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2 years ago

The diagram shows one side of a storage barn.

Mathematics

1 answer:

EastWind [94]2 years ago

5 0

Answer to A and B.

The area of rectangle: 22.8×14.5=330.6 ft²The area of rectangle: 22.8×14.5=330.6 ft²

The area of triangle: 12⋅12⋅22.8=136.8 ft²The area of triangle: 12·12·22.8=136.8 ft²

The total area of figure: 330.6+136.8=467.4 ft²The total area of figure: 330.6+136.8=467.4 ft²

B: In order to find how many gallons of paint are needed, we need to divide the total area that needs to be painted (467.4 square ft) by the area one gallon covers (350 square ft)

467.4 ÷ 350 ≈ 1.34 gallons

Since only whole gallons of paint can be purchased, you will need 2 gallons of paint.

At $20 each, the cost will be 2 x $20 or $40.

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3 years ago

Solve the system of equations using any appropriate method: 5x + 2y = -4 and -x + 2y = 8

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Step-by-step explanation:

-x + 2y = 8

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+ x. -2y. -8

6x = -12

÷6. ÷6

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3 years ago

Let P be the parabola with focus (0,4) and directrix y=x.Write an equation whose graph is a parabola with a vertical directrix t

prisoha [69]

Answer:

y²=4√2.x

Step-by-step explanation:

The focus is at (0,4) and directrix is y=x or x-y =0, for a parabola P.

The distance between the focus and the directrix of the parabola P is

$\frac{ |0-4| }{\sqrt{(1)^{2}+(-1)^{2} } }$ = $\frac{4}{\sqrt{2} }$

{Since the perpendicular distance of a point (x1, y1) from the straight line ax+by+c =0 is given by $\frac{ |ax1+by1+c| }{\sqrt{a^{2}+b^{2} } }$ }

Let us assume that the equation of the parabola which is congruent with parabola P is y²=4ax

{Since the parabola has vertical directrix}

Hence, the distance between focus and the directrix is 2a = $\frac{4}{\sqrt{2} }$ , {Two parabolas are congruent when the distances between their focus and the directrix are same}

⇒ a=√2

Therefore, the equation of the parabola is y²=4√2.x (Answer)

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3 years ago