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mr_godi [17]
2 years ago
14

Can someone please do this fast

Mathematics
1 answer:
Dvinal [7]2 years ago
3 0

Answer: 2, 8, 96cm^2, 35 miles

<h3>Explanation:</h3>

What we know:

  • We need to solve all of the given problems
  • We have the information we need
  • We can use ratios to our advantage

How to solve:

    By using our knowledge of ratios and substitution, we can solve these problems.

<h3>Process:</h3>

First problem

Set up ratio                                                             7.5:15

Find GCF                                                                (7.5:15)/7.5

Simplify                                                                   1:2

Solution:                                                                  2  

Second problem

Set up equation                                                     (x/10) = (6/7.5)

Rewrite                                                                   (x/10) = (60/75)

Simplify                                                                   (x/10) = (4/5)

Common denominator                                          (x/10) = (8/10)

Isolate variable                                                      [(x/10) = (8/10)]*10

Simplify                                                                    x = 8

Solution:                                                                  8

Third Question

<em>where x represents the new width, y represents the new length, and A represents the new area.</em>

Set up equation                                                    A = xy

Substitute                                                              A = (2*4)(2*6)

Simplify                                                                  A = (8)(12)

Simplify                                                                  A = 96

Solution:                                                                96 cm^2                                                      

Fourth Question

<em>Where x represents the unknown length in miles</em>

Set up equation                                                    (21:3) = (x:5)

Rewrite in fraction form                                        [(21/3)] /3 = (x/5)

Simplify                                                                   (7/1) = (x/5)

GCF                                                                        5(7/1) = (x/5)

Isolate variable                                                       [(35/5) = (x/5)]*5

Solution:                                                                  35 miles = x

<h3>Answer: 2, 8, 96 cm^2, 35 miles</h3><h3>Check:</h3>

Problem 1:

If the scale factor is 2, then the area of a square with the side measurement of 7.5 units should be (due to areas being squared) 1/2^2 of the square with the side measurement of 15 units. Let's solve this:

(1/2^2)(15*15) = (7.5*7.5)

(1/4)(15^2) = (7.5^2)

225/4 = 56.25

56.25 = 56.25

Therefore, a scale factor of 2 is correct.

Problem 2:

If x = 8, then 8/10 should equal 6/7.5. Let's solve this:

when x = 8:

8/10 = 6/7.5

0.8 = 0.8

Therefore, x = 8 is a correct solution.

Problem 3:

If a scale factor of 2 creates the new area of 96 cm^2, then the old area of (6*4) should be (due to areas being squared) 1/2^2 of the new area. Let's solve this:

(1/2^2)(96) = (6*4)

(96/4) = 24

24 = 24

Therefore, the new area is 96 cm^2.

Problem 4:

If the houses are 35 miles apart, then 3 in./21 mi. should be equal to 5 in./35 mi. Let's solve this:

(21/3) = (35/5)

7 = 7

Therefore, the houses are 35 miles apart.

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