Find the equation of the line that contains the point (4, - 2) and is perpendicular to the line y = - 2x + 5.

Mathematics

2 answers:

Licemer1 [7]2 years ago

5 0

<h3>Answer:</h3>

y=1/2x

<h3>Solution:</h3>

The slopes of perpendicular lines are opposite reciprocals of each other.
The simplest way to determine a number's reciprocal is to flip it over, like so:
$-2 ~ - > -\displaystyle\frac{1}{2}$
Now, change the sign:
$\displaystyle\frac{1}{2}$
So we have the <em>slope </em>of the line that's <em>perpendicular </em>to the given line.
Now, let's find the line's equation.
First, let's write it in Point-Slope Form:
y-y1=m(x-x1)
y-(-2)=1/2(x-4)
y+2=1/2x-2 (Point slope)
Now, convert to slope-intercept:
y=1/2x+2-2
y=1/2x

Hope it helps.

Do comment if you have any query.

klasskru [66]2 years ago

3 0

Answer:

y=1/2x

Step-by-step explanation:

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What is the value of v?<br> 1 / 4 (v – 7) = 2

belka [17]

1/4 (v - 7) = 2

1/4v - 1/4 (7/1) = 2

1/4v - 7/4 = 2

1/4v = 15/4

Multiply by 4/1 on both sides to get v

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3 years ago

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 110 engines

slava [35]

Answer:

we will fail to reject the null hypothesis and conclude that the mean pressure is not different from 4.7 psi

Step-by-step explanation:

Let's first define the hypothesis;

Null hypothesis: H0: μ = 4.7

Alternative hypothesis: Ha: μ ≠ 4.7

We have;

Sample size; n = 110

Sample mean; x¯ = 4.6

Variance: σ² = 0.64

Standard deviation; σ = √0.64 = 0.8

Formula for test statistic is;

z = (x¯ - μ)/(σ/√n)

z = (4.6 - 4.7)/(0.8/√110)

z = -0.1/0.0763

z = -1.31

From online p-value from z-score calculator attached, using; z = -1.31, two tailed hypothesis, significance value of 0.1, we have;

P-value = 0.190196

The p-value is greater than the significance value and thus we will fail to reject the null hypothesis and conclude that the mean pressure is not different from 4.7

σ μ