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3 years ago

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7x+2y=16 Find the equation of the line which passes through the point (−1,−12) and is parallel to the given line. Express your a

nswer in slope-intercept form. Simplify your answer.

1 answer:

Snowcat [4.5K]3 years ago

7 0

Answer:

The answer would be 7x+2y=-31, or in slope-intercept form, y=-7/2x-31/2

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Evaluate the definite integral using the graph of f(x)<br> (Image included)

Tanya [424]

a) The first integral corresponds to the area under y = f(x) on the interval [0, 3], which is a right triangle with base 3 and height 5, hence the integral is

$\displaystyle \int_0^3 f(x) \, dx = \frac12 \times 3 \times 5 = \boxed{\frac{15}2}$

b) The integral is zero since the areas under the curve over [3, 4] and [4, 5] are equal but opposite in sign. In other words, on the interval [3, 5], f(x) is symmetric and odd about x = 4, so

$\displaystyle \int_3^5 f(x) \, dx = \int_3^4 f(x) \, dx + \int_4^5 f(x) \, dx = \int_3^4 f(x) \, dx - \int_3^4 f(x) \, dx = \boxed{0}$

c) The integral over [5, 9] is the negative of the area of a rectangle with length 9 - 5 = 4 and height 5, so

$\displaystyle \int_5^9 f(x) \, dx = -4\times5 = -20$

Then by linearity, we have

$\displaystyle \int_0^9 f(x) \, dx = \left\{\int_0^3 + \int_3^5 + \int_5^9\right\} f(x) \, dx = \frac{15}2 + 0 - 20 = \boxed{-\frac{25}2}$

8 0

2 years ago

Find the slope in fraction form

nlexa [21]

Answer:

-1/3

Step-by-step explanation:

Taking two points on the graph (I took (0,9) and (6,7)

Slope=(y2-y1)/(x2-x1)

(7-9)/(6-0)=-2/6

=-1/3

7 0

3 years ago

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Solve the following system of equations by elimination

olya-2409 [2.1K]

Answer:

y = -6

x = 1

Step-by-step explanation:

-x + 2y = -13

-x - 2y = 11

Sum the equations:

-x -x = -2x

+2y - 2y = 0

-13 + 11 = -2

then

-2x = -2

x = -2/-2

x = 1

from the first eq.

-x + 2y = -13

-1 + 2y = -13

2y = -13 + 1

2y = -12

y = -12/2

y = -6

check:

from the second eq.

-x -2y = 11

-1 -(2*-6) = 11

-1 -(-12) = 11

-1 + 12 = 11

5 0

2 years ago

Construct the discrete probability distribution for the random variable described. Express the probabilities as simplified fract

lisov135 [29]

Answer:

$P(X = 0) = 0.03125$

$P(X = 1) = 0.15625$

$P(X = 2) = 0.3125$

$P(X = 3) = 0.3125$

$P(X = 4) = 0.15625$

$P(X = 5) = 0.03125$

Step-by-step explanation:

For each toss, there are only two possible outcomes. Either it is tails, or it is not. The probability of a toss resulting in tails is independent of any other toss, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Fair coin:

Equally as likely to be heads or tails, so $p = 0.5$

5 tosses:

This means that $n = 5$

Probability distribution:

Probability of each outcome, so:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{5,0}.(0.5)^{0}.(0.5)^{5} = 0.03125$

$P(X = 1) = C_{5,1}.(0.5)^{1}.(0.5)^{4} = 0.15625$

$P(X = 2) = C_{5,2}.(0.5)^{2}.(0.5)^{3} = 0.3125$

$P(X = 3) = C_{5,3}.(0.5)^{3}.(0.5)^{2} = 0.3125$

$P(X = 4) = C_{5,4}.(0.5)^{4}.(0.5)^{1} = 0.15625$

$P(X = 5) = C_{5,5}.(0.5)^{5}.(0.5)^{0} = 0.03125$

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2 years ago

There is a group of 10 people who are ordering pizza. If each person gets 2 slices and each pizza has 4 slices, how many pizzas

Sonbull [250]

Answer:

5 pizzas

Step-by-step explanation: If you have 10 people and each will get two slices then you will need 20 pieces of pizza because 10x2 is 20. If each pizza has 4 slices then you will need 5 pizzas because 4/20 is 5.

6 0

3 years ago

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