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3 years ago

Section 1 - Topic 9 Parallel and Perpendicular Lines - Part 2 (please help)

Mathematics

1 answer:

RUDIKE [14]3 years ago

6 0

9514 1404 393

Answer:

y = -1/7x
y = 2x -7

Step-by-step explanation:

1. The slope of the given line is the x-coefficient, 7. The slope of the perpendicular line is the negative reciprocal of this: -1/7. Since the line goes through the origin, the y-intercept is zero.

y = -1/7x

2. The first part of this problem is to find the solution to the given system of equations. We can substitute for x to do that:

3(5 -y)-2y = 10

15 -5y = 10 . . . simplify

-3 +y = -2 . . . . divide by -2

y = 1, x = 4 . . . add 3 to find y; subtract y from 5 to find x

The second part of this problem requires we note the slope of the parallel line. It is the x-coefficient, 2. The y-intercept can be found from ...

b = y -mx = 1 -2(4) = -7

So, the desired line in y=mx+b form is ...

y = 2x -7

_____

The first attachment shows the perpendicular lines of problem 1.

The second attachment shows the parallel lines of problem 2.

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Read 2 more answers

In one region, the September energy consumption levels for single-family homes are found to be normally distributed with a mean

Otrada [13]

Answer:

$a=1050 -0.126*218=1022.532$

So the value of height that separates the bottom 45% of data from the top 55% is 1022.532.

Step-by-step explanation:

1) Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

2) Solution to the problem

Let X the random variable that represent the consumption levels of a population, and for this case we know the distribution for X is given by:

$X \sim N(1050,218)$

Where $\mu=1050 kWh$ and $\sigma=218kWh$

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.55$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.45 of the area on the left and 0.55 of the area on the right it's z=-0.26. On this case P(Z<-0.126)=0.45 and P(z>-0.126)=0.55

If we use condition (b) from previous we have this:

$P(X$