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zubka84 [21]
3 years ago
12

Find the value of each variable

Mathematics
1 answer:
ohaa [14]3 years ago
6 0

9514 1404 393

Answer:

  11.  x = 13, y = 13√2

  12.  x = 8, y = 4√3

  13.  x = 14√3, y = 7√3

  14.  x = y = 11√2

  15.  x = 12√2, y = 12, z = 12√3

Step-by-step explanation:

The ratios of side lengths in the "special" triangles are (shortest to longest)

  1 : 1 : √2 . . . . . isosceles right triangle

  1 : √3 : 2 . . . . 30°-60°-90° triangle

These ratios make answering these questions much easier.

__

11. 13 : x : y = 1 : 1 : √2

  x = 13, y = 13√2

__

12. 4 : y : x = 1 : √3 : 2

  x = 8, y = 4√3

__

13. y : 21 : x = 1 : √3 : 2

  y = 21/√3 = 7√3

  x = 14√3

__

14. x : y : 22 = 1 : 1 : √2

  x = 22/√2 = 11√2

  x = y = 11√2

__

15. Let 'a' represent the altitude. Then we have ...

  a : z : 24 = 1 : √3 : 2

  a = 12, z = 12√3

and ...

  a : y : x = 1 : 1 : √2

  y = 12, x = 12√2

_____

<em>Additional comment</em>

It is worth remembering that 1/√n = (√n)/n. This is useful when you have to divide by √2 or √3 in the above problems.

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Answer:

5

Step-by-step explanation:

75/15=5

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Answer:

It is A and I am positive its A

Step-by-step explanation:

6 0
2 years ago
How many solutions exist for the given equation?<br> 12x + 1 = 3(4x + 1) - 2
VladimirAG [237]

Answer:

Infinite

Step-by-step explanation:

3(4x + 1) - 2

= 12x + 3 - 2 (Multiply the sum in the bracket by 3)

= 12x + 1 (Simplify)

This means that:

12x + 1 = 3(4x + 1) - 2

is the same as

12x + 1 = 12x + 1

Hence, anything that is used to substitute x is correct.

4 0
3 years ago
Graham is hiking at an altitude of 14,040 feet and is descending 50 feet each minute. Max is hiking at an altitude of 12,500 fee
alina1380 [7]

Graham: -50x + 14,040

Max:  20x + 12,500

   Graham      =        Max

-50x + 14,040 = 20x + 12,500

<u>+50x               </u>   <u>+50x               </u>

            14,040 = 70x + 12,500

<u>          -12,500  </u>  <u>         -12.500 </u>

             1,540  = 70x

              \frac{1,540}{70} = \frac{70x}{70}

                220 = x

Answer: 220 minutes <em>(3 hours 40 minutes)</em>

5 0
3 years ago
Read 2 more answers
It is given that ∠ABC and ∠CBD are Response area. So, m∠ABC+m∠CBD=90° using the Response area. It is also given that ​m∠ABC=35°​
zhenek [66]

THE QUESTION CAN BE WRITTEN AS THIS;

It is given that ∠ABC and ∠CBD are a____________ So, m∠ABC+m∠CBD=90° using the b____________. It is also given that ​m∠ABC=35°​. Using the substitution property of equality, you have c________+ ​m∠CBD=90°​. Therefore, using the subtraction property of equality, ​m∠CBD=55°

Answer:

a)COMPLIMENTARY ANGLE

b)DEFINITION OF COMPLEMENTARY ANGLES

c)35°+ m<CBD = 90 degrees.

Step by step Explanation:

a)It's given that <ABC and <CBD are (COMPLIMENTARY ANGLE)

We know that the Sum of Complementary angles equal to 90 degrees.Those angles don't have to be next to each other, just so long as the total is 90 degrees. That's why the Sum of m<ABC and m<CBD equals 90 degrees that is m<ABC + m<CBD = 90 degrees

b)using the (DEFINITION OF COMPLEMENTARY ANGLES) It is also given that m<ABC = 35 degrees.

c)Using substitution property of equality, you have (35°+ m<CBD = 90 degrees.)

If we subtract 35 from both sides, we get 35-35+ m<CBD = 90-35.

Therefore, m<CBD = 55 degrees.

PLEASE CHECK THE ATTACHED FIGURE TO SEE HOW THE QUESTION LOOKS LIKE

8 0
3 years ago
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