MATHEMATICS HIGH SCHOOL

Let f(x) = 8x3 − 22x2 − 4 and g(x) = 4x − 3. Find f of x over g of x . 2x2 − 4x − 3 − (13/4x-3)
2x2 − (4x − 3/13)
2x2 − 7x − 1
2x2 − 7x − 5 +(x-4/4x-3)

Answers

Answer 1

Answer:

Answer:

Option 1 - $(2x^2-4x-3)(-13)/((4x-3))$

Step-by-step explanation:

Given : $f(x)=8x^3-22x^2-4$ and $g(x)=4x-3$

To find : f of x over g of x.

Solution :

$f(x)=8x^3-22x^2-4$ and $g(x)=4x-3$

f of x over g of x is $(f(x))/(g(x))$

Substitute the value in the formula,

$(f(x))/(g(x))=(8x^3-22x^2-4)/(4x-3)$

Now, We have to divide the numerator by denominator with the help of calculator.

Refer the attached figure below.

Here, Dividend is $f(x)=8x^3-22x^2-4$

Divisor is $g(x)=4x-3$

We get, Quotient is $2x^2-4x-3$

and Remainder is -13.

The form is $\text{Dividend}=\text{Quotient}* \text{Divisor}+\text{Remainder}$

i.e. $(8x^3-22x^2-4)=(2x^2-4x-3)*(4x-3)+(-13)$

or in mixed fraction it is written as $(2x^2-4x-3)(-13)/((4x-3))$

Therefore, Option 1 is correct.

Answer 2

Answer: I hope this helps you

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A line with a slope of 10 passes through the point (9, 3). What is its equation in point-slope form?

Answers

Answer:

y=10(x-9)+3

Step-by-step explanation:

Point Slope Formula: y=m(x-x1)+y

y=10(x-9)+3

A vendor sells hot dogs and bags of potato chips. A customer buys 5 hotdogs and 2 bags of potato chips for $11.50. Another customer buys 3 hotdogs and 5 bags of potato chips for $9.75. Find the cost of each items.

Answers

Answer:

Hotdogs cost $2 and potato crisps $0.75.

Step-by-step explanation:

Let the hotdogs cost $h and the crisps $p

5h + 2p = 11.5

3h + 5p = 9.75

Multiply the first equation by -5 and the second by 2:

-25h - 10p = -57.5

6h + 10p = 19.5 Adding these 2 equations:

-19h = -38

h = $2.

Substitute h = 2 into the first equation:

5h + 2p = 11.5

10 + 2p = 11.5

2p = 1.5

p = $0.75.

Translate the sentence into an equation.Nine times the sum of a number and 3 is 5.
Use the variable x for the unknown number.

Answers

Answer: 9 (3 + x) = 5

Step-by-step explanation: hope this helps

Answer:

9(X) x 3 =5

Step-by-step explanation:

Question of the day! Someone steals your N500. Same person owes you N100. So he uses the stolen N500 to pay you your N100, and you give him N400 change... How much did you lose??

Answers

N500 because in total you owe the person N600 (N500 stolen, N100 owe) and you give the person you stole money from N500 and the person gives you N400 change + the N100 you still have remainder giving you N500 in total

Someone steals 500, your balance is -500
Same person gives you 100, your balance is -400
You give them the 400 change, your balance is -800

Write an algebraic expression to represent each of these 6 verbal expressions.1. 7 less than fifteen times a number
2. the difference of nine times a number and the quotient of 6 and the same number
3. the sum of 100 and four times a number
4. the product of 3 and the sum of 11 and a number
5. four times the square of a number increased by five times the same number
6. 23 more than the product of 7 and a number

Answers

Answer:

1. 15n - 7

2. 9n - (6/n)

3. 4n + 100

4. 3(11 + n)

5. 4n^2 + 5n

6. 7n + 23

Step-by-step explanation:

1. "7 less than fifteen times a number" can be represented as 15n - 7, where n represents the unknown number. This expression means that you take the number, multiply it by 15, and then subtract 7 from the result.

2. "The difference of nine times a number and the quotient of 6 and the same number" can be represented as 9n - (6 / n), where n represents the unknown number. This expression means that you take the number, multiply it by 9, and then subtract the quotient of 6 divided by the same number.

3. "The sum of 100 and four times a number" can be represented as 4n + 100, where n represents the unknown number. This expression means that you take the number, multiply it by 4, and then add 100 to the result.

4. "The product of 3 and the sum of 11 and a number" can be represented as 3(11 + n), where n represents the unknown number. This expression means that you take the number, add 11 to it, and then multiply the sum by 3.

5. "Four times the square of a number increased by five times the same number" can be represented as 4n^2 + 5n, where n represents the unknown number. This expression means that you square the number, multiply the result by 4, and then add the product of the number and 5.

6. "23 more than the product of 7 and a number" can be represented as 7n + 23, where n represents the unknown number. This expression means that you take the number, multiply it by 7, and then add 23 to the result.

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