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beks73 [17]
3 years ago
11

Solve x2 + 14x = −24 by completing the square.

Mathematics
2 answers:
Artyom0805 [142]3 years ago
7 0

Answer:

A. -12, -2

Step-by-step explanation:

Just took an Edge quiz.

Aleks04 [339]3 years ago
6 0

Option A

The solution set of the equation is {-12, -2}

<h3><u>Solution:</u></h3>

Given equation is:

x^2 + 14x = -24

We have to find the solution set of this equation by completing the square

First, rearrange the equation so that only zero will be on the right side:

x^2 + 14x + 24 = 0 ----- eqn 1

<em><u>The general form of quadratic equation is:</u></em>

ax^2 + bx + c = 0 where a \neq 0

On comparing the given eqn 1 with general quadratic equation, we get

a = 1

b = 14

c = 24

In completing the square, we take half of coefficient of middle term "x" and then square it. Then we add it on both sides of the equation

So to complete the square, add (\frac{b}{2})^2 to both sides of the equation

x^2 + 14x + 24 + (\frac{14}{2})^2 = (\frac{14}{2})^2

x^2 + 14x + 24 + 7^2 = 7^2\\\\x^2 + 14x + 24 + 49 = 49

x^2 + 14x + 24 + 49 = 49\\\\x^2 + 14x + 49 = 49 - 24\\\\x^2 + 14x + 49 = 25\\\\(x + 7)(x + 7) = 25\\\\(x + 7)^2 = 25

Take square root on both sides

x + 7 = \sqrt{25}

x+7=\pm 5

Now make two equations

x + 7 = + 5 and x + 7 = -5

x = +5 - 7 = -2

x = -2

And,

x + 7 = -5

x = -5 - 7 = -12

x = -12

Therefore, the solution set of the equation is {-12, -2} and option A is correct

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To solve this problem, we make use of the z statistic. What we have to do here is to find for the z score using the given data and from the standard probability tables for z, we locate the proportion of the fish longer than 12 inches.

 

The formula for calculating the z score is:

z = (x – μ) / σ

where,

x = the sample value = 12 inches

μ = the sample mean = 11 inches

σ = 2 inches

 

so,

z = (12 – 11) / 2

z = 1 / 2

z = 0.5

 

Since we are looking for the values greater than 12, so this is a right tailed test. Using the tables, the value of p at this value of z is:

p (z = 0.5) = 0.3085

 

Therefore there is a 30.85% probability that the fish is longer than 12 inches.

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The area of a rectangular parking lot is 7031m? If the with of the parking lot is 79m, what is its length?
serg [7]
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To find the length, we can abide by the following formula:

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Find the exact location of all the relative and absolute extrema of the function. HINT [See Examples 1 and 2.] (Order your answe
icang [17]

Answer:

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  • (2, -32) absolute minimum
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Step-by-step explanation:

There will be extremes at the ends of the domain interval, and at turning points where the first derivative is zero.

The derivative is ...

  h'(t) = 24t^2 -48t = 24t(t -2)

This has zeros at t=0 and t=2, so that is where extremes will be located.

We can determine relative and absolute extrema by evaluating the function at the interval ends and at the turning points.

  h(-1) = 8(-1)²(-1-3) = -32

  h(0) = 8(0)(0-3) = 0

  h(2) = 8(2²)(2 -3) = -32

  h(∞) = 8(∞)³ = ∞

The absolute minimum is -32, found at t=-1 and at t=2. The absolute maximum is ∞, found at t→∞. The relative maximum is 0, found at t=0.

The extrema are ...

  • (-1, -32) absolute minimum
  • (0, 0) relative maximum
  • (2, -32) absolute minimum
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_____

Normally, we would not list (∞, ∞) as being an absolute maximum, because it is not a specific value at a specific point. Rather, we might say there is no absolute maximum.

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7/8 = /48 <br> A. 1 <br> B. 6 <br> C. 42 <br> D. 13
Vsevolod [243]
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Your final answer is B. 42<span>.</span>
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