Triangle DEF has vertices D(4,8), E(12,16), and F(-4,-12). The triangle is dilated with a scale factor of ¼ . What are the coordinates of D’E’F’?

Answer:

[tex]f(g(x))=x[/tex]

[tex]g(f^{-1}(x))=\dfrac{-1}{x-1}[/tex]

[tex]g^{-1}(x)=\dfrac{1}{1-x}[/tex]

Step-by-step explanation:

[tex]f(x)=\dfrac{1}{1-x} \ \ \textsf{and} \ \ g(x)=\dfrac{x-1}{x}[/tex]

[tex]f(g(x))=\dfrac{1}{1-(\frac{x-1}{x})}[/tex]

[tex]\implies f(g(x))=\dfrac{1}{\frac{x}{x}-\frac{(x-1)}{x}}[/tex]

[tex]\implies f(g(x))=\dfrac{1}{\frac{x-x+1}{x}}[/tex]

[tex]\implies f(g(x))=\dfrac{1}{\frac{1}{x}}[/tex]

[tex]\implies f(g(x))=x[/tex]

[tex]x=\dfrac{1}{1-y}[/tex]

[tex]\implies 1-y=\dfrac{1}{x}[/tex]

[tex]\implies y=1-\dfrac{1}{x}[/tex]

[tex]\implies f^{-1}(x)=1-\dfrac{1}{x}[/tex]

[tex]g(f^{-1}(x))=1-\dfrac{1}{1-\frac{1}{x}}[/tex]

[tex]\implies g(f^{-1}(x))=1-\dfrac{1}{\frac{x-1}{x}}[/tex]

[tex]\implies g(f^{-1}(x))=1-\dfrac{x}{x-1}[/tex]

[tex]\implies g(f^{-1}(x))=\dfrac{x-1-x}{x-1}[/tex]

[tex]\implies g(f^{-1}(x))=\dfrac{-1}{x-1}[/tex]

[tex]x=\dfrac{y-1}{y}[/tex]

[tex]\implies xy=y-1[/tex]

[tex]\implies 1=y-xy[/tex]

[tex]\implies 1=y(1-x)[/tex]

[tex]\implies y=\dfrac{1}{1-x}[/tex]

[tex]\implies g^{-1}(x)=\dfrac{1}{1-x}[/tex]

Answer:

Step-by-step explanation:

A side of a square garden is represented by the expression 2s + 5. Which expression represents the area of the garden?

Area = s * s ( side x side or side²)

(2s + 5) * (2s + 5)

or

(2s + 5)²

Vertical angles are always congruent, which means that they are equal. Adjacent angles are angles that come out of the same vertex. Adjacent angles share a common ray and do not overlap. The size of the angle xzy in the picture above is the sum of the angles A and B.

Answer:

Length of rectangular lawn =72 meters

Breadth of rectangular lawn =18 meters

Perimeter of rectangle =2(Length+Breadth)

So, Perimeter of rectangle =2(72+18)=2(90)=180 meters

If three shrubs can be planted in a meter of hedge.

Then, Number of shrubs planted in whole perimeter will be=3×180=540

Step-by-step explanation:

Based on the amount of money that Randy has more than Sandy and Mandy, the amount that Sandy has is $1,728.

First find out how much Randy has.

This can be found as:

= Amount that Mandy has x ( 1 + 20%)

= 1,800 x 1.2

= $2,160

The amount that Sandy has is:

= Amount Randy has / ( 1 + 25%)

= 2,160 / 1.25

= $1,728

In conclusion, Sandy has $1,728.

Find out more on percentages at https://brainly.com/question/990406.

Answer:

B. Caleb's experiment had 100 bacteria and Jenna's experiment had 2500 bacteria.

Step-by-step explanation:

[tex]\displaystyle Jenna \hookrightarrow 2500 = 50^2 \\ Caleb \hookrightarrow 100 = [2][50][/tex]

Take a clocer look at the keywourds next to each name. When you square a quantity, you duplicate and multiply it, but when you double a quantity, you multiply by two.

I am joyous to assist you at any time.

Amount of money made by adult ticket = 10x

Amount of money made by student ticket = 5y

Total amount made = 10x + 5y

Hope that helps!

y represents the number of  adults

x represents the number of students

THIS IS AN EXPRESSION SO THERE IS NO EQUAL SIGN!!!

ANSWER:   10y+5x

Answer:

residents that read at least two newspapers is 9,600

residents that read exactly one newspaper is 9,200

Step-by-step explanation:

Add up the percentages of a certain group of people from the venn diagram then find that percentage from the number 20,000

Answer:

this is the answer I came up with hope this helps

Answer:

E. The absolute value and square root function share an x-intercept.

Step-by-step explanation:

Pre-Calc on Edge 2022

Answer:

see explanation

Step-by-step explanation:

[tex]\frac{2}{1+e^{-2} }[/tex] ← evaluate [tex]e^{-2}[/tex] using calculator

= [tex]\frac{2}{1+0.135}[/tex]

= [tex]\frac{2}{1.135}[/tex]

= 1.762.....

≈ 1.8 ( to 1 dec. place )

Step-by-step explanation:

i hope its clear enough and that it helps

Here's a pic. hope it helps

Answer:

68×32= 2176

Step-by-step explanation:

Answer:

a) 44

b) 84

Step-by-step explanation:

210/60 = space for every child (3.5m)

For a 154m^2 ground, 154/3.5 = 44

b) I’m not sure but I think it is 24*3.5 = 84

The probability that the combination starts with 2 is 1/3

Probability is the likelihood or chance that an event will occur.

Probability = expected/total outcome

The total outcome  = 3! = 6

The expected outcome if the combination starts with 2 is given as 2! = 2

Pr(the combination starts with 2) = 2/6 = 1/3

Hence the probability that the combination starts with 2 is 1/3

Learn more on probability here: https://brainly.com/question/25870256

Answer:

Step-by-step explanation:

25) hypotenuse² = base² + altitude²

                            = 10² + 8²

                            = 100 + 64

                            = 164

hypotenuse = √164 = 12.8

Perimeter = 10  +8 + 8 + 12.8 + (12.8 -10)

                 = 10 + 8 + 8 + 12.8 + 2.8

                 = 41.6

Answer:

\overline{OQ}

OQ

​

. Given OQ=2x,OQ=2x, OP=x,OP=x, and PQ=10,PQ=10, determine \overline{OQ}.

Oq

Check the picture below.

what other relationship?, well, we can also say 2(midsegment) = base.

Answer:

x = 16

Angle p = 50°

Angle q = 40°

Step-by-step explanation:

"complementary" means the angles add up to 90°.

So,

3x+2 + 3x-8 =90

combine like terms.

6x - 6 = 90

add 6

6x = 96

divide by 6

x = 16

If x = 16,

then Angle p=

3x + 2

= 3(16) + 2

= 48 + 2

= 50

Angle p = 50°

And,

Angle q

= 3x - 8

= 3(16) - 8

= 48 - 8

= 40

Angle q = 40°

Check:

40° + 50° = 90°

Answer:

you earn 8.50 an hour

he has 288 inches of fabric

Step-by-step explanation:

Answer:

1. Kevins unit rate is $8.50 per hour

To find the unit rate, we need to divide 6 by 51. 51/6 = 8.50 Kevin earns $8.50 per hour

2.  there are 288 inches in 8 yards so tony has 288 inches of fabric.

1 yard is 36 inches 8 * 36 is 288

Step-by-step explanation:

Answer:

y = 45 + 5(x - 5)

where y is the total cost of the ad, and x is the total number of lines in the ad

Step-by-step explanation:

Let x = number of lines in the ad

Let y = total cost

If the cost of the ad is $45 for the first 5 lines and $5 for each additional line then the expression for the total cost of the ad is:

y = 45 + 5(x - 5)

Answer:

equation: y = 5(x-5) + 45

Explanation:

Here "y" represents the total money earned. "x" represents the earning from additional line. the constant variable is "45" and does not change.

The square prism would contain more seed than the cone because it has a larger volume.

Volume is the amount of space occupied by a three dimensional shape or object.

The volume of cone = (1/3) * π * radius² * height = (1/3) * π * 2.5² * 10 = 65.45 cm³

The volume of square prism =  base² * height = 5² * 2.5 = 62.5 cm³

The square prism would contain more seed than the cone because it has a larger volume.

Find out more on Volume at: https://brainly.com/question/1972490

[tex](\stackrel{x_1}{-5}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{(-5)}}}\implies \cfrac{-6}{5+5}\implies \cfrac{-6}{10}\implies -\cfrac{3}{5}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{-\cfrac{3}{5}}(x-\stackrel{x_1}{(-5)}) \implies y-1=-\cfrac{3}{5}(x+5) \\\\\\ y-1=-\cfrac{3}{5}x-3\implies y=-\cfrac{3}{5}x-2[/tex]

Answer:

Step-by-step explanation:

The given formula can be used to find the area when the radius is known.

  r = 3, A = 3²π = 9π

  r = 1/2, A = (1/2)²π = 1/4π

The formula can be solved to give the radius when the area is known:

  r = √(A/π)

  A = 16π, r = √(16π/π) = 4

  A = 100π, r = √(100π/π) = 10

Answer:2/16

Step-by-step explanation:

~Shoto Todoroki here~

Answer:

hope this helps :))

Answer:

  the value of hi changes from 58 to 0:

  h(t) = -4.9t^2 +19.8t

Step-by-step explanation:

If the initial height changes, then the term in the equation that represents that height will change. The initial height term is hi, so it changes from 58 to 0.

  [tex]h(t)=-4.9t^2+19.8t+0\\\\\boxed{h(t)=-4.9t^2+19.8t}[/tex]

Answer:

m=-2

Step-by-step explanation:

You want to isolate the variable on one side (m).

Divide each side by 7.

m+5=3

Subtract 5 from both sides

m=-2

Answer:

m = -2.

Step-by-step explanation:

First divide both sides by 7; m + 5 = 3.

Then subtract 5 from both sides; m = -2.

Answer:

x=3+2i,3−2i

Step-by-step explanation:

one of those two i think