Use the domain and range of each of the following relations to determine which is a function.

Remainder Theorem says that if there is any Polynomial equation P(x), which is to be divided by (x - a) then remainder can be calculated by substituting value of a in equation P(x).

$2x^{4} +x^{2}-10x-1$ = P(x) divided by $(x+2)$

Step 1: Find a

To find a we will have to convert (x+2) into (x - a) form

i.e. (x+2) = (x - (-2))

therefore, a = -2

Step 2: Substitute value of a in P(x),

By substitution we get,

$2(-2)^{4}+(-2)^{2}-10(-2)-1$

= $2(16) + 4 +20 -1$

= $32 +4 + 20 - 1$

= $55$ = Remainder

Hence, Remainder is 55.

8 0

3 years ago

The sum of 5 consecutive odd integers is 2,555. What is the sum of the first, third, and last integer?

Lilit [14]

Answer:

The sum of the first, third, and last integer is 1533.

Step-by-step explanation:

Step 1: You need to create a equation first:

n + n + 2 + n + 4 + n + 6 + n + 8 = 2555

How did I make the equation?

If n is odd number, n + 2 must be the consecutive odd number

5 , 5 + 2 , 5 + 4 , 5 + 6 , 5 + 8

5, 7, 9, 11, 13 ALL CONSECUTIVE ODD NUMBERS

Step 2: Simplifying the equation

n + n + 2 + n + 4 + n + 6 + n + 8 = 2555

5n + 20 = 2555

Step 3: Solving the equation, with explanation

5n + 20 = 2555 Subtract 20 on both sides

5n = 2535 Isolate the variable by dividing 5 on both sides

n = 507

Step 4: Plug in the value

n + n + 2 + n + 4 + n + 6 + n + 8

507, 507 + 2 , 507 + 4 , 507 + 6 , 507 + 8

507, 509, 511, 513, 515

Step 5: Solve the sum of the first, third, and last integer

507 + 511 + 515 = 1533

Step 6: THE ANSWER

1533

<h3>Hope this helps!!! </h3><h3>Please mark this as brainliest!!! </h3><h3>Thank You!!! </h3><h3>:)</h3>

8 0

3 years ago

The grounds keeper of Estofer Park has to mow 14,623 sq. ft. of grass. He can mow 13 sq. ft of grass in one minute. How many min

MA_775_DIABLO [31]

Answer: $1,124\frac{11}{13}\ minutes$

Step-by-step explanation:

Let be "x" the time in minutes that will take him to mow the entire park.

You know that he can mow 13 square feet in 1 minute and he has to mow 14,623 square feet.

Then, you can write the following proportion:

$\frac{1}{13}=\frac{x}{14,623}$

Solving for "x", you get:

$x=\frac{14,623}{13}\ min$

To write that improper fraction as a mixed number:

- The quotient when you divide the numerator by the denominator of the fraction obtained, is $1,124$ (This will be the whole number).

- The remainder of that division is $11$ (This will be the numerator of the fraction).

- The denominator does not change.

Then:

$x=1,124\frac{11}{13}\ min$

8 0

3 years ago