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3 years ago

What is 8n=3m 1;n=-2,2,4

1 answer:

5 0

8n = 3m + 1
~~~~~~~~~~~~~~~~~~~
8(-2) = 3m + 1
-16 = 3m + 1
-1 -1
-17 = 3m
--- ---
3 3
-17/3 = m
~~~~~~~~~~~~~~~~~~~
8(2) = 3m + 1
16 = 3m + 1
-1 -1
15 = 3m
--- ---
3 3
5 = m
~~~~~~~~~~~~~~~~~~~
8(4) = 3m + 1
32 = 3m + 1
-1 -1
31 = 3m
--- ---
3 3
31/3 = m

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9+y=6 help me please

Phoenix [80]

Y=-3
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4 years ago

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Which expression represents a quadratic expression in standard form? *

vovikov84 [41]

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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 $(4x^2 - 12x + 38)$ .

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4 years ago

Simplify the algebraic expression:<br><br> 5 + 3(2y - 4) - 11y

Iteru [2.4K]

5 + 6 − 1 2 − 1 1 -11y 5+6y−12−11y − 7 + 6 − 1 1

− 7 + 6 − 1 1 −7+6y−11y − 7 − 5

− 7 − 5 −7−5y − 5 − 7

Solution: −5y−7

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3 years ago

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The coordinates of rhombus ABCD are A(–4, –2), B(–2, 6), C(6, 8), and D(4, 0). What is the area of the rhombus? Round to the nea

Trava [24]

Answer:

The rhombus ABCD has an area of 22 square units.

Step-by-step explanation:

The coordinates of rhombus ABCD are shown in the image attached below. The area of the rhombus can be found in terms of their diagonals, which are now calculated by Pythagorean Theorem:

$AC = \sqrt{[6-(-4)]^{2}+[8-(-4)]^{2}}$