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2 years ago

Angle A and angle B are supplementary (180°)

Mathematics

2 answers:

Nonamiya [84]2 years ago

5 0

Answer:

65° and 115°

Step-by-step explanation:

Given: Angle A and Angle B are supplementary

Let x represent Angle A. Since the angles have a difference of 50, Angle B would be x+50.

We are given that Angle A and Angle B are supplementary which means they add up to 180°. We can use this information to set up an equation.

Angle A + Angle B = 180

Substitute the variables we used to represent Angle A and B into the equation

x+x+50=180

Combine like terms

2x+50=180

Subtract both sides by 50

2x=130

Divide both sides by 2

x=65

x+50=65+50=115

The measure of the angles are 65° and 115°

Gnoma [55]2 years ago

3 0

Answer:

65 and 115 degrees.

Step-by-step explanation:

Set up and define the variables.

Angle A: x

Angle B: x + 50 {this is because one is 50 degrees more than the other}

Set up equation.

- {supplementary angles have a combined sum of 180}

x + x + 50 = 180

Solve equation.

2x + 50 = 180

2x = 130

x = 65

Substitute answers into original setup of variables.

A: 65

B: 65+50= 115

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lys-0071 [83]

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3 years ago

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Tresset [83]

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Now if you were reflecting across Y = 0, the x values would just be inverse ( opposite signs).

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Now since the reflection line is y = -1, which is a one unit shift to the left of y = 0, subtract 1 unit from each X value.

The locations are now: A'(3,4), B'(1,3) and C'(4,2)

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3 years ago

Line DE contains the points D (–1, –4) and E (3, 3). Line FG contains the point F (–3, 3). Which set of coordinates for point G

Bond [772]

Answer:

The set of coordinates for point G that make the two lines perpendicular are given through the relation

7y = -4x + 9

Step-by-step explanation:

The condition for perpendicularly of two lines is that the products of the slope of the two lines, m₁ and m₂ must be equal to -1.

For a line whose two points (x₁, y₁) and (x₂, y₂)

on the line are known, the slope of the line, m, is given as

m = (Δy/Δx) = (y₁ - y₂) ÷ (x₁ - x₂)

points D (–1, –4) and E (3, 3).

Let the slope of DE be m₁ and the slope of FG be m₂

Since the two lines are perpendicular,

m₁m₂ = -1

m₁ = (Δy/Δx) = (-4 - 3) ÷ (-1 -3) = (7/4) = 1.75

Since, m₁m₂ = -1, this means that,

m₂ = (-1/m₁) = (-1/1.75) = -(4/7)

Let the coordinates of point G be (x, y)

m₂ = (3 - y) ÷ (-3 - x)

(-4/7) = [(3-y)/(-3-x)]

-4(-3-x) = 7(3-y)

12 + 4x = 21 - 7y

7y = -4x + 9

Hope this Helps!!!

8 0

3 years ago

About 16 % of the population of a large country is allergic to pollen. If two people are randomly selected, what is the probabil

Vinvika [58]

Answer:

(a) 0.0256

(b) 0.2944

Step-by-step explanation:

For solving this exercise we can apply the binomial distribution. The equation that give as the probability is:

$P(x,n,p)=(nCx)*p^{x} *(1-p)^{n-x}$

Where n is the number of identical events, p is the probability that the event has a success and x is the number of success in the n identical events.

Additionally, nCx is calculated as:

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

So, in this case we have 2 identical events because we are going to select two people randomly and the probability p of success is the probability that the person is allergic to pollen and this probability is 16%.

Then, for the first case, x is 2 because their are asking for the probability that both are allergic to pollen. Replacing the values of x, n and p we get:

$P(2,2,0.16)=(2C2)*0.16^{2} *(1-0.16)^{2-2}$

P(2,2,0.16)=0.0256

For the second case, their are asking for the probability that at least one is allergic to pollen, that means that we need to sum the probability that both are allergic to pollen with the probability that just one is allergic to pollen.

Using the same equation to calculate P(1,2,0.16) we get:

$P(1,2,0.16)=(2C1)*0.16^{1} *(1-0.16)^{2-1}$

P(1,2,0.16)=0.2688

So, the probability that at least one person is allergic to pollen is 0.2944 and it is calculated as:

0.0256 + 0.2688 = 0.2944

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3 years ago

There are 10 students in class and the number of siblings in their families are given by {1,1,1,1,2,3,3,4,4,4}. Consider the exp

Svetllana [295]

Answer:

a. Check the attached image

b. The Pr(Y > 2) = ½

c. The mean is 2.4

d. The standard deviation is: 2.72

e. The exact value is 1 because it is certain from the given data that any probability will fall within that range.

Step-by-step explanation:

a. An image showing the step by step solution is attached.

b. P(Y > 2) = P(3) + P(4)

= 2/10 + 3/10 = 5/10 = ½

c. The mean is 2.4

d. The standard deviation is: 2.72

e. Check the attached image for the steps.

7 0

3 years ago