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1 year ago

G(x) = −5x + 2, find g(–4).

Mathematics

1 answer:

Anika [276]1 year ago

8 0

Answer:

g(x)=22

Step-by-step explanation:

Substitute -4 into the equation.

g(x)= -5x+2

g(-4)= -5(-4)+2

g(-4)= 20+2

g(-4)= 22

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Ariel travels 400 miles in 8 hours. What is her rate of change or rate?

Leviafan [203]

Hello there.

Ariel travels 400 miles in 8 hours. What is her rate of change or rate?

Rate of change is defined as
change in distance
change in time

400 ÷ 8 = 50

Answer: B) 50 miles per hour

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4 years ago

Read 2 more answers

Find an equation of the tangent line to the curve 2(x2+y2)2=25(x2−y2) (a lemniscate) at the point (−3,1). An equation of the tan

valina [46]

$2(x^2+y^2)^2=25(x^2-y^2)$

Let $y=y(x)$ , so that differentiating both sides wrt $x$ gives

$4(x^2+y^2)\left(2x+2y\dfrac{\mathrm dy}{\mathrm dx}\right)=25\left(2x-2y\dfrac{\mathrm dy}{\mathrm dx}\right)$

If $x=-3$ and $y=1$ , the above reduces to

$40\left(-6+2\dfrac{\mathrm dy}{\mathrm dx}\right)=25\left(-6-2\dfrac{\mathrm dy}{\mathrm dx}\right)\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac9{13}$

This is the slope of the tangent line, which has equation

$y-1=\dfrac9{13}(x+3)\implies\boxed{y=\dfrac{9x+40}{13}}$

7 0

3 years ago

A rock is released from rest and freely falls 70 m to the ground. What is its velocity just before impact? A. 1.2 m/s B. 7.0 m/s

Yuri [45]

Answer:

37.04 m/s

Step-by-step explanation:

we can use the equation x = x0 + v0t + 1/2at^2

a = -9.8 m/s^2, the acceleration due to gravity

x0 = 70 m, the starting point of x

v0 = 0 m/s

x = 0

this will allow us to solve for time

0 = 70 + 0 +-4.9t^2

t = 3.779

now we can use the equation v = v0 + at

v = 0 + 9.8(3.77)

v = 37.04 m/s

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3 years ago

The average score of all golfers for a particular course has a mean of 71 and a standard deviation of 3. Suppose 36 golfers play

Zielflug [23.3K]

Answer:

.0228

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .