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3 years ago

Re-write the linear function in slope-intercept form -6x+9y=24

Mathematics

1 answer:

Pachacha [2.7K]3 years ago

6 0

Answer:

y = 2/3x + 8/3

Step-by-step explanation:

-6x + 9y = 24

~Add 6x to both sides

9y = 24 + 6x

~Divide 9 to everything

y = 24/9 + 6/9x

~Simplify

y = 8/3 + 2/3x

~Reorder

y = 2/3x + 8/3

Best of Luck!

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Kay earns $78,400 per year. She takes a standard deduction of $5,700 and pays tax at a 21% rate. What is the amount of Kay's inc

Alex787 [66]

Answer:

$15,267

Step-by-step explanation:

Kay earns $78,400 per year and gets a standard deduction of $5,700.

Her taxable income is amount of money that she can pay tax on and that is:

Income - Standard Deduction

= $78,400 - $5,700 = $72,700

She pays tax at a 21% rate, hence, her income tax is:

$\frac{21}{100} * 72,700$

= $15,267

Her income tax is $15,267.

6 0

3 years ago

Which of the following functions are solutions of the differential equation y'' + y = 3 sin x? (select all that apply)

DiKsa [7]

Answer:

Step-by-step explanation:

We must compute the derivatives and check if the equation is satisfied.

A. $y'=(3\sin x)'=3\cos x$ . Differentiate again to get $y''=(3\cos x)'=-3\sin x$ , then $y''+y=-3\sin x+3\sin x=0\neq 3\sin x$ so this choice of y doesn't solve the equation.

B. $y'=3\sin x+3x\cos x-5\cosx +5x\sin x=(5x+3)\sin x+(3x-5)\cos x$ and $y''=5\sin x+(5x+3)\cos x+3\cos x-(3x-5)\sin x=(10-3x)\sin x+(5x+6)\cos x$ , then $y''+y=10\sin x+6\cos x\neq 3\sin x$ so y is not a solution

C. $y'=\frac{-3}{2}\cos x+\frac{3}{2}x\sin x$ hence $y''=\frac{3}{2}\sin x+\frac{3}{2}\sin x+\frac{3}{2}x\cos x=3\sin x+\frac{3}{2}x\cos x$ . Then $y''+y=3\sin x+\frac{3}{2}x\cos x-\frac{3}{2}x\cos x=3\sin x$ so y is a solution.

D. $y'=-3\sin x$ and $y''=-3\cos x$ , then $y''+y=0$ thus y isn't a solution

E. $y'=\frac{3}{2}\sin x+\frac{3}{2}x\cos x$ hence $y''=\frac{3}{2}\cos x+\frac{3}{2}\cos x-\frac{3}{2}x\sin x=3\cos x-\frac{3}{2}x\cos x$ . Then $y''+y=3\cos x-\frac{3}{2}x\cos x-\frac{3}{2}x\cos x=3\cos x\neq 3\sin x$ then y is not a solution.