2x + 3y = -14 y = 6x + 22

Pls help this is due in a little bit I don't wanna failllll

Fittoniya [83]

The answer is 8 3/4. Hope this helps

6 0

3 years ago

What is the quotient when 4x3 + 2x + 7 is divided by x + 3?

Arte-miy333 [17]

Answer:

The quotient of this division is $(4x^2 -12x + 38)$ . The remainder here would be $-26$ .

Step-by-step explanation:

The numerator $4x^3 + 2x + 7$ is a polynomial about $x$ with degree $3$ .

The divisor $x + 3$ is a polynomial, also about $x$ , but with degree $1$ .

By the division algorithm, the quotient should be of degree $3 - 1 = 2$ , while the remainder shall be of degree $1 - 1 = 0$ (i.e., the remainder would be a constant.) Let the quotient be $a\,x^2 + b\, x + c$ with coefficients $a$ , $b$ , and $c$ .

$4x^3 + 2x + 7 = \left(a\,x^2 + b\, x + c\right)(x + 3)$ .

Start by finding the first coefficient of the quotient.

The degree-three term on the left-hand side is $4 x^3$ . On the right-hand side, that would be $a\, x^3$ . Hence $a = 4$ .

Now, given that $a = 4$ , rewrite the right-hand side:

$\begin{aligned}&\left(4\,x^2 + b\, x + c\right)(x + 3) \cr =& \left(4x^2 + (b\, x + c)\right)(x + 3) \cr =& 4x^2(x + 3) + (bx + c)(x + 3) \cr =& 4x^3 + 12x^2 + (bx + c)(x + 3)\end{aligned}$ .

Hence:

$4x^3 + 2x + 7 = 4x^3 + 12x^2 + (b\,x + c)(x + 3)$

Subtract $\left(4x^3 + 12x^2\right$ from both sides of the equation:

$-12x^2 + 2x + 7 = (b\,x + c)(x + 3)$ .

The term with a degree of two on the left-hand side has coefficient $(-12)$ . Since the only term on the right hand side with degree two would have coefficient $b$ , $b = -12$ .

Again, rewrite the right-hand side:

$\begin{aligned}&\left(-12 x + c\right)(x + 3) \cr =& \left(-12 x+ c\right)(x + 3) \cr =& (-12x)(x + 3) + c(x + 3) \cr =& -12x^2 -36x + (bx + c)(x + 3)\end{aligned}$ .

Subtract $-12x^2 -36x$ from both sides of the equation:

$38x + 7 = c(x + 3)$ .

By the same logic, $c = 38$ .

Hence the quotient would be $(4x^2 - 12x + 38)$ .

6 0

4 years ago

Two months ago, a car dealership sold 150 cars. Thirty of the cars were red. Last month, the dealership sold 200 cars. Predict t

Romashka-Z-Leto [24]

Do you know what colors they had?

4 0

3 years ago

Read 2 more answers

Determine whether each number is prime, composite, or neither.

givi [52]

Alright lets start by defining both prime and composite.

A natural number that has exactly two factors, one and itself, is called a prime number.
And natural number, other than one, that is not prime, is composite.

So lets start on #1: 8. We should know right off the bat that this is an even number and therefore can be divided by 2 (8/2=4). Since 8 is not one, we know that it is a composite number.

On #2 the number is 13. Now try some random numbers (2,3...) and you will find that nothing will give you a whole number (other than one). This means this number is prime.

#3 is the number 24 which is also even and can be divided by two, therefore is it composite.

33 is the number on #4. Now this one you should look at and realize that it can be divided by 11. Any two numbers that are the same (11, 22, 33, 44, 55...) can be divided by 11. This number is composite.

#5, the last one, is number 89. 89 is not a composite number, because it's only divisors are one and itself. This would make is a prime number.

Sorry this was kinda long, but I hope it helps! If you have any questions, feel free to ask!

4 0

4 years ago

Find the probability of drawing a 4 card on the first draw, replacing it and drawing a 10 card on the second draw.(no joker incl

BigorU [14]

The probability with no joker included is 75%

7 0

4 years ago