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3 years ago

Can someone tell me the answer to both of these

Mathematics

2 answers:

borishaifa [10]3 years ago

6 0

First 8.5 h, and second question is 2

omeli [17]3 years ago

3 0

Answer:

First question --> C) 8.5h

Second question --> D) 2

Step-by-step explanation:

First question

Terry earns $10 per hour

Jill earns 20% less which is $2 less

Jill earns $8 per hour

Jerry earns $0.50 more per hour than Jill

Jerry earns $8.50 per hour

Second question

x = 2

y = 4

(2x + 3y) / 4 - 2 = ?

Use PEMDAS

so Parentheses first, then divide, then subtract

So.... (2x + 3y) = (2*2 + 3*4) = (4 + 12) = 16

Then divide

16/4 = 4

Then subtract

4 - 2 = 2

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Use a half-angle identity to find the exact value of tan 22.5°.

dusya [7]

Answer:

$\sqrt{2} -1$

Step-by-step explanation:

22.5 degrees is half of 45 degrees (special angle for which we know exactly the value of all three basic trigonometric functions (sine, cosine, and tangent).

So we start recalling the formula for tangent of a half angle: $tan(\frac{\alpha }{2} )= \frac{1-cos(\alpha) }{sin(\alpha) }$

We need just the values of:

$sin(\alpha )=sin(45^o)=\frac{\sqrt{2} }{2}$

and of

$cos(\alpha )=cos(45^o)=\frac{\sqrt{2} }{2}$

to answer the question. Then, we use those values in the original formula for tangent of a half angle:

$tan(\frac{\alpha }{2} )= \frac{1-cos(\alpha) }{sin(\alpha) }\\tan(22.5^o)=\frac{1-\frac{\sqrt{2} }{2} }{\frac{\sqrt{2} }{2}} =\frac{2-\sqrt{2} }{\sqrt{2} } =\frac{2\sqrt{2}-2 }{2} =\sqrt{2} -1$