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mel-nik [20]
2 years ago
11

Which expression is equivalent to the given expression?

Mathematics
1 answer:
jasenka [17]2 years ago
8 0

Answer:

C.) 2(x-3)(x-4)

Step-by-step explanation:

I think so

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Suppose you know that the volume of the following prism is represent by V(x) = -2x^3 + 14x^2 + 120x.
erastova [34]

Step-by-step explanation:

-2x³ + 14x² + 120x

= -2x(x² - 7x - 60)

= -2x(x - 12)(x + 5).

The other 2 dimensions are -2x and (x + 5).

When using a graphing calculator to maximise the volume of the prism, we get x = 7.378. However this value is not reasonable as it makes -2x and (x - 12) negative, which are the sides of the prism.

8 0
3 years ago
How do you write 0.000056 in scientific notation?
anygoal [31]
5.6 × 10^-5 = 0.000056
8 0
3 years ago
What is the vertex of y=x^2+4x+3
AnnyKZ [126]

Answer:

(-2, -1)

Step-by-step explanation:

This is a quadratic equation in standard form, and a = 1, b = 4 and c = 3.

The x-coordinate of the vertex is given by the formula

        -b                                                                         -4

x = --------- which here has the numerical value x = -------- = -2

        2a                                                                           2

Finally, we evaluate y=x^2+4x+3 at x = -2 to find the y-coordinate of the vertex:

y = (-2)^2 + 4(-2) + 3 = -1

The vertex is at (-2, -1).

7 0
3 years ago
I need help please. Thanks!
Karolina [17]

Answer:

A

Step-by-step explanation:

We are given the function f and its derivative, given by:

f^\prime(x)=x^2-a^2=(x-a)(x+a)

Remember that f(x) is decreasing when f'(x) < 0.

And f(x) is increasing when f'(x) > 0.

Firstly, determining our zeros for f'(x), we see that:

0=(x-a)(x+a)\Rightarrow x=a, -a

Since a is a (non-zero) positive constant, -a is negative.

We can create the following number line:

<-----(-a)-----0-----(a)----->

Next, we will test values to the left of -a by using (-a - 1). So:

f^\prime(-a-1)=(-a-1-a)(-a-1+a)=(-2a-1)(-1)=2a+1

Since a is a positive constant, (2a + 1) will be positive as well.

So, since f'(x) > 0 for x < -a, f(x) increases for all x < -a.

To test values between -a and a, we can use 0. Hence:

f^\prime(0)=(0-a)(0+a)=-a^2

This will always be negative.

So, since f'(x) < 0 for -a < x < a, f(x) decreases for all -a < x < a.

Lasting, we can test all values greater than a by using (a + 1). So:

f^\prime(a+1)=(a+1-a)(a+1+a)=(1)(2a+1)=2a+1

Again, since a > 0, (2a + 1) will always be positive.

So, since f'(x) > 0 for x > a, f(x) increases for all x > a.

The answer choices ask for the domain for which f(x) is decreasing.

f(x) is decreasing for -a < x < a since f'(x) < 0 for -a < x < a.

So, the correct answer is A.

3 0
3 years ago
1000 divided by 4 equal to what
Nesterboy [21]

Answer:

250?

Step-by-step explanation:

1000÷4=250

I think this is the right answer.

5 0
2 years ago
Read 2 more answers
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