PLEASE HELP !!
Quadrilateral ABCD has vertices at A (0, 0), B (0, 3), C (5, 3), and D (5, 0). Find the vertices of the
quadrilateral after a dilation with scale factor 2.5.
Answers
According to the dilation formula, the location of the four vertices of the quadrilateral A'B'C'D' are A'(x, y) = (0, 0), B'(x, y) = (0, 7.5), C'(x, y) = (12.5, 7.5) and D'(x, y) = (12.5, 0).
How to determine the coordinates of the vertices of the dilated rectangle
Dilation are a kind of rigid transformations defined by the following formula:
P'(x, y) = O(x, y) + r · [P(x, y) - O(x, y)] (1)
Where:
O(x, y) - Center of dilationr - Dilation factorP(x, y) - Original pointP'(x, y) - Resulting pointIf we know that r = 2.5, O(x, y) = (0, 0), A(x, y) = (0, 0), B(x, y) = (0, 3), C(x, y) = (5, 3) and D(x, y) = (5, 0), then the resulting points are obtained:
A'(x, y) = (0, 0) + 2.5 · [(0, 0) - (0, 0)]
A'(x, y) = (0, 0)
B'(x, y) = (0, 0) + 2.5 · [(0, 3) - (0, 0)]
B'(x, y) = (0, 7.5)
C'(x, y) = (0, 0) + 2.5 · [(5, 3) - (0, 0)]
C'(x, y) = (12.5, 7.5)
D'(x, y) = (0, 0) + 2.5 · [(5, 0) - (0, 0)]
D'(x, y) = (12.5, 0)
Lastly, we proceed to graph the two figures.
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Related Questions
In a New York State daily lottery game, a sequence of five digits (not necessarily different) in the range 0-9 are selected at random. Find the probability that four of the five digits are the same.
Answers
The probability that four of the five digits are the same is 0.036.
There are 10,000 (10*10*10*10) possible sequences. There are 4C3 ways, 4, of having exactly three digits be the same value. The differing digit can be any of the four positions. There are 10P2 ways, 90 (10*9), to choose the digits of the sequence since we have 10 choices for the digit to be repeated, then 9 more options or the differing digit. The product of the combination arrangements and permutation selection, 4*90, shows there are 360 sequences with three of the same digit. Thus the probability is 360/10,000 or 0.036 or 3.6%.
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Triangle A B C has centroid G. Lines are drawn from each point through the centroid to the midpoint of the opposite side to form line segments A F, B D, and C E. The length of line segment A G is 19 x + 14 and the length of line segment D G is 9 x + 2.
G is the centroid of triangle ABC.
What is the length of GF?
units
Answers
Based on the calculations, the length of GF is equal to 26 units.
How to find the length of GF?In Geometry, the centroid of any triangle always divides the lines in a ratio of 2:1. Thus, G divides line B F as follows:
2DG = BD
2(9x + 2) = 40
18x + 4 = 40
18x = 40 - 4
x = 36/18
x = 2.
Similarly, G divides line A F as follows:
2GF = A F
GF = A F/2
GF = (19x + 14)/2
GF = (19(2) + 14)/2
GF = 52/2
GF = 26 units.
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Answer: 26 units
Step-by-step explanation: Trust Me!
The answer is correct on Edge. I did it and got it right!
The distance between adelaide and melbourne is 450 miles. For the first 200 miles, Mila drives her car at X miles per hour. For the remaining distance, Mila drives her car at (X+30) mph. The average speed of the whole trip is 30 mph. What is the value of X?
Answers
Time taken= 200/x
Second part of the trip:
Time taken= 250/(x+30)
Average:
Time taken= 450/30
Time taken= 15 hours
200/x + 250/(x+3)= 15
-15x^2+405x+600=0
x=28.40805152
Identify the expression that has two terms.
6 x + 4
x/4
2 x
5
Answers
Answer:
A
Step-by-step explanation:
Comment
The first one. Such an expression requires an isolation plus or minus sign and two terms that are not alike.
Answer
A
Answer:
6x+4
Step-by-step explanation:
A term can be a constant(like 7,4,3 etc) or a variable (x,y etc) which is separated by a multiplication, division,addition or subtraction sign.
Find all solutions to the equation in the interval [0,2pi]. Enter the solutions in increasing order. sin 2x = sin x
please explain how you got the answer
Answers
Step-by-step explanation:
[tex]sin2x=sinx\\sin2x-sinx=0\\2*sinx*cosx-sinx=0\\sinx*(2*cosx-1)-0\\sinx=0 \\x=\pi n\ \ \ \ \ x\in[0;2\pi ]\ \ \ \ \Rightarrow\\x_1=0\ \ \ \ x_2=\pi .\\2*cosx-1=0\\2*cosx=1\ |:2\\cosx=\frac{1}{2} \\x=б\frac{\pi }{3} +2\pi n\ \ \ \ \ x\in[0;2\pi ]\ \ \ \ \Rightarrow\\x_3=\frac{\pi }{3} \ \ \ \ \ x_4=\frac{5\pi }{3}.\\[/tex]
[tex]Answer: x=0,\ \frac{\pi }{3} ,\ 1\pi ,\ \frac{5\pi }{3} .[/tex]
Jacob made 93 cups of lemonade.
He and his sisters drank 5½ cups.
How much lemonade is left?
Give your answer as a mixed number in simplest form
Enter the number that belongs in the green box.
[?] cups
Answers
Answer:
I think it's 87.5 or 87½
Step-by-step explanation:
I hope it helps you.
HELP HELP HELP
I have so many 50 point easy algebra 1 questions, just look into my profile and click questions I really need help.
Tysm! :)
Answers
What is the sum of k° + i°?
180°
360°
110°
290°
Answers
Answer:
k+i =290
Step-by-step explanation:
The three angles added together form a circle, which is 360 degrees
k+i + 70 = 360
We want to find the sum of k+i, so we subtract 70 from each side
k+i + 70-70 = 360-70
k+i =290
Consider u = ⟨5, –2⟩ and v = ⟨10, –4⟩. what is the relationship between u and v?
Answers
Answer:
v = 2u
Step-by-step explanation:
note that
2u = 2 (5, - 2 ) ← multiply each component by 2
= (10, - 4) = v , then
v = 2u
Jim’s Gym has an initial fee of $300 to join the gym and then charges $3 per visit. Sally’s Salon has an initial fee of $250 and then charges $5 per visit. Write a system of equations that represent the total fees charged for each plan. How many visits does it take before the plans are equal? Separate your equations and final number of visits by comas
Answers
The system of equation is y = 300 + 3x and y = 250 + 5x and the number of visits is 25
The system of equationsThe given parameters are:
Jim's Gym
Initial fee = $300Charges = $3 per visitSally's Salon
Initial fee = $250Charges = $5 per visitThe equation is calculated as:
Total (y) = Initial * Charges * Number of visits (x)
So, the system of equation is
y = 300 + 3x
y = 250 + 5x
Number of visits before the plans are equalWe have:
y = 300 + 3x
y = 250 + 5x
Substitute y = 300 + 3x in y = 250 + 5x
300 + 3x = 250 + 5x
Evaluate the like terms
-2x = -50
Divide by -2
x= 25
Hence, the number of visits is 25
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1. Taking your eyes off the road for ____ seconds at 60 miles per hour means you have traveled blindly for half the length of a football field.
Answers
Answer:
4.09 seconds
Step-by-step explanation:
simplify miles per hour to feet per second how many feet is a mile and how many seconds are in an hour you end up with 88 fps from 60 mph
now simply a football field is 360 feet so 360/88 is 4.09090909 etc
Your eyes off the road for 4.09 seconds.
What is speed?The rate of change of position of an object in any direction is called the speed.
Given that, Taking your eyes off the road for how many seconds at 60 miles per hour means you have travelled blindly for half the length of a football field,
Converting 60 mph into fps
60 mph = 88 fps
The length of a football field = 360 ft
Time = 350/88
= 4.09 seconds.
Hence, you travelled for 4.09 seconds.
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Question 2 of 10
If a basketball player missed 53 free throws out of 100, what fraction and
what percentage of free throws did the player make? Choose two answers.
Answers
Answer:
47/100 and 47%
Step-by-step explanation:
He missed 53 out of 100 so that means he made 47 out of a 100 and there you go... 47/100 and 47%
what is the probability of hitting a triangle on this dashboard?
Answers
Answer: 9/110
Step-by-step explanation:
11*20=220
3*3/2*4=18
18/220=9/110
Answer:
P = 9/110
Step-by-step explanation:
Area of all triangles
[tex]4(\frac{(3)(3)}{2}) =4(\frac{9}{2}) =18[/tex]
Area of the rectangle
[tex](20)(11)=220[/tex]
Probability of hit
[tex]P=\frac{18}{220}= \frac{9}{110}[/tex]
Hope this helps
The graph of the function f(x) = -(x+3)(x-1) is shown
below.
64-2
Mark this and return
6
A
2
-2-
-4
-6
2
4
6
X
Which statement about the function is true?
O The function is positive for all real values of x where
x < -1.
The function is negative for all real values of x where
x <-3 and where .x > 1.
O The function is positive for all real values of x where
x > 0.
O The function is negative for all real values of x where
x <-3 or x>-1.
Save and Exit
Next
Submit
Answers
The true statement about this function is that: B. the function is negative for all real values of x, where x < -3 and where x > 1.
What is a function?A function is a mathematical expression which can be used to define and indicate the relationship existing between two or more variables in a data set.
By critically observing the graph which models the given function (see attachment), we can logically deduce that the true statement about this function is that it's negative for all real values of x, where x is less than -3 and where x is greater than 1.
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Question 10 How many cubic yards of sand will it take to fill a child's play area that measures 10 yards long, 8 yards wide, and 1/3 yard deep
Answers
Answer:
26.6 cubic yards
Step-by-step explanation:
Remark
What you have is a rectangle prism. It has an easy enough formula.
Formula
V = L *w * h
Givens
L = 10 yards
w = 8 yards
h = 1/3 yards
Solution
V = L*w*h
V = 10 * 8 * 1/3
V = 26.66 yds^3
What is the volume of the following rectangular prism? Volume ==equals units^3 3
Answers
The volume of the rectangular prism is 1/10 cubic units
Volume of a rectangular prismThe formula for calculating the volume of a rectangular prism is expressed as;
V = Bh
B is the base area
h is the height
Given the following parameters
B = 3/20 units²
h = 2/3 units
Substitute
V = 3/20 * 2/3
V = 2/20
V = 1/10 cubic units
Hence the volume of the rectangular prism is V = 1/10 cubic units
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Answer:8 1/2^3
Step-by-step explanation:
The table shows the information about the length of time, in minutes, it took students to do their maths homework.
Draw a histogram.
Answers
The histogram is a chart for comparing the data by plotting it in a rectangular form in the chart. The histogram for the given data is attached with the answer below.
What is a histogram?The histogram is a diagram with rectangles whose width is similar to the specified range and whose area is equal to the regularity of variables.
The histogram is a chart for comparing the data by plotting it in a rectangular form in the chart.
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Assume that all conditions are met. The mean of the differences was 1. 33 and the standard deviation of those differences was 2. 90. What is the test statistic for this procedure?.
Answers
The test static used for this procedure is Aspin Welch's t-test.
What is Aspin Welch's T-test?
A variation of the Student's t-test used to determine if two sample means are substantially different is known as the Aspin Welch's T - test for Unequal Variances (also known as Welch's t-test, Welch's adjusted T, or unequal variances t-test). The test's degrees of freedom have been changed, which generally boosts the test's power for samples with unequal variance.
The means being equal is the test's null hypothesis.The notion that the means are not equal serves as the test's alternate hypothesis.Formula for Aspin Welch's T - test
The t-statistic in Aspin Welch's T-test is given as,
t = [tex]\frac{X' - X}{\sqrt{\frac{S1^{2} }{N1^{2} } -\frac{S2^{2} }{N2^{2} } } }[/tex]
Here, X' is the mean of the sample
X is the mean of the population
S1 and S2 are the respective standard deviations for the two samples
N1 and N2 are the respective strength of samples.
Calculating t-statistic for Aspin Welch's T-test
Given that,
X'-X = 1.33
[tex]\sqrt{\frac{S1^{2} }{N1^{2} } -\frac{S2^{2} }{N2^{2} } } = 2.90[/tex]
∴ t = 1.33/2.90
t=0.458
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What is the solution to the system of equations? "-6x2/5y=8" 1/2x+3y=29
(10, –2)
(10, 2)
(2, 10)
(–2, 10)
Answers
The answer choice which represents a solution to the system of equations is; (–2, 10).
Which answer choice is a solution to the systems of equations?The system of equations as given in the task content is;
-6x - (2/5)y = 8
(1/2)x +3y = 29
Hence, by making x subject in equation 1 and substitution; we have;
x = (-0.4y -8)/6
Hence; (0.4y -8)/12 + 3y = 29.
(0.4y -8) + 36y = 348
35.6y = 356
y = 10
and x = (-0.4(10) -8)/6 = -2.
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If sin θ = cos θ, what are the possible values of θ from 0 < θ < 2π?
A.) π/4
B.) 3π/4
C.) 5π/4
D.) 7π/4
Answers
The possible values is θ = π/4 and 5π/4
What is Trigonometry?The branch of mathematics concerned with specific functions of angles and their application to calculations.
Given:
sin θ = cos θ
The above condition satisfied for θ = π/4 and 5π/4
sin π/4 = cos π/4 = 1/√2
sin 5π/4 = cos 5π/4 = -1/√2
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5. Sally took money from her bank account to go
out of town for an audition. She spent $54.00
for a round-trip ticket and 1/2 of the remaining
money for her hotel bill. She spent $7.90 for
food and arrived home with $15.10. How much
money did Sally take from her bank account?
Answers
Answer:
110
Step-by-step explanation:
Sally takes $110 from her bank account if she spent $54.00 for a round-trip ticket.
What are expenses?It is defined as the money spends on the utility, the amount of money is required to buy something, in other words, it is the outflow of money from the sole earner's income or the money incurred by any organization.
We have:
Sally took money from her bank account to go out of town for an audition.
The expeses = (7.90 + 15.10) ÷ (1 - 1/2) = $46
Total money = 54 + 46
Total money = $110
Thus, Sally takes $110 from her bank account if she spent $54.00 on a round-trip ticket.
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Find the rate of change for the given table of values.
Answers
Answer:
-40
Step-by-step explanation:
First you have to look at the difference between 8 and 10. which is 80, then because it takes two steps to go from 8 to 10 you divide 80 by two, which is 40. And because the values are decreasing it is -40.
The coordinates of the vertices of quadrilateral ABCD are A(−5, 1), B(−2, 5), C(5, 3), and D(2, −1). Drag and drop the choices into each box to correctly complete the sentences. The slope of AB¯¯¯¯¯ is Response area, the slope of BC¯¯¯¯¯ is Response area, the slope of CD¯¯¯¯¯ is Response area, and the slope of AD¯¯¯¯¯ is Response area. Quadrilateral ABCD is Response area because Response area.
Answers
Slope of AB = 4/3, Slope of BC = -2/7, Slope of CD = 4/3, Slope of AD = -2/7 and Quadrilateral ABCD is a parallelogram because both pairs of opposite sides are parallel.
How to find the slope of a quadrilateral?We are given the coordinates of the quadrilateral ABCD as;
A(−5, 1), B(−2, 5), C(5, 3), and D(2, −1).
Slope of AB = (5 - 1)/(-2 + 5) = 4/3
Slope of BC = (3 - 5)/(5 + 2) = -2/7
Slope of CD = (-1 - 3)/(2 - 5) = 4/3
Slope of AD = (-1 - 1)/(2 + 5) = -2/7
Thus we can see that both pairs of slope are equal which denotes that both pairs are parallel.
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20² + 15¹ = ? Help me!!
Answers
Answer:
415
Step-by-step explanation:
20x20=400+15= 415
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathbf{20^2 + 15^1}[/tex]
[tex]\huge\textbf{Solving:}[/tex]
[tex]\mathbf{20^2 + 15^1}[/tex]
[tex]\mathbf{= 20\times 20 + 15\times 1}[/tex]
[tex]\mathbf{= 400 + 15}[/tex]
[tex]\mathbf{= 415}[/tex]
[tex]\huge\textbf{Answer:}[/tex]
[tex]\huge\boxed{\mathsf{415}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
please answer this paper
Answers
The computation shows that the total number of chocolate bars when there are 280 orange flavored bars will be
How to compute the values?The total number of chocolate bars when there are 280 orange flavored bars will be:
= Coconut + Honeycomb + Coffee + Orange + Strawberry
= (4/6 × 280) + (5/6 × 280) + (1/6 × 280) + 280 + (4/6 × 280)
= 1033
The total number when there are 960 coconut bars will be:
= Coconut + Honeycomb + Coffee + Orange + Strawberry
= 960 + (5/4 × 960) + (1/6 × 960) + (6/4 × 960) + 960
= 960 + 1200 + 160 + 1440 + 960
= 4720
The mean of 7, 2, and 9 will be:
= (7 + 2 + 9)/3
= 6
The mean of 5, 6, 6, and 5 will be:
= (5 + 6 + 6 + 5)/4
= 22/4
= 5.5
The mean of 2, 1, 2, 3, 3, 1 will be:
= (2 + 1 + 2 + 3 + 3 + 1) / 6
= 15/6
= 2.5
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In a school, lessons are 55 minutes long.
A maths lesson starts at 9:15am
At what time does the lesson end?
Answers
Answer:
6:10am from my point of view
Solve this identity, where the angles involved are acute angles.
[tex] \dfrac{\tan\theta}{1 -\cot\theta } + \dfrac{\cot\theta}{1 -\tan \theta } = 1 + \sec \theta \cosec\theta[/tex]
Answers
[tex]\therefore \sf{ LHS = \dfrac{tan \theta}{1 – cot \theta } + \dfrac{cot \theta}{1 – tan \theta}}[/tex]
[tex]\\[/tex]
[tex]\therefore\sf{ LHS = \dfrac{tan \theta}{1 – \dfrac{1}{tan \theta}} + \dfrac{ \dfrac{1}{tan \theta}}{1 – tan \theta} }[/tex]
[tex]\\[/tex]
[tex]\therefore\sf{ LHS = \dfrac{ tan^{2} \theta }{tan \theta – 1} + \dfrac{1}{tan \theta (1–tan \theta) } }[/tex]
[tex]\\[/tex]
[tex] \therefore\sf{ LHS = \dfrac{tan^{2} \theta}{tan \theta–1} – \dfrac{1}{tan \theta(tan \theta – 1 )}}[/tex]
[tex]\\[/tex]
[tex]\therefore \sf{LHS = \dfrac{tan^{3}\theta–1}{tan \theta(tan \theta –1)}}[/tex]
[tex]\\[/tex]
[tex]\therefore\sf{LHS = \dfrac{tan^{3}\theta–(1)^{3}}{tan\theta(tan\theta–1)}}[/tex]
[tex]\\[/tex]
[tex] \therefore\sf{ LHS = \dfrac{ (tan \theta -1)(tan^{2}\theta+tan\theta .1 + (1)^{2})} {tan \theta (tan\theta(tan \theta –1 )}}[/tex]
[tex]\\[/tex]
[tex] \therefore\sf{ LHS = \dfrac{(tan^{2} \theta×tan\theta .1+1)}{tan \theta}}[/tex]
[tex]\\[/tex]
[tex] \therefore\sf{ LHS = \dfrac{(sec^{2}\theta+tan\theta)}{tan\theta}}[/tex]
[tex]\\[/tex]
[tex] \therefore\sf{ LHS = \dfrac{sec^{2}\theta}{tan\theta} + \dfrac{tan \theta}{tan\theta}}[/tex]
[tex]\\[/tex]
[tex] \therefore\sf{ LHS = sec^{2}\theta \times cot \theta + 1 }[/tex]
[tex]\\[/tex]
[tex] \therefore\sf{ LHS = \dfrac{1}{cos^{2}\theta} \times \dfrac{cos \theta }{sin\theta}+1}[/tex]
[tex]\\[/tex]
[tex] \therefore\sf{ LHS = \left( \dfrac{ 1}{cos \theta} \times \dfrac{1}{sin \theta} \right) + 1}[/tex]
∴ LHS = 1 + secθ.cosecθ = RHS━━━━━━━━━━━━━━━━━━━━━━━We have proven that the trigonometric identity [(tan θ)/(1 - cot θ)] + [(cot θ)/(1 - tan θ)] equals 1 + (secθ * cosec θ)
How to solve Trigonometric Identities?We want to prove the trigonometric identity;
[(tan θ)/(1 - cot θ)] + [(cot θ)/(1 - tan θ)] = 1 + sec θ
The left hand side can be expressed as;
[(tan θ)/(1 - (1/tan θ)] + [(1/tan θ)/(1 - tan θ)]
⇒ [tan²θ/(tanθ - 1)] - [1/(tan θ(tanθ - 1)]
Taking the LCM and multiplying gives;
(tan³θ - 1)/(tanθ(tanθ - 1))
This can also be expressed as;
(tan³θ - 1³)/(tanθ(tanθ - 1))
By expansion of algebra this gives;
[(tanθ - 1)(tan²θ + tanθ.1 + 1²)]/[tanθ(tanθ(tanθ - 1))]
Solving Further gives;
(sec²θ + tanθ)/tanθ
⇒ sec²θ * cotθ + 1
⇒ (1/cos²θ * cos θ/sin θ) + 1
⇒ (1/cos θ * 1/sin θ) + 1
⇒ 1 + (secθ * cosec θ)
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Which triangles could not be similar to triangle ABC ?
triangle a b c where angle b is a right angle. side a b is 15 cm. side b c is 8 cm. side a c is 17 cm.
Select each correct answer.
(See image for details.)
Answers
Similar triangles are those triangles whose corresponding sides are in the same ratio. The triangles that are similar to ΔABC are ΔDEF and ΔJKL.
What are similar triangles?Similar triangles are those triangles whose corresponding sides are in the same ratio. And the corresponding angles measure the same.
For two triangles to be similar there sides should be in the same ratio.
For ΔABC ~ ΔMNO,
AB/MN should be equal to BC/NO,
AB/MN = 15/35 = 0.4286
BC/NO = 8/12 = 0.66
Thus, there are not similar triangles.
For ΔABC ~ ΔDEF,
AB/MN should be equal to BC/NO,
AB/DE = 15/22.5 = 0.66
BC/EF = 8/12 = 0.66
Thus, there are similar triangles.
For ΔABC ~ ΔGHI,
AB/GH should be equal to BC/HI,
AB/MN = 15/77 = 0.1948
BC/NO = 8/36 = 0.222
Thus, there are not similar triangles.
For ΔABC ~ ΔJKL,
AB/MN should be equal to BC/NO,
AB/JK = 15/60 = 0.250.25
BC/KL = 8/32 = 0.66
Thus, there are similar triangles.
Hence, the triangles that are similar to ΔABC are ΔDEF and ΔJKL.
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Julia examines the two triangles below and determines that Triangle F G H is similar to triangle L N M.
Triangle F G H. Angle F is 98.6 degrees and angle G is 61.1 degrees. Triangle L N M. Angle M is 18.3 degrees and angle L is 98.6 degrees.
Which best describes the accuracy of Julia’s solution?
Accurate. The triangles are similar and the congruent angles are listed in corresponding order.
Inaccurate. The triangles are not similar because the sum of the angles in each triangle is not 180º.
Inaccurate. The triangles are similar, but the triangles are named incorrectly. The vertices are listed out of corresponding order.
Inaccurate. The triangles are not similar because angle M is not congruent to angle H, and angle N is not congruent to angle G.
Answers
The correct option regarding whether the triangles are similar is given by:
Inaccurate. The triangles are not similar because angle M is not congruent to angle H, and angle N is not congruent to angle G.
What are similar triangles?Similar triangles are triangles that have congruent angles, that is, angles with the same measure.
Considering that the sum of the internal angles of a triangle is of 180º, the third angle of triangle FGH is given as follows:
98.6 + 61.1 + x = 180
x = 180 - (98.6 + 61.1)
x = 20.3º.
The second triangle has an angle of 20.3º, hence they are not similar, and the correct option is given by:
Inaccurate. The triangles are not similar because angle M is not congruent to angle H, and angle N is not congruent to angle G.
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convert the Function to Degrees Fahrenheit:
3. Suppose you want to represent the desert temperature in degrees Fahrenheit instead. How would you transform the function C(t) to make the new function, F(t)? (2 points: 1 point for each transformation)
Note: The conversion rule for Celsius to Fahrenheit is .
F(t)=95(-0.30(t-12)2+40)+32
f(t)=-0.54(t-12)2+72+32
4. Take your values from the previous chart (in question 2) and convert them from Celsius to Fahrenheit. Follow the example below, and use the conversion rule to fill out the chart for degrees Fahrenheit when t = 12 and t = 24. (2 points: 1 point for each row)
t
0
12
(12,24)
c(0)=95(24)+32
24
5. Use the conversion formula to write the equation for the new function, F(t).
(4 points: 2 points for setting up the equation, 2 points for the answer)
Hint: Substitute the equation for C(t) into .
6. Plot the points from the Fahrenheit chart in question 4 onto the graph below. Use the plotted points to sketch out the graph of F(t). (3 points: 2 points for correct coordinates, 1 point for correct shape)
7. Compare the graph in question 6 (F(t)) with the graph in question 2 (C(t)). What changes were made to the graph of C(t) to transform it to F(t)? (1 point)
Answers
The changes that transform C(t) to F(t) is that the function C(t) is stretched vertically to form the function F(t)
How to transform the function?The Fahrenheit function
The Celsius function is given as:
C(t) = -0.30 (t – 12)² + 40
The conversion from Celsius to Fahrenheit is
F(t) = 9/5 * C(t)
Hence, the Fahrenheit function is F(t) = 9/5 * C(t)
Convert values from Celsius to Fahrenheit
The values are t = 0, 12 and 24.
So, we have:
F(0) = -0.54(0 - 12)² + 72 = -5.76
F(12) = -0.54(12 - 12)² + 72 = 72
F(24) = -0.54(24 - 12)² + 72 = -5.76
The new function F(t)
The conversion from Celsius to Fahrenheit is
F(t) = 9/5 * C(t)
So, we have:
F(t) = 9/5 * (-0.30 (t – 12)² + 40)
Expand
F(t) = -0.54(t – 12)² + 72
Hence, the new function is F(t) = -0.54(t – 12)² + 72
The graph of function F(t)
See attachment for the graph of function F(t)
The changes that transform C(t) to F(t)
We have:
C(t) = -0.30 (t – 12)² + 40
F(t) = 9/5 * C(t)
The above implies that the function C(t) is stretched vertically to form the function F(t)
Read more about composite functions at:
https://brainly.com/question/20379727
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