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loris [4]
3 years ago
13

Find the value of x in each case. Give reasons to justify your solutions!

Mathematics
2 answers:
Savatey [412]3 years ago
8 0

Answer: x = 52^{0}

Step-by-step explanation:

The exterior angle of a triangle = sum of the opposite interior angle.

The interior angles given are : 34^{0} and 90^{0}

Which are opposite to x + 72

Therefore :

x + 72 = 34^{0} + 90^{0}

x + 72 = 124^{0}

x = 124^{0} - 72^{0}

x = 52^{0}

White raven [17]3 years ago
4 0
All angles in a triangle add up to 180, so you can do 180-90-34 to get angle Q (56). Since there is a straight line, both angle and add up to 180. 56+x+72=180. X is 52
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Help please!!! Thxxx
Gnom [1K]

Answer:

F = 7: 16

Step-by-step explanation:

Equating 1 : x and 7:2

x = 2:7

Substituting x into the other equation we have

1: 16/7

Which is equal to 7: 16

5 0
3 years ago
WILL GIVE BRAINLIEST!!! Write the equation represented by the table.
atroni [7]

Answer: y = 2x+12

Step-by-step explanation:

y = mx + b

the Ys are going down by 6 each time

the Xs are going adding up by 3 each time

radio: 6/3 = 2

that's our slope

--------------------------------

when x is 0 then the y will be our b

which is 12

all together

y = 2x+12

4 0
3 years ago
Look at the picture of a scaffold used to support construction workers. The height of the scaffold can be changed by adjusting t
Vikki [24]

Answer:

Triangle PQR is a right triangle therefore you can use the pythagorean theorem to find the length of PR which is the same as the hypothenuse

Step-by-step explanation:

Theorem:

(QP)² + (QR)² = (PR)²

(6)² + (14)² = 232 ⇒  (PR)² = 232  then PR = √232 = 15.23

If PR is adjusted to 16 feet then we use the Pythagorean theorem again to find the height QR

(QR)² + (14)² = (16)²

(QR)² = 256 - 196 = 60 ⇒ QR = √60 = 7.75.

8 0
3 years ago
Using the law of cosines, write an algebraic proof to show that the angles in an equilateral triangle must equal 60°. Use "∧" to
bekas [8.4K]

The algebraic proof shows that the angles in an equilateral triangle must equal 60° each

<h3>Laws of cosines </h3>

From the question, we are to use the law of cosines to write an algebraic proof that shows that the angles in an equilateral triangle must equal 60°.

Given any triangle ABC, the measures of angles A, B, and C by the law of cosines are

cos A = (b^2 + c^2 - a^2)/2bc

cos B= (a^2 + c^2 - b^2)/2ac

cos C = (a^2 + b^2 - c^2)/2ab  

Now, given that the triangle is equilateral, with each of the side lengths equal to s

That is, a = b = c = s

Then, we can write that

cos A = (s^2 + s^2 - s^2)/(2s×s)

cos A = (s^2 )/(2s^2)

cos A = 1/2

cos A = 0.5

∴ A = cos⁻¹(0.5)

A = 60°

Also

cos B = (s^2 + s^2 - s^2)/(2s×s)

cos B = (s^2 )/(2s^2)

cos B = 1/2

cos B = 0.5

∴ B = cos⁻¹(0.5)

B = 60°

and

cos C = (s^2 + s^2 - s^2)/(2s×s)

cos C = (s^2 )/(2s^2)

cos C = 1/2

cos C = 0.5

∴ C = cos⁻¹(0.5)

C = 60°

Thus,

A = 60°, B = 60° and C = 60°

Hence, the algebraic proof above shows that the angles in an equilateral triangle must equal 60° each.

Learn more on The law of cosines here: brainly.com/question/2866347

#SPJ1

3 0
2 years ago
At an ice cream store, a family ordered 1 banana split and 2 hot fudge sundaes, paying a total of $11 for their order. The next
Vladimir [108]

Answer:

$5 and $3

Step-by-step explanation:

Cost of banana split = b

Cost of hot fudge sundae = s

  • b + 2s = 11
  • 4b + 3s = 29

<u>From the first equation we get: </u>

  • b = 11 - 2s

<u>Replacing in the second equation:</u>

  • 4(11 - 2s) + 3s = 29
  • 44 - 8s + 3s = 29
  • 44 - 29 = 5s
  • 15 = 5s
  • s = 15/5
  • s = 3

Then

  • b = 11 - 2*3 = 11 - 6 = 5

So banana split costs $5 and hot fudge sundae costs $3

8 0
3 years ago
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