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bogdanovich [222]
2 years ago
15

I need help with this someone please

Mathematics
1 answer:
Alex2 years ago
7 0
3/1 is your slope for that
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Find the area of a plane figure bounded by lines
natulia [17]

Answer: 4.5

<u>Step-by-step explanation:</u>

First, find the points of intersection by solving the system.

y = x² + 2x + 4

y = x + 6

Solve by substitution:

x² + 2x + 4 = x + 6   ⇒   x² + x - 2 = 0   ⇒   (x + 2)(x - 1) = 0   ⇒   x = -2, x = 1

Now, integrate from x = -2 to x = 1

\int\limits^1_2 {(x+6)-(x^{2}+2x+4) } \,    <em>the bottom of the integral is -2 </em>

= \int\limits^1_2 {x+6-x^{2}-2x-4 } \,

= \int\limits^1_2 {-x^{2}-x+2 } \,  

= \frac{-x^{3}}{3} - \frac{x^{2}}{2}+2x\int\limits^1_2 {} \,

= (\frac{-1^{3}}{3} - \frac{1^{2}}{2}+2(1)) - (\frac{-(-2)^{3}}{3} - \frac{(-2)^{2}}{2}+2(-2))

= (\frac{-1}{3} - \frac{1}{2} +2) - (\frac{8}{3} -\frac{4}{2} -4)

= \frac{-9}{3} + \frac{3}{2} +6

= -3 + 1.5 + 6

= 4.5


3 0
3 years ago
If you pick a card at random from a well shuffled deck, what is the probability that you get a face card or a spade?
tankabanditka [31]
P(Face card) =16/52 = 4/13
P(Spade) = 13/52 =1/4
P(Face ∪ Spade) = 4/13 + 1/4 = 29/52 = 0.557

7 0
3 years ago
An athletic coach conducted an experiment to test whether a four-week stretching and flexibility program reduces the number of m
nirvana33 [79]

Answer: This study uses a control group, this study uses repeated measures design, and this study uses random sampling

Step-by-step explanation:

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I think is B

Step-by-step explanation:

I dont know I thont know

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\frac{1}{2}

Step-by-step explanation:

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