Given that:
Parent equation : [tex]y=x[/tex]
Transformed function : [tex]c(x)=\dfrac{5}{9}(x-32)[/tex]
Solution:
Let Parent equation be [tex]f(x)=x[/tex]. Then,
[tex]c(x)=\dfrac{5}{9}f(x-32)[/tex] ...(1)
The translation is defined as
[tex]c(x)=kf(x+a)+b[/tex] .... (2)
Where, k is stretch factor, a is horizontal shift and b is vertical shift.
If 0<k<1, then the graph compressed vertically by factor k and if k>1, then the graph stretch vertically by factor k.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
On comparing (1) and (2), we get
[tex]k=\dfrac{5}{9}<1[/tex] , So graph of parent function compressed vertically by factor [tex]\dfrac{5}{9}[/tex].
[tex]a=-32<0[/tex], so the graph of parent function shifts 32 units right.
[tex]b=0[/tex], so there is no vertical shift.
Therefore, the graph of parent function compressed vertically by factor [tex]\dfrac{5}{9}[/tex] and shifts 32 units right to get the graph of c(x).
horizontal translation
vertical compression
Step-by-step explanation:
the first 2
Which figures demonstrate a reflection? Select each correct answer.
top right and bottom right
The figures demonstrate a reflection are option (B) and option (D) are the correct answer.
What is a reflection of transformation?A reflection is a type of transformation. It maps one shape onto another. The function retains its basic shape; however, by including a negative sign in the appropriate place in the equation, the graph of the function will flip over one or the other of the axes.
For the given situation,
The options shows the different figures. we need to select the figure that correctly demonstrates the reflection.
Option A:
Here, the figure is not flipped on the axes.
The figure in option A does not show the transformation of reflection.
Option B:
Here, the figure is flipped on the axes.
The figure in option B shows the transformation of reflection.
Option C:
Here, the figure is not flipped on the axes.
The figure in option C does not show the transformation of reflection.
Option D:
Here, the figure is flipped on the axes.
The figure in option D shows the transformation of reflection.
Hence we can conclude that the figures demonstrate a reflection are option (B) and option (D) are the correct answer.
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The width of a rectangle is 5 feet less than the length. The perimeter is 62. Find the length and width of the rectangle.
Variables: ___________________________
Model equation: ______________________________
Length of the rectangle: ______________________________
Width of the rectangle: ______________________________
Perimeter formula: p = 2(w + l)
The perimeter is 62.
p = 62
The width of a rectangle is 5 feet less than the length.
w = l - 5
Substitute and solve.
62 = 2[(l - 5) + l)]
62 = 2l + 2l - 10
62 = 4l - 10
72 = 4l
18 = l
Substitute and solve for the width
w = 18 - 5
w = 13
Therefore, the length is 18 and the width is 13.
Best of Luck!
Answer:
see below and attached.
Step-by-step explanation:
Perimeter (P) = 2 L (Length) + 2 W (Width)
where P = 62
W = L - 5
P = 2L + 2W
62 = 2L + 2(L -5)
62 = 2L + 2L - 10
72 = 4L
L = 72/4
L = 18
W = L - 5
W = 18 - 5
W = 15
Variables : P, L, W
Model equation: P = 2L + 2W
Length of the rectangle: 18
Width of the rectangle: 13
Please Help!!!! 50 Points
Answer:
D
Step-by-step explanation:
Answer: D.
Step-by-step explanation:
HELPPPPP
1. How can you prove that a line parallel to one side of a triangle divides the other 2 sides proportionally?
2. In an isosceles triangle, how do you prove the base angles are congruent?
Answer:
1. You can prove that a line parallel to one side of a triangle divides the other 2 sides proportionally by using the Triangle Proportionality Theorem.
2. You prove the base angles are congruent by constructing the angle bisector through the vertex angle of an isosceles triangle. By constructing the angle bisector, we designed two congruent triangles and then used CPCTC to show that the base angles are congruent.
Step-by-step explanation:
Mrs. Wheeler is finishing a craft and needs a piece of yarn that is 5.4 feet long. If Mrs. Wheeler has 54 inches of yarn, she __________. A. has enough yarn because 54 inches is 18 feet of yarn B. has enough yarn because 54 inches is 5.4 feet C. does not have enough yarn because 54 inches is 0.54 feet of yarn D. does not have enough yarn because 54 inches is 4.5 feet of yarn
Answer:
D
Step-by-step explanation:
ello
-_-
Evaluate when a = 8 and b = -4 a(a - b) ÷ (a + b) A) -12 B) 8/3 C) 10 D) 24 what the answer
Answer:
Step-by-step explanation:
a = 8 and b = -4 a(a - b) ÷ (a + b)
A) -12
B) 8/3
C) 10
D) 24
ANSWER IS D) 24
I need help with this ASAP!!!
Answer:
Step-by-step explanation:
12.5= 25/2
Ln (25/2).. change decimal to fraction
Ln ((5^2)/2)...change 25 to 5^2
(2ln 5)/2... log rule.. move exponent to the front
Ln 5 .. . Simplify the top and bottom 2's
The metal in a penny is about 0.505 cents. How many cents is this written as a fraction in simplest form?
I need help with this
Answer:
90°
Step-by-step explanation:
5x+20=9x
20=4x
5=x
<DEG=5x+20+9x=5(5)+20+9(5)=25+20+45=90
Natalie has 27 aples to give to her classmates,she give away 12 to the boys in her class and 15 to the girls in her class. How many aples does natalie have left?
Answer:
Natalie has zero apples left because she gave 27 away
Step-by-step explanation:
hope it helps
Norma Ann planned a rectangular courtyard, as shown in the scale drawing below. She decides to change the width, the shorter side of the courtyard, from 45 ft to 40 ft. Which expression finds the change in the scale factor? PLSS HELP!
Answer: 45 / 40 ft
Step-by-step explanation:
Given that She decides to change the width, the shorter side of the courtyard, from 45 ft to 40 ft. Which expression finds the change in the scale factor?
Actual width of shorter side = 45 ft
New width of shorter side = 40 ft
Scale factor is the ratio of the actual length to the new or intended length
Scale factor = Actual width / New width
Hence, scale factor :
45 ft / 40 ft
Whats the answer to this question
Answer:
a. 37
Step-by-step explanation:
1. Given the function f(x)=x2-3
find f(2)
Answer:
f(2) = 1
Step-by-step explanation:
f(x) = x^2-3
x=2
f(2) = (2)^2-3
f(2)=4-3
f(2)=1
what is 16=4f+4 please help me
Answer:
f=3
Step-by-step explanation:
16=4f+4
16-4=4f
12=4f
12/4=f
f=3
hope that was answer you were looking for
6 cm
63 cm
the area of the rectangle
Answer:
Area of a rectangle is length *width
Therefore the area is 378cm square
In the following figure, three layers of cubes are stacked on top of each other. How many cubes of any size are in the figure?
Answer:
14
Step-by-step explanation:
It's 3x3, 2x2, and 1x1
9+4+1=14
Answer:
14 cubes
Step-by-step explanation:
The figure, there are 3 layers, so we can split up the layers.
In the 1st layer is just 1 cube.
In the 2nd layer:
2 x 2 = 4 cubes.
In the 3rd and final layer:
3 x 3 = 9 cubes.
We then add them:
1 + 4 + 9, giving us a total of 14 cubes.
A map scale compares a map distance with?
Answer:
RATIO
Step-by-step explanation:
Francis did this work to solve an equation. Did he make an error?
3x = 10 - 2x
-2x
-2x
x = 10
Answer:
Yes he did. The error is that you are supposed to add 2x to 3x to get 5x. So 5x = 10, x = 2
Step-by-step explanation:
find the cube of 2/3
Answer:
8/27
Step-by-step explanation:
[tex] \huge \bigg( \frac{2}{3} \bigg)^{3 } = \frac{ {2}^{3} }{ {3}^{3} } = \frac{8}{27} \\ [/tex]
You purchased a computer for your business for $800. Using straight-line depreciation, the amount of depreciation allowed for each year after the purchase is given by the function f (x) = 800 − 114.29x. What type of function can you use to model the data?
Answer:
linear function
Step-by-step explanation:
The given function is linear function.
What is linear function?A linear function is a function that represents a straight line on the coordinate plane. For example, y = 3[tex]x[/tex] - 2 represents a straight line on a coordinate plane and hence it represents a linear function. Since y can be replaced with g([tex]x[/tex]), this function can be written as g([tex]x[/tex] )= 3[tex]x[/tex] - 2.
A linear function is of the form g([tex]x[/tex]) = m[tex]x[/tex] + b where 'm' and 'b' are real numbers. Here,
'm' is the slope of the line'b' is the y-intercept of the line'[tex]x[/tex]' is the independent variable'y' (or g([tex]x[/tex])) is the dependent variableGiven:
y = 800 - 114.29[tex]x[/tex]
year accumulated
depreciation
0 0
1 114.29
2 228.58
3 342.87
4 457.16
5 571.45
6 685.74
7 800
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the average of 3,3,16,19, and y is 10. what is y+6?
Answer:
y=9
9+6=15
y+6=15
Step-by-step explanation:
3+3+16+19+y=41+y
41+y/5=10
multiply both sides by 5
205+y/5=50
41+y=50
Rearrange the equation so y is isolated.
y= 50-41
y=9
Check:
3+3+16+19+9=50
50/5=10
y=9
y+6=?
9+6=15
Hope this helps :)
Given h(x) = 3x - 9
Find the value of q such that h^2(2q/3) = 36
I will make you the brainliest
Answer:
q= (9,-9)
Step-by-step explanation:
Evaluate
h^2(2(q/3))
then set it equal to
36
Hope this helps!
-10|b-4| <-10
Solve the inequality
Answer:
b>5 or b<3
(i hope this helps)
What is the best way to determine the graph of a situation?
Answer:
iys answer can be
by drawing
The diagram shows several points and lines.
4 intersecting lines are shown. A horizontal line contains points K, N, R. A vertical line contains points M, N, Q. Another line intersects the lines at points K and M. Another line has points J, K, and Q. Points L and P are not on the lines.
Which statements are true based on the diagram? Select two options.
Points K, M, and N are collinear.
Points J, K, and Q are collinear.
Point R is the intersection of line KN and line MQ.
Lines JQ, KM, and MQ all intersect at point K.
There is only one line that can be drawn through points L and P.
Answer:
B and E 2020
Step-by-step explanation:
Answer:
Points J, K, and Q are collinear. There is only one line that can be drawn through points L and P.
Step-by-step explanation:
i took the class
Which is the value of 362 – b when b = 5?
Hey there! I'm happy to help!
Since b=5, we can replace the b in the expression with 5 and evaluate!
362-5
357
Have a wonderful day! :D
Answer:
357
Step-by-step explanation:
I need help with this
Answer:
I think it's 18 don't quote me on it.
Step-by-step explanation:
What is the measure of angle B? Someone please help ASAP!!
A bakery used 61/4 cups of flour this morning to make 5 batches of cookies how much flour went into each batch of cookies ?
Answer:
15.25 cups per batch
Step-by-step explanation:
What is the probability of a spinner stopping on Y?
Answer:
Step-by-step explanation:
1/8.
There is. One Y and 8 choices
