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2 years ago

Please help me with 9 I really need it

Mathematics

1 answer:

MissTica2 years ago

4 0

Answer:

605 boys

Step-by-step explanation:

If the ratio of boys to girls is 5:7

and there are 847 girls

we can plug this value into the ratio by doing something like:

5:7

= 5/7

= x/847

Because the ratio has to be the same, we can substitute x for the number of boys and solve by the cross method or whatever you guys call it.

5 x

--- x ------

7 847

The x in the middle is just to show the direction you are multiplying.

the 5 is multiplied by the 847 and the 7 is multiplied by x.

847 * 5 = 4,235

4,235 divided by 7 is 605

605 is your answer.

The cross method can be used in most situations.

* is used to represent multiplication btw

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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:

The complete question is

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

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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

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Answer:

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Step-by-step explanation:

Let the required number be a.

Given,

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= > Ten times of a + seven times of it's square = 152

= > 10( a ) + 7( a )^2 = 152

= > 10a + 7a^2 - 152 = 0

= > 7a^2 + 10a - 152 = 0

= > 7a^2 + ( 38 - 28 )a - 152 = 0

= > 7a^2 + 38a - 28a - 152 = 0

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= > ( a - 4 )( 7a + 38 ) = 0

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