe, we need to know the proportion of the initial 40 neighbors who felt safe. Let's say that 25 of the 40 neighbors surveyed felt safe.
Then, we can estimate the proportion of the larger group of 120 neighbors (the initial 40 plus the additional 80) who will feel safe as follows:
proportion feeling safe = number feeling safe / total number surveyed
proportion feeling safe = 25 / 40
proportion feeling safe = 0.625
We can use this proportion to estimate the number of the 80 additional neighbors who will feel safe:
number feeling safe = proportion feeling safe x total number surveyed
number feeling safe = 0.625 x 80
number feeling safe ≈ 50
So based on the information given, we can predict that around 50 of the additional 80 neighbors will feel safe in the neighborhood.
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PLEASE HELP ASAP I HAVE 10 MIN 30 PTS
A 72. 0-gram piece of metal at 96. 0 °C is placed in 130. 0 g of water in a calorimeter at 25. 5 °C. The final temperature in the calorimeter is 31. 0 °C. Determine the specific heat of the metal. Show your work by listing various steps, and explain how the law of conservation of energy applies to this situation.
The specific heat of the metal is approximately 0.392 J/g°C. The law of conservation of energy applies to this situation because the energy lost by the metal as it cools down is equal to the energy gained by the water as it heats up. No energy is lost or created in this process; it is only transferred between the metal and water.
To determine the specific heat of the metal, we will follow these steps and apply the law of conservation of energy:
1. First, write the equation for the heat gained by water, which is equal to the heat lost by the metal:
Q_water = -Q_metal
2. Next, write the equations for heat gained by water and heat lost by the metal using the formula Q = mcΔT:
m_water * c_water * (T_final - T_initial, water) = -m_metal * c_metal * (T_final - T_initial, metal)
3. Plug in the known values:
(130.0 g) * (4.18 J/g°C) * (31.0 °C - 25.5 °C) = -(72.0 g) * c_metal * (31.0 °C - 96.0 °C)
4. Solve for the specific heat of the metal (c_metal):
c_metal = [(130.0 g) * (4.18 J/g°C) * (5.5 °C)] / [(72.0 g) * (-65.0 °C)]
5. Calculate the value:
c_metal = 0.392 J/g°C
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A rectangular garden has an area of 100 square meters. The length of the garden is 10 meters more than the width. What is the perimeter of the garden?
Answer:
40 meters
Step-by-step explanation:
Let's assume the width of the garden is x meters, then the length of the garden would be (x+10) meters since we know that the length is 10 meters more than the width.
We also know that the area of the garden is 100 square meters, therefore:
Area = Length x Width
100 = (x+10) x x
Expanding the equation we get:
100 = x^2 + 10x
Rearranging the terms we have:
x^2 + 10x - 100 = 0
Solving for x using the quadratic formula, we get:
x = 5 or x = -20
Since the width cannot be negative, we discard the negative solution and conclude that the width of the garden is 5 meters. Therefore, the length of the garden is (5+10) = 15 meters.
The perimeter of the garden is the sum of the four sides, which is:
Perimeter = 2 x (Length + Width)
Perimeter = 2 x (15 + 5)
Perimeter = 2 x 20
Perimeter = 40 meters
Therefore, the perimeter of the garden is 40 meters.
Answer:
Let's start by using algebra to solve for the width of the garden:
- Let w be the width of the garden.
- Then the length of the garden is w + 10.
- The area of the garden is length x width, so we can write the equation: (w + 10)w = 100.
- Expanding the left side of the equation, we get: w^2 + 10w = 100.
- Rearranging the equation, we get: w^2 + 10w - 100 = 0.
- Factoring the left side of the equation, we get: (w + 20)(w - 10) = 0.
- Solving for w, we get: w = -20 or w = 10. Since the width cannot be negative, we have w = 10.
Now that we know the width of the garden is 10 meters, we can find the length by adding 10 meters:
- Length = width + 10 = 10 + 10 = 20 meters.
Finally, we can find the perimeter of the garden by adding up the lengths of all four sides:
- Perimeter = 2(length + width) = 2(20 + 10) = 2(30) = 60 meters.
Therefore, the perimeter of the garden is 60 meters.
Explain how you can determine if (x + 3) is a factor of the given polynomial through factoring and polynomial division:
(A-APR. 2) (A1. 26. A, A1. 26. B)
x3-x2-12x
fast with step by step explanation if possible please!
To determine whether (x + 3) is a factor of the polynomial x^3 - x^2 - 12x, we can use polynomial division.
Step 1: Write the divisor, (x + 3), on the left side of a long division symbol and the dividend, x^3 - x^2 - 12x, on the right side.
x + 3 | x^3 - x^2 - 12x
Step 2: Divide the first term of the dividend, x^3, by the first term of the divisor, x, and write the result, x^2, on top of the division symbol. Multiply the divisor by this quotient, and write the result under the dividend.
lua
x^2 - 4x
___________________
x + 3 | x^3 - x^2 - 12x
- (x^3 + 3x^2)
----------
-4x^2
Step 3: Bring down the next term of the dividend, -12x, and write it next to the remainder, -4x^2.
lua
Copy code
x^2 - 4x
___________________
x + 3 | x^3 - x^2 - 12x
- (x^3 + 3x^2)
----------
-4x^2 - 12x
Step 4: Divide the first term of the new dividend, -4x^2, by the first term of the divisor, x, and write the result, -4x, on top of the division symbol. Multiply the divisor by this quotient, and write the result under the previous subtraction.
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Use the figure below to determine the value of the variable and the
lengths of the requested segments. Your answers may be exact or
rounded to the nearest hundredth. The figure may not be to scale.
Using tangents theorem, we can find the value of the missing length,
n = 18.7units.
Define a tangent?"To touch" is how the word "tangent" is defined. The same idea is conveyed by the Latin word "tangere". A tangent, in general, is a line that, while never entering the circle, precisely touches it at one point on its circumference. A circle has a number of tangents. They make a straight angle with the radius.
Here in the diagram,
We can see that as per the central angle and tangent theorem,
AB/BC = ED/DC
⇒ 17/10 = n/11
Cross multiplying:
⇒ 17 × 11 = n × 10
⇒ 10n = 187
⇒ n = 187/10
⇒ n = 18.7
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find scale factor of the dilation
Answer:
Step-by-step explanation:
The original image is the the black one. The dilated image is blue. It got bigger. So it is an enlargment.
Each side got bigger by times 2
So the dilation is 2
What is the meaning of a relative frequency of 0. 56
A relative frequency of 0.56 means that out of the total number of observations in a given sample or population, 56% of those observations belong to a particular category or have a certain characteristic.
In other words, it is the proportion or fraction of the observations that fall into that particular category or have that characteristic, relative to the total number of observations. For example, if we had a sample of 100 people and 56 of them had brown hair, then the relative frequency of brown hair would be 0.56 or 56%.
To calculate relative frequency, you divide the frequency of a specific event or category by the total number of observations. In this case, the specific event or category occurs 56% as often as the total events or categories observed.
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I would like to see the process steps of solving this as well please! Thank you!
You must begin to brake 234643.2 feet from the intersection.
What is stopping distance?In Mathematics and Science, stopping distance can be defined as a measure of the distance between the time when a brake is applied by a driver to stop a vehicle that is in motion and the time when the vehicle comes to a complete stop (halt).
Based on the information provided above, the speed of this car is represented by the following equation;
s = √(30fd)
Where:
f is the coefficient of friction.d is the stopping distance (in feet).By substituting the given parameters, we have:
20 = √(30(0.3)d)
400 = 9d
d = 400/9
d = 44.44
Conversion:
1 mile = 5,280 feet.
44.44 miles = 234643.2 feet.
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