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Serggg [28]
3 years ago
6

Which of these equations is for a line perpendicular to y-3=5(x-2)?

Mathematics
1 answer:
olasank [31]3 years ago
6 0

Answer:

C

Step-by-step explanation:

y-3=5(x-2)  (rearrange this to be in slope- intercept from) (add 3 to both sides)

y = 5(x-2) + 3   (distribute parentheses)

y = x(5) - 2(5) + 3

y = 5x -10 + 3

y = 5x - 7

recall that for a line with gradient m, the gradient of the perpendicular line will be - (1/m)

hence in our case, our gradient of the original line is 5, hence the gradient of the perpendicular line is -1/5

From the choices, the only one that is consistent with this is C

i.e choice C:

5y + x = 25

5y = -x + 25

y = -(1/5) x + 5   ===> gradient of -1/5

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What is the slope of the line through the points (-3, -5) and (-4, -2)
Ede4ka [16]

Answer:

slope= -3

Step-by-step explanation:

the slope formula is \frac{y_{2} -y_{1} }{x_{2} -x_{1} }

plug in your numbers: \frac{(-2)-(-5)}{(-4)-(-3)}

solve:\frac{3}{-1}

simplify: -3

5 0
3 years ago
A box contains 5 red and 5 blue marbles. Two marbles are withdrawn randomly. If they are the same color, then you win $1.10; if
topjm [15]

Answer:

a) The expected value is \frac{-1}{15}

b) The variance is  \frac{49}{45}

Step-by-step explanation:

We can assume that both marbles are withdrawn at the same time. We will define the probability as follows

#events of interest/total number of events.

We have 10 marbles in total. The number of different ways in which we can withdrawn 2 marbles out of 10 is \binom{10}{2}.

Consider the case in which we choose two of the same color. That is, out of 5, we pick 2. The different ways of choosing 2 out of 5 is \binom{5}{2}. Since we have 2 colors, we can either choose 2 of them blue or 2 of the red, so the total number of ways of choosing is just the double.

Consider the case in which we choose one of each color. Then, out of 5 we pick 1. So, the total number of ways in which we pick 1 of each color is \binom{5}{1}\cdot \binom{5}{1}. So, we define the following probabilities.

Probability of winning: \frac{2\binom{5}{2}}{\binom{10}{2}}= \frac{4}{9}

Probability of losing \frac{(\binom{5}{1})^2}{\binom{10}{2}}\frac{5}{9}

Let X be the expected value of the amount you can win. Then,

E(X) = 1.10*probability of winning - 1 probability of losing =1.10\cdot  \frac{4}{9}-\frac{5}{9}=\frac{-1}{15}

Consider the expected value of the square of the amount you can win, Then

E(X^2) = (1.10^2)*probability of winning + probability of losing =1.10^2\cdot  \frac{4}{9}+\frac{5}{9}=\frac{82}{75}

We will use the following formula

Var(X) = E(X^2)-E(X)^2

Thus

Var(X) = \frac{82}{75}-(\frac{-1}{15})^2 = \frac{49}{45}

7 0
3 years ago
7-3(10 divided by 2) divided by 1
Misha Larkins [42]

Answer:

-8

Step-by-step explanation:

Remember pemdas

7 - 3*(10:2):1 =

7-3*5:1=

7-15:1=

7- 15=

-8

4 0
1 year ago
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Problem situation: Bernie spends $6.50 on ingredients and cups for his lemonade stand. He charges $1.50 for each cup of lemonade
salantis [7]

Answer:

Answer:

18 cups.

Step-by-step explanation:

We are given that Bernie spends $6.50 on ingredients and cups for his lemonade stand. He charges $1.50 for each cup of lemonade. Inequality that represents this situation: .

To find number of cups x to make a profit of at least  $20 we will use our given inequality.

Therefore, in order to make a profit of at least $20 Bernie need to sell 18 cups of lemonade.

3 0
3 years ago
Ms.Jackson went to the local market to buy 50 pieces of fruit. Out of the 50 pieces of fruit she bought, 14 were apples. What fr
harkovskaia [24]

Answer:

A

Good luck kid mark me most brainliest!

8 0
3 years ago
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