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Bogdan [553]
3 years ago
10

How do you solve -178=-5x+4(-4x-13)

Mathematics
1 answer:
Effectus [21]3 years ago
5 0

Answer:

x = 6

Step-by-step explanation:

  • <em><u>Pull out like factors: </u></em>

-4x - 13  =   -1 • (4x + 13)

  • <em><u>Equation at the end of step 2: </u></em>

 -178 -  (-5x +  -4 • [4x + 13] )  = 0

  • <em><u>Pull out like factors: </u></em>

  21x - 126  =   21 • (x - 6)

  • <em><u>Equation at the end of step 4: </u></em>

 21 • (x - 6)  = 0

  • <em><u>Solve:</u></em>

x-6 = 0  

  • <em><u>Add 6 to both sides of the equation:</u></em>

x = 6

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Find the value of the integral that converges.<br> ∫^-5_-[infinity] x^-2 dx.
Bingel [31]

Answer:

\int_{-\infty}^{-5} x^{-2}dx= \frac{1}{5} + \lim_{x\to -\infty} \frac{1}{x} =\frac{1}{5}

Because the \lim_{x\to -\infty} \frac{1}{x} =0

The integral converges to \frac{1}{5}

Step-by-step explanation:

For this case we want to find the following integral:

\int_{-\infty}^{-5} x^{-2}dx

And we can solve the integral on this way:

\int_{-\infty}^{-5} x^{-2}dx= \frac{x^{-2+1}}{-2+1} \Big|_{-\infty}^{-5}

\int_{-\infty}^{-5} x^{-2}dx= -\frac{1}{x} \Big|_{-\infty}^{-5}

And if we evaluate the integral using the fundamental theorem of calculus we got:

\int_{-\infty}^{-5} x^{-2}dx= \frac{1}{5} + \lim_{x\to -\infty} \frac{1}{x} =\frac{1}{5}

Because the \lim_{x\to -\infty} \frac{1}{x} =0

The integral converges to \frac{1}{5}

8 0
3 years ago
Find the x &amp; y-intercepts of the function. f(x)=2(x−1)(x+2)(x−3)
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Step-by-step explanation:

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To find the equation we will put the values of x and y in the equations and then check if LHS=RHS.

\large\red{\sf{y=3x-1}}

  • x=1
  • y=9

\begin{gathered}\\ \sf\longmapsto 9=3(1)-1\end{gathered}

\begin{gathered}\\ \sf\longmapsto 9=3-1\end{gathered}

\begin{gathered}\\ \sf\longmapsto 9≠2 \end{gathered}

\large\green{\sf{y=5x+4}}

\begin{gathered}\\ \sf\longmapsto 9=5(1)+4\end{gathered}

\begin{gathered}\\ \sf\longmapsto 9=5+4\end{gathered}

\begin{gathered}\\ \sf\longmapsto 9=9\end{gathered}

\large\blue{\sf{y=-2x-8}}

\begin{gathered}\\ \sf\longmapsto 9=-2(1)-8\end{gathered}

\begin{gathered}\\ \sf\longmapsto 9=-2-8\end{gathered}

\begin{gathered}\\ \sf\longmapsto 9≠10\end{gathered}

\large\pink{\sf{y=6x-8}}

\begin{gathered}\\ \sf\longmapsto 9=6(1)-8\end{gathered}

\begin{gathered}\\ \sf\longmapsto 9=6-8\end{gathered}

\begin{gathered}\\ \sf\longmapsto 9≠-2\end{gathered}

Hence, Option B. y=5x+4 satisfies the system (1,9)

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