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3 years ago

If 3x^2 -2x+7=0, then(x-1/3)^2=

1 answer:

5 0

3x² - 2x + 7 = 0.

Using method of completing the square.

3x² - 2x = 0 - 7

3x² - 2x = -7 Divide through by 3.

x² - 2/3x = -7/3 ...........(d)

Coefficient of x = -2/3, half of it = 1/2*-2/3 = -1/3 square of it = (-1/3)² = 1/9

We add (1/9) to both sides of equation (d)

x² - 2/3x = -7/3

x² - 2/3x + 1/9 = -7/3 + 1/9

We factorize it by making using of half of the coefficient, -1/3

(x - 1/3)² = -7/3 + 1/9

(x - 1/3)² = -20/9

That's the answer as asked by the question. -20/9

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A square napkin is folded in half on the diagonal and placed on the diameter of a round plate (see diagram below). If the folded

Crank

Answer:

$A=81(\pi-1)\ in^2$

Step-by-step explanation:

step 1

Find the area of the plate

The area of a circle is given by the formula

$A=\pi r^{2}$

we have

$r=18/2=9\ in$ ---> the radius is half the diameter

substitute

$A=\pi (9)^{2}\\A=81\pi\ in^2$

step 2

Find the area of the square napkin folded (is a half of the area of the square napkin)

we know that

The diagonal of the square is the same that the diameter of the plate

Applying Pythagorean theorem

$D^2=2b^2$

where

b is the length side of the square

we have

$D=18\ in$

substitute

$18^2=2b^2$

solve for b^2

$b^2=162\ in^2$ -----> is the area of the square

Divide by 2

$162/2=81\ in^2$

step 3

Find the area of the space on the plate that is NOT covered by the napkin

we know that

The area of the space on the plate that is NOT covered by the napkin, is equal to subtract the area of the square napkin folded (is a half of the area of the square napkin) from the area of the plate

$A=(81\pi-81)\ in^2$

simplify

$A=81(\pi-1)\ in^2$

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3 years ago

Write the expression as either the sine, cosine, or tangent of a single angle.

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3 years ago

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Sarah is the oldest out of here four sisters. Her youngest sister is half her age. The 2 other sisters are twin and are 2 years

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Sarah is 14
The twins are 12
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