Hey can anyone help with this question please and thank you

Mathematics

2 answers:

Law Incorporation [45]3 years ago

6 0

Answer:

x = 16

Step-by-step explanation:

7x + 9 = 9x - 23

9 + 23 = 9x - 7x

32 = 7x

32 / 7 = x

16 = x

Viefleur [7K]2 years ago

4 0

Since < (7x + 9) is an interior angle and < (9x - 23) an exterior angle — these angles are on the same side of the transversal, line t. Therefore, they are corresponding angles with the same measure.

Hence, we can establish the following equality statement to solve for x:

< (7x + 9) = < (9x - 23)

Subtract 7x from both sides:

7x - 7x + 9 = 9x - 7x - 23
9 = 2x - 23

Add 23 on both sides:

9 + 23 = 2x - 23 + 23
32 = 2x

Divide both sides by 2 to solve for x:

32/2 = 2x/2
16 = x

Therefore, x = 16.

Substitute x = 16 into the equality statement to verify whether it is the correct value:

< (7x + 9) = < (9x - 23)
7(16) + 9 = 9(16) - 23
112 + 9 = 144 - 23
121 = 121 (True statement. Therefore, x = 16 is the correct answer).

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Which of the following are possible values of r? <img src="https://tex.z-dn.net/?f=%20%7Br%7D%5E%7B2%20%7D%20%20%3D%20%20%5Cf

marshall27 [118]

Answer:

$r=\frac{\sqrt{3} }{4}$ and $r=-\frac{\sqrt{3} }{4}$

Step-by-step explanation:

when you solve for r in the given equation, you need to apply the square root property, which gives positive and negative answers (both should therefore be considered):

$r^2=\frac{3}{16} \\r=+/-\sqrt{\frac{3}{16}} \\r=+/-\frac{\sqrt{3} }{4}$