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2 years ago

I can't seem to figure this one out, this is all the info that was given:

Mathematics

1 answer:

vazorg [7]2 years ago

7 0

Answer:

4a + 4

Step-by-step explanation:

f(x) = x² + 2

f(a) = a² + 2

f(a+2) = (a+2)² + 2

f(a+2) − f(a) = (a+2)² + 2 − (a² + 2)

f(a+2) − f(a) = a² + 4a + 4 + 2 − a² − 2

f(a+2) − f(a) = 4a + 4

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Which equation represents a line that passes through (-2, 4) and has a slope of 1/2?

jok3333 [9.3K]

Answer:

$\large\boxed{y-4=\dfrac{1}{2}(x+2)\text{- point-slope form}}\\\boxed{y=\dfrac{1}{2}x+5\text{- slope-intercept form}}$

Step-by-step explanation:

The point-slope form of an equation of a line:

$y-y_1=m(x-x_1)$

m - slope

We have the slope $m=\dfrac{1}{2}$ and the point $(-2, 4)$ .

Substitute:

$y-4=\dfrac{1}{2}(x-(-2))$

$y-4=\dfrac{1}{2}(x+2)$ - point-slope form

Convert to the slope-intercept form (y = mx + b):

$y-4=\dfrac{1}{2}(x+2)$ <em> use the distributive property</em>

$y-4=\dfrac{1}{2}x+1$ <em>add 4 to both sides</em>

$y=\dfrac{1}{2}x+5$ - slope-intercept form

3 0

2 years ago

A physicist examines 25 water samples for nitrate concentration. The mean nitrate concentration for the sample data is 0.165 cc/

xz_007 [3.2K]

Answer:

The 80% confidence interval for the the population mean nitrate concentration is (0.144, 0.186).

Critical value t=1.318

Step-by-step explanation:

We have to calculate a 80% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=0.165.

The sample size is N=25.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

$s_M=\dfrac{s}{\sqrt{N}}=\dfrac{0.078}{\sqrt{25}}=\dfrac{0.078}{5}=0.016$

The degrees of freedom for this sample size are:

$df=n-1=25-1=24$

The t-value for a 80% confidence interval and 24 degrees of freedom is t=1.318.

The margin of error (MOE) can be calculated as:

$MOE=t\cdot s_M=1.318 \cdot 0.016=0.021$

Then, the lower and upper bounds of the confidence interval are:

$LL=M-t \cdot s_M = 0.165-0.021=0.144\\\\UL=M+t \cdot s_M = 0.165+0.021=0.186$

The 80% confidence interval for the population mean nitrate concentration is (0.144, 0.186).

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3 years ago

HELP if correct I give the best rating.

Charra [1.4K]

What do you need help in?

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3 years ago

What does m represent in the equation y = mx + b?

dexar [7]

Answer:

B. the slope of the graph of y = mx + b

Step-by-step explanation:

m is the slope.

y is the y value

x is the x value

b is the y intercept

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2 years ago

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Answer:

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Step-by-step explanation:

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