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1 year ago

Simplify the rational expression: x^2+13x+42/x^2+15x+56

Mathematics

1 answer:

ANTONII [103]1 year ago

8 0

Answer:

x+6/x+8

Step-by-step explanation:

First, factor out each of the expressions. You will use the AM method, where the last term is the factors multiplied together, and the middle term is the two added together. For the top, you would get (x+7) and (x+6) as your factors, and for the bottom you'd get (x+7) and (x+8). Based off of that, you can simplify your answer. The two (x+7)'s can cancel out, leaving you with a (x+6) over (x+8) as your answer.

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If you are paid $5.50/hour for mowing yards, and you take 1 3 3 hours to mow a yard, how much money are you owed

mamaluj [8]

The correct question is
If you are paid $5.50/hour for mowing yards, and you take 3 1/3 hours to mow a yard, how much money are you owed
see the attached figure

we know that
3 1/3 hours-----> (3*3+1)/3----> 10/3 hours
Multiply $5.50/hour by (10/3) hour
so
5.5*10/3----> $18.33

the answer is
$18.33

6 0

2 years ago

(2b) A rectangular prism measures 2 & 2/5 inches by 3 & 1/5 inches by 2 inches. How many cubes with edge length 1/5 inch

erastova [34]

Answer:

1920 cubes.

Step-by-step explanation

Turn both the mix numbers into improper fractions.

2 2/5 = 12/5

3 1/5 = 16/5

Then you will turn 1/5 into its reciprocal and multiply both the improper fractions by it. You can just casually multiply 2 and 5.

12/5 * 5/1 = 12

16/5 * 5/1 = 16

2 * 5 = 10

Next you multiply all together to get 1920 cubes.

(I could be missing a step. I apologize if I did.)

3 0

2 years ago

How Many Solutions? 3x - 7 = 3(x - 3) + 2 No Solution One Solution Infinite Solution

prisoha [69]

Answer:

Infinite Solutions

Step-by-step explanation:

3x-7=3x(x-3)+2

3x-7=3x-9+2 - Distributive Property

3x-7=3x-7 - adding the right side together

3 0

2 years ago

What is the answer for this equation P=r+s-6

Alexeev081 [22]

3x-x+2=4
P = t + r + s
P - r - s = t + r - r + s - s
P - r - s = t

6 0

2 years ago

The radius of a cone is decreasing at a constant rate of 7 inches per second, and the volume is decreasing at a rate of 948 cubi

inessss [21]

Answer:

The height of cone is decreasing at a rate of 0.085131 inch per second.

Step-by-step explanation:

We are given the following information in the question:

The radius of a cone is decreasing at a constant rate.

$\displaystyle\frac{dr}{dt} = -7\text{ inch per second}$

The volume is decreasing at a constant rate.

$\displaystyle\frac{dV}{dt} = -948\text{ cubic inch per second}$

Instant radius = 99 inch

Instant Volume = 525 cubic inches

We have to find the rate of change of height with respect to time.

Volume of cone =

$V = \displaystyle\frac{1}{3}\pi r^2 h$

Instant volume =

$525 = \displaystyle\frac{1}{3}\pi r^2h = \frac{1}{3}\pi (99)^2h\\\\\text{Instant heigth} = h = \frac{525\times 3}{\pi(99)^2}$

Differentiating with respect to t,

$\displaystyle\frac{dV}{dt} = \frac{1}{3}\pi \bigg(2r\frac{dr}{dt}h + r^2\frac{dh}{dt}\bigg)$

Putting all the values, we get,

$\displaystyle\frac{dV}{dt} = \frac{1}{3}\pi \bigg(2r\frac{dr}{dt}h + r^2\frac{dh}{dt}\bigg)\\\\-948 = \frac{1}{3}\pi\bigg(2(99)(-7)(\frac{525\times 3}{\pi(99)^2}) + (99)(99)\frac{dh}{dt}\bigg)\\\\\frac{-948\times 3}{\pi} + \frac{2\times 7\times 525\times 3}{99\times \pi} = (99)^2\frac{dh}{dt}\\\\\frac{1}{(99)^2}\bigg(\frac{-948\times 3}{\pi} + \frac{2\times 7\times 525\times 3}{99\times \pi}\bigg) = \frac{dh}{dt}\\\\\frac{dh}{dt} = -0.085131$

Thus, the height of cone is decreasing at a rate of 0.085131 inch per second.

3 0

2 years ago