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3 years ago

Solve the equation for x.

Mathematics

1 answer:

Degger [83]3 years ago

4 0

Answer:

$x=-\frac{11}{8}$

Step-by-step explanation:

Hi there!

$(x - 4) - (x + 7) = 8x$

Open up the parentheses

$x - 4 - x - 7 = 8x$

Combine like terms

$x -x - 4 - 7 = 8x\\-4-7=8x\\-11=8x$

Divide both sides by 8 to isolate $x$

$-\frac{11}{8}=x$

I hope this helps!

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P(x)= 3x^3-5x^2-14x-4

nexus9112 [7]

$\displaystyle\\
P(x)=3x^3-5x^2-14x-4\\\\
D_{-4}=\{-4;~-2;~\underline{\bf -1};~1;~2;~4\}\\\\
\text{We observe that } \frac{-1}{3} \text{ is a solution of the equation:}\\
3x^3-5x^2-14x-4=0\\\\
$

$\displaystyle\\
\text{Verification}\\\\
3x^3-5x^2-14x-4=\\\\
=3\times\Big(-\frac{1}{3}\Big)^3-5\times\Big(-\frac{1}{3}\Big)^2-14\times\Big(-\frac{1}{3}\Big)-4=\\\\
=-\frac{1}{9}-\frac{5}{9}+\frac{14}{3}-4=\\\\
=-\frac{6}{9}+\frac{14}{3}-4=\\\\
=-\frac{6}{9}+\frac{42}{9}- \frac{4\times 9}{9}=\\\\
 =-\frac{6}{9}+\frac{42}{9}- \frac{36}{9}= \frac{42-6-36}{9}=\frac{42-42}{9}=\frac{0}{9}=0\\\\
\Longrightarrow~~~P(x)~\vdots~\Big(x+ \frac{1}{3}\Big)\\\\
\Longrightarrow~~~P(x)~\vdots~(3x+1)$

$\displaystyle\\
3x^3-5x^2-14x-4=0\\
~~~~~-5x^2 = x^2 - 6x^2\\
~~~~~-14x =-2x-12x \\
3x^3+x^2 - 6x^2-2x-12x-4=0\\
x^2(3x+1)-2x(3x+1) -4(3x+1)=0\\
(3x+1)(x^2-2x -4)=0\\\\
\text{Solve: } x^2-2x -4=0\\\\
x_{12}= \frac{-b\pm \sqrt{b^2-4ac}}{2a}=\\\\=\frac{2\pm \sqrt{4+16}}{2}=\frac{2\pm \sqrt{20}}{2}=\frac{2\pm 2\sqrt{5}}{2}=1\pm\sqrt{5}\\\\
x_1 =1+\sqrt{5}\\
x_2 =1-\sqrt{5}\\
\Longrightarrow P(x)= 3x^3-5x^2-14x-4 =\boxed{(3x+1)(x-1-\sqrt{5})(x-1+\sqrt{5})}$

7 0

3 years ago

A mix of factoring by grouping. Factor the exressions. 17ax+17a-x-1 Please explain/show steps on how to do this!

mario62 [17]

Answer:

$(x+1)(17a-1)$

Step-by-step explanation:

We are given that

$17ax+17a-x-1$

We have to factorize the given expression.

Pair up the terms

$(17ax+17a)+(-x-1)$

Now, taking common factor

$17a(x+1)-1(x+1)$

Taking common (x+1)

$(x+1)(17a-1)$

Now, we get

$(x+1)(17a-1)$

This is required factors of given expression.

4 0

3 years ago

use the factor theorem to find all the zeros of f(x)=2x^3+7x^2-77x-40 given that (x-5) is a factor of the polynomial

Soloha48 [4]

Because the factor would divide it into two

5 0

3 years ago

The monthly output P of a light bulb factory is given by the formula P = 450LK, where L is the amount invested in labor and K th

Tems11 [23]

Answer:

C(p) = 4,96 (in thousands of dollars)

l = 2980 $ invest in labor

k = 2980 $ invest in equipment

Step-by-step explanation:

Information we have:

Monthly output P = 450*l*k ⇒ k = P/450*l

But the production need to be 4000

Then k = 4000/450*l

Cost of production = l * k (in thousands of dollars)

C(l) = l + 4000/450*l

Taking derivatives (both members of the equation)

C´(l) = 1 - 400 /45*l² ⇒ C´(l) = 0 ⇒ 1 - 400/45l² = 0

45*l² - 400 = 0 ⇒ l² = 400/45

l = 2.98 (in thousands of dollars)

l = 2980 $ And

k = 400/45*l ⇒ k 400/45*2.98

k = 2.98 (in thousands of dollars)

C(p) = l + k

C(p) = 2980 + 2980

C(p) = 5960 $

4 0

3 years ago

60 Points !!!!!

zheka24 [161]

Answer:

A yes ; it can be rotated 360° or less and match the original figure

8 0

3 years ago