The function f(x) = g(x), where f(x) = 2x - 5 and g(x) = x2

In rectangle ABCD, AB = 10 cm and BC = 14 cm. If rectangle EFGH is the image after a dilation, which could be its side lengths?

lana [24]

Answer is D

After dilation the image remain same but it is stretched or shrinked to the original size.

That means the ratio of the sides and the angles between the sides remain same .

Here we did dilation of ABCD which made it to EFGH.

Hence the ratio of the corresponding sides of the original rectangle ABCD should remain same even after dilation.

the corresponding sides are : AB and EF

BC and FG

CD and GH

DA and HE

* Let us find ratio of the sides AB and BC

given that AB= 10 and BC= 14

AB/BC= 10/14 = 5 /7 ( 10 and 14 both are multiple of 2 so we reduced them by a factor of 2 )

* the raio of the corresponding sides EF and FG should be same ( 5/7)

in the option D EF= 25 and FG= 35

so EF/FG= 25/35 = 5 /7 ( both are multiple of 5 so we reduced them by the factor of 5 )

Since ratio of the corresponding sides are coming out to be same for the EFGH given in option D it should be the dilation of the ABCD

4 0

2 years ago

Read 2 more answers

Jonah drives from his car to and from work. The total length of the trip to and from work is 19.2 miles. In August, Jonah worked

natita [175]

ANSWER

The total length of the trip to and from work in August is

$403.2 \: miles$

EXPLANATION

The total length of the trip to and from work is

$19.2 \: miles$

If Jonah worked 21 days in August,

Then, the total length of the trip to and from work is
$= 21 \times 19.2 \: miles$

Change the decimal to fraction and multiply,

$= 21 \times \frac{192}{10} miles$

$= \frac{21 \times 192}{10}$

$= \frac{4032}{10} miles$

Convert back to decimal

$= 403.2 \: miles$

6 0

3 years ago

PLEASE HELP

Nookie1986 [14]

For the square with side length n, the diagonal measures:

$d = \sqrt{2} *n$

<h3>How to get the length of the diagonal?</h3>

The sidelength of the square is n, and we want to get the length of the diagonal d.

Notice that the diagonal is the hypotenuse of a right triangle whose catheti measure n.

Then we can use the Pythagorean theorem, which says that the square of the hypotenuse is equal to the sum of the squares of the cathetus;

$d^2 = n^2 + n^2\\\\d^2 = 2n^2\\\\d = \sqrt{2n^2} \\\\d = \sqrt{2}*n$

That is the length of the diagonal.

If you want to learn more about right triangles:

brainly.com/question/2217700

#SPJ1

6 0

1 year ago

What is the answer to this equation “A = ?”<br><br> G(a + h) = M

sasho [114]

Answer:

a = M -Gh/G

Step-by-step explanation:

in order to make a the subject of fomular , you will open the bracket first and then combine the like terms.

G(a + h) = M

Ga + Gh = M

Ga = M - Gh

since G is disturbing a from standing alone, we divide both sides by G

Ga/G = M- Gh/ G

a = M -Gh/G

7 0

2 years ago

Slove the simoltanous equation by using substitution or elimination method 5x-3y=1 3x+2y=1<br>

xxTIMURxx [149]

<u>By substitution method </u>

5x - 3y =1

3x + 2y = 1

_____o____o____

$5x - 3y = 1 \\ 5x = 1 + 3y \\ x = \frac{1 + 3y}{5}$

______o____o_____

$3x + 2y = 1 \\ 3( \frac{1 + 3y}{5} ) + 2y = 1 \\ \frac{3 + 9y}{5} + 2y = 1 \\ \frac{3 +9y + 10y}{5} = 1 \\ \frac{3 + 19y}{5} = 1 \\ 3 + 19y = (1)(5) \\ 3 + 19y = 5 \\ 19y = 5 - 3 \\ 19y = 2 \\ y = \frac{2}{19}$

______o_____o____

$x = \frac{1 + 3y}{5} = \frac{1 + 3 \frac{2}{19} }{5} \\ x = \frac{1 + \frac{6}{19} }{5} = \frac{ \frac{19 + 6}{19} }{5} = \frac{ \frac{25}{19} }{5} \\ x = \frac{25}{19} \div 5 \\ x = \frac{25}{19} \times \frac{1}{5} \\ x = \frac{5}{19}$

I hope I helped you^_^

7 0

2 years ago

The function f(x) = g(x), where f(x) = 2x - 5 and g(x) = x2 - 6.