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3 years ago

Quadrilateral ABCD is similar to Quadrilateral EFGH. The scale factor is 3:2. If AB = 18, find EF.

Mathematics

2 answers:

nasty-shy [4]3 years ago

6 0

The answer is A. 12

do you want to know how I got my answer...

meriva3 years ago

5 0

Answer: 12

Step-by-step explanation: The correct answer is 12. This problem can be solved by setting up a proportion and cross multiplying.

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BabaBlast [244]

$\underline{\bf{Given \:equation:-}}$

$\\ \sf{:}\dashrightarrow ax^2+by+c=0$

$\sf Let\:roots\;of\:the\: equation\:be\:\alpha\:and\beta.$

$\sf We\:know,$

$\boxed{\sf sum\:of\:roots=\alpha+\beta=\dfrac{-b}{a}}$

$\boxed{\sf Product\:of\:roots=\alpha\beta=\dfrac{c}{a}}$

$\underline{\large{\bf Identities\:used:-}}$

$\boxed{\sf (a+b)^2=a^2+2ab+b^2}$

$\boxed{\sf (√a)^2=a}$

$\boxed{\sf \sqrt{a}\sqrt{b}=\sqrt{ab}}$

$\boxed{\sf \sqrt{\sqrt{a}}=a}$

$\underline{\bf Final\: Solution:-}$

$\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}$

$\bull\sf Apply\: Squares$

$\\ \sf{:}\dashrightarrow (\sqrt{\alpha}+\sqrt{\beta})^2= (\sqrt{\alpha})^2+2\sqrt{\alpha}\sqrt{\beta}+(\sqrt{\beta})^2$

$\\ \sf{:}\dashrightarrow (\sqrt{\alpha}+\sqrt{\beta})^2 \alpha+\beta+2\sqrt{\alpha\beta}$

$\bull\sf Put\:values$

$\\ \sf{:}\dashrightarrow (\sqrt{\alpha}+\sqrt{\beta})^2=\dfrac{-b}{a}+2\sqrt{\dfrac{c}{a}}$

$\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}=\sqrt{\dfrac{-b}{a}+2\sqrt{\dfrac{c}{a}}}$

$\bull\sf Simplify$

$\\ \sf{:}\dashrightarrow \underline{\boxed{\bf {\sqrt{\boldsymbol{\alpha}}+\sqrt{\boldsymbol{\beta}}=\sqrt{\dfrac{-b}{a}}+\sqrt{2}\dfrac{c}{a}}}}$

$\underline{\bf More\: simplification:-}$

$\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}=\dfrac{\sqrt{-b}}{\sqrt{a}}+\dfrac{c\sqrt{2}}{a}$

$\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}=\dfrac{\sqrt{a}\sqrt{-b}+c\sqrt{2}}{a}$

$\underline{\Large{\bf Simplified\: Answer:-}}$

$\\ \sf{:}\dashrightarrow\underline{\boxed{\bf{ \sqrt{\boldsymbol{\alpha}}+\sqrt{\boldsymbol{\beta}}=\dfrac{\sqrt{-ab}+c\sqrt{2}}{a}}}}$

5 0

2 years ago

Read 2 more answers

Select the Expressions that are equivalent to -2(4-3x)+(5x-2) PLZ help do tommorrow

Alborosie

Answer is B.........

5 0

4 years ago

Cheryl climbed a set of stairs and stopped at the middle step. She then walked down 2 steps, up 4 steps, down 3 steps, and up 5

Sedaia [141]

Answer:

There were 8 total steps

Step-by-step explanation:

Okay, so we start in the middle.

-2 + 4 = 2. We're back in the middle.

2 - 3 = -1. One away from the middle.

-1 + 5 = 4. Now you're at the top.

4 x 2 = 8

5 0

3 years ago

Find the lateral surface area of the figure.

Brut [27]

Surface area of the cylinder = 816.4 sq. ft.

Solution:

Height of the cylinder = 21 ft

Diameter of the cylinder = 10 ft

Radius of the cylinder = 10 ÷ 2 = 5 ft

Use the value of $\pi$ = 3.14

Surface area of the cylinder = $2 \pi r h+2 \pi r^{2}$

Substitute the given values in the surface area formula, we get

Surface area of the cylinder $$=2\times3.14\times 5\times 21+2 \times3.14\times 5^2$

$=659.4+157$

$=816.4$ ft²

Hence the surface area of the cylinder is 816.4 sq. ft.

7 0

3 years ago

Read 2 more answers

What is between 280 and 560?

nikitadnepr [17]

420 would be the middle number.

Hoped I Could Help:)

3 0

3 years ago