All categories

3 years ago

Complete the point-slope equation of the line through (-1,-10) and (5,2).

Mathematics

1 answer:

iris [78.8K]3 years ago

7 0

Answer:

y-2 = 2(x-5)

Step-by-step explanation:

We have two points, we use

m = (y2-y1)/(x2-x1) to get the slope

m = (2--10)/(5--1)

= (2+10)/(5+1)

=12/6

We will write the equation in point slope form

y-y1 = m(x-x1)

Given that it starts with y-2. we will use the point (5,2)

y-2 = 2(x-5)

You might be interested in

Solve the equation:<br><br> 3x + 34 when x = 4<br><br> Show work!

balandron [24]

3x + 34

x = 4

Substitute x:

3 times 4 = 12

12 + 34 = 46

The answer is 46.

Hope this helped

4 0

3 years ago

Read 2 more answers

An airplane takes off from an airport and travels 1100 miles east and then travels 600 miles north. This trip can be plotted on

IgorLugansk [536]

Answer:

The plane is now at (1100, 600) in unit mile

Step-by-step explanation:

The airport is the point (0 ,0) and the plane travels from there 1100 miles east and thereafter 600 miles north. If the unit is in mile then we may say that the planes co -ordinates are now (1100 , 600)

Since,

positive x -axis points towards east and positive y-axis points towards north.

4 0

3 years ago

Round to the nearest thousand 5.2182

steposvetlana [31]

Answer:

5.218

Step-by-step explanation:

5 or more, you add one. Four or less, you change it to zero.

6 0

3 years ago

Many, many snails have a one-mile race, and the time it takes for them to finish is approximately normally distributed with mean

Mamont248 [21]

Answer:

a) The percentage of snails that take more than 60 hours to finish is 4.75%.

b) The relative frequency of snails that take less than 60 hours to finish is 95.25%.

c) The proportion of snails that take between 60 and 67 hours to finish is 4.52%.

d) 0% probability that a randomly-chosen snail will take more than 76 hours to finish

e) To be among the 10% fastest snails, a snail must finish in at most 42.32 hours.

f) The most typical 80% of snails take between 42.32 and 57.68 hours to finish.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 50, \sigma = 6$

a. The percentage of snails that take more than 60 hours to finish is

This is 1 subtracted by the pvalue of Z when X = 60.

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

$Z = \frac{60 - 50}{6}$

$Z = 1.67$

$Z = 1.67$ has a pvalue 0.9525

1 - 0.9525 = 0.0475

The percentage of snails that take more than 60 hours to finish is 4.75%.

b. The relative frequency of snails that take less than 60 hours to finish is

This is the pvalue of Z when X = 60.

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

$Z = \frac{60 - 50}{6}$

$Z = 1.67$

$Z = 1.67$ has a pvalue 0.9525

The relative frequency of snails that take less than 60 hours to finish is 95.25%.

c. The proportion of snails that take between 60 and 67 hours to finish is

This is the pvalue of Z when X = 67 subtracted by the pvalue of Z when X = 60.

X = 67

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

$Z = \frac{67 - 50}{6}$

$Z = 2.83$

$Z = 2.83$ has a pvalue 0.9977

X = 60

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

$Z = \frac{60 - 50}{6}$

$Z = 1.67$

$Z = 1.67$ has a pvalue 0.9525

0.9977 - 0.9525 = 0.0452

The proportion of snails that take between 60 and 67 hours to finish is 4.52%.

d. The probability that a randomly-chosen snail will take more than 76 hours to finish (to four decimal places)

This is 1 subtracted by the pvalue of Z when X = 76.

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

$Z = \frac{76 - 50}{6}$

$Z = 4.33$

$Z = 4.33$ has a pvalue of 1

1 - 1 = 0

0% probability that a randomly-chosen snail will take more than 76 hours to finish

e. To be among the 10% fastest snails, a snail must finish in at most hours.

At most the 10th percentile, which is the value of X when Z has a pvalue of 0.1. So it is X when Z = -1.28.

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

$-1.28 = \frac{X - 50}{6}$

$X - 50 = -1.28*6$

$X = 42.32$

To be among the 10% fastest snails, a snail must finish in at most 42.32 hours.

f. The most typical 80% of snails take between and hours to finish.

From the 50 - 80/2 = 10th percentile to the 50 + 80/2 = 90th percentile.

10th percentile

value of X when Z has a pvalue of 0.1. So X when Z = -1.28.

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

$-1.28 = \frac{X - 50}{6}$

$X - 50 = -1.28*6$

$X = 42.32$

90th percentile.

value of X when Z has a pvalue of 0.9. So X when Z = 1.28

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

$1.28 = \frac{X - 50}{6}$

$X - 50 = 1.28*6$

$X = 57.68$

The most typical 80% of snails take between 42.32 and 57.68 hours to finish.

5 0

3 years ago

What is the prime factorization of 312?

Fofino [41]

You find the prime factorization by breaking the number down into other numbers that are prime. Start by breaking up 312 into 39 * 8. 39 breaks up into 3 * 13, and 8 breaks up into 4 * 2 which breaks up into 2 * 2. So the prime factorization of 312 is 3 * 13 * 2 * 2 * 2 or $3*13* 2^{3}$ . When you multiply those together you'll get 312.

5 0

3 years ago

Read 2 more answers