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2 years ago

15

The table shows the amount of money a plumber charges for different numbers of hours that he works. The plumber graphed this inf

ormation.
What is the slope of the line that represents this situation?

Hours worked| 2 4 7 9
Amount charged ($)| 96 192 336 432

1 answer:

OLEGan [10]2 years ago

3 0

Y=ax+b
A=y/x
= 192-96/4-2
= 96/2
=48
So y=48x+b
Lets replace y and x
96=48.2+b
B= 96-96
=0
So y=48x

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asambeis [7]

Given:

$\cos^4 \alpha+\sin^4\alpha=\dfrac{1}{4}(3+\cos 4 \alpha)$

To prove:

The given statement.

Proof:

We have,

$\cos^4 \alpha+\sin^4\alpha=\dfrac{1}{4}(3+\cos 4 \alpha)$

$LHS=\cos^4 \alpha+\sin^4\alpha$

$LHS=(\cos^2 \alpha)^2+(\sin^2 \alpha)^2$

$LHS=(\cos^2 \alpha+\sin^2\alpha)^2-2\sin ^2\alpha\cos^2 \alpha$ $[\because a^2+b^2=(a+b)^2-2ab]$

$LHS=(1)^2-2(1-\cos^2 \alpha)\cos^2 \alpha$ $[\because \cos^2 \alpha+\sin^2\alpha=1]$

$LHS=1-2\cos^2 \alpha+2\cos^4 \alpha$

Now,

$RHS=\dfrac{1}{4}(3+\cos 4 \alpha)$

$RHS=\dfrac{1}{4}[3+(2\cos^2 2\alpha-1)]$ $[\because \cos 2\theta=2\cos^2\theta -1]$

$RHS=\dfrac{1}{4}[2+2\cos^2 2\alpha]$

$RHS=\dfrac{1}{4}[2+2(2\cos^2 \alpha-1)^2]$ $[\because \cos 2\theta=2\cos^2\theta -1]$

$RHS=\dfrac{1}{4}[2+2(4\cos^4 \alpha-4\cos \alpha+1)]$ $[\because (a-b)^2=a^2-2ab+b^2]$

$RHS=\dfrac{1}{4}[2+8\cos^4 \alpha-8\cos \alpha+2]$

$RHS=\dfrac{1}{4}[4+8\cos^4 \alpha-8\cos \alpha]$

$RHS=1+2\cos^4 \alpha-2\cos \alpha$

$RHS=1-2\cos^2 \alpha+2\cos^4 \alpha$

$LHS=RHS$

Hence proved.

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2 years ago

vicki made a fruit tart and cut it into six equal pieces. vicki, silvia, and Elena each took 2 pieces of the tart home. vicki sa

CaHeK987 [17]

Vicki is correct!
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2 years ago

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Darya [45]

Answer: y = 1

Step-by-step explanation:

Step 1) Simplifying

2(y + 2) = 6

Step 2) Reorder the terms:

2(2 + y) = 6

(2 * 2 + y * 2) = 6

(4 + 2y) = 6

Step 3) Solving

4 + 2y = 6

Step 4) Solving for variable 'y'.

Step 5) Move all terms containing y to the left, all other terms to the right.

Step 6) Add '-4' to each side of the equation.

4 + -4 + 2y = 6 + -4

Step 7) Combine like terms: 4 + -4 = 0

0 + 2y = 6 + -4

2y = 6 + -4

Step 8) Combine like terms: 6 + -4 = 2

2y = 2

Step 9) Divide each side by '2'.

y = 1

Step 10) implifying

y = 1

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2 years ago

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Answer:

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Step-by-step explanation:

width x length = area

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65 x 95 = 6175

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