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3 years ago

15

(01.06 LC) Expand and simplify: (2x + 5y) (x - 3y) (5 points)

1 answer:

laiz [17]3 years ago

4 0

Answer:

2x² - xy - 15y²

Step-by-step explanation:

(2x + 5y)(x - 3y)

Each term in the second factor is multiplied by each term in the first factor, that is

2x(x - 3y) + 5y(x - 3y) ← distribute parenthesis

= 2x² - 6xy + 5xy - 15y² ← collect like terms

= 2x² - xy - 15y²

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8n - (2n+11 - 54)<br>simplify

Serjik [45]

Answer:

8n - (2n + 11 - 54) =

Step-by-step explanation:

6n + 43, I used a calculator !

5 0

3 years ago

Which expression is equivalent to this expression? x(2x + 3) A) 2x2 + 3 B) 2x2 + 3x C) 2x2 - 3x Eliminate D) 3x + 3

ira [324]

Answer:

B

Step-by-step explanation:

x(2x + 3)

Expand the brackets.

x(2x)+x(3)

Multiply the terms.

2x² + 3x

The answer is 2x² + 3x.

3 0

3 years ago

Read 2 more answers

Find all of the equilibrium solutions. Enter your answer as a list of ordered pairs (R,W), where R is the number of rabbits and

zloy xaker [14]

Answer:

$(0,0)$ $(4000,0)$ and $(500,79)$

Step-by-step explanation:

Given

See attachment for complete question

Required

Determine the equilibrium solutions

We have:

$\frac{dR}{dt} = 0.09R(1 - 0.00025R) - 0.001RW$

$\frac{dW}{dt} = -0.02W + 0.00004RW$

To solve this, we first equate $\frac{dR}{dt}$ and $\frac{dW}{dt}$ to 0.

So, we have:

$0.09R(1 - 0.00025R) - 0.001RW = 0$

$-0.02W + 0.00004RW = 0$

Factor out R in $0.09R(1 - 0.00025R) - 0.001RW = 0$

$R(0.09(1 - 0.00025R) - 0.001W) = 0$

Split

$R = 0$ or $0.09(1 - 0.00025R) - 0.001W = 0$

$R = 0$ or $0.09 - 2.25 * 10^{-5}R - 0.001W = 0$

Factor out W in $-0.02W + 0.00004RW = 0$

$W(-0.02 + 0.00004R) = 0$

Split

$W = 0$ or $-0.02 + 0.00004R = 0$

Solve for R

$-0.02 + 0.00004R = 0$

$0.00004R = 0.02$

Make R the subject

$R = \frac{0.02}{0.00004}$

$R = 500$

When $R = 500$ , we have:

$0.09 - 2.25 * 10^{-5}R - 0.001W = 0$

$0.09 -2.25 * 10^{-5} * 500 - 0.001W = 0$

$0.09 -0.01125 - 0.001W = 0$

$0.07875 - 0.001W = 0$

Collect like terms

$- 0.001W = -0.07875$

Solve for W

$W = \frac{-0.07875}{ - 0.001}$

$W = 78.75$

$W \approx 79$

$(R,W) \to (500,79)$

When $W = 0$ , we have:

$0.09 - 2.25 * 10^{-5}R - 0.001W = 0$

$0.09 - 2.25 * 10^{-5}R - 0.001*0 = 0$

$0.09 - 2.25 * 10^{-5}R = 0$

Collect like terms

$- 2.25 * 10^{-5}R = -0.09$

Solve for R

$R = \frac{-0.09}{- 2.25 * 10^{-5}}$

$R = 4000$

So, we have:

$(R,W) \to (4000,0)$

When $R =0$ , we have:

$-0.02W + 0.00004RW = 0$

$-0.02W + 0.00004W*0 = 0$

$-0.02W + 0 = 0$

$-0.02W = 0$

$W=0$

So, we have:

$(R,W) \to (0,0)$

Hence, the points of equilibrium are:

$(0,0)$ $(4000,0)$ and $(500,79)$

4 0

3 years ago

What is the volume of the cylinder below?

Anestetic [448]

Answer:

B

Step-by-step explanation:

The formula for volume of cylinder is given below:

volume of cylinder = $\pi r^2 h$

Where r is the radius (here, it is given as 3)

h is the height, the perpendicular distance from base to top (here, it is 4 NOT 5 since 5 is the 'slant height')

Plugging in the available info , we get our answer:

$\pi r^2 h\\=\pi (3)^2 (4)\\=36\pi$

B is the correct answer

3 0

3 years ago

Read 2 more answers

Evaluate 4x² + 3x for x=6

Sloan [31]

Answer:

162

Step-by-step explanation:

Given algebraic expression:

4x² + 3x

To:

Evaluate this expression,with : x = 6

Solution:

4x²+3x

Simplify by plugging x = 6

4(6)²+3(6)
4(36) + 18
144 + 18
162

<em>We can conclude:</em>

By evaluating this expression by x = 6 , the answer will be 162.

3 0

2 years ago