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2 years ago

Which equation represents the line through (4,5) and (0,-3)

Mathematics

1 answer:

MatroZZZ [7]2 years ago

7 0

The linear equation that represents the line that passes through the points (4,5) and (0,-3) is given by:

B. y = 2x - 3

<h3>What is a linear function?</h3>

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

The line passes through (0,-3), that is, when x = 0, y = -3, hence the y-intercept is of b = -3.

The slope is given by the <u>change in y divided by the change in x</u>, hence:

m = (5 - (-3))/(4 - 0) = 2

Hence the equation is:

y = 2x - 3.

Which means that option B is correct.

More can be learned about linear equations at brainly.com/question/24808124

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2 years ago

An anthropologist studies a woman's femur that was uncovered in Madagascar. To estimate the woman's height, he uses the equation

Lelu [443]

Answer:

The inequality $f>40$ represents the length of the femur for which the woman had a height greater than 160cm.

Step-by-step explanation:

The given equation is

$h=60+2.5f$

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If woman's height is greater than 160cm, then

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$60+2.5f>160$

Substract 60 from both sides.

$2.5f>100$

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Therefore the inequality $f>40$ represents the lengths of the femur for which the woman had a height greater than 160cm.

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3 years ago

Solve for x.<br>3 - |8x-6I = 3<br><br>x= or x=

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Answer:

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Step-by-step explanation:

Since 3 - 0 gives us the 3, we do this:

$0 = -|8x - 6|$

0 = -8x + 6 >> Distributive Property

-6 - 6

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3 years ago

To help consumers assess the risks they are taking, the Food and Drug Administration (FDA) publishes the amount of nicotine foun

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Answer:

We conclude that the mean nicotine content is less than 31.7 milligrams for this brand of cigarette.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 31.7 milligrams

Sample mean, $\bar{x}$ = 28.5 milligrams

Sample size, n = 9

Alpha, α = 0.05

Sample standard deviation, s = 2.8 milligrams

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 31.7\text{ milligrams}\\H_A: \mu < 31.7\text{ milligrams}$

We use One-tailed t test to perform this hypothesis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{28.5 - 31.7}{\frac{2.8}{\sqrt{9}} } = -3.429$

Now, $t_{critical} \text{ at 0.05 level of significance, 8 degree of freedom } = -1.860$

Since,

$t_{stat} < t_{critical}$

We fail to accept the null hypothesis and accept the alternate hypothesis. We conclude that the mean nicotine content is less than 31.7 milligrams for this brand of cigarette.

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3 years ago

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