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Colt1911 [192]
3 years ago
15

If the sales tax on 150 is 7.50, what is the percent of sales tax?​

Mathematics
1 answer:
Pachacha [2.7K]3 years ago
7 0
Let “T” represent the tax rate...
$150 x T = $7.50
Divide both sides by 150 to solve for T...
T = 7.5/150 = .05
So the tax is 5% (.05)
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A rectangle that has an area of 357 square inches is 17 inches wide. Using the formula for area (A=lw), how long is the rectangl
Lynna [10]
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Formula
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Area of rectangle = Length x Width

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Find Length
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357 = Length x 17

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Divide by 17 through
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Length = 357 ÷ 7
Length = 51 inches

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Answer: The length of the rectangle is 51 inches
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7 0
3 years ago
Evaluate the line integral, where c is the given curve. (x + 9y) dx + x2 dy, c c consists of line segments from (0, 0) to (9, 1)
viktelen [127]
\displaystyle\int_C(x+9y)\,\mathrm dx+x^2\,\mathrm dy=\int_C\langle x+9y,x^2\rangle\cdot\underbrace{\langle\mathrm dx,\mathrm dy\rangle}_{\mathrm d\mathbf r}

The first line segment can be parameterized by \mathbf r_1(t)=\langle0,0\rangle(1-t)+\langle9,1\rangle t=\langle9t,t\rangle with 0\le t\le1. Denote this first segment by C_1. Then

\displaystyle\int_{C_1}\langle x+9y,x^2\rangle\cdot\mathbf dr_1=\int_{t=0}^{t=1}\langle9t+9t,81t^2\rangle\cdot\langle9,1\rangle\,\mathrm dt
=\displaystyle\int_0^1(162t+81t^2)\,\mathrm dt
=108

The second line segment (C_2) can be described by \mathbf r_2(t)=\langle9,1\rangle(1-t)+\langle10,0\rangle t=\langle9+t,1-t\rangle, again with 0\le t\le1. Then

\displaystyle\int_{C_2}\langle x+9y,x^2\rangle\cdot\mathrm d\mathbf r_2=\int_{t=0}^{t=1}\langle9+t+9-9t,(9+t)^2\rangle\cdot\langle1,-1\rangle\,\mathrm dt
=\displaystyle\int_0^1(18-8t-(9+t)^2)\,\mathrm dt
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Finally,

\displaystyle\int_C(x+9y)\,\mathrm dx+x^2\,\mathrm dy=108-\dfrac{229}3=\dfrac{95}3
5 0
3 years ago
Which proportion can be used to show that the slope of JL is equal to the slope of MP
Ilya [14]

Answer:

See below and attached

Step-by-step explanation:

<u>As per the graph we have:</u>

  • Coordinates of JL are J(-7, 4), L(-4, 0)
  • Coordinates of MP are M(-10, 8), P(-1, -4)

<u>Slope formula is:</u>

  • m = (y₂ - y₁)/(x₂ - x₁)

<u>Slope of JL:</u>

  • (0 - 4)/(-4-(-7)) = - 4 / 3

<u>Slope of MP:</u>

  • (-4 -8)/(-1- (-10)) = -12 / 9 = - 4/3

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Step-by-step explanation:

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