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soldi70 [24.7K]
2 years ago
5

Please help me with this homework!

Mathematics
1 answer:
ZanzabumX [31]2 years ago
5 0
<h2><u>Part 1: Define</u></h2><h3>Part 1i) Defining "adjacent angles"</h3>

In this case, adjacent angles are such pairs of angles that are alongside each other. Therefore, we can say that the sum of the two adjacent angles forms a bigger angle.

<h3>Part 1ii) Defining "vertical angles"</h3>

In this case, vertical angles are such angles that are on opposite sides of the intersection between two lines. It is understood that vertically opposite angles are equivalent.

<h2><u>Part 2: Solve</u></h2><h3>Problem 8:</h3>

Clearly, we can see that two angles (one angle known as ∠x and the other angle) are alongside each other. Therefore, we can tell the angles are adjacent angles.

As we can see a \square, we can tell that the sum of the measure of ∠x and the other angle is 90°. Therefore, we obtained;

  • ⇒ ∠x + 35 = 90
  • ⇒ ∠x = 90 - 35
  • ⇒ ∠x = 65°

Therefore, the measure of ∠x is 65°.

<h3 /><h3>Problem 9:</h3>

Clearly, we can see that two angles (one angle known as ∠x and the other angle) are on opposite sides. Therefore, we can tell that the angles are vertically opposite angles.

As stated in part 1ii, vertical angles are equivalent. Since ∠x and the other angles are vertically opposite angles, the measure of ∠x is 128°.

<h3 /><h3>Problem 10:</h3>

Clearly, we can see that two angles (one angle known as ∠x and the other angle) are alongside each other. Therefore, we can tell the angles are adjacent angles.

Since the line shown, is a straight line, we can tell that the sum of 117 and x is 180. Therefore, we obtain the following equation;

  • 117 + ∠x = 180°

<u>When isolating x, we get;</u>

  • ⇒ 117 + ∠x - 117 = 180° - 117
  • ⇒ ∠x = 180° - 117
  • ⇒ ∠x = 63°

Therefore, the measure of ∠x is 63°

Learn more about this topic: brainly.com/question/14355129

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Sharon can buy cards in boxes of 12 and stamps in packages of 20 what is the least number of boxes of cards she should buy?
-Dominant- [34]

The least number of boxes Sharon should buy is 5 boxes.

Step-by-step explanation:

Given,

Number of cards in box = 12

Number of stamps in packages = 20

We will find least common multiple of 12 and 20.

12 = 12,24,36,48,60,.....

20 = 20,40,60,80,....

The LCM of 12 and 20 is 60.

Now,

12 cards = 1 box

60 cards = \frac{60}{12}\ boxes

60 cards = 5 boxes

The least number of boxes Sharon should buy is 5 boxes.

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Step-by-step explanation:

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6x-4(3x-5)=2 solve for x.
jeka57 [31]

Answer:

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Step-by-step explanation:

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(2^8 \times 5^{-5} \times 19^0)^{-2} \times (\dfrac{5^{-2}}{2^3})^4 \times 2^{28} =

= 2^{-16} \times 5^{10} \times 1 \times \dfrac{5^{-8}}{2^{12}} \times 2^{28}

= 2^{-16} \times 5^{10} \times 5^{-8} \times 2^{-12} \times 2^{28}

= 2^{-16} \times 2^{-12} \times 2^{28} \times 5^{10} \times 5^{-8}

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