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2 years ago

Factor 5a^2-30a+45, and 2x^5+x^4-2x-1.

Mathematics

1 answer:

Mrrafil [7]2 years ago

6 0

Step-by-step explanation:

${5a}^{2} - 30a + 45$

$5( {a}^{2} - 6a + 9)$

5(a-3)(a-3)

5(a-3)^2

${2x}^{5} + {x}^{4} - 2x - 1$

X^4(2x+1) - (2x+1)

(x^4-1)(2x+1)

(x^2-1)(x^2+1)(2x+1)

(x-1)(x-1)(x^2+1)(2x+1)

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PLEASE HELP! Daniela has a rectangular yard with a pool in the shape of a semicircle. How many square feet of grass does Daniela

GalinKa [24]

Answer:

Part 1) Area of rectangle $3,600\ ft^{2}$

Part 2) Area of semicircle $1,413\ ft^{2}$

Par 3) Total area of grass $2,187\ ft^{2}$

Step-by-step explanation:

we know that

The total area of grass is equal to the area of rectangle minus the area of semicircle

step 1

Find the area of rectangle

The area of rectangle is equal to

$A=45*80=3,600\ ft^{2}$

step 2

Find the area of semicircle

The area of semicircle is equal to

$A=\frac{1}{2}\pi r^{2}$

we have

$r=60/2=30\ ft$ -----> the radius is half the diameter

substitute

$A=\frac{1}{2}(3.14)(30)^{2}$

$A=1,413\ ft^{2}$

step 3

Find the total area of grass

$3,600\ ft^{2}-1,413\ ft^{2}=2,187\ ft^{2}$

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$\large{ \tt{❃ \: EXPLANATION}} :$

You'll have to know : Mid-point theorem states that A straight line segment joining the mid-points of any two triangle is parallel to the third side and it is equal to half of the length of the third side.