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3 years ago

What is the equation of a line that is perpendicular to the line y - 1 = -2 (x + 5) and

Mathematics

2 answers:

a_sh-v [17]3 years ago

8 0

Step-by-step explanation:

Write the equation in the form of Y=mX+C so that it is easuer to find the gradientor slope

$y - 1 = - 2(x + 5) \\ y - 1 = - 2x - 10 \\ y = - 2x - 9$

the slope is -2 .

since we need to find a perpendicular equation, the gradient or slope should be negative reciprocal of the gradient we have now which is -2

the perpendicular gradient = 1/2

coordinates: (-3,2)

$y - y1 = m(x - x1) \\ y - 2 = \frac{1}{2} (x - ( - 3)) \\ 2y - 4 = x + 3 \\ 2y = x + 7$

RSB [31]3 years ago

3 0

Answer:

y - 2 = $\frac{1}{2}$ (x + 3)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

y - 1 = - 2(x + 5) ← is in point- slope form

with slope m = - 2

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{-2}$ = $\frac{1}{2}$

and (a, b) = (- 3, 2), thus

y - 2 = $\frac{1}{2}$ (x - (- 3) ), that is

y - 2 = $\frac{1}{2}$ (x + 3) ← equation of perpendicular line

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What is the slope of a line parallel to the line that passes through (4, -3) and (3, -1)?

FinnZ [79.3K]

Answer:

-2

Step-by-step explanation:

find rise over run with y1-y2/x1-x2 = -2/1 = -2

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3 years ago

Dave’s Automatic Door, referred to in Exercise 29, installs automatic garage door openers. Based on a sample, following are the

HACTEHA [7]

The question is not complete and the full question says;

Calculate the (a) range, (b) arithmetic mean, (c) mean deviation, and (d) interpret the values. Dave’s Automatic Door installs automatic garage door openers. The following list indicates the number of minutes needed to install a sample of 10 door openers: 28, 32, 24, 46, 44, 40, 54, 38, 32, and 42.

Answer:

A) Range = 30 minutes

B) Mean = 38

C) Mean Deviation = 7.2

D) This is well written in the explanation.

Step-by-step explanation:

A) In statistics, Range = Largest value - Smallest value. From the question, the highest time is 54 minutes while the smallest time is 24 minutes.

Thus; Range = 54 - 24 = 30 minutes

B) In statistics,

Mean = Σx/n

Where n is the number of times occurring and Σx is the sum of all the times occurring

Thus,

Σx = 28 + 32 + 24 + 46 + 44 + 40 + 54 + 38 + 32 + 42 = 380

n = 10

Thus, Mean(x') = 380/10 = 38

C) Mean deviation is given as;

M.D = [Σ(x-x')]/n

Thus, Σ(x-x') = (28-38) + (32-38) + (24-38) + (46-38) + (44-38) + (40-38) + (54-38) + (38-38) + (32-38) + (42-38) = 72

So, M.D = 72/10 = 7.2

D) The range of the times is 30 minutes.

The average time required to open one door is 38 minutes.

The number of minutes the time deviates on average from the mean of 38 minutes is 7.2 minutes

4 0

3 years ago

In June 2005, a CBS News/NY Times poll asked a random sample of 1,111 U.S. adults the following question: "What do you think is

Shtirlitz [24]

Answer:

The appropriate null hypothesis is $H_0: p = 0.25$

The appropriate alternative hypothesis is $H_1: p < 0.25$

Step-by-step explanation:

Exactly a year prior to this poll, in June of 2004, it was estimated that roughly 1 out of every 4 U.S. adults believed (at that time) that the war in Iraq was the most important problem facing the country.

At the null hypothesis, we test if the proportion is still the same, that is, of $\frac{1}{4} = 0.25$ . So

$H_0: p = 0.25$

We would like to test whether the 2005 poll provides significant evidence that the proportion of U.S. adults who believe that the war in Iraq is the most important problem facing the U.S. has decreased since the prior poll.

Decreased, so at the alternative hypothesis, it is tested if the proportion is less than 0.25, that is:

$H_1: p < 0.25$

3 0

3 years ago

160% of what number 56?

Bogdan [553]

Answer:

160% of 35 is 56.

Step-by-step explanation:

$\frac{56}{y} :\frac{160}{100}$

y · 160 = 56 · 100

160y = 5600

160y ÷ 160 = 5600 ÷ 160

y = 35

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3 years ago

Smith's age is 8 and his mother is 42.in how many years will the mother be three times as his son

frozen [14]

Let’s make an equation
Let’s say x = amount of years after
Smith = 8, mother = 42
3(8 + x) = 42 + x
24 + 3x = 42 + x
2x = 18, x = 9
Solution: after 9 years

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3 years ago