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4 years ago

7y + 5 = 3y – 31

Mathematics

2 answers:

Alex73 [517]4 years ago

8 0

Answer: y=-9

Step-by-step explanation:

I go step-by-step in the image!

KiRa [710]4 years ago

8 0

7y+5=3y-31
7y-3y= -31 -5
4y = -36
y=-36/4
y = - 9
The answer is -9

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A building casts a shadow 48ft long. At the same time, a 40ft tall flagpole casts a shadow 9.6ft long

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Answer:

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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:

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

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

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3 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

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shusha [124]

Complete question

To find $\sqrt{5}$ , Beau found $2^2 = 4$ and $3^2 = 9$ . He said that since 5 is between 4 and 9, $\sqrt{5}$ , is between 2 and 3. Beau thinks a good estimate for $\sqrt{5}$ , is $\frac{2 + 3}{2} = 2.5$ Is his estimate high or low? How do you know?

Answer:

The estimation is high because 5 is very close to 4 so $\sqrt{5}$ will also be very close to $\sqrt{4}$ which is lower than the estimate

In order to get a good estimate

The first step is to choose a number between 2 and 3 let say 2.8 , 2,85 , 2.9 and the square them

i.e

$2.1^2 = 4.41$

$2.2^2 = 4.84$

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From here we can see that $\sqrt{5}$ lies between 2.2 and 2.3 but is closer to 2.2

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Step-by-step explanation:

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3 years ago

7​y​ + 5 = 3​y​ – 31

7y + 5 = 3y – 31