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3 years ago

Find the slope of the line that contains the points named. R(0, 4), S(5, 0)

Mathematics

2 answers:

HACTEHA [7]3 years ago

4 0

Slope = (0 - 4) / (5-0) = -4/5

hope that helps

Nat2105 [25]3 years ago

4 0

Answer:

The slope of the line that contains the points R(0, 4) , S(5, 0) is $m = \frac{-4}{5}$ .

Step-by-step explanation:

Formula

The slope of the line is defined as

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

As given in the question

The line contains the points R(0, 4), S(5, 0) .

$x_{1}=0$

$y_{1}=4$

$x_{2}=5$

$y_{2}=0$

Put all the points in the formula

$m = \frac{0-4}{5-0}$

$m = \frac{-4}{5}$

Therefore the slope of the line that contains the points R(0, 4) , S(5, 0) is $m = \frac{-4}{5}$ .

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What is the area of the triangle

Anna11 [10]

Answer:

Step-by-step explanation:

1. The area of triangle is = (A*h)/2, where h is the height grounded on side A.

2. Given the height 5 and the side 4 we get S(area)=(5*4)/2=10.

4 0

3 years ago

Random samples of size 81 are taken from an infinite population whose mean and standard deviation are 200 and 18, respectively.

TiliK225 [7]

Answer:

d. 200 and 2

Step-by-step explanation:

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 $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

Mean = 200

Standard deviation = 18

Sample size: 81

Standard error: $s = \frac{18}{\sqrt{81}} = 2$

So the correct answer is:

d. 200 and 2

7 0

3 years ago

Read 2 more answers

The vertex of the parabola below is at the point (2,4), and the point (3,6) is

lukranit [14]

Answer:

A. y= 2(x - 2)2 + 4

Step-by-step explanation:

vertex having an x value of 2 means the phrase in paren must be x - 2.

This eliminates B and D

vertex having a y value of 4 is of no help as the remaining two equations will result in 4 if the x term is 2

plugging in x = 3 makes y = 6 in equation A, but not in equation C where y = 10

3 0

3 years ago

Can someone please explain this to me? Thanks!

Makovka662 [10]

Answer: Choice D

$\displaystyle F\ '(x) = 2x\sqrt{1+x^6}\\\\$

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Explanation:

Let g(t) be the antiderivative of $g'(t) = \sqrt{1+t^3}$ . We don't need to find out what g(t) is exactly.

Recall by the fundamental theorem of calculus, we can say the following:

$\displaystyle \int_{a}^{b} g'(t)dt = g(b)-g(a)$

This theorem ties together the concepts of integrals and derivatives to show that they are basically inverse operations (more or less).

So,

$\displaystyle F(x) = \int_{\pi}^{x^2}\sqrt{1+t^3}dt\\\\ \displaystyle F(x) = \int_{\pi}^{x^2}g'(t)dt\\\\ \displaystyle F(x) = g(x^2) - g(\pi)\\\\$

From here, we apply the derivative with respect to x to both sides. Note that the $g(\pi)$ portion is a constant, so $g'(\pi) = 0$

$\displaystyle F(x) = g(x^2) - g(\pi)\\\\ \displaystyle F \ '(x) = \frac{d}{dx}[g(x^2)-g(\pi)]\\\\\displaystyle F\ '(x) = \frac{d}{dx}[g(x^2)] - \frac{d}{dx}[g(\pi)]\\\\ \displaystyle F\ '(x) = \frac{d}{dx}[x^2]*g'(x^2) - g'(\pi) \ \text{ .... chain rule}\\\\$

$\displaystyle F\ '(x) = 2x*g'(x^2) - 0\\\\ \displaystyle F\ '(x) = 2x*g'(x^2)\\\\ \displaystyle F\ '(x) = 2x\sqrt{1+(x^2)^3}\\\\ \displaystyle F\ '(x) = \boldsymbol{2x\sqrt{1+x^6}}\\\\$

Answer is choice D

5 0

2 years ago

Read 2 more answers

A science teacher has a supply of 50% sugar solution and a supply of 80% sugar solution. How much of each solution should the te

mash [69]

How much of each solution should the teacher mix together to get 105 ML of 60% sugar solution for an experiment?

1. Look at how 60% is closer to the solution of lower concentration (50%). You can deduce that you will be mixing a higher volume of the 50% solution.

2. All 4 answers add up to 105ml.

3. The intuitive answer is the first option:
70 ML of the 50% solution and 35 ML of the 80% solution

4. Let's check whether point 3 is true.
70ml/105ml X 0.5 + 35ml/105ml X 0.8 = (35 + 28)/105= 63/105= 60% / 105 ml = 105ml of 60% sugar solution

3 0

3 years ago