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3 years ago

Solve for R using cross multiplication

Mathematics

1 answer:

topjm [15]3 years ago

8 0

R/ r+ 15 = 3/8

Cross multiply: top of one side multiplied by bottom of other side:

R x 8 = 3 x r+ 15

Simplify:

8r = 3r + 45

Subtract 3r from both sides:

5r = 45

Divide both sides by 5:

R = 9

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The isosceles trapezoids, ABCD and EFGH, are similar quadrilaterals. The scale factor between the trapezoids is 2:3, = 6 centime

Bingel [31]

Answer:

Part A) see the explanation

Part B) see the explanation

Part C) The perimeter of trapezoid ABCD is 32 centimeters and the perimeter of trapezoid EFGH is 48 centimeters

Step-by-step explanation:

<u><em>The complete question is</em></u>

The isosceles trapezoids, ABCD and EFGH, are similar quadrilaterals. The scale factor between the trapezoids is 2:3, GH = 6 centimeters, AD = 8 centimeters, and AB is three times the length of DC

Part A) Write a similarity statement for each of the four pair of corresponding sides

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional

The corresponding sides are

AB and EF

BC and FG

CD and GH

AD and EH

$\frac{AB}{EF}=\frac{BC}{FG}=\frac{CD}{GH}=\frac{AD}{EH}$

Part B) Write a congruence statement for each of the four pair of corresponding angles.

we know that

If two figures are similar, then its corresponding angles are congruent

The corresponding angles are

∠A and ∠E

∠B and ∠F

∠C and ∠G

∠D and ∠H

∠A ≅ ∠E

∠B ≅ ∠F

∠C ≅ ∠G

∠D ≅ ∠H

Part C) Determine the perimeter for each of the isosceles trapezoids

we have

The scale factor between the trapezoids is 2:3, GH = 6 centimeters, AD = 8 centimeters, and AB is three times the length of DC

step 1

Find the measure of CD

Remember that

The ratio between corresponding sides is proportional and this ratio is the scale factor

Let

z ----> the scale factor

$z=\frac{2}{3}$

$\frac{2}{3}=\frac{CD}{GH}}$

we have

$GH=6\ cm$

substitute

$\frac{2}{3}=\frac{CD}{6}}\\\\CD=4\ cm$

step 2

Find the measure of AB

Remember that

AB is three times the length of DC

$AB=3DC$

$DC=CD=4\ cm$

substitute

$AB=3(4)=12\ cm$

step 3

Find the measure of BC

Remember that in an isosceles trapezoid, the legs are equal

BC=AD

we have

$AD=8\ cm$

therefore

$BC=8\ cm$

step 4

Find the perimeter of trapezoid ABCD

$P=AB+BC+CD+AD$

substitute the values

$P=12+8+4+8=32\ cm$

step 5

Find the perimeter of trapezoid EFGH

we know that

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

Let

z ---> the scale factor

x ----> the perimeter of trapezoid ABCD

y ----> the perimeter of trapezoid EFGH

$z=\frac{x}{y}$

we have

$z=\frac{2}{3}$

$x=32\ cm$

substitute

$\frac{2}{3}=\frac{32}{y}$

$y=32(3)/2=48\ cm$

therefore

The perimeter of trapezoid EFGH is 48 centimeters

3 0

2 years ago

What is the length of AA' ?

natali 33 [55]

The length of AA' is the squareroot of 29.

5 0

3 years ago

-5,-2,1,4 is models by the equation an=3n-8 find the 42 term

sleet_krkn [62]

A(42) = 3(42) - 8
The 42nd term is 118.

7 0

3 years ago

How many solutions can be found for the equation 4z + 2(z - 4) = 3z + 11

Gnom [1K]

4z+2(z-4)=3z+11 perform indicated multiplication on left side

4z+2z-8=3z+11 combine like terms on left side

6z/-8=3z+11 add 8 to both sides

6z=3z+19 subtract 3z from both sides

3z=19 divide both sides by 3

z=19/3

z=6 1/3

So there is only one solution when z=6 1/3

4 0

3 years ago

Read 2 more answers

Explain each step for solving x^2 - 4x=6 by the method of completing the square.

deff fn [24]

Answer:

If you aren't looking for the quadratic solving method then comment it down below and tell me what you're looking for

QUADRATIC EQUATION

x²- 4x = 6

(x - 2)²- 4 = 6

(x - 2)² = 10

x - 2 = ±10

x = ±10+2

x = -8, 12

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3 years ago