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3 years ago

Algebra Help! I appreciate any assistance.

Mathematics

2 answers:

katrin [286]3 years ago

7 0

Hello!

Given the integer in form of fraction, we should know the denominator. We know the denominator n is 3^x * 5^y.

We should know the greatest divisor of 90.

You have to prime factorize 90.

90|2
45|3
15|3
5|5
1

So 90 = 2 × 3^2 × 5^1

We take the greatest numbers with highest exponents.

That means 3^2 × 5 = 45 <- answer

Kruka [31]3 years ago

4 0

90 = 2 · 3 · 3 · 5 = 2 · 3² · 5¹

If n has the form $3^x5^y$ and $\frac{90}{n}$ is an integer, then greatest possible value of n = 3² · 5¹ = 45

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3 years ago

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

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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

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∠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

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

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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

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$DC=CD=4\ cm$

substitute

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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

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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

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

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substitute

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

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

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