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Annette [7]
3 years ago
13

How do I Rewrite the function by completing the square x^2+8x-29

Mathematics
1 answer:
Flura [38]3 years ago
5 0

Answer:

  (x +4)^2 -45

Step-by-step explanation:

The square of a binomial has the form ...

  (x +a)^2 = x^2 +2ax +a^2

That is, the constant term (a^2) is the square of half the coefficient of the linear term: (2a/2)^2 = a^2.

To "complete the square", you add 0 in the form of the desired constant added to its opposite. Here, we want the constant for the square to be (8/2)^2 = 16. So, we can add 0 = 16 -16 to the expression:

  x^2 +8x +16 -29 -16

  (x^2 +8x +16) -45 . . . . group the terms that make the square

  (x +4)^2 -45 . . . . rewritten after completing the square

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Solve the inequality x+1<3/4 and write the solution in interval notation.
Darya [45]

The solution to the inequality in interval form is (-∞, -1/4)

<h3>Inequality expressions</h3>

Inequality are expressions not separates by an equal sign. Given the inequality below;

x+1<3/4

Subtract 1 from both sides to have;

x + 1 - 1 < 3/4 - 1

x < 3/4 - 1

x < (3-4)/4

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Hence the solution to the inequality in interval form is (-∞, -1/4)

Learn more on inequality here: brainly.com/question/24372553

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1 year ago
Write the slope-intercept form of the equation of the line; (-5,-4) and prep. To y equals 5x plus 1
ohaa [14]

Answer:

y=-\frac{1}{5} x-5

Step-by-step explanation:

The given line is defined by:  y=5x+1, where we see that the slope is 5 and the y-intercept 1.

In order to find a line perpendicular to the given one, we need it to have a slope that is the "opposite of the reciprocal" of the given slope.

"Opposite" means it would have its sign inverted (in our case from positive to negative); and "reciprocal means that instead of 5, it would be its reciprocal: \frac{1}{5}.

We can write this new line with such slope, and try to find its y-intercept (b) by using the given condition that requires it to go through the point (-5,-4) on he plane:

y=-\frac{1}{5} x+b

we require then that when x=-5, the value of y=-4.

Therefore: -4=-\frac{1}{5} (-5)+b\\-4=\frac{5}{5} +b\\-4=1+b\\b=-4-1=-5

Then our final answer is that the new line should have the form: y=-\frac{1}{5} x-5

4 0
3 years ago
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Alexus [3.1K]
Why is it so complicated? Volume of one cube is 1/2 * 1/2 * 1/2 = 1/8 cm^3

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2 years ago
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2 years ago
Solve for x 4x+8=28
liraira [26]

x = 5.

I attached an image of my work!

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