Reese is selling lemonade at the parade. He gets to keep 50% of the money he collects. A large lemonade is

Yuri [45]

$f(x) = \dfrac{x}{2} - 2$

$g(x) = 2x^2 + x - 3$

$(f + g)(x) = \dfrac{x}{2} - 2+ 2x^2 + x - 3$

$(f + g)(x) = 2x^2 + \dfrac{3}{2}x - 5$

7 0

3 years ago

The polynomial of degree 4, P ( x ) has a root of multiplicity 2 at x = 4 and roots of multiplicity 1 at x = 0 and x = − 1 . It

Svetlanka [38]

To have roots as described, that means we have the following factors: From multiplicity 2 at x=1 has (x-1)^2 as its factor From multiplicity 1 at x=0 has x as a factor From multiplicity 1 at x = -4 has a factor of x+4 Putting these together we get that P(x) = A (x) (x+4) (x-1)^2 Multiply these out and find P(x) = A (x^2 + 4x) (x^2 - 2x + 1) A ( x^4 - 2x^3 + x^2 + 4x^3 - 8x^2 + 4x ) Combine like terms and find P(x) = A (x^4 + 2x^3 - 7x^2 + 4x) To find A, we use the point they gave us (5, 72) P(5) = A [ (5)^4 + 2(5)^3 - 7(5)^2 + 4(5) ] = 72 A [ 625 + 250 - 175 + 20 ] = 72 A [ 720 ] = 72 Divide both sides by 720 and find that A = 0.1 Final answer: P(x) = 0.1 ( x^4 + 2x^3 - 7x^2 + 4x) or P(x) = 0.1 x^4 + 0.2 x^3 - 0.7x^2 + 0.4x

4 0

2 years ago

Which expression is equivalent to sqrt128x^5y^6/2x^7y^5 ? Assume x 0 and y > 0.

kolbaska11 [484]

Answer:

$\frac{8\sqrt{y} }{x}$

Step-by-step explanation:

We are given the following expression and we are to simplify it:

$\sqrt {\frac {128x^5y^6} {2x^7y^5} }$

To make it easier to solve, we can also write this expression as:

$\sqrt {\frac{128}{2} * \frac {x^5} {x^7} * \frac {y^6} {y^5}}$

Now we will cancel out the like terms to get:

$\sqrt {64*\frac{1} {x^2}*y }$

Taking the square root of the terms to get:

$8*\frac {1}{x} .\sqrt{y}$

$\frac{8\sqrt{y} }{x}$

4 0

3 years ago

Read 2 more answers

-3 | -8n – 8 | = -120 Can you guys solve for absolute value??

alexandr1967 [171]

Answer:

n = -6 or n = 4.

Step-by-step explanation:

-3 | -8n – 8 | = -120

Divide both sides by -3:

| -8n – 8 | = 40

This gives us 2 equations because the expression in the absolute signs can be positive or negative:

-8n - 8 = 40

so -8n = 48

n = -6.

and

-8n - 8 = -40

-8n = -32

n = 4.

3 0

3 years ago

You randomly choose one of the morales.Without replacing the first marble, you choose a second marble. What is the probability o

IrinaK [193]

Let’s say, hypothetically speaking, you chose the second marble without replacing the first marble so, events are hypothetically dependent. Events are dependent if the occurrence of one hypothetical event hypothetically does affect the likelihood that the other events occur. The probably of two or more dependent events A and B is the probability of A times the probability of B after A hypothetically occurs

P(A and B) = P(A) x P(B after A)

Choose the first marble

The total number of hypothetical marbles are, hypothetically speaking, 4 on a hypothetical basis, and there is one red marble.

P(red)=1/4

Choose the second marble

Without hypothetically replacing the hypothetical first marble, you choose the hypothetical marble, hypothetically speaking. So, the total hypothetical number of marbles are, hypothetically, 3, and there is, hypothetically, one green marble.

P(green) = 1/3

The probability of choosing red and then, hypothetically, green is:

P(red and green) = P(red) x P(green)
=1/4 x 1/3

= 1/12

P(red and green) is hypothetically equal to 1/12 on a hypothetical account.

Final hypothetical answer: 1/12

4 0

2 years ago