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3 years ago

3 A pair of vertical angles is formed as shown.

Mathematics

2 answers:

Jobisdone [24]3 years ago

6 0

Its A 29 plug in each number in replacement of X

stepan [7]3 years ago

3 0

Answer:

A - 29

Step-by-step explanation:

5x + 30 = 175

5x +30 -30 = 175 - 30

5x = 145

5x ÷ 5 = 145 ÷ 5

X = 29

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9 9. What is the slope of the line y = 3x + 2?

gregori [183]

Answer:

Step-by-step explanation:

this equation is written in the form of

y = mx + b

where m = slope

so the slope is 3

6 0

3 years ago

A school wishes to enclose its rectangular playground using 480 meters of fencing.

Harlamova29_29 [7]

Answer:

Part a) $A(x)=(-x^2+240x)\ m^2$

Part b) The side length x that give the maximum area is 120 meters

Part c) The maximum area is 14,400 square meters

Step-by-step explanation:

The picture of the question in the attached figure

Part a) Find a function that gives the area A(x) of the playground (in square meters) in terms of x

we know that

The perimeter of the rectangular playground is given by

$P=2(L+W)$

we have

$P=480\ m\\L=x\ m$

substitute

$480=2(x+W)$

solve for W

$240=x+W\\W=(240-x)\ m$

Find the area of the rectangular playground

The area is given by

$A=LW$

we have

$L=x\ m\\W=(240-x)\ m$

substitute

$A=x(240-x)\\A=-x^2+240x$

Convert to function notation

$A(x)=(-x^2+240x)\ m^2$

Part b) What side length x gives the maximum area that the playground can have?

we have

$A(x)=-x^2+240x$

This function represent a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

The x-coordinate of the vertex represent the length that give the maximum area that the playground can have

Convert the quadratic equation into vertex form

$A(x)=-x^2+240x$

Factor -1

$A(x)=-(x^2-240x)$

Complete the square

$A(x)=-(x^2-240x+120^2)+120^2$

$A(x)=-(x^2-240x+14,400)+14,400$

$A(x)=-(x-120)^2+14,400$

The vertex is the point (120,14,400)

therefore

The side length x that give the maximum area is 120 meters

Part c) What is the maximum area that the playground can have?

we know that

The y-coordinate of the vertex represent the maximum area

The vertex is the point (120,14,400) -----> see part b)

therefore

The maximum area is 14,400 square meters

Verify

$x=120\ m$

$W=(240-120)=120\ m$

The playground is a square

$A=120^2=14,400\ m^2$

8 0

3 years ago

A binomial experiment has 5 trials in which p = 0.7. What is the

Nonamiya [84]

Answer:

Answer

InesWalston

Ambitious

1.3K answers

7.2M people helped

Answer with Step-by-step explanation:

For a given Binomial event with probability of success 'p' the probabolity of 'r' success in 'n' trails is given by

Thus for given 4 trails (n = 4) we have

Part 1)

Probability of 1 success is

Part 2)

Probability of 2 successes

Part 3)

Probability of at least 1 success

Step-by-step explanation:

8 0

3 years ago

ANSWER FAST PLZ 65 POINTS!!!!!!!!!!!!!!!!!!

Snezhnost [94]

Area of a circle is found using the formula: A = PI x r^2 where r is the radius of the circle, which is half the diameter.

Using the information in the problem you have:

A= PI x 15^2

A = PI x 225

A = 706.5 sq. In.

8 0

3 years ago

Read 2 more answers

What should be done to both sides of the equation in order to solve w - 9 1/2 = 15? Add 15. Subtract 15. Add 9 1/2. Subtract 9 1

krek1111 [17]

You want to undo the (-9 1/2), so you will add 9 1/2 to each side

8 0

3 years ago

Read 2 more answers