To solve the problem, we need to find Julian's average speed, given that he started biking from a position behind the simulated biker at a speed of 20 km/h, and after 15 minutes, his position was reported as -214 km.
We can use the formula for average speed:
Average speed = total distance / total time
To find the total distance, we need to calculate the displacement of Julian from the initial position of -d (where d is the distance between Julian and the simulated biker when he started biking) to the position of -214 km after 15 minutes.
Displacement = final position - initial position
Displacement = (-214 km) - (-d) = d - 214 km
The total distance covered by Julian is equal to the absolute value of the displacement, since the direction of the motion does not matter when computing distance.
Total distance = |d - 214 km|
To find the total time, we need to convert 15 minutes to hours:
Total time = 15 minutes / 60 minutes/hour = 0.25 hours
Now we can substitute the values into the formula for average speed:
Average speed = total distance / total time
Average speed = |d - 214 km| / 0.25 hours
Since Julian was traveling at a constant speed of 20 km/h, we can also express the distance in terms of time:
Average speed = (20 km/h) x t / 0.25 hours
where t is the time Julian biked in hours.
Setting the two expressions for average speed equal to each other, we can solve for t:
|d - 214 km| / 0.25 hours = (20 km/h) x t / 0.25 hours
|d - 214 km| = 20 km/h x t
Solving for t:
t = |d - 214 km| / 20 km/h
Now we can substitute this expression for t into either expression for average speed:
Average speed = (20 km/h) x t / 0.25 hours
Average speed = |d - 214 km| / 0.25 hours
Substituting the expression for t:
Average speed = |d - 214 km| x 4 / |d - 214 km|
Simplifying:
Average speed = 80 km/h
Therefore, Julian's average speed so far has been 80 km/h.
An annual depreciation rate is the percent that the value of an item decreases each year. A company purchases technology for $5,000. The company uses the function $r=1-\sqrt[3]{\frac{S}{5000}}$
to relate the annual depreciation rate $r$ (in decimal form) and the value $S$ (in dollars) of the technology after 3 years. Find $S$ when $r=0.15$ .
if a clock shows it is 3 o'clock, how could you describe the smaller angle made my the two hands of the clock? solve this problem any way you choose
The smaller angle made by the two hands of the clock at 3 o'clock is 90 degrees.
What is an angle?A figure known as an angle is created by two rays or line segments that meet at a place known as the vertex of the angle. The sides or legs of the angle are other names for the rays or line segments.
According to question:To determine the smaller angle made by the two hands of a clock when it is 3 o'clock, we can use the following formula:
angle = |(11/2) * m - 30h|
where:
m is the number of minutes past the hour (in this case, since it is 3 o'clock, m = 0)
h is the hour (in this case, h = 3)
By using this formula, we get:
angle = |(11/2) * 0 - 30(3)| = |0 - 90| = 90
Therefore, the smaller angle made by the two hands of the clock at 3 o'clock is 90 degrees.
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Help pleaseeeee I would appreciate it
(1) The result of the row operation R₂ ↔ R₃ is [ -5 1 0 8]
[ 8 8 -7 5 ]
[ 2 2 6 -5]
(2) The result of the row operation 3R₁ ↔ R₁ is [24 - 27 -21 - 18]
[8 9 -4 -5]
[2 2 -7 -8]
What is the result of the row operation?
The result of the row operation in the matrix is calculated as follows;
R₂ ↔ R₃, implies changing row 2 and row, and the result would be;
[ -5 1 0 8]
[ 8 8 -7 5 ]
[ 2 2 6 -5]
The result of obtained from 3R₁;
3R₁ = [24 - 27 -21 - 18]
3R₁ ↔ R₁ is determined as; (the row interchange)
[24 - 27 -21 - 18]
[8 9 -4 -5]
[2 2 -7 -8]
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From the observation deck of a skyscraper, Brandon
The horizontal distance from the base of the skyscraper out to the ship will be 1140 feet.
How to solveGiven that:-
The angle is = 45
The height of the skyscraper is 1140 feet.
The horizontal distance will be calculated by applying the angle property in the right angle triangle.
tan45 = ( P / B )
B = P / tan45
B = P Since ( tan45 =1 )
B = 1140 feet.
Therefore the horizontal distance from the base of the skyscraper out to the ship will be 1140 feet.
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From the observation deck of a skyscraper, Brandon measures a 45^{\circ} ∘ angle of depression to a ship in the harbor below. If the observation deck is 1140 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest tenth of a foot if necessary.
Please help fast. Thanks! (:
The value of variable y from the system of vertical angles is equal to 125.
How to find the values of a variable associated with system of vertical anglesIn this problem we need to determine by algebra properties the value of a variable y from a system of two pairs of vertical angles. The system is represented by the following expression:
x + 20 = 3 · x - 50
2 · x = 70
x = 35
Then, by definition of supplementary angles:
(x + 20) + y = 180
55 + y = 180
y = 125
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The formula for the volume of a prism is V = area of base x height. What is the volume and surface area of each of these prisms? Show your thinking
The volume of the prism is V = 4000 cm³
Given data ,
Let the volume of the prism be represented as V
Now , the value of V is
Let the height of the prism be h = 10 cm
Let the width of the prism be w = 20 cm
Let the length of the prism be l = 20 cm
So , the base area of prism = l x w
Base area = 400 cm²
Now , the volume of the prism is V = 400 x 10
V = 4000 cm³
Hence , the volume of prism is V = 4000 cm³
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What is the midpoint of the line segment with the given endpoints (4,6) (3,-3)
Help it’s urgent
The coordinates of the midpoints of the given line segment is:
(3.5, 1.5)
How to find the midpoints of a line segment?The midpoint of a line segment is simply referred to as the center of that specific line segment.
Thus, the coordinates at that point will be referred to as the coordinates of the midpoint.
The coordinates of the endpoints of the line are:
(4,6) and (3,-3)
The formula to find the coordinates of the midpoint of the line is:
(x, y) = (x₁ + x₂)/2, (y₁ + y₂)/2
Thus, we have:
(x, y) = (4 + 3)/2, (6 - 3)/2
= (3.5, 1.5)
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Several trusses are needed to build the frame of the shed roof. Each roof truss is 16 inches apart, as measured from the centers of the beam widths.
The roof could be constructed so that the ridgeline of the roof is parallel to the longest dimension of the shed (first picture below) or it could be constructed so that the ridgeline of the roof is parallel to the shortest dimension of the shed (second picture below).
The number of roof trusses that would be needed for the longest length is 2
Calculating the number of roof trusses that would be neededThe longest lengths from the question are given
Longest lengths = 28 and 22
Next, we expand the lengths of the roof trusses
This is to calculate the greatest common factor (GCF) of the lengths
So, we have
28 = 2 * 2 * 7
22 = 2 * 11
Multiplying the common factors gives the GCF
So, we have
GCF = 2
This means that the number of roof trusses that would be needed for the longest length is 2
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La distancia entre Bay Town y Oak Glen es de 175 millas. Si la ecuación y = -x +175 representa la distancia que queda por recorrer hasta Oak Glen, ¿qué representa el dominio? ¿Qué es el dominio?
The correct answer is: D) distance traveled since leaving Bay Town; x ≥ 0
How to solveThe equation y = -x + 175 represents the distance left to travel to Oak Glen.
In this equation, x is the distance traveled since leaving Bay Town, and y is the distance left to reach Oak Glen.
The domain represents the possible values of x, which is the distance traveled since leaving Bay Town.
Since distance traveled cannot be negative, the domain is x ≥ 0. Therefore, the correct answer is:
D) distance traveled since leaving Bay Town; x ≥ 0
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The question in English is:
The distance between Bay Town and Oak Glen is 175 miles. If the equation y = -x +175 represents the distance to go to Oak Glen, what does the domain represent? What is the domain?
The distance between Town P and Town Q is 237.5 Km. At 11.30 a.m a van travels from
Town P to Town Q at an average speed of 35 km/h. At the same time, a car travels from
Town Q to Town P along the same route at an average speed of 60 km/h.
a)At what time will the vehicles meet on the way?
b) How far will each vehicle have travelled when they meet?
Answer:
So when the two vehicles meet, the van has travelled 87.5 km and the car has travelled 150 km.
Step-by-step explanation:
(a) Let's call the time it takes for the two vehicles to meet "t". We know that the distance between the two towns is 237.5 km, and the combined speed of the two vehicles is 35 km/h + 60 km/h = 95 km/h. Using the formula distance = speed × time:
237.5 = 95t
Solving for t:
t = 237.5/95
t ≈ 2.5 hours
So the two vehicles will meet on the way 2.5 hours after 11.30 a.m., which is at 2.00 p.m.
(b) To find how far each vehicle has traveled when they meet, we can use the formula distance = speed × time again. The van travels at 35 km/h for 2.5 hours, so it travels:
distance = speed × time = 35 km/h × 2.5 hours = 87.5 km
The car travels at 60 km/h for 2.5 hours, so it travels:
distance = speed × time = 60 km/h × 2.5 hours = 150 km
So when the two vehicles meet, the van has traveled 87.5 km and the car has traveled 150 km.
reasoning.
19. Challenge: Find the lengths of BC, DE, and FG in the diagram
below.
A
1
30°
B
0.5
C
D
E
-1.5√3
F
G
The length of BC, DE and FG are 0.5, 0.75 and 1.5 respectively. This can be solved by using trigonometric functions.
What are trigonometric functions?Trigonometric functions are used to describe relationships involving angles and sides of triangles. They are used to calculate the sizes of angles and distances between points. These include sine, cosine, tangent, secant, cosecant and cotangent.
This can be solved by using trigonometric functions.
First we need to find the length of FA to solve the question further.
FA = 1.5+ FD
AG = FA cos 30
AG = 1.5 √3
AG = 1.5 FD √3/2 = 1.5√3 (as cos 30 = √3/2)
DF = 1.5
Thus, FA = AB+BD+FD
FA = 1 + 0.5 + 1.5
So, the length of FA is 3.
Now, for the triangle, ΔABC
as ∠BAC= 30
BC = AB/2
= 0.5
This is because the angle of the right triangle is 30°and we know that when the angle of a right triangle is 30° the length of opposite side is exactly equal to half of the length of the hypotenuse.
For ΔADE,
as ∠DAE= 30, and AD= 1.5
DE= AD/2
= 0.75
For ΔGAF,
as ∠GAF= 30, and FA= 3
FG = FA/2
= 1.5
The length of BC, DE and FG are 0.5, 0.75 and 1.5 respectively.
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an expression that is equivelent to 12x-3x
Answer:
it would be 9x
Step-by-step explanation:
because subtract 3 from 12 and leave the x
What is the equation of a parabola with a vertical axis, vertex (h, k), and directrix y = k – p, where p is a nonzero real number? How can the equation be simplified if the vertex is at the origin?
The equation of a parabola with a vertical axis and vertex (h, k) is given by:
(x - h)² = 4p(y - k)
How to explain the equationIn the equation, where p is the distance from the vertex to the focus (and also the distance from the vertex to the directrix).
If the vertex is at the origin (h=0, k=0), then the equation simplifies to:
x² = 4py
where p is still the distance from the vertex to the focus (and also the distance from the vertex to the directrix).
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I don’t know how to do this question if anyone does please put the steps thank you.
If the third term is 31, then let's get the second term. We have to use the rule we were given and work backwards. So, we will add three and then divide by 2.
31 + 3 = 34
34 / 2 = 17
17 is the second term. Let's do the same thing we just did to find the first term: add three, divide by 2.
17 + 3 = 20
20 / 2 = 10
Answer: the first term is 10
Hope this helps!
You deposit $300 each month into an account earning 2% interest compounded
monthly.
a) How much will you have in the account in 30 years?
b) How much total money will you put into the account?
c) How much total interest will you earn?
a) The future value of the account after 30 years can be calculated using the formula:
FV = P * ((1 + r/n)^(n*t))
where P is the monthly deposit, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
In this case, P = $300, r = 0.02, n = 12 (monthly compounding), and t = 30. Plugging these values into the formula, we get:
FV = $300 * ((1 + 0.02/12)^(12*30)) = $150,505.60
So you will have $150,505.60 in the account after 30 years.
b) The total amount of money you will put into the account is simply the monthly deposit multiplied by the number of months in 30 years, which is 30*12 = 360 months. So the total amount of money you will put into the account is:
$300 * 360 = $108,000
c) The total interest earned can be calculated by subtracting the total amount deposited from the future value of the account. So the total interest earned is:
$150,505.60 - $108,000 = $42,505.60
Answer:
a) you will have approximately $133,381.85 in the account in 30 years.
b) a total of $108,000 into the account over 30 years.
c) a total of $25,381.85 in interest over 30 years.
Step-by-step explanation:
A can of soda is placed inside a cooler. As the soda cools its temperature C (t) in degrees Celsius after t minutes is given by the following exponential function.
C(t)=18(0.91)t
The initial temperature of the soda is 18 degrees Celsius.
Its temperature after 20 minutes is 2.73 degrees Celsius.
What is an exponential function?In Mathematics, an exponential function can be modeled by using this mathematical expression:
f(x) = a(b)^x
Where:
a represents the base value, initial value, or y-intercept.x represents time.b represents the rate of change.When time, t = 0, the initial value can be calculated as follows;
[tex]C(t)=18(0.91)^{t}\\\\C(0)=18(0.91)^{0}[/tex]
C(0) = 18(1)
C(0) = 18 degrees Celsius.
When time, t = 0 = 20, the temperature can be calculated as follows;
[tex]C(t)=18(0.91)^{t}\\\\C(20)=18(0.91)^{20}[/tex]
C(20) = 2.73 degrees Celsius.
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Complete Question:
A can of soda is placed inside a cooler. As the soda cools its temperature C (t) in degrees Celsius after t minutes is given by the following exponential function.
[tex]C(t)=18(0.91)^{t}[/tex]
Find the initial temperature of the soda and its temperature after 20 minutes?
Find a pair of integers whose difference gives zero.
A)8 and 1
B)8 and 2
C)8 and 3
D)-8 and -8
Answer:
Answer is D.
Please mark my answer as Brainliest if you found this one helpful.
sin negative-1 (-3sqrt/2) in radians
The given trigonometric expression sin⁻¹(-3√(2)/2) in radians is approximately -2.2143 radians.
As we know that sin⁻¹(x) = -cos⁻¹(x) + π/2, which is the angle in the fourth quadrant whose cosine is 3sqrt(2)/2.
We have:
cos²θ + sin²θ = 1
Since sine is negative and cosine is positive, we know that:
sinθ = -sqrt(1 - cos²θ)
Substituting cosθ = 3√(2)/2, we get:
sinθ = -√(1 - (3√(2)/2)²) = -√(1 - 9/8) = -√(1/8) = -√(2)/2
Therefore, sin^(-1)(-3sqrt(2)/2) = -cos^(-1)(3sqrt(2)/2) + π/2.
Since cosine is positive in the fourth quadrant, we have:
cos⁻¹(3√(2)/2) = π/4
Substituting this value, we get:
sin⁻¹(-3√(2)/2) = -π/4 + π/2 = π/4
Therefore, sin⁻¹(-3√(2)/2) in radians is approximately -2.2143 radians.
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Given that X is a normal random variable with a mean of 40 and a standard deviation of 8 what is P (34
The probability is given as follows:
P(34 < X < 46) = 0.5468 = 54.68%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 40, \sigma = 8[/tex]
The probability is the p-value of Z when X = 46 subtracted by the p-value of Z when X = 34, hence:
Z = (46 - 40)/8
Z = 0.75
Z = 0.75 has a p-value of 0.7734.
Z = (34 - 40)/8
Z = -0.75
Z = -0.75 has a p-value of 0.2266.
Hence:
0.7734 - 0.2266 = 0.5468 = 54.68%.
Missing InformationThe probability is:
P(34 < X < 46).
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(x^2-1)^3=64(X^2-1)^2
Answer:
x = ±1, ±√65
Step-by-step explanation:
You want the solution to (x² -1)³ = 64(x² -1)².
SolutionSubtracting the right side, we have ...
(x² -1)³ -64(x² -1) = 0
(x² -1)²(x² -1 -64) = 0
Zero product ruleThe solutions make the factors zero:
x² -1 = 0 ⇒ x = ±1
x² -65 = 0 ⇒ x = ±√65
Solutions are x = ±1 and x = ±√65.
__
Additional comment
The solutions ±1 are each multiplicity 2.
Two cars are traveling in the same direction. The first car is going 45 mi/h and the second car is going 60 mi/h. The first car left 2 hours before the second car. How many hours will it take for the second car to travel the same distance as the first car
The time taken for the second car to travel the same distance as the first car is 6 hours.
What is the time of motion of the second car?
The time taken for the second car to travel the same distance as the first car is calculated as follows;
let the time taken for the second car to travel the same distance = t
distance traveled by second car = 60t
the time taken for the first car = t + 2
distance traveled by the first car = 45(t + 2)
Since both distance are equal, we will have the following equations;
60t = 45 (t + 2)
60t = 45t + 90
15t = 90
t = 90/15
t = 6
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What linear function equation is represented by this graph?
ANSWER: 1
3
x−4 just took the test
Answer:
The linear function is y = (1/3)x - 4.
Step-by-step explanation:
The y-intercept is -4. Starting at (0, -4), go up 1 unit and then right 3 units. You will end at (3, -1). So the slope of this line is 1/3, and it follows that the function is
y = (1/3)x - 4.
to manufacturing floor
T
30 in.
72 in.
to loading dock
D
48 in.
36 in.
g) What is the longest rod that can be carried to the loading dock? Round to
the nearest tenth of an inch.
Answer:
To determine the longest rod that can be carried to the loading dock, we want to find the shortest distance from point T to line segment CD. We can use the Pythagorean theorem for this.
First, we need to find the equation of the line containing segment CD. We can find the slope of the line CD as:
m = (y2 - y1) / (x2 - x1) = (36 - 48) / (48 - 0) = -12/48 = -1/4
where (x1, y1) = (0, 48) and (x2, y2) = (48, 36).
Using point-slope form, we get the equation of the line CD as:
y - 48 = (-1/4)(x - 0)
y = (-1/4)x + 48
Now, we can find the perpendicular distance from point T to the line CD as follows:
d = |(-1/4)(30) + 72 - 48| / sqrt((-1/4)^2 + 1)
d = 42 / sqrt(17) ≈ 10.21
Therefore, the longest rod that can be carried to the loading dock is approximately 10.2 inches long (rounded to the nearest tenth of an inch).
Please help if I don't finish this today my parents gonna take my phone away
Find the slope to solve the problem.
Sue drives 200 miles by 1:00 pm. She drives 350 miles by 4:00 pm if she continues at the same rate, how far will she drive by 5:00 pm?
To find the slope in this problem, we can use the formula for calculating slope, which is change in distance divided by change in time. In this case, the change in distance is 350 miles - 200 miles = 150 miles, and the change in time is 4:00 pm - 1:00 pm = 3 hours.
So, the slope (rate of driving) is 150 miles / 3 hours = 50 miles per hour.
Now, to find how far Sue will drive by 5:00 pm, we can use the slope and the additional time of 1 hour (from 4:00 pm to 5:00 pm).Distance driven by 5:00 pm = Slope * Time = 50 miles per hour * 1 hour = 50 miles.Therefore, Sue will drive an additional 50 miles by 5:00 pm, making her total distance driven by 5:00 pm 200 miles + 150 miles + 50 miles = 400 miles. So, Sue will drive 400 miles by 5:00 pm if she continues at the same rate. Note that in this problem, we are assuming that Sue maintains a constant speed throughout her drive. If her speed changes, the solution may be different.
3. Rochelle helped in the garden 7 days during the last 4 weeks. Use the
numbers in the box to complete the sentences comparing her time in
the garden.
Numbers can be used more than once. Write each number in the
appropriate box.
For every day(s) Rochelle helped, she did not help
For every
day(s).
1 3 4 7 28
day(s).
day(s) Rochelle did not help, she helped
For every 3 days Rochelle helped, she did not help for 1 day.
For every 4 days Rochelle helped, she did not help for 1 day.
For every 7 days Rochelle helped, she did not help for 6 days.
For every 28 days Rochelle helped, she did not help for 21 days.
Let's use the terms provided to complete the sentences comparing Rochelle's time in the garden.
Since Rochelle helped in the garden for 7 days during the last 4 weeks, we can calculate the total number of days in 4 weeks and then find the number of days she did not help.
There are 7 days in a week, so in 4 weeks, there are 4 x 7 = 28 days.
Rochelle helped for 7 days, so she did not help for 28 - 7 = 21 days.
Now, let's complete the sentences:
For every 1 day(s) Rochelle helped, she did not help for 3 day(s).
For every 3 day(s) Rochelle did not help, she helped 1 day(s).
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Can anyone help with this part of my geometry notes ?
From the interior angle theorem:
m∠1 = ¹/₂(m∠AD + m∠BC)m∠2 = 180 - m∠1m∠AED = 77°m∠AEB = 103°m∠LK = 50°What is the interior angle theorem?The Interior Angle Theorem states that if two secants or chords intersect inside a circle, then the measure of the angle formed is equal to half the sum of the measures of the intercepted arcs.
Considering the given circles:
m∠AED = ¹/₂(45 + 109)
m∠AED = 77°
m∠AEB = 180 - 77
m∠AEB = 103°
m∠LK = (2 * 62) - 74)
m∠LK = 50°
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The cubic polynomial shown below has zeroes at x=-1and x= only and has a relative maximum at (3,8). Which of the following is its y-value when x=5?
The cubic polynomial is given as y = 0.25(x³ - 12x + 16). Then the value of y when x = 6 will be 40.
Therefore the option C is correct.
What is polynomial?A polynomial expression is described as an algebraic expression with variables and coefficients.
If the zeroes of the polynomial are negative 4, 2, and 2.
Then the factors will be (x + 4), (x - 2), and (x - 2).
Then the cubic polynomial will be
→ (x + 4) (x - 2) (x - 2)→ (x + 4) (x² - 4x + 4)→ (x³ - 12x + 16)we can write the polynomial equation as:
y = C(x³ - 12x + 16)
Then the polynomial is maximum at (-2, 8) then the value of C will be 0.25.
y = 0.25 (x³ - 12x + 16)
y = 0.25 (6³ - 12 × 6 + 16)
y = 0.25 (216 - 72 + 16)
y = 0.25 (160)
y = 40
Note that there was no diagram provides, i solved a similar question
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PLS HELP ASAP PLSSSSSS
Answer:
a) |x -8| = 6
b) |x -15| = 0
Step-by-step explanation:
You want the values of 'b' and 'c' for the cases where the solutions to the equation |x -b| = c are ...
2 and 1415SolutionsThe solutions to |x -b| = c are the solutions to ...
x -b = c ⇒ x = b +c
x -b = -c ⇒ x = b -c
ParametersGiven the two solutions P and Q, the values of 'b' and 'c' can be found from ...
P = b +c
Q = b -c
Adding these two equations gives ...
P +Q = 2b ⇒ b = (P +Q)/2
Subtracting the second equation from the first gives ...
P -Q = 2c ⇒ c = (P -Q)/2
a) Solutions 2 and 14b = (2 +14)/2 = 8
c = (14 -2)/2 = 6
The equation is ...
|x -8| = 6
b) Solutions 15 and 15b = (15 +15)/2 = 15
c = (15 -15)/2 = 0
The equation is ...
|x -15| = 0
The sides of a square are increased
by a scale factor of 3. The area of
the larger square is what percent of
the area of the smaller square?
So the area of the larger square is 900% of the area of the smaller square.
What is area?Area is a measure of the size of a two-dimensional surface or region. It is typically expressed in square units, such as square meters (m²) or square feet (ft²). To find the area of a shape, you need to measure the length and width of the surface or region and then multiply those measurements together.
Here,
If the sides of a square are increased by a scale factor of 3, then the new square will have sides that are 3 times as long as the original square. The area of a square is proportional to the square of its sides, so the area of the new square will be 3² = 9 times as large as the area of the original square. Therefore, the area of the larger square is 900% of the area of the smaller square.
Alternatively, we can use the formula for the area of a square, A = s², where A is the area and s is the side length. If the side length is increased by a scale factor of 3, then the new side length is 3s. Therefore, the area of the new square is:
A' = (3s)²
= 9s²
The ratio of the area of the new square to the area of the original square is:
A' / A = (9s²) / (s²)
= 9
Multiplying by 100% to convert to a percentage, we get:
A' / A = 900%
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Carson is organizing textbooks on his bookshelf. He has a Spanish textbook, a math textbook, a history textbook, and a health textbook. How many different ways can he line the textbooks up on his bookshelf?
Carson can line up his textbooks on his bookshelf in 24 different ways
What is Permutation?
Permutations are a way to count the number of ways that a set of objects can be arranged in a particular order. A permutation is an ordered arrangement of objects.
What is Combination?
The combination is a way to count the number of ways that a set of objects can be selected without regard to order. A combination is an unordered selection of objects.
According to the given information:
Carson has four textbooks that he wants to line up on his bookshelf. The number of different ways that he can do this is given by the permutation formula:
n! / (n - r)!
where n is the total number of objects (in this case, 4 textbooks), and r is the number of objects that he wants to arrange in a particular order (in this case, all 4 textbooks).
On substituting the values in the formula,
4! / (4 - 4)! = 4! / 0! = 4 x 3 x 2 x 1 / 1 = 24
Therefore, Carson can line up his textbooks on his bookshelf in 24 different ways.
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