We first integrate with respect to z from 2 to (3x + 4y), then with respect to y from 0 to 2, and finally with respect to x from 0 to 1.
To integrate the given function over the region, we would use triple integration with the bounds of integration as follows:
∫ from 0 to 1 ∫ from 0 to 2 ∫ from 2 to (3x + 4y) f(x, y, z) dz dy dx
This is because the region is defined by the inequalities 0 ≤ x ≤ 1, 0 ≤ y ≤ 2, and 0 ≤ z ≤ (3x + 4y).
Therefore, we first integrate with respect to z from 2 to (3x + 4y), then with respect to y from 0 to 2, and finally with respect to x from 0 to 1.
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Given that segment KL is parallel to segment MN and that segment KN bisects segment ML, prove that segment KO is congruent to segment NO
If that segment KL is parallel to segment MN and that segment KN bisects segment ML, then segment KO is congruent to segment NO.
To prove that segment KO is congruent to segment NO, we need to show that triangle KNO is an isosceles triangle, with KO ≅ NO.
From the given information, we know that KL is parallel to MN, which means that angle KLN is congruent to angle MNL (corresponding angles). Also, KN bisects segment ML, which means that angle KNO is congruent to angle NMO (angle bisector theorem).
Therefore, we have:
angle KNO = angle NMO
angle KLN = angle MNL
Adding these two equations gives us:
angle KNO + angle KLN = angle NMO + angle MNL
But angle KLN + angle NMO + angle MNL = 180 degrees (as they form a straight line). So we can substitute this into the equation:
angle KNO + 180 degrees = 180 degrees
Simplifying, we get:
angle KNO = 0 degrees
This means that KO and NO are on the same line, so they must be congruent. Therefore, we have proven that segment KO is congruent to segment NO.
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what's the solution?
Answer:
(1, 1.5)
Step-by-step explanation:
If x = 1, plug it into the other equation, y = 1/2x + 1, and y = 1.5.
Randy divides (2x4 – 3x3 – 3x2 7x – 3) by (x2 – 2x 1) as shown below. what error does randy make? x squared minus 2 x 1 startlongdivisionsymbol 2 x superscript 4 baseline minus 3 x cubed minus 3 x squared 7 x minus 3 endlongdivisionsymbol. minus 2 x superscript 4 baseline minus 4 x cubed 2 x squared to get a remainder of x cubed minus 5 x squared 7 x. minus x cubed minus 2 x squared x to get a remainder of negative 3 x squared 6 x minus 3. minus negative 3 x squared 6 x minus 3 to get a remainder of 0 and a quotient of 2 x squared x 3. he makes a subtraction error. he makes an error writing the constant term in the quotient. he makes an error choosing the x-term in the quotient. he makes an error rewriting the problem in long division.
By subtracting this from the dividend, the next step would be:
[tex](2x^4 - 3x^3 - 3x^2 + 7x - 3) - (-5x^3 + 10x^2 - 5x) = 2x^4 + 2x^3 - 13x^2 + 12x - 3[/tex]
This error occurs because he forgets to distribute the -2 in [tex]-2(x^2 - 2x + 1)[/tex]when subtracting from [tex]2x^4[/tex]. This leads to a mistake in the next step when he subtracts [tex]x^3 - 2x^2[/tex] from [tex]x^3 - 5x^2[/tex] to get [tex]-3x^2[/tex]instead of [tex]-3x^2 + 6x[/tex]. This error then leads to the incorrect constant term in the quotient.
Therefore, the error Randy makes is a subtraction error in the first step of the long division. It is important to pay attention to signs and distribute coefficients correctly when performing long division with polynomials.
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Answer: A. x + 2
Step-by-step explanation:
Edge 2023
4. Use the data below for the calculations.
Average hours sleeping per weeknight: 4, 5, 8, 12, 10, 6, 7, 9, 8, 8, 6, 6, 4, 3, 9
Mean:
Median:
Mean Absolute Deviation:
Absolute Deviation from Median:
The mean is 7
The median is the middle value, which is 7.
Mean Absolute Deviation: 2
How to solve for the mean absolute deviationStep 3: Find the absolute deviation of each value from the mean:
|4-7.067|, |5-7.067|, |8-7.067|, |12-7.067|, |10-7.067|, |6-7.067|, |7-7.067|, |9-7.067|, |8-7.067|, |8-7.067|, |6-7.067|, |6-7.067|, |4-7.067|, |3-7.067|, |9-7.067|
These absolute deviations are: 3.067, 2.067, 0.933, 4.933, 2.933, 1.067, 0.067, 1.933, 0.933, 0.933, 1.067, 1.067, 3.067, 4.067, 1.933.
Step 4: Find the mean of these absolute deviations to find the mean absolute deviation:
Mean Absolute Deviation = (3.067+2.067+0.933+4.933+2.933+1.067+0.067+1.933+0.933+0.933+1.067+1.067+3.067+4.067+1.933) / 15 = 2
Step 5: Find the absolute deviation of each value from the median:
|4-8|, |5-8|, |6-8|, |6-8|, |6-8|, |7-8|, |8-8|, |8-8|, |8-8|, |9-8|, |9-8|, |10-8|, |12-8|, |8-8|, |3-8|
These absolute deviations are: 4, 3, 2, 2, 2, 1, 0, 0, 0, 1, 1, 2, 4, 0, 5.
Therefore, the absolute deviation from the median is 5.
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D. Larry has a new plan. Whenever his need for the car exceeds the number of slots he has rented the car for, he returns the car on time to avoid the fine, and uses his bicycle for the remaining deliveries. Unfortunately, bike deliveries take 3 times longer than car deliveries. Suppose he rents the car for 5 slots (75 minutes). If he needs 7 slots, then he uses the car for 5 slots, and the remaining 2 slots are done by bicycle, which take 6 slots (1. 5 hours). How much time does he expect to bicycle on average (in terms of slots)
Larry uses the car for the first 5 slots (75 minutes) and returns it on time to avoid any fine. He then uses his bike for the remaining 2 slots, which takes 6 slots (3 times longer than using the car).
Therefore, in total, Larry uses the car for 5 slots and the bike for 6 slots, for a total of 11 slots.
On average, Larry expects to use the bike for (6/11) of his total slots. Since each bike delivery takes 3 times longer than a car delivery, we can say that Larry expects to spend 3 times as much time on the bike as he would in the car. Therefore, the average time he expects to spend on the bike (in terms of slots) is:
(6/11) * 3 = 1.636 slots
So, Larry expects to spend an average of 1.636 slots (or about 24.5 minutes) on the bike for each delivery.
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Compute the number of 12 letter combination of the 26 letters in alphabet.
key answer:
9,675,700
To compute the number of 12 letter combinations of the 26 letters in the alphabet, we can use the formula for combinations, which is:
nCr = n! / r!(n-r)!
where n is the total number of items (26 letters in this case), r is the number of items to choose (12 letters in this case), and ! means factorial (the product of all positive integers up to that number).
Using this formula, we can plug in the numbers:
26C12 = 26! / 12!(26-12)!
= (26 x 25 x 24 x 23 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15) / (12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)
= 9,675,700
Therefore, there are 9,675,700 possible 12 letter combinations of the 26 letters in the alphabet.
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Find the x- and y-intercepts of the graph of 4x+8y=20. State each answer as an integer or an improper fraction in simplest form
The cordinate points with x- and y-intercepts of the graph of a linear equation, 4x+ 8y = 20, are equals to the (5,0) and (0, 5/2).
We have an equation, 4x + 8y = 20 --(1) which is linear equation with two variables. We have to determine the the x- and y-intercepts of the graph of equation (1). The graph of line (1) is present in above figure. Slope intercept form of equation (1) is written as [tex]y = - \frac{1}{2}x + \frac{5}{2}[/tex],
The x-intercept is point where a line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis. As we know, two points determine any line, we can graph lines using the x- and y-intercepts. To determine the x-intercept, we substitute y=0 and solve for x. So, when y = 0 then 4x + 0 = 20
=> x = 5
similarly to determine the y-intercept, set x=0 and solve for y. When x = 0
=> 8y = 20
=> y = 5/2.
Hence, required value are (5,0) and (0,5/2).
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Find the exact location of all the relative and absolute extrema of the function. (Order your answers from smallest to largest t.)
f(t) = 4t3 + 4t with domain [−2, 2]
f has (select)(a relative minimum, a relative maximum, an absolute minimum, an absolute maximum, no extremum,) at (x, y) = ____________
f has (select)(a relative minimum, a relative maximum, an absolute minimum, an absolute maximum, no extremum,) at (x, y) = ____________
The derivative of the given function is:
f'(t) = 12t^2 + 4
Setting f'(t) = 0 to find critical points, we get:
12t^2 + 4 = 0
t^2 = -1/3
This equation has no real solutions, which means there are no critical points on the interval [-2, 2]. Since the interval is closed and bounded, the function attains its maximum and minimum values at the endpoints of the interval.
We can find the values of the function at the endpoints:
f(-2) = -24
f(2) = 24
Therefore, the function has an absolute maximum of 24 at t = 2 and an absolute minimum of -24 at t = -2. There are no relative extrema.
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Which is the better deal: an account that pays 4% interest compounded daily or one that pays 3.95% compounded continuously?
Answer:
compounded continuously
Step-by-step explanation:
compounded continuously occurs more frequently than daily
Emma doesn’t have $300 now, but she plans to get a job when she gets to college. she wants to find out how much it will cost her if she doesn’t pay off her credit card until after college. find how much she’ll owe in four years. these are the terms of her credit card:
it has a 15% yearly interest rate.
the interest is compounded monthly.
the card has $0 minimum payments for the first four years it is active.
If it has a 15% yearly interest rate and the interest is compounded monthly and the card has $0 minimum payments for the first four years it is active. Therefore, Emma will owe approximately $529.27 in four years.
To calculate how much Emma will owe in four years, we need to use the compound interest formula: A = P (1 + r/n)^(n*t)
where:
A = the amount of money at the end of the investment period
P = the principal amount (the initial amount of money borrowed)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time period in years
In this case, the principal amount is $300, the annual interest rate is 15%, and the interest is compounded monthly (so n = 12). The time period is four years.
Plugging in the values, we get:
A = 300(1 + 0.15/12)^(12*4)
A ≈ $529.27
Therefore, Emma will owe approximately $529.27 in four years if she doesn't pay off her credit card until after college.
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Select the correct answer.
The parallelogram has an area of 20 square inches. What are the dimensions of the parallelogram, to the nearest hundredth of an inch?
X
40°
4 in
ОА
I=
B.
=
3. 06 in, h = 6. 54 in
I = 6. 22 in, h = 3. 23 in
OC. I = 2. 57 in, h = 7. 78 in
1 = 4. 00 in, h 5. 00 in
OD
Options A and D both give an area of 20 square inches
To find the correct dimensions of the parallelogram with an area of 20 square inches, you can use the formula for the area of a parallelogram: Area = base * height.
Given the options:
A. base = 3.06 in, height = 6.54 in
B. base = 6.22 in, height = 3.23 in
C. base = 2.57 in, height = 7.78 in
D. base = 4.00 in, height = 5.00 in
Check each option by plugging the base and height into the formula:
A. 3.06 * 6.54 ≈ 20.00
B. 6.22 * 3.23 ≈ 20.08
C. 2.57 * 7.78 ≈ 19.98
D. 4.00 * 5.00 = 20.00
Options A and D both give an area of 20 square inches. Since the question asks for dimensions to the nearest hundredth of an inch, option A (base = 3.06 in, height = 6.54 in) is more precise and is the correct answer.
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If i walked 14 out of the 20 days in February, which value is equivalent to the fraction of the school days in February that i walked to school?
The fraction of the school days in February that you walked to school is 7/10 or 0.7 when expressed as a decimal.
What is the fraction of school days in February that you walked to school if you walked 14 out of 20 days?
The fraction of the school days in February that you walked to school can be represented as:
(number of days you walked) / (total number of school days in February)
Since you walked 14 out of 20 days in February, we can substitute these values into the formula:
(number of days you walked) / (total number of school days in February) = 14 / 20
Simplifying the fraction by dividing both the numerator and denominator by their greatest common factor (2), we get:
(number of days you walked) / (total number of school days in February) = 7 / 10
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A $750 gift was shared equally by 5 people. After spending $90 of her share, Clarissa divided the amount remaining into 2 equal parts. What amount of money is now in each part of Clarissa's money?
Answer:
$30 for each part
Step-by-step explanation:
$750 ÷ 5 = $150 each people
Clarissa's money is $150
$150 - $90 = $60
Clarissa's money after she spent is $60
$60 ÷ 2 = $30
Clarissa's money for each part out of 2 parts is $30
How much would it cost to buy a cover for the pool that cost $0.30 per square foot
It would cost $735 to buy a cover for the pool at $0.30 per square foot
How much would it cost to buy a cover for the poolFrom the complete question (see attachment), we have the following parameters that can be used in our computation:
Unit rate = $0.30 per square foot
Dimensions = 10 inches by 20 inches
Scale = 2 inches : 7 feet
Using the above as a guide, we have the following:
Total cost = Unit rate * Area of pool
Where
Area of the pool = 10 inches * 20 inches
Using the scale, we have
Area of the pool = (10 * 7/2)* (20 * 7/2) square feet
Area of the pool = 2450 square feet
Substitute the known values in the above equation, so, we have the following representation
Total cost = $0.30 per square feet * 2450 square feet
This gives
Total cost = $735
Hence, it would cost $735 to buy a cover for the pool
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Complete question
The blueprint of a pool has a scale of 2 inches equals 7 feet. The scale drawing is shown below (see attachment)
How much would it cost to buy a cover for the pool that cost $0.30 per square foot
Find the volume generated when the area bounded by the curve y?=x, the line x=4 and the
x-axis is revolved about the y-axis.
To find the volume generated, we need to use the formula for volume of revolution. We are revolving the area bounded by the curve y=x, the line x=4 and the x-axis about the y-axis.
First, we need to find the limits of integration for x. The curve y=x intersects the line x=4 at y=4, so we integrate from x=0 to x=4.
Next, we need to find the radius of the rotation. The radius is the distance from the y-axis to the curve at each value of x. Since we are revolving about the y-axis, the radius is simply x.
Using the formula for volume of revolution, we get:
V = π∫(radius)^2 dx from 0 to 4
V = π∫x^2 dx from 0 to 4
V = π[x^3/3] from 0 to 4
V = π[(4^3/3) - (0^3/3)]
V = (64π/3)
Therefore, the volume generated when the area bounded by the curve y=x, the line x=4 and the x-axis is revolved about the y-axis is (64π/3).
To find the volume generated when the area bounded by the curve y=x^2, the line x=4, and the x-axis is revolved around the y-axis, we'll use the disk method. The formula for the disk method is:
Volume = π * ∫ [R(x)]^2 dx
Here, R(x) is the radius function and the integral is taken over the given interval on the x-axis. In this case, R(x) = x and the interval is from 0 to 4.
Volume = π * ∫ [x]^2 dx, with the integral from 0 to 4
Now, we'll evaluate the integral:
Volume = π * [ (1/3)x^3 ](0 to 4)
Volume = π * [ (1/3)(4)^3 - (1/3)(0)^3 ]
Volume = π * [ (1/3)(64) - 0 ]
Volume = π * [ (64/3) ]
So, the volume generated is (64/3)π cubic units.
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Ver en español
Of the last 20 contestants on a game show, 8 won a prize. What is the experimental probability that the next contestant will win a prize?
The probability that the next contestant will win a prize is 2/5.
What is probability?
Probability is a way of calculating how likely something is to happen. It is difficult to provide a complete prediction for many events. Using it, we can only forecast the probability, or likelihood, of an event occurring. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.
Experimental probability is based on the result of an experiment that has been carried out multiples times.
probability that the next contestant will win a prize = number of contestants that won in the last games / total number of contestants in the last games
=> 8/20
To transform to the simplest form. divide both the numerator and the denominator by 4
=> 2/5
Hence the probability that the next contestant will win a prize is 2/5.
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Color the stars so it would be likely but not certain you would choose a yellow one.
A survey of North middle school staff included staff members ages the ages were complied and displayed in a histogram which of the following statements best describes the data
The number of staff members under the age of 40 are 28 and the number of staff members 40 and older are 22.
From the given histogram,
A. Between the age 20-29 there are 10 members.
B. Under the age of 40 = 10+18
= 28
40 and older = 12+7+2+1
= 22
C) Total staff members = 28+22=50
D) Number of staff members are 50 years or older
= 7+2+1
= 10
Therefore, the number of staff members under the age of 40 are 28 and the number of staff members 40 and older are 22.
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Based on the box-and-whisker plot shown below, match each term with the correct value. PLEASE ANSWER QUICKLY!!!
The value of the median is 18. The range of this plot is 6. The 25th percentile is 17 and the 75th percentile is 20. The interquartile range is 3.
We are given a box-and-whisker plot and we have to find the correct value of the median, range, 25th percentile, 75th percentile, and inter-quartile range with the help of this box-and-whisker plot.
We find the median with the help of the box. The line which splits the box into two halves is the median for the given data. Therefore, the median will be 18. To find the range, we subtract the minimum value from the maximum value. The minimum value is 15 and the maximum value is 21. Therefore, the range will be (21 - 15) = 6.
From the plot, we can see that the 25th percentile is 17, Q1, and the 75th percentile is 20, Q3. Now, we have to find the interquartile range. To find the interquartile range, we subtract Q1 from Q3. Therefore, our interquartile range will be (20 -17) = 3.
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Mr. Woodley invested $1200 at 5% simple interest at the beginning of each year for a period of 8 years. Find the total accumulated value of all the investments at the end of the 8-year period.
It would be helpful if u used a geometric or arithmetic sequence formula.
Answer:
$1680
Step-by-step explanation:
PV = $1200
i = 5%
n = 8
Simple interest formula:
FV = PV (1 + i × n)
FV = 1200 (1 + 5% x 8)
FV = $1680
if r=11 units and x = 15 units, then what is the volume of the cylinder shown above?
The volume of the cylinder V = πr²h. Therefore, we need to have more information about the cylinder's height in order to solve this problem.
To find the volume of the cylinder, we first need to know the height of the cylinder. However, the height is not given in the question. Therefore, we cannot determine the volume of the cylinder with the given information.
We can use the formula for the volume of a cylinder, which is V = πr²h, where V is the volume, r is the radius, and h is the height.
Since r = 11 units and x = 15 units, we can find the diameter of the base of the cylinder by multiplying r by 2, which gives us 22 units. However, we still do not know the height of the cylinder.
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3. Suppose a simple random sample of 150 college students is drawn. Among sampled students, the average IQ score is 115 with a standard deviation of 10. What is the 95% confidence interval for the ents^ prime IQ score?
Answer: is approximately between 113.39 and 116.61
To calculate the 95% confidence interval for the students' average IQ score, we'll use the given information: sample size (n=150), sample mean (X=115), and sample standard deviation (s=10). We'll use the t-distribution since the population standard deviation is unknown.
First, we need to find the t-value for a 95% confidence interval with n-1 (149) degrees of freedom. Using a t-table or calculator, we find the t-value to be approximately 1.976.
Next, we'll calculate the standard error (SE) using the formula: SE = s/√n. In this case, SE = 10/√150 ≈ 0.816.
Now, we can find the margin of error (ME) using the formula: ME = t-value × SE. For this problem, ME = 1.976 × 0.816 ≈ 1.61.
Finally, to calculate the 95% confidence interval, we'll use the formula: X ± ME. Thus, the 95% confidence interval is 115 ± 1.61, which is approximately (113.39, 116.61).
So, the 95% confidence interval for the students' average IQ score is approximately between 113.39 and 116.61.
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EXAMPLE 1 A spring with a mass of 6 kg has a natural length of 0.3 m. A force of 38.4 N is required to maintain it stretched to a length of 0.7 m. If the spring is stretched to a length of 0.7 m and then released with initial velocity 0, find the position of the mass at time t. SOLUTION From Hooke's Law, the force required to stretch the spring is k(0.4) = 38.4 so k = 38.4/0.4 = 96. Using this value of the spring constant k, together with m = 6, we have d²x 6 = 0. + dt2 As in the earlier general discussion, the solution of this equation is X(t) = ( cos(4t) + C2 sin(4t). We are given the initial condition that x(0) = 0.4. But, from the previous equation, x(0) = cz. Therefore cn = . Differentiating, we get x'(t) = -4c sin(4t) + 4c2 cos(4t). Since the initial velocity is given as x'(O) = 0, we have cz = 0 and so the solution is = x(t) =
The equation given in the solution is X(t) = (cos(4t) + C2sin(4t)). This equation represents the position of the mass at time t after the spring has been released with an initial velocity of 0. The terms "spring" and "stretch" indicate that Hooke's Law is being used to determine the spring constant k.
The term "velocity" is used to describe the initial velocity of the mass, which is given as 0. The position of the mass at time t is determined by the value of X(t), which is a function of time. Therefore, the position of the mass at any given time can be found by plugging in the value of t into the equation X(t) = (cos(4t) + C2sin(4t)).
Hi! Based on the information provided, you have a spring with a mass of 6 kg and a natural length of 0.3 m. A force of 38.4 N is required to stretch it to 0.7 m. The spring constant, k, is determined to be 96. The spring is then stretched to 0.7 m and released with an initial velocity of 0. To find the position of the mass at time t, you can use the equation:
x(t) = C1 * cos(4t) + C2 * sin(4t)
Given the initial condition x(0) = 0.4, we find that C1 = 0.4. The initial velocity x'(0) is 0, leading to the conclusion that C2 = 0. Therefore, the equation for the position of the mass at time t is:
x(t) = 0.4 * cos(4t)
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In 2016 there were approximately 7,040 college and university libraries in the United States. A survey found that 65% of those libraries participated in an electronic "book-sharing" program. Based on this information, how many college and university libraries participated in the electronic "book-sharing" program in 2016?
To calculate the approximate number of libraries that participated in the book-sharing program in 2016, we multiply the total number of college and university libraries (7,040) by the percentage of libraries participating (65%).
By multiplying 7,040 by 0.65, we find that approximately 4,576 libraries participated in the book-sharing program in 2016.
This calculation assumes that the percentage given accurately represents the proportion of libraries participating in the program. However, it's important to note that this is an approximation based on the given information. The actual number of participating libraries may vary slightly due to factors such as reporting discrepancies or changes in participation rates over time.
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The notation (x,y)→(−x,y) means a reflection across the y axis.
Answer:
This is true.
Step-by-step explanation:
To prove this as true what we can do is draw a graph. On one of the graphs, we will have a point at (-7,1). If we were going to reflect it over the y-axis by counting the distance it is from the y-axis and counting it in the other direction. When we do this we get a point of (7,1). We can infer that because it was flipped in the y-axis the y value stayed the same while the x-axis changed.
This is how we can prove this to be true.
QR has endpoints at Q(5, –6) and R(6, 3). Find the midpoint M of QR.
Answer:
(5.5, -1.5)
Step-by-step explanation:
(x, y)midpoint = (x1 + x2)/2 , (y1 + y2)/2
= (6 + 5)/2, (3 - 6)/2
= (11/2, -3/2)
= (5.5, -1.5)
Please upload a picture of a piece of paper with the problem worked out, and draw the graph for extra points, there will be 6 of these, so go to my profile and find the rest, and do the same, for extra points.
for questions 3 and 4, solve the system using the substitution method.
The value of X and y using substitution method for the quadratic equation given above would be = -3.6 and - 2.8 respectively.
How to calculate the unknown values using substitution method?The equations given are;
2x - 7y = 13. ----> equation 1
3x + y = 8 --------> equation 2
From equation 2 make y that subject of formula;
y = 8 - 3x
Substitute y = 8 - 3x into equation 1
2x - 7(8 - 3x) = 13
2x - 56 - 21x = 13
-19x = 13+56
-19x = 69
X = -69/19
X = - 3.6
Substitute X = -3.6 into equation 2
3(-3.6) + y = 8
y= 8 - 10.8
= - 2.8
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A food company is designing box for several products each box is a rectangular prism. The food company is now designing soup boxes. The largest box of soup will be a dilation of the smallest box using a scale factor of two. The smallest box must hold eight fluid ounces or about 15 in. ³ of soup. Find a set of dimensions for the largest box round to the nearest tenth
The set of dimensions for the largest box is: 4 in x 4 in x 3.8 in.
We know that the smallest box must hold 8 fluid ounces or 15 in³ of soup. Let's assume the dimensions of the smallest box to be x, y, and z.
Then, we have:
[tex]x * y * z = 15[/tex]
Now, the largest box will be a dilation of the smallest box using a scale factor of 2. This means that every dimension of the smallest box will be multiplied by 2 to get the dimensions of the largest box.
So, the dimensions of the largest box will be 2x, 2y, and 2z.
Now, we need to find the dimensions of the smallest box. We can start by solving the equation x * y * z = 15 for one of the variables, say z:
[tex]z = 15 / (x * y)[/tex]
Substituting this value of z in the expression for the dimensions of the largest box, we get:
[tex]2x * 2y * (15 / (x * y))[/tex]
Simplifying this expression, we get:
[tex]4 * 15 = 60[/tex]
So, the dimensions of the largest box are approximately 4 in by 4 in by 3.8 in (rounded to the nearest tenth).
Therefore, the set of dimensions for the largest box is: 4 in x 4 in x 3.8 in.
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Marshall and oliver went to an arcade where the machines took tokens. marshall played 10 games of skee ball and 8 games of pinball, using a total of 44 tokens. at the same time, oliver played 3 games of skee ball and 8 games of pinball, using up 30 tokens. how many tokens does each game require?
Each game of skee ball requires 2 tokens and each game of pinball requires 2 tokens.
Let the number of tokens required for each game of skee ball be x and for each game of pinball be y.
From the given information, we can form two equations:
10x + 8y = 44 ... (1)
3x + 8y = 30 ... (2)
Multiplying equation (2) by 3, we get:
9x + 24y = 90 ... (3)
Subtracting equation (1) from equation (3), we get:
- x + 16y = 46
Solving for x, we get:
x = 16y - 46
Substituting this value of x in equation (2), we get:
3(16y - 46) + 8y = 30
Simplifying and solving for y, we get:
y = 2
Substituting this value of y in equation (1), we get:
10x + 8(2) = 44
Solving for x, we get:
x = 2
Therefore, each game of skee ball requires 2 tokens and each game of pinball requires 2 tokens.
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A cylindrical jar of peanut butter has a height of 4 inches and a diameter of 3 inches. How many cubic inches of peanut butter can the jar hold? Use π = 3.14.
28.26 in3
37.68 in3
113.04 in3
150.72 in3
The jar can hold 28.26 cubic inches of peanut butter
How to calculate the amount of cubic inches of peanut butter?The first step is to write out the parameters
A cylindrical jar of peanut has a height of 4 inches
The diameter is 3 inches
The next step is to calculate the radius, this is done by dividing the diameter by 2
radius= 3/2
= 1.5
The formula used to calculate the cubic inches of peanut butter is
V= πr²h
= 3.14 × 1.5² × 4
= 3.14 × 2.25 × 4
= 28.26
Hence the jar can hold 28.26 cubic inches of peanut butter
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