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3 years ago

Express the quotient in simplest form. x^2 - 4/ x^3 + 7x^2 divided by x^3 - x^2 - 6x/x^2 + 4x - 21

Mathematics

1 answer:

amm18123 years ago

8 0

You must first transform into a multiplication and then factor to see what you can eliminate.

Explanation:

To transform a fractional division into a multiplication, you have to inverse the numerator and the denominator of the second fraction.

x2−4x3+7x2×x2+4x−21x3−x2−6x

(x+2)(x−2)x2(x+7)×(x+7)(x−3)x(x−3)(x+2)

Since aa=1,a= all real numbers, we can proceed by eliminating factors that appear in the numerator and the denominator.

We are left with x−2/x^3

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The angles below are supplementary. What is the value of x? 5 7.5 15 30

OLEGan [10]

Answer:

x=30

Step-by-step explanation:

The two angles are supplementary. They add to 180

4x+20 + 40 =180

Combine like terms

4x+60 =180

Subtract 60 from each side

4x+60-60 = 180-60

4x = 120

Divide each side by 4

4x/4 = 120/4

x = 30

7 0

3 years ago

Read 2 more answers

___,36 ,108 ,324 ,972

hjlf

12

First figure out of it is a arithmetic or geometric sequence, in this case it is a geometric sequence because you have to multiply, not add to find the next number.

Divide one number, I'll pick 324 by the number before it, 108, you get three.

Now divide 36 by 3, you get 12.

To check, multiply 12 by 3, you get 36, multiply that by 3, you get 108, and so on and so forth.

3 0

3 years ago

Dylan borrowed $2100 from the bank for 15 months. The bank discounted the loan at 2.6%. How much was the interest? $ State your

melomori [17]

Answer:

actual rate of interest is 2.08 %

Step-by-step explanation:

Given data

borrowed = $2100

time = 15 months

rate = 2.6%

to find out

interest and receive from the bank and actual rate of interest

solution

we know bank discounted the loan at 2.6%

so interest will be 2.6% of $2100

that is = 2.6/100 × 2100

interest = $54.60

so receive from the bank is borrowed money - interest

receive = 2100 - 54.60

receive from the bank is $2045.40

and we can say that interest is directly proportional to time

so interest of 12 months / interest of 15 month = 12 month time/ 15 month time

here interest of 12 months = 12/15 × interest of 15 month

interest of 12 months = 12/15 × 54.60

interest of 12 months is $43.68 (annually)

now we can calculate actual rate of interest

that is = interest / borrowed money × 100

actual rate of interest = 43.68/2100 × 100

actual rate of interest is 2.08 %

6 0

3 years ago

Translate the sentence into an inequality. The difference of twice a number and 3 is greater than 29. Use the variable y for the

Licemer1 [7]

Answer:

The sentence you need is ##### ###### ### ### #####

Step-by-step explanation:

7 0

2 years ago

A rectangular parking area measuring 5000 ft squared is to be enclosed on three sides using chain-link fencing that costs $5.5

kaheart [24]

Answer:

Dimensions: 75.3778 ft and 66.3325 ft

Minimum price: $1658.31

Step-by-step explanation:

Let's call the length of the parking area 'x', and the width 'y'.

Then, we can write the following equations:

-> Area of the park:

x * y = 5000

-> Price of the fences:

P = 2*x*5.5 + y*5.5 + y*7

P = 11*x + 12.5*y

From the first equation, we have that y = 5000/x

Using this value in the equation for P, we have:

P = 11*x + 12.5*5000/x = 11*x + 62500/x

To find the minimum of this function, we need to take its derivative and then make it equal to zero:

dP/dx = 11 - 62500/x^2 = 0

x^2 = 65000/11

x = 250/sqrt(11) = 75.3778 ft

This is the x value that gives the minimum cost.

Now, finding y and P, we have:

x*y = 5000

y = 5000/75.3778 = 66.3325

P = 11*x + 62500/x = $1658.31

5 0

3 years ago