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Schach [20]
2 years ago
12

Find two integers whose sum is -9 and product is -10

Mathematics
1 answer:
BigorU [14]2 years ago
5 0

Step-by-step explanation:

if the two integers are x and y

xy=-10

x+y=-9

x+(-10/x)=-9

x2+9x-10=0

(x-1)(x+10)=0

x=1 or x=-10

if x=1, y=-10

if x=-10, y=1

so the two integers are 1 and -10

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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
Tickets for a family of 6 to go skiing cost $48. whats the unit price ?
Molodets [167]
The unit price would be $8.

48/6 = 8
4 0
2 years ago
A group of students were asked how many times they exercised in the past week. The results were: 0,0,0,0,0,1,1,1,1,1,1,2,2,2,2,3
Digiron [165]

Answer:

Kindly check attached picture for histogram plot

Step-by-step explanation:

Given the data:

0,0,0,0,0,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,4,5,6,7,7,7

The range [0,2), [2,4), is the same as ;

Class range __ frequency

0 - 1 __________ 11

2 - 3 __________ 8

4 - 5 __________ 6

6 - 7 __________ 4

Kindly see picture for histogram plot

5 0
3 years ago
Rice weighing 3 3/4 pounds was divided equally and placed in 4 containers. How many ounces of rice were in each?​
IRINA_888 [86]

Answer:

Solution

To solve the problem first we have simplify the improper fraction.

⇒ 33/4 ÷ 4 pounds.

= (4 × 3 + 3) /4 ÷ 4 pounds.

= 15/4 ÷ 4 pounds.

= 15/4 × 1/4 pounds.

= 15/16 pounds.

Now we know that, 1 pound = 16 ounces.

Therefore, 15/16 pounds .

= 15/16 × 16 ounces.

= 15/1

= 15

= 15 ounces.

Answer: 15 ounces.

4 0
2 years ago
Read 2 more answers
Can someone help me please?
Molodets [167]
-2 should be correct. It is an input for that given graph.
5 0
3 years ago
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