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3 years ago

−2x=x2−6 Rewrite the equation by completing the square.

Mathematics

1 answer:

V125BC [204]3 years ago

6 0

Answer:

(x + 1)² = 7

Step-by-step explanation:

Given:

-2x = x² - 6

We'll start by rearranging it to solve for zero:

x² + 2x - 6 = 0

The first term is already a perfect square so that's fine. Normally, if that term had a non-square coefficient, you would need to multiply all terms a value that would change that constant to a perfect square.

Because it's already square (1), we can simply move to the next step, separating the -6 into a value that can be doubled to give us the 2, the coefficient of the second term. That value will of course be 1, giving us:

x² + 2x + 1 - 1 - 6 = 0

Now can group our perfect square on the left and our constants on the right:

x² + 2x + 1 - 7= 0

x² + 2x + 1 = 7

(x + 1)² = 7

To check our answer, we can solve for x:

x + 1 = ± √7

x = -1 ± √7

x ≈ 1.65, -3.65

Let's try one of those in the original equation:

-2x = x² - 6

-2(1.65) = 1.65² - 6

- 3.3 = 2.72 - 6

-3.3 = -3.28

Good. Given our rounding that difference of 2/100 is acceptable, so the answer is correct.

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3 years ago

Please solve for x.... 13x+13=104

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3 years ago

Complete the table below for the function y = -3x+7

KiRa [710]

Answer:

(x,y)--> (2,1), (4, -5), (7, -14), (9, -20), (11, -26)

Step-by-step explanation:

y = -3x + 7

substituting x-values in y= -3x + 7

x = 2

y= -3 × 2 + 7

= -6 + 7

= 1

x=4

y= -3 × 4 + 7

= -12 + 7

= -5

x=7

y= -3 × 7 + 7

= -21 + 7

= -14

x=9

y= -3 × 9 + 7

= -27 + 7

= -20

x=11

y= -3 × 11 + 7

= -33 + 7

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6 0

3 years ago

Three right triangles are drawn in the coordinate plane,

SashulF [63]

Answer:

Triangle A:

- smaller leg = 3

- longer leg = 10

- hypotenuse = 10.4

Traingle B:

- smaller leg = 4

- longer leg = 13

- hypotenuse = 13.6

Triangle C:

- smaller leg = 5

- longer leg = 7

- hypotenuse = 8.6

Step-by-step explanation:

Let's find the distance of the legs for the 3 right triangles.

Triangle A

The smaller leg (SL) is from (2,5) to (2,8), so the length is given by the distance in the y-axis:

$SL_{A} = 8 - 5 = 3$

Hence, the lenght of the smaller leg is 3.

The longer leg (LL) is from (-8, 8) to (2, 8), so the length is given by the distance in the x-axis:

$LL_{A} = 2 - (-8) = 10$

Then, the length of the longer leg is 10.

Now, we can find the hypotenuse (H) by using Pitagoras:

$H_{A} = \sqrt{SL_{A}^{2} + LL_{A}^{2}} = \sqrt{3^{2} + 10^{2}} = 10.4$

Triangle B

The SL is from (3, -9) to (7, -9)

The length of the SL is:

$SL_{B} = 7 - 3 = 4$

The LL is from (7, -9) to (7, 4)

The length of the LL is:

$LL_{B} = 4 - (-9) = 13$

The hypotenuse is:

$H_{B} = \sqrt{4^{2} + 13^{2}} = 13.6$

Triangle C

The SL is from (-10, -6) to (-10, -1)

The length of the SL is:

$SL_{C} = -1 - (-6) = 5$

The LL is from (-10, -6) to (-3, -6)

The length of the LL is:

$LL_{C} = -3 - (-10) = 7$

The hypotenuse is:

$H_{C} = \sqrt{5^{2} + 7^{2}} = 8.6$

I hope it helps you!

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3 years ago

Super easy problem its just graphing!! will mark brainliest <33

Sonbull [250]

Answer:

$y\ =\ \left|\frac{1}{2}x-2.5\right|+3$

Step-by-step explanation:

Look at the image below ↓

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3 years ago

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