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lukranit [14]
3 years ago
15

A first number plus twice a second number is 1. twice the first number plus the second totals 26. find the numbers.

Mathematics
1 answer:
spayn [35]3 years ago
5 0
{x+2y=1
{2x+y=26
{x+y=9
{x+2y=1
y=-8
x=17
The first number is 17
The second number is -8

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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
Timothy stated that the sum of 0.9 + (-9/10) was 18/20.
Evgesh-ka [11]

Answer:

18/10

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Find two numbers whose sum is 44 and whose difference is 6.<br> smaller number<br> larger number
Anna [14]
X+ y = 44
x - y = 6
—————
2x = 50

x = 25
y = 44-x = 19
3 0
3 years ago
Lily, Louis, and Ben went to an arcade and won tokens for prizes. Louis won 4.5 times as many tokens as Ben. Lily won 8 more tok
lana66690 [7]

<em><u>The expression that describes the number of tickets won by Lily is:</u></em>

a = 8 + 4.5c where "a" is the number of tokens won by Lily and "c" is the number of tokens won by Ben

<em><u>Solution:</u></em>

Given that Lily, Louis, and Ben went to an arcade and won tokens for prizes

Let "a" be the number of tokens won by Lily

Let "b" be the number of tokens won by Louis

Let "c" be the number of tokens won by Ben

<em><u>Given that Louis won 4.5 times as many tokens as Ben</u></em>

So we can frame a equation as:

number of tokens won by Louis =  4.5 times as many tokens as Ben

number of tokens won by Louis  = 4.5 x number of tokens won by Ben

b = 4.5 \times c

b = 4.5c

<em><u>Given that Lily won 8 more tokens than Louis</u></em>

number of tokens won by Lily = 8 + number of tokens won by Louis

a = 8 + b

Substituting the value of b = 4.5c in above expression

a = 8 + 4.5c

Thus the expression that describes how many tokens Lily won is found

7 0
3 years ago
I think its B can I get someone's opinion. Its not too hard. Plzzz Help.
shusha [124]

Answer:

I agree with you,I also think its B

Step-by-step explanation:

8 0
3 years ago
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