All categories

2 years ago

What is the value of x? x = ___

Mathematics

1 answer:

iVinArrow [24]2 years ago

5 0

Answer:

x = 9

Step-by-step explanation:

The triangle is split into two similar triangles. They have the same shape but not the same size. To solve, write a proportion.

$\frac{9}{81}=\frac{3x-20}{3x+36}$

Cross multiply to solve for x.

9(3x+36) = 81(3x-20)

27x + 324 = 243x -1,620

1,944 = 216x

9 = x

You might be interested in

Based on the pattern table what is the value of a?

kirza4 [7]

The answer is D. The bottom number is multiplied by two each time.

6 0

3 years ago

Read 2 more answers

WHat are the correct answers to this?

iogann1982 [59]

Answer:

1st blank _ 36

2nd blank _ -30

last blank _ 6

7 0

2 years ago

Read 2 more answers

50 POINTS!!! In rectangle ABCD, AB = 6 cm, BC = 8 cm, and DE = DF. The area of triangle DEF is one-fourth the area of rectangle

aalyn [17]

Answer:

$EF=4\sqrt{3}$

Step-by-step explanation:

In rectangle ABCD, AB = 6, BC = 8, and DE = DF.

ΔDEF is one-fourth the area of rectangle ABCD.

We want to determine the length of EF.

First, we can find the area of the rectangle. Since the length AB and width BC measures 6 by 8, the area of the rectangle is:

$A_{\text{rect}}=8(6)=48\text{ cm}^2$

The area of the triangle is 1/4 of this. Therefore:

$\displaystyle A_{\text{tri}}=\frac{1}{4}(48)=12\text{ cm}^2$

The area of a triangle is half of its base times its height. The base and height of the triangle is DE and DF. Therefore:

$\displaystyle 12=\frac{1}{2}(DE)(DF)$

Since DE = DF:

$24=DF^2$

Thus:

$DF=\sqrt{24}=\sqrt{4\cdot 6}=2\sqrt{6}=DE$

Since ABCD is a rectangle, ∠D is a right angle. Then by the Pythagorean Theorem:

$(DE)^2+(DF)^2=(EF)^2$

Therefore:

$(2\sqrt6)^2+(2\sqrt6)^2=EF^2$

Square:

$24+24=EF^2$

Add:

$EF^2=48$

And finally, we can take the square root of both sides:

$EF=\sqrt{48}=\sqrt{16\cdot 3}=4\sqrt{3}$

6 0

3 years ago

Read 2 more answers

(5x+1)3=15x3 que Propiedad pertenece

Aneli [31]

Answer:

Step-by-step explanation:

1) Reagrupar términos.

3(5x + 1) = 15x^3

2) Divide ambos lados por tres.

5x + 1 = 5x^3

3) Mueva todos los términos a un lado.

5x + 1 - 5x^3 = 0

4) No se encontró ninguna raíz algebraicamente. Sin embargo, las siguientes raíces se encontraron por métodos numéricos.

x=−0.878886,−0.209148,1.088033

6 0

2 years ago

The Stillwater Storm team consists of 16 players Each player needs a uniform set. The uniform set includes two jerseys, a pair o

Alexandra [31]

Answer:

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers