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3 years ago

Which equation represents the line that is perpendicular to y = 5 and passes through (-4,-3)?

Mathematics

1 answer:

kenny6666 [7]3 years ago

6 0

Answer:

The required equation is: y=-3

Option D is correct.

Step-by-step explanation:

We need to write equation of line that is perpendicular to y = 5 and passes through (-4,-3).

The equation of line in slope-intercept form is expressed as: $y=mx+b$

where m is slope and b is y-intercept.

Finding Slope:

Comparing with the given equation y=5, the slope m =0

The slope of required line will be opposite reciprocal of 0 as both lines are perpendicular. so it will be m=0

Finding y-intercept

The y-intercept can be found using slope m=0 and point (-4,-3)

$y=mx+b\\-3=0(-4)+b\\b=-3$

So, y-intercept b is b=-3

The equation of required line having slope m=0 and y-intercept b=-3 is

$y=mx+b\\y=0(x)-3\\y=-3$

So, required equation is: y=-3

Option D is correct.

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In one area, the lowest angle of elevation of the sun in winter is 27.5°. Find the minimum distance x that a plant needing full

Alex73 [517]

Answer:

The minimum distance x that a plant needing full sun can be placed from a fence that is 5 feet high is 4.435 ft

Step-by-step explanation:

Here we have the lowest angle of elevation of the sun given as 27.5° and the height of the fence is 5 feet.

We will then find the position to place the plant where the suns rays can get to the base of the plant

Note that the fence is in between the sun and the plant, therefore we have

Height of fence = 5 ft.

Angle of location x from the fence = lowest angle of elevation of the sun, θ

This forms a right angled triangle with the fence as the height and the location of the plant as the base

Therefore, the length of the base is given as

Height × cos θ

= 5 ft × cos 27.5° = 4.435 ft

The plant should be placed at a location x = 4.435 ft from the fence.

8 0

3 years ago

A track star runs two races on a certain day. The probability thathe wins the first race is 0.7, the probability that he wins th

NARA [144]

Answer:

a) 80% probability that he wins at least one race.

b) 30% probability that he wins exactly one race.

c) 20% probability that he wins neither race.

Step-by-step explanation:

We solve this problem building the Venn's diagram of these probabilities.

I am going to say that:

A is the probability that he wins the first race.

B is the probability that he wins the second race.

C is the probability that he does not win any of these races.

We have that:

$A = a + (A \cap B)$

In which a is the probability that he wins the first race but not the second and $A \cap B$ is the probability that he wins both these races.

By the same logic, we have that:

$B = b + (A \cap B)$

The probability that he wins both races is 0.5.

This means that $A \cap B = 0.5$

The probability that he wins the second race is 0.6

This means that $B = 0.6$

$B = b + (A \cap B)$

$0.6 = b + 0.5$

$b = 0.1$

The probability that he wins the first race is 0.7.

This means that $A = 0.6$

$A = a + (A \cap B)$

$0.7 = a + 0.5$

$a = 0.2$

A) he wins at least one race.

This is

$P = a + b + (A \cap B) = 0.2 + 0.1 + 0.5 = 0.8$

There is an 80% probability that he wins at least one race.

B) he wins exactly one race.

This is

$P = a + b = 0.2 + 0.1 = 0.3$

There is a 30% probability that he wins exactly one race.

C) he wins neither race

Either he wins at least one race, or he wins neither. The sum of these probabilities is 100%.

From a), we have that there is an 80% probability that he wins at least one race.

So there is a 100-80 = 20% probability that he wins neither race.

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3 years ago

Two factory plants are making TV panels. Yesterday, Plant A produced 7000 fewer panels than Plant B did. Four percent of the pan

amid [387]

Step-by-step explanation:

17000

Let the number of panels Plant B produced be x.

$7000(0.04)+0.02x=620 \\ \\ 0.02x=340 \\ \\ x=17000$

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1 year ago

I need to find the value of x

nexus9112 [7]

Answer:

15°

Step-by-step explanation:

x= 89-44-30= 15°

:))

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2 years ago

Raina bought three books at a bookstore. Here are their prices (in dollars). 18.8, 4, 9.38 What is the total amount Raina paid a

artcher [175]

Answer:

$32.18

Step-by-step explanation:

It's really just addition. No explanation necessary.

4 0

3 years ago