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EleoNora [17]
2 years ago
13

A line passes through the two points (-4,6) and (2,-5). Calculate the following parts:

Mathematics
1 answer:
Viktor [21]2 years ago
8 0

A line passes through the two points (-4,6) and (2,-5). 11x +6y - 80 = 0 is the given line equation.

<h3>What is the slope of a line which passes through points ( p,q) and (x,y)?</h3>

Its slope would be:

m = \dfrac{y-q}{x-p}

The slope of parallel lines are same. Slopes of perpendicular lines are negative reciprocal of each other.

The slope m of the line is given as

m = \dfrac{y-q}{x-p}\\\\ m = \dfrac{-5-6}{2+4}\\\\ m = \dfrac{-11}{6}

The equation of a line is  

( y -y_0) = m (x - x_0)\\\\( y -6) = \dfrac{-11}{6}  (x+4)\\\\6( y -6) = (-11)  (x+4)\\\\6y -36 = (-11x +44)\\\\11x +6y - 80 = 0

Hence, the equation is  11x +6y - 80 = 0

Learn more about slopes here:

brainly.com/question/2503591

#SPJ4

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olga2289 [7]

50-10 = 40. 40 divided by 6 = around 6/7. So about 6/7 weeks

5 0
3 years ago
If f(x)= 3x + 1 and f^(-1)= x-1/3, then the ordered pair of f^(-1)(10)=
iragen [17]

The answer is B

The correct inverse of 3x+1 is actually (1/3)x - 1/3

plug in 10 to the inverse

10/3 - 1/3 = 9/3 or 3

this gives you the point (10,3)

8 0
3 years ago
A new roller coaster at an amusement park requires individuals to be at least​ 4' 8" ​(56 ​inches) tall to ride. It is estimated
Maksim231197 [3]

Answer:

a) 34.46% of​ 10-year-old boys is tall enough to ride this​ coaster.

b) 78.81% of​ 10-year-old boys is tall enough to ride this​ coaster

c) 44.35% of​ 10-year-old boys is tall enough to ride the coaster in part b but not tall enough to ride the coaster in part​ a

Step-by-step explanation:

When the distribution is normal, we use 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 question, we have that:

\mu = 54, \sigma = 5

a. What proportion of​ 10-year-old boys is tall enough to ride the​ coaster?

This is 1 subtracted by the pvalue of Z when X = 56.

So

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

Z = \frac{56 - 54}{5}

Z = 0.4

Z = 0.4 has a pvalue of 0.6554

1 - 0.6554 = 0.3446

34.46% of​ 10-year-old boys is tall enough to ride this​ coaster.

b. A smaller coaster has a height requirement of 50 inches to ride. What proportion of​ 10-year-old boys is tall enough to ride this​ coaster?

This is 1 subtracted by the pvalue of Z when X = 50.

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

Z = \frac{50 - 54}{5}

Z = -0.8

Z = -0.8 has a pvalue of 0.2119

1 - 0.2119 = 0.7881

78.81% of​ 10-year-old boys is tall enough to ride this​ coaster.

c. What proportion of​ 10-year-old boys is tall enough to ride the coaster in part b but not tall enough to ride the coaster in part​ a?

Between 50 and 56 inches, which is the pvalue of Z when X = 56 subtracted by the pvalue of Z when X = 50.

From a), when X = 56, Z has a pvalue of 0.6554

From b), when X = 50, Z has a pvalue of 0.2119

0.6554 - 0.2119 = 0.4435

44.35% of​ 10-year-old boys is tall enough to ride the coaster in part b but not tall enough to ride the coaster in part​ a

5 0
3 years ago
What is the opposite of -21? show all work
bogdanovich [222]
21 is the opposite of -21
8 0
3 years ago
Answer this if you're cool
GalinKa [24]
I’m doing this to in 8th grade I don’t understand it neither
7 0
3 years ago
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