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Elodia [21]
3 years ago
8

Use the diagram to solve for the three variables so that the quadrilateral will be a rhombus. Show all of your work for full cre

dit.

Mathematics
1 answer:
satela [25.4K]3 years ago
3 0

Answer:

  • x = 4
  • y = 4
  • z = 7

Step-by-step explanation:

Each triangle is a right triangle, and all are congruent. So ...

  90 -m∠CAB = (1/2)m∠CDA

  90 -(4x +33) = (1/2)(12x +34)

  57 -4x = 6x +17 . . . . . . . eliminate parentheses

  40 = 10x . . . . . . . . . . . . .add 4x-17

  4 = x

We also have ...

  2m∠CAD = m∠BCD

  2(3z +28) = 10z +28

  6z +56 = 10z +28 . . . . . eliminate parentheses

  28 = 4z . . . . . . . . . . . . . .subtract 6z+28

  7 = z . . . . . . . . . . . . . . . . divide by 4

Since BC = CD ...

  x = y = 4

The values of the three variables are ...

  x = 4, y = 4, z = 7.

You might be interested in
Problem #1: Mrs. Grape has 90 students. On her last test, 3/10 of these students earned an A. Of those students, 1/9 got a perfe
ser-zykov [4K]

Answer:

3 students got a perfect score.

Step-by-step explanation:

Total number of students in Mrs. Grape's class = 90

Number of students who earned an A = 3/10 of 90

= \frac{3}{10}\times 90

= 27 students

Out of 27 students the number of students who got perfect score

= \frac{1}{9}\times 27

= 3 students

3 students got a perfect score.

5 0
3 years ago
A package is secured with ribbon. Two pieces of ribbon,
lutik1710 [3]

Answer:

A total of 387 centimeters of ribbon are used.

Step-by-step explanation:

We already know that two out of three pieces of ribbon are 1.25 meters.

The third piece of ribbon is 120 millimeters (mm) longer.

1 millimeters = 0.001 meters

120 x 0.001 = 0.12

That means that the third piece of ribbon is 0.12 meters longer than the first two. The length of the third ribbon is 1.25 m + 0.12 m = 1.37 m

In order to find the total number of meters of ribbon used, we need to do addition.

1.25 m + 1.25 m + 1.37 m = 3.87 m

But, the question is asking us the number of centimeters of ribbon that are used.

1 m = 100 cm

3.87 x 100 = 387 cm

Therefore, a total of 387 centimeters of ribbon are used.

Hope this helps! Have a blessed day! :)

7 0
2 years ago
Find the mean absolute deviation (MAD) of the following data set. Round your answer to TWO decimal places.
mario62 [17]

Answer:

the correct answer is 10

3 0
3 years ago
Read 2 more answers
Ana uses Talk-A-Lot and Peter uses Talk-to-Me. Each company charges
mr Goodwill [35]

Answer:

They both talk for a different amount of time

7 0
3 years ago
What is the slope of a horizontal line?
Margarita [4]
The slope is rise/run
rise=up and down
run=left and right

the rise is 0
the run is inifnity
so 0/inifnity=0

the slope is 0
6 0
3 years ago
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