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never [62]
3 years ago
8

Find the equation of the line with slope = 6 and passing through (6,43). Write your equation in the form y = m x + b .

Mathematics
1 answer:
gayaneshka [121]3 years ago
5 0

Answer:

y = 6x + 7.

Step-by-step explanation:

Using the point-slope form of a line

y - y1 = m(x - x1)

m = 6, x1 = 6 and y1 = 43:

y - 43 = 6(x - 6)

y - 43 = 6x - 36

y = 6x - 36 + 43

y = 6x + 7.

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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
Pls help ASAP!!!!! I will mark as brainlist!!
juin [17]

Answer:

Isjsjsjjekeekkddkdkdkdjdjdjdjdjdj

Step-by-step explanation:

Susjjssjjswiwiwiwi2

3 0
3 years ago
Read 2 more answers
Can I get some help plz?
Anika [276]

Answer:

X=20 degree

Step-by-step explanation:

∆A+∆D+∆O=180

2x+10+2x+90=180

collect like terms

2x+2x=180-100

4x=80

(4x)/4=(80)/4

x=20 degree

6 0
2 years ago
Read 2 more answers
The total cost, c, of bananas is proportional to the number of pounds, p, purchased. Bananas are selling for 79 cents per pound
mrs_skeptik [129]

Answer:

C = 0.79p

Step-by-step explanation:

This equation means that the cost of the bananas is 0.79 cents per pound.

If this answer is correct, please make me Brainliest!

4 0
3 years ago
Joni has a box that has a mass of 67 dekagrams. She converts this to centigrams. Her work is shown below. 67 dekagrams over 1,00
hichkok12 [17]

Answer: I think it’s B

Step-by-step explanation:

3 0
3 years ago
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