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3 years ago

choose the point slope form of the equation below that represents the like that passes through the points (-6,4) and (2, 0)

Mathematics

1 answer:

mariarad [96]3 years ago

6 0

Answer:

y = -1/2(x -2)

y - 4 = -1/2(x + 6)

Step-by-step explanation:

Point-slope form: y - y1 = m(x - x1)

For point-slope form, you need two things:

A point (x1, y1)
The slope (m)

Given:

Points (-6, 4) and (2,0)

You already have at least one point, but you still need to find the slope.

To find the slope (m), use the formula: m = y2 - y1/x2 - x1

Select which point is your (x2, y2) and which is your (x1, y1)
NOTE: It doesn't matter which one you pick as long as you don't "mix-and-match" your x and y-coordinates
For example: you can't choose (-6,0) for a point.

I've chosen:

(x2, y2) = (2, 0)
(x1, y1) = (-6, 4)

Plug in the info into m = y2 - y1/x2 - x1:

m = 0 - 4/2 -(-6) = -4/2 + 6 = -4/8
Simplify: -4/8 = -1/2
m = -1/2

Now plug in the slope and ONE of the points into point-slope form

Tip: It doesn't matter which point you choose but I'd recommend choosing the point with all positive numbers, if you can, to prevent the confusion of double negatives:

Answers could be:

y = -1/2(x -2)
y - 4 = -1/2(x + 6)

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2 years ago

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3 years ago

HELP!!!!!!!!!!!

Svetradugi [14.3K]

Using the mean concept, it is found that:

Relative to Sabrina's goal, her average swim time over the last five weeks is 0.1 hours.

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

The mean of a data-set is given by the sum of all observations divided by the number of observations.

In this problem:

The data-set is her swim time relative to her goal, which is: {1.25, -1, 2.25, 0, -2.}

5 observations.

Thus, the mean is:

$M = \frac{1.25 - 1 + 2.25 + 0 - 2}{5} = 0.1$

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A similar problem is given at brainly.com/question/24787716

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3 years ago

Exhibit 6-5 The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation o

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Answer:

46.18% of the items will weigh between 6.4 and 8.9 ounces.

Step-by-step explanation:

We are given that the weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces.

Let X = weight of items produced by a machine

The z-score probability distribution for is given by;

Z = $\frac{ X -\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = mean weight = 8 ounces

$\sigma$ = standard deviation = 2 ounces

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.

So, percentage of items that will weigh between 6.4 and 8.9 ounces is given by = P(6.4 < X < 8.9) = P(X < 8.9 ounces) - P(X $\leq$ 6.4 ounces)

P(X < 8.9) = P( $\frac{ X -\mu}{\sigma}$ < $\frac{ 8.9-8}{2}$ ) = P(Z < 0.45) = 0.67364 {using z table}

P(X $\leq$ 70) = P( $\frac{ X -\mu}{\sigma}$ $\leq$ $\frac{ 6.4-8}{2}$ ) = P(Z $\leq$ -0.80) = 1 - P(Z < 0.80)

= 1 - 0.78814 = 0.21186

Now, in the z table the P(Z $\leq$ x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 0.45 and x = 0.80 in the z table which has an area of 0.67364 and 0.78814 respectively.

Therefore, P(6.4 < X < 8.9) = 0.67364 - 0.21186 = 0.4618 or 46.18%

Hence, 46.18% of the items will weigh between 6.4 and 8.9 ounces.

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