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katovenus [111]
3 years ago
11

What is the equation, in slope-intercept form, of the line that is perpendicular to the line

Mathematics
2 answers:
hjlf3 years ago
5 0
B) is the correct answer hope this helps :D
Digiron [165]3 years ago
4 0
The correct answer is D
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Answer:

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Step-by-step explanation:

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8. Write the equation of the line that is parallel to the line 2x + 5y = 15 and passes through the
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Answer:

\sf y = \bold -\frac{2}{5} x -3

Explanation:

part A identification for slope:

\sf 2x + 5y = 15

\sf 5y = -2x + 15

\sf y = \frac{-2x + 15}{5}

\sf y = -\frac{2 }{5} x+3

comparing with slope intercept form: y = mx + b

we can find that here the slope is \bold -\frac{2}{5}

part B, solving the equation:

if the line is parallel, then the slope will be same.

given coordinates: ( - 10, 1 )

using the equation:

y - y₁ = m( x - x₁ )

\sf y - 1 = \bold -\frac{2}{5} (x --10)

\sf y = \bold -\frac{2}{5} x -4 + 1

\sf y = \bold -\frac{2}{5} x -3

Extra information:

check the image below. this proves that the line is parallel and passes through point (-10, 1). the blue line is question line and red the answer line.

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3 years ago
Ms. Sloane earns an 8% commission on her total sales. In February, Ms. Sloane's total sales were $29,250. In March, Ms. Sloane's
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Answer:

$278

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3 years ago
From a thin piece of cardboard 30 in. by 30 in., square corners are cut out so that the sides can be folded up to make a box. Wh
Brilliant_brown [7]

Answer:

Dimensions 5in x 10in x 10in will yeild a box with a max. volume of  500 cubic inches

Step-by-step explanation:

Volume =  height x length x width

considering 'x' as the length of the square corners that has been cut out from the cardboard and also, that is height of the cardboard box.

square corners are cut out so that the sides can be folded up to make a box, cardboard sides would reduce by 2x

therefore,

V = x  (30-2x) (30-2x) ---> eq(1)

V=( 30x - 2x²) (30-2x)

V= 900x- 60x² - 60x² + 4x³

V=  4x³ - 120 x²+ 900x

Taking derivative w.r.t 'x'

dV/dx = 12x² - 240 x +900

dV/dx = 4 (3x² - 60x +225)

For maximum dV/dx, make it equal zero

dV/dx = 0

so,  4 (3x² - 60x +225)=0

3x² - 60x+225=0   (taking 3 common)

x² - 20x + 75 =0

Solving this quadratic equation

x² - 15x -5x + 75 =0

x(x-15) - 5(x-15) =0

Either (x-15)=0

x=15

Or x-5=0

x = 5

if we substitute x=15 in eq(1), volume becomes zero.

therefore, x cannot be 15

When x= 5

eq(1)=>V = 5  (30-2(5)) (30-2(5))

V= 5 (10) (10)

V= 500 cubic inches,

Therefore, Dimensions 5in x 10in x 10in will yeild a box with a max. volume of  500 cubic inches

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4 years ago
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