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2 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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An equivalent expression with a rational denominator is...

Whitepunk [10]

Given the expression,

$(8x-56x^2)/(\sqrt{14x-2})$

We will have to rationalize the denominator first. To rationalize the denominator we have to multiply the numerator and denominator both by the square root part of the denominator.

$[(8x-56x^2)(\sqrt{14x-2})]/[(\sqrt{14x-2})(\sqrt{14x-2})]$

If we have $(\sqrt{a})(\sqrt{a})$ , we will get $\sqrt{a^2}$ by multiplying them. And $\sqrt{a^2} = a$ .

So here in the problem, we will get,

$[(8x-56x^2)(\sqrt{14x-2})]/(14x-2)$

Now in the numerator we have $(8x-56x^2)$ . We can check 8x is common there. we will take out -8x from it, we will get,

$-8x(-1+7x)$

$-8x(7x-1)$

And in the denominator we have $14x-2$ . We can check 2 is common there. If we take out 2 from it we will get,

$2(7x-1)$

So we can write the expression as

$[(-8x)(7x-1)(\sqrt{14x-2})]/[2(7x-1)]$

$(7x-1)$ is common to the numerator and denominator both, if we cancel it we will get,

$(-8x)(\sqrt{14x-2})/2$

We can divide -8 by the denominator, as -8 os divisible by 2. By dividing them we will get,

$(-4x)(\sqrt{14x-2})$

$(-4x)(14x-2)^(1/2)$

So we have got the required answer here.

The correct option is the last one.

4 0

2 years ago

I need help its a review form a few years ago i cant rember pls answer both

nalin [4]

Answer:

u didnt add the picture

Step-by-step explanation:

3 0

2 years ago

1. What is the slope of the line that passes through the points E(3, 0) and F (6, -3)?

Mama L [17]

Answer:

1. m=- -1 2. -1+1

Step-by-step explanation:

Ok for the first one you need to label 3 x1 0 y1 6 x2

and -3 y2

Next you need to do y2-y1 over x2-x1 so fill that in and your equasion is (-3-0)

------------ = -3

( 6-3) ----

That reduces to -1 because -3 divided by 3 is -1

As for number 2 we need to find b to do this pick any of the y's from before we can go with 0 so the 0 is y in the equasion and we already learned slope is -1 so your equasion should be 0=--1+b ok to solve this you need to add -1 to both sides since its a negitive so you add 1 to 0 which is 1 and when you add 1 to -1 it cancells it out so you have 1=b so b is 1 for the equsion you just fill it in so it is y=- -1+1

I hope I helped

5 0

2 years ago

Trapezoid QRST has two right angles. A 5-in.altitude can be drawn dividing QRDT into a rectangle and an isosceles right triangle

Vika [28.1K]

Answer:

The area of the trapezoid is 57.5 square inches

Step-by-step explanation:

we know that

The trapezoid QRST can be divided into a rectangle QRDT and an isosceles right triangle RSD

see the attached figure to better understand the problem

step 1