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3 years ago

8

7n^2-4n-14=21 complete the square

1 answer:

Galina-37 [17]3 years ago

4 0

Answer: (7n - 2)² = 249

Explanation:

1) Given expression: 7n² - 4n - 14 = 21

2) Transpose - 14 =>

7n² - 4n = 21 + 14

3) Combine like terms =>

7n² - 4n = 35

4) multiply both terms by 7 =>

(7n)² - 4(7n) = 35×7

5) form the squared binomial:

(7n - 2)² - 4 = 35×7

6) Transpose - 4 =>

(7n - 2)² = 35×7 + 4

7) Do the operations on the right side:

(7n - 2)² = 249 or (7n - 2)² - 249 = 0

8) Verify the equivalence by expanding the binomial:

(7n)² - 2(7n) + 4 - 249 = 0

(7n)² - 14n - 245 = 0

Divide by 7: 7n² - 2n - 35 = 0 or 7n² - 2n = 35, which is equivalent to the given expression.

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The midpoint of AB is M(1, -4). If the coordinates of A are (-3,-6), what are the coordinates of B?

kramer

Answer:

The coordinates of B is (5,-2)

Step-by-step explanation:

In order to find the coordinates of B, you have to use midpoint formula. Then substitute the following values into the formula :

$m = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2} )$

Let (x1,y1) be A (-3,-6),

Let (x2,y2) be B,

Let midpoint be M (1,-4),

$(1, - 4) = (\frac{ - 3 + x2}{2} , \frac{ - 6 + y2}{2} )$

$by \: comparison, \:$

$\frac{ - 3 + x2}{2} = 1$

$- 3 + x2 = 2$

$x2 = 5$

$\frac{ - 6 + y2}{2} = - 4$

$- 6 + y2 = - 8$

$y2 = - 2$

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3 years ago

Samaria has 6 more than three times as many pieces of candy as Sydney. Samaria has 36 pieces of candy. How many does Sydney have

Vlad1618 [11]

Sam=3syd+6 and sam=36, since sam=sam we can say:

3syd+6=36

3syd=30

syd=10

So Sydney has 10 pieces of candy.

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2 years ago

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Andru [333]

Answer:

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Step-by-step explanation:

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2 years ago

What is the value of x ÷ y - z if x = 32, y = 4, and z = 2.75?

katen-ka-za [31]

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2 years ago

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I have to determine the length please show me the steps

iogann1982 [59]

Answer:

c = 11.03 m

Step-by-step explanation:

In this given <em>right isoceles triangle</em>, one of the sides are labeled as 7.8 m. We'll label this side as "a."

The length of side "a" is congruent to the other side. Therefore, the measurement of the other side is also 7.8 m.

We can use the Pythagorean Theorem to solve for the measurement of the hypotenuse, side "c."

According to the Pythagorean Theorem: $c^{2} = a^{2} + a^{2}$ .

We'll plug in the values for side "a" and side "b" into the formula:

$c^{2} = a^{2} + a^{2}$

$c^{2} = 2a^{2}$

$c^{2} = 2(7.8 m)^{2}$

$c^{2} = 121.68 m^{2}$

To calculate the value of "c," we must take the squared root of $2a^{2}$ :

$\sqrt{c^{2}} = \sqrt{121.68}$

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By the way, the value of c = <em>a </em> $\sqrt{2}$

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2 years ago