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2 years ago

The graph of the function f(x) = (x − 3)(x + 1) is shown.

Mathematics

2 answers:

Nuetrik [128]2 years ago

7 0

Answer:

The answer is A

Nutka1998 [239]2 years ago

6 0

Option A. All the real values of x where x < -1

Procedure
Solve the inequality:
(x -3)(x+1)>0
That happens in two cases.

1) When both factors >0
x-3>0 and x+1>0
x>3 and x >-1

The intersection is x >3

2) When both factors <0
x-3<0 and x+1<0
x<3 and x<-1

the intersection is x<-1.

We have obtained that the function is positive for the intervals x < -1 and x > 3. But in one of those intervals the function is decresing and in the other is increasing.

You can recognize that the function given is a parabola and, because the coefficient of the quadratic term is positive, the parabola opens upward. Then the function is decreasing in the first interval and increasing in the second interval.

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Solve for x

Anon25 [30]

Answer:

3. x = y - 3

Step-by-step explanation:

You want to move all numbers on the same side of x to the other side with y. Whenever doing this, we have to reverse the operation. In this problem, we have + 3 with x. So we will need to subtract 3 from both sides.

x + 3 = y

x = y - 3

6 0

2 years ago

Y varies inversely with x y = 132 when x = 6 What is the value of k, the constant of inverse variation?

malfutka [58]

The answer to this question is i think a or b.

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2 years ago

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What is the following product? <br>(4x square root 5x^2 + 2^2 square root 6)^2

tangare [24]

The product is $104 x^{4}+16 \sqrt{30} x^{4}$

Explanation:

The given expression is $\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}$

We need to determine the product of the given expression.

First, we shall simplify the given expression.

Thus, we have,

$\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=\left(4 x \sqrt{5} x+2 x^{2} \sqrt{6}\right)^2$

$\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=\left(4 x^{2} \sqrt{5}+2 x^{2} \sqrt{6}\right)^2$

Expanding the expression, we have,

$\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=\left(4 x^{2} \sqrt{5}+2 x^{2} \sqrt{6}\right)\left(4 x^{2} \sqrt{5}+2 x^{2} \sqrt{6}\right)$

Now, we shall apply FOIL, we get,

$\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=\left(4 x^{2} \sqrt{5}\right)^{2}+2 ( 2 x^{2} \sqrt{6})(4 x^{2} \sqrt{5})+\left(2 x^{2} \sqrt{6}\right)^{2}$

Simplifying the terms, we have,

$\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=16 \cdot 5 x^{4}+16 \sqrt{30} x^{4}+4 \cdot 6 x^{4}$

Multiplying, we get,

$\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=80 x^{4}+16 \sqrt{30} x^{4}+24 x^{4}$

Adding the like terms, we get,

$\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=104 x^{4}+16 \sqrt{30} x^{4}$

Thus, the product of the given expression is $104 x^{4}+16 \sqrt{30} x^{4}$

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2 years ago

What is a common denominator for 5/12 and 2/9

hram777 [196]

because the denominator is on the bottom, you have to find a number which both 12 and 9 can be divided by. In this case the only answer that isn't a decimal is 3

4 0

2 years ago

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Which system of equations can be used to find the roots of the equation 4x^2=x^3+2x?

irina [24]

Next time, please share the answer choices.
Starting from scratch, it's possible to find the roots:

<span>4x^2=x^3+2x should be rearranged in descending order by powers of x:

x^3 - 4x^2 + 2x = 0. Factoring out x: </span>x(x^2 - 4x + 2) = 0

Clearly, one root is 0. We must now find the roots of (x^2 - 4x + 2):

Here we could learn a lot by graphing. The graph of y = x^2 - 4x + 2 never touches the x-axis, which tells us that (x^2 - 4x + 2) = 0 has no real roots other than x=0. You could also apply the quadratic formula here; if you do, you'll find that the discriminant is negative, meaning that you have two complex, unequal roots.

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2 years ago

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