## Problem 992

By air, the distance from city A to city B is 3009 miles less than the distance form city C to city D. If the total of these two distance is 7821 miles, find the distance from city C to city D.

Solution:-

5415 miles

## Problem 991

Write the sentence as an equation.

Four times the difference of -17 and 9 amounts to -104.

Solution:-

The sentence ”four times the difference of -17 and 9 amount to -104” written as an equation is 4(-17 – 9) = -104.

## Problem 990

Write the following phrase as a variable expression. Use x to represent “a number.”

nineteen decreased by a number.

Solution:-

The translation is 19 – x.

## Problem 989

Write the following phrase as a variable expression. Use x to represent “a  number.”

The total of a number and eleven

Solution:-

The variable expression is x + 11.

## Problem 988

Write the following sentence as an equation.

The quotient of 216 and twice 27 is equal to 4.

Solution:-

Separate the sentence into logical parts and translate each part.

In words:  The quotient of 216 and twice 27 is equal to 4

Translate = 4

Next put together all parts to get the final equation.

= 4

## Problem 987

Write the sentence as an equation.

The product of -4 and -26 gives 104.

Solution:-

To translate the sentence into an equation, write each part in symbols. First translate “the product of -4 and -26” into symbols.

In words: the product of -4 and -26 given 104

Translate: (-4)(-26)

Now translate the word ”given” into a symbol.

In words: the product of -4 and -26 gives 104

Translate: (-4)(-26) = 104

The number 104 remains the same.

Therefore , the sentence “the product of -4 and -26 gives 104” written as an equation is (-4)(-26) = 104.

## Problem 986

Polynomial conditions.

a)   If the degree is even and the leading coefficient is positive, the polynomial rises on the left and rises on the right.

b)   If the degree is even and the leading coefficient is negative, the polynomial falls on the left and falls on the right.

c)    If the degree is odd and the leading coefficient is positive, the polynomial falls on the left and rises on the right.

d)   If the degree is odd and the leading coefficient is negative, the polynomial rises on the left and fall on the right.

## Problem 985

Consider the polynomial function

f(x) = 8x5– x2+ 3x6 – 4

a)   Find the degree of this polynomial function.?

b)   Find the most number of x-intercepts this function can have.?

c)    Find the most number of turning points this function can have.?

Solution:-

a)   The degree of this polynomial function is 6.

b)   The most number of x-intercepts this function can have is 6.

c)    The most number of turning points this function can have is 5.

## Problem 984

A Hepplewhite sofa costs 1940 in cash. Jaquanna Wilson will purchase the sofa in 36 monthly installment payment. A 13% per year finance charge will be assessed on the amount financed. Find the finance charge, the installment price, and the monthly payment.

Solution:-

To obtain the finance charge, first find the number of years Jaquanna Wilson will pay for the sofa. Divide the number of monthly payments by 12.

= 3

The down payment is 0. Therefore, the amount financed is equal to the cash price.

To find the finance charge, multiply the amount financed by the annual finance charge in percent times the number of years to pay off the amount.

Finance charge = 1940*13%*3

=756.60

To find the installment price, add the finance charge to the cash price.

Installment price = cash price + finance charge

= 1940 + 756.60

= 2696.60

To obtain the monthly payment, divide the installment price by the number of monthly payments.

Monthly payment =

=

74.91

Thus,  the finance charge is 756.60, the installment price is 2696.60 and the monthly payment is 74.91

## Problem 983

A computer with software costs 2965, and Catherine Stevens has agreed to pay an 18% per year finance charge on the cash price. If she contracts to pay the loan in 18 months, how much will she pay each month?

Solution:-

First determine the cash price of the computer. The cash price of the computer is 2965.

Next find the percentage rate of the finance charge per 18 months.

Rate per 18 months = *18 = *18 = 27%

State the determine equivalent of 27%.

27%  = 0.27

Find the finance charge.

Finance charge = finance charge rate period * cash price

= 0.27 *2965

=800.55

Find the installment price.

Installment price = finance charge + cash price

=800.55 + 2965

= 3765.55

Recall the formula.

Installment price = total of installment payments + down payment

In our problem there is no down payment, therefore we can use the formula below.

Total of installment payment = installment price = 3765.55

Finally, divide the total of the installment payments by the number of payments, 18.

Installment payment = total of installment payments/number of payments = = 209.20

So, her monthly payment is 209.20.