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3 years ago

Write Absolute value equation that has the given solutions 4 and 11

1 answer:

4 0

| x + a | = | x + a |
As given in the question x=3 or x=9, replace first x by 3 and the other x by 9
| 3 + a | = | 9 + a |
3 + a = - ( 9 + a)
3 + a = -9 - a (Solving for a )
2a = -12
a = -12/2
a= -6
now, | x + a | = | 3 - 6 | = |-3| = 3
| x + a | = | 9 - 6 | = |3| = 3
Therefore, the answer is | x - 6 | = 3

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Determine the range of the function.

Naya [18.7K]

Answer:

$Solution: f(x)\ge-5\\Interval:[-5,\infty)$

Step-by-step explanation:

Equation: $\frac{1}{4} x^2-5 = y$

1). $\frac{1}{4} x^2-5 = y$ → $\frac{x^2}{4}-5=y$

2). $\frac{x^2}{4}-5=y$ ∴ $a=\frac{1}{4}, b=0, c=-5$

3). $x_v=-\frac{b}{2a}$

$=-\frac{0}{2(\frac{1}{4})}$

$=0$

4). now plug $x_v$ into $y_v$

$y_v=\frac{0^2}{4}-5$

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5). Minimum (0,-5) ∴ $f(x)\ge-5$

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3 years ago

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nekit [7.7K]

Answer:

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Step-by-step explanation:

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3 years ago

Find the value of that makes m ll n.

Alja [10]

Answer: x = 108

Step-by-step explanation: In this problem, we're given a diagram and

we're asked to find the value of x that would make m ll n.

We can see that the angles that are marked in the diagram

are same-side interior angles since they lie on the same side

of the transversal and they lie on the interior of lines m and n.

Therefore, in order for line m to be parallel to line n,

these angles must be supplementary.

In other words, they must add to 180 degrees.

So we can setup the equation x + 72 = 180.

Subtracting 72 from both sides gives us x = 108.

So the value of x that would make line m ll n is 108.

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2 years ago

What is the approximate value of x in the diagram below? (Hint: You will need

Delicious77 [7]

Answer:

B. 39.59

Step-by-step explanation:

So 43 degrees, you know the length of the opposite side (27) and the angle (43 degrees), the only unknown is the hypotenuse. So you're looking for a trigonometric ratio that uses the angle (all of them do, except technically the inverse don't), the opposite side, and the hypotenuse. Sine is defined as $\frac{opposite}{hypotenuse}$ . So let's plug in known values: