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1 year ago

Identify the equation in slope-intercept form for the line containing the point (0,7) and perpendicular to y=−5/4x+11/4.

Mathematics

1 answer:

g100num [7]1 year ago

4 0

Answer:

4/5x + 7

Step-by-step explanation:

the slope-intercept form is y = ax+b

a is the slope, to figure it out the line is perpendicular to y = -5/4x+11/4

There is a rule said if two lines are perpendiculars, the multiplication of their slopes = -1, so -5/4 * a = 1, solve for a = 4/5

b is the intercept to get it use the point (0,7)

so y = 4/5x+b, 7 = 4/5 * 0 + b, then b = 7

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Find the distance between the points

Tasya [4]

Answer:

5 units

Step-by-step explanation:

Calculate the distance d using the distance formula

d = $\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }$

with (x₁, y₁ ) = (2, 1) and (x₂, y₂ ) = (6, 4)

d = $\sqrt{(6-2)^2+(4-1)^2}$

= $\sqrt{4^2+3^2}$

= $\sqrt{16+9}$

= $\sqrt{25}$

= 5

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2 years ago

Read 2 more answers

What is the irrational number between 5.5and5.2

levacccp [35]

Answer:
<span>The irrational number between 5.5 and 5.2 is square root of 30. </span>

6 0

2 years ago

Identify the independent and dependent variables in the following situation Julie notices that her plant grows one inch for ever

LUCKY_DIMON [66]

Answer:

Independent variable: amount of water

Dependent variable: growth of the plant

Step-by-step explanation:

In the statement "Julie notices that her plant grows one inch for every liter of water that it receives" it is implied that the growth of the plant is related proportionally to the amount of water it receives.

We know the amount of growth in function of the amount of water

The dependant variable, the result, is the growth of the plant.

Then, the independent variable is the amount of water, as it is the input to calculate the amount of growth.

4 0

2 years ago

Justine earned $28,000 during the first year of her job at city hall. After each year she received a 6% raise. Find her total ea

Verdich [7]

Answer:

$ 157838.60 in 5 years

Step-by-step explanation:

r = 1.06

sum of geometric seq = a1 ( 1-r^n)/(1-r) n = 5

28000 ( 1 - 1.06^5) / ( 1-1.06) = 157838.60

5 0

1 year ago

In one town, the number of burglaries in a week has a poisson distribution with a mean of 1.9. find the probability that in a ra

tester [92]

Let X be the number of burglaries in a week. X follows Poisson distribution with mean of 1.9

We have to find the probability that in a randomly selected week the number of burglaries is at least three.

P(X ≥ 3 ) = P(X =3) + P(X=4) + P(X=5) + ........

= 1 - P(X < 3)

= 1 - [ P(X=2) + P(X=1) + P(X=0)]

The Poisson probability at X=k is given by

P(X=k) = $\frac{e^{-mean} mean^{x}}{x!}$

Using this formula probability of X=2,1,0 with mean = 1.9 is

P(X=2) = $\frac{e^{-1.9} 1.9^{2}}{2!}$

P(X=2) = $\frac{0.1495 * 3.61}{2}$

P(X=2) = 0.2698

P(X=1) = $\frac{e^{-1.9} 1.9^{1}}{1!}$

P(X=1) = $\frac{0.1495 * 1.9}{1}$

P(X=1) = 0.2841

P(X=0) = $\frac{e^{-1.9} 1.9^{0}}{0!}$

P(X=0) = $\frac{0.1495 * 1}{1}$

P(X=0) = 0.1495

The probability that at least three will become

P(X ≥ 3 ) = 1 - [ P(X=2) + P(X=1) + P(X=0)]

= 1 - [0.2698 + 0.2841 + 0.1495]

= 1 - 0.7034

P(X ≥ 3 ) = 0.2966

The probability that in a randomly selected week the number of burglaries is at least three is 0.2966

5 0

2 years ago