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earnstyle [38]
2 years ago
8

write an equation for the line that passes through the given point and has the given slope m (4,-5);m= -1/4

Mathematics
1 answer:
EastWind [94]2 years ago
5 0

-------------------------------------------------------------------------------------------------------------

Answer:  \textsf{y = -1/4x - 4}

-------------------------------------------------------------------------------------------------------------

Given: \textsf{Slope = -1/4, Point through = (4, -5)}

Find:  \textsf{Equation for the line that passes through the given point}

Solution: In order to get the equation, we need to first use the point-slope form to help us sort out our information and then we solve for y.

<u>Plug in the values</u>

  • \textsf{y - y}_1\textsf{ = m(x - x}_1\textsf{)}
  • \textsf{y - (-5) = -1/4(x - 4)}

<u>Simplify and solve for y</u>

  • \textsf{y + 5 = -1/4(x - 4)}
  • \textsf{y + 5 = -1/4x + 1}
  • \textsf{y + 5 - 5 = -1/4x + 1 - 5}
  • \textsf{y = -1/4x - 4}

Therefore, the final answer would be that the equation that has a slope of -1/4 and passes through (4, -5) is y = -1/4x - 4.

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Which table represents the function y = -3x + 2?
Nat2105 [25]

Answer:

first one

Step-by-step explanation:

if you plug the inputs into the equation, you can see that all of the outputs match the ones in the first chart

0 --> 2

1 --> -1

2 --> -4

3 0
3 years ago
According to records, the amount of precipitation in a certain city on a November day has a mean of inches, with a standard devi
Mekhanik [1.2K]

Answer:

The probability that the mean daily precipitation will be of X inches or less for a random sample of n November days is the p-value of Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}, in which \mu is mean amount of inches of rain and \sigma is the standard deviation.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

Mean \mu, standard deviation \sigma

n days:

This means that s = \frac{\sigma}{\sqrt{n}}

Applying the Central Limit Theorem to the z-score formula.

Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

What is the probability that the mean daily precipitation will be of X inches or less for a random sample of November days?

The probability that the mean daily precipitation will be of X inches or less for a random sample of n November days is the p-value of Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}, in which \mu is mean amount of inches of rain and \sigma is the standard deviation.

5 0
2 years ago
What is the equation of the line that passes through (-2, 2) and (1, -4)?
poizon [28]

Answer:

y = - 2x - 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \frac{y_{2}-y_{1}  }{x_{2}-x_{1}  }

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

m = \frac{-4-2}{1+2} = \frac{-6}{3} = - 2, thus

y = - 2x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (- 2, 2), then

2 = 4 + c ⇒ c = 2 - 4 = - 2

y = - 2x - 2 ← equation of line

3 0
2 years ago
What is the slope of the line that passes through the points (-2, 7) and (2,-5)?
Deffense [45]

Answer:

Denote that line: y = ax + b

Line passes (-2, 7) and (2,-5):

=> -2a + b =7

=>  2a + b = -5

Add both side of above equations:

=> 2b = 2

=> b = 1

=> a = (-5 - 1)/2 = -3

=> Slope a = -3

Hope this helps!

:)

4 0
2 years ago
what is the surface area of a rectangular prisim with a base length of 9 yd, base width of 7 yd,and a height of 4 yd?
krek1111 [17]

Answer:

254 yds²

Step-by-step explanation:

There are 6 faces of the prism we need to calculate the area of for a rectangular prism.

The base and top of the prism measure 9x7 yards each, so there are two faces with an area of 63 yds²                 (9 x 7 = 63)

The sides of the prism measure 4x7 yards each, so there are two faces with an area of 28 yds²    (4 x 7 = 28)

The front and back face of the prism measure 9x4 yards each, so there are two faces with an area of 36 yds²     (9 x 4 = 36)

The total surface area is

2(63) + 2(28) + 2(36) = 254 yds²

3 0
3 years ago
Read 2 more answers
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