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mel-nik [20]
2 years ago
11

Which expression is equivalent to the given expression?

Mathematics
1 answer:
jasenka [17]2 years ago
8 0

Answer:

C.) 2(x-3)(x-4)

Step-by-step explanation:

I think so

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Consider the region bounded by the curves y=|x^2+x-12|,x=-5,and x=5 and the x-axis
Tasya [4]
Ooh, fun

what I would do is to make it a piecewise function where the absolute value becomse 0

because if you graphed y=x^2+x-12, some part of the garph would be under the line
with y=|x^2+x-12|, that part under the line is flipped up

so we need to find that flipping point which is at y=0
solve x^2+x-12=0
(x-3)(x+4)=0
at x=-4 and x=3 are the flipping points

we have 2 functions, the regular and flipped one
the regular, we will call f(x), it is f(x)=x^2+x-12
the flipped one, we call g(x), it is g(x)=-(x^2+x-12) or -x^2-x+12
so we do the integeral of f(x) from x=5 to x=-4, plus the integral of g(x) from x=-4 to x=3, plus the integral of f(x) from x=3 to x=5


A.
\int\limits^{-5}_{-4} {x^2+x-12} \, dx + \int\limits^{-4}_3 {-x^2-x+12} \, dx + \int\limits^3_5 {x^2+x-12} \, dx

B.
sepearte the integrals
\int\limits^{-5}_{-4} {x^2+x-12} \, dx = [\frac{x^3}{3}+\frac{x^2}{2}-12x]^{-5}_{-4}=(\frac{-125}{3}+\frac{25}{2}+60)-(\frac{64}{3}+8+48)=\frac{23}{6}

next one
\int\limits^{-4}_3 {-x^2-x+12} \, dx=-1[\frac{x^3}{3}+\frac{x^2}{2}-12x]^{-4}_{3}=-1((-64/3)+8+48)-(9+(9/2)-36))=\frac{343}{6}

the last one you can do yourself, it is \frac{50}{3}
the sum is \frac{23}{6}+\frac{343}{6}+\frac{50}{3}=\frac{233}{3}


so the area under the curve is \frac{233}{3}
6 0
3 years ago
Michelle bought five packs of crayons for 13.75. what is the cost of a pack ,in dollars, if all the packs cost the same​
Schach [20]

Answer:

2.75

Step-by-step explanation:

Divide 13.75 by five.

5 0
3 years ago
(5x-7)+(6+33)<br> solve the equation
Vinil7 [7]

Answer: 5x + 32

Step-by-step explanation:

4 0
3 years ago
Which cannot be used in a proof?
Gwar [14]
Hello,

you may not used what you are going to prove in a proof (la thèse)
4 0
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Help<br>evaluate 12-3×2+1​
Feliz [49]

Answer:

7 hope this helps(✿◠‿◠)

Step-by-step explanation:

5 0
3 years ago
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