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Lena [83]
3 years ago
5

Leah hangs 6 posters in a row, each 14 inches wide, on a bedroom wall. There are 4 inches between each poster. For the posters a

t each end, there are 3 inches between each poster and the end of the wall. What is an appropriate strategy for Leah to use to find the width of the wall?
Mathematics
1 answer:
goldfiish [28.3K]3 years ago
8 0

Answer:

62 sq in of wall is covered

Step-by-step explanation:

6 x 14 = 84 -22 = 62

this is for the total

4 x 4 = 16

this is for the inches of the inside wall

2 x 3 = 6

this is for the inches of the outside wall

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f(x)=x^2; vertical shrink by a factor of 1/2 and a reflection in the y-axis, followed by a translation 1 unit down​
NeX [460]

The image of the function f(x) after vertical shrink by a factor of 1/2

and a reflection in the y-axis, followed by a translation 1 unit down​

is g(x) = \frac{1}{2} x² - 1

Step-by-step explanation:

Lets revise:

1. The vertical shrink

A vertical shrinking is the squeezing of the graph toward the x-axis.

if 0 < k < 1 (a fraction), the graph of y = k•f(x) is the graph of f(x) vertically

shrunk by multiplying each of its y-coordinates by k

2. The reflection

If the function f(x) reflected across the y-axis, then its image is g(x) = f(-x)

3. Vertical translation

If the function f(x) translated vertically up  by m units, then its image

is g(x) = f(x) + m

If the function f(x) translated vertically down  by m units, then its image

is g(x) = f(x) - m

Now let us solve the problem

∵ f(x) = x²

∵ f(x) shrunk by a factor of \frac{1}{2}

∴ The image of f(x) = \frac{1}{2} x²

∵ The image of f(x) reflected across y-axis

∴ The sign of x will change

∴ The new image of f(x) = \frac{1}{2} (-x)²

∵ The new image of f(x) translated 1 unit down

∴ We will subtract the new image of f(x) by 1

∴ The last image of f(x) is g(x) = \frac{1}{2} (-x)² - 1

<em>V.I.Note:</em>

(-x)² = x² because even exponents reject the negative sign

The image of the function f(x) after vertical shrink by a factor of 1/2

and a reflection in the y-axis, followed by a translation 1 unit down​

is g(x) = \frac{1}{2} x² - 1

The attached graph for more understand

Learn more:

you can learn more about transformation in brainly.com/question/2415963

#LearnwithBrainly

4 0
3 years ago
Which three types of transformations result in congruent shapes?
Aleks [24]

Answer:

There are three main types of congruence transformations: reflections (flips), rotations (turns), and translations (slides). These congruence transformations can be used to obtain congruent shapes or to verify that two shapes are congruent

6 0
3 years ago
Three numbers add up to 210. The second number is 10 more than the first and the third number is 3 times the first. Find the num
svp [43]

Answer:

I. First number, a = 40.

II. Second number, b = 50.

III. Third number, c = 120.

Step-by-step explanation:

Let the three numbers be a, b and c respectively.

Given the following data;

Translating the word problem into an algebraic equation, we have;

a + b + c = 210

b = a + 10

c = 3a

Substituting the value of b and c into the equation, we have;

a + a + 10 + 3a = 210

5a + 10 = 210

5a = 210 - 10

5a = 200

a = 200/5

<em>a = 40</em>

To find the value of b;

b = a + 10

b = 40 + 10

<em>b = 50</em>

To find c

c = 3a

c = 3*40

<em>c = 120</em>

5 0
3 years ago
Plzzzzzzzzz anyone helpppppp10points
BlackZzzverrR [31]

when is 9 = 15.2 - 0.537x

         9 = 15.2 - 0.537x

  -15.2      -15.2                 subtract 15.2 from both sides

      -6.2   =   -0.537x  

/-0.537           /-0.537    divide -0.537 from both sides

11.55  = x   or 12 feet round to nearest whole foot


5 0
3 years ago
Find any 3 (x,y) pairs that are solutions for the equation 2x-5y=10 . Show your work
Alla [95]

Answer:

(0,-2), (5,0) and (10,2).

Step-by-step explanation:

Given equation is 2x-5y=10.

Now we need to find 3 pairs of solutions in (x,y) form for the given equation.

As 2x-5y=10 is a linear equation so we are free to pick any number for x like x=0, 5, 10

Plug x=0 into 2x-5y=10, we get:

2(0)-5y=10

0-5y=10

-5y=10

y=\frac{10}{-5}

y=-2

Hence first solution is (0,-2)

We can repeat same process with x=5 and 10 to get the other solutions.

Hence final answer is (0,-2), (5,0) and (10,2).

5 0
3 years ago
Read 2 more answers
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