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3 years ago

Determine the next step for solving the quadratic equation by completing the square.

Mathematics

2 answers:

Nataly_w [17]3 years ago

8 0

Answer:

A) StartFraction negative 7 Over 2 EndFraction = –2(x – StartFraction 1 Over 2 EndFraction)2

Step-by-step explanation:

–3 + = –2(x² – x + )

-3 + -2(½)² = -2(x² - 2(x)(½) + (½)²)

-3 - ½ = -2(x - ½)²

-7/2 = -2(x - ½)²

Lady_Fox [76]3 years ago

6 0

Answer:

-7/2 = -2(x-1/2)^2

Step-by-step explanation:

0 = –2x^2 + 2x + 3

Subtract 3 from each side

-3 = –2x^2 + 2x

Factor out the -2

-3 =- 2(x^2 -x)

Take the coefficient of x and divide by 2 and square it

-1 /2 = -1/2 ^2 = 1/4

Add it to each side Remember the -2 on the outside so we need to multiply it by -2

-2 *1/4 = -1/2

-3 -1/2= -2(x^2 -x +1/4)

-7/2 = -2(x^2 -x +1/4)

-7/2 = -2(x-1/2)^2

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2. Given a quadrilateral with vertices (−1, 3), (1, 5), (5, 1), and (3,−1):

zlopas [31]

<h2>Explanation:</h2>

In every rectangle, the two diagonals have the same length. If a quadrilateral's diagonals have the same length, that doesn't mean it has to be a rectangle, but if a parallelogram's diagonals have the same length, then it's definitely a rectangle.

So first of all, let's prove this is a parallelogram. The basic definition of a parallelogram is that it is a quadrilateral where both pairs of opposite sides are parallel.

So let's name the vertices as:

$A(-1,3) \\ \\ B(1,5) \\ \\ C(5,1) \\ \\ D(3,-1)$

First pair of opposite sides:

<u>Slope:</u>

$\text{For AB}: \\ \\ m=\frac{5-3}{1-(-1)}=1 \\ \\ \\ \text{For CD}: \\ \\ m=\frac{1-(-1)}{5-3}=1 \\ \\ \\ \text{So AB and CD are parallel}$

Second pair of opposite sides:

<u>Slope:</u>

$\text{For BC}: \\ \\ m=\frac{1-5}{5-1}=-1 \\ \\ \\ \text{For AD}: \\ \\ m=\frac{-1-3}{3-(-1)}=-1 \\ \\ \\ \text{So BC and AD are parallel}$

So in fact this is a parallelogram. The other thing we need to prove is that the diagonals measure the same. Using distance formula:

$d=\sqrt{(y_{2}-y_{1})^2+(x_{2}-x_{1})^2} \\ \\ \\ Diagonal \ BD: \\ \\ d=\sqrt{(5-(-1))^2+(1-3)^2}=2\sqrt{10} \\ \\ \\ Diagonal \ AC: \\ \\ d=\sqrt{(3-1)^2+(-5-1)^2}=2\sqrt{10} \\ \\ \\$

So the diagonals measure the same, therefore this is a rectangle.

5 0

3 years ago

lars has been approved for$420,000, 20-year mortgage with an APR of 5.125%.What is his monthly payment ? How much interest would

olya-2409 [2.1K]

The answer is in the question

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3 years ago

Read 2 more answers

TIMED QUESTION NEED HELP FASTWhat values of b satisfy 3(2b + 3)2 = 36?

egoroff_w [7]

Answer:

$\frac{-3+ 2\sqrt{3}}{2}\textrm{ and }\frac{-3- 2\sqrt{3}}{2}$

Step-by-step explanation:

$3(2b+3)^{2}=36\\\frac{3(2b+3)^{2}}{3}=\frac{36}{3}\\(2b+3)^{2}=12$

Taking square root both sides, we get

$\sqrt{(2b+3)^{2}}=\pm \sqrt{12}\\2b+3=\pm \sqrt{4\times 3}\\2b+3=\pm 2\sqrt{3}\\2b+3-3=\pm 2\sqrt{3}-3\\2b=-3\pm 2\sqrt{3}\\b=\frac{-3\pm 2\sqrt{3}}{2}\\b=\frac{-3+ 2\sqrt{3}}{2}\textrm{ or }b=\frac{-3- 2\sqrt{3}}{2}$