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3 years ago

(a) has no solutions.(b) has infinitely many solutions.(c) has exactly one solution.

Mathematics

1 answer:

grandymaker [24]3 years ago

6 0

Answer and Step-by-step explanation:

Given

ax + by = c

qx + ry = s

(a) the equation has no solutions if a/q = b/r ≠ c/s, when this happens, we say the system of equations has no solution. For example

x + y = 3

x + y = 5

Subtracting first equation from the second we have:

0 = 2 which is impossible.

(b) the equations have infinite solutions if a/q = b/r = c/s, for example

x + y = 2

Subtracting the first equation from the second we have

0 = 0, since this is always true, then it has infinite solutions.

x + y = 2

x – y = 1

Adding the first and second equation we have

2x = 3, we can get x from here and definitely y, so we have just one solution.

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height of second rectangular prism is 5 meters

Step-by-step explanation:

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3 years ago

If you are smart in ranges, graphs, and functions, pls help me out. Look at the screenshot below!

jeka94

Answer:

<u>Graph of the equation y = 2/5x - 1</u>

Please check the attached graph of the equation where:

The point (0, -1) represents the y-intercept, it is the point where the line crosses the y-axis.

The point (2.5, 0) represents the x-intercept, it is the point where the line crosses the x-axis.

Step-by-step explanation:

Given the equation

y = 2/5x - 1

<u>Determining the y-intercept:</u>

We know that the value of the y-intercept can be determined by setting x = 0 and determining the corresponding value of y.

As the equation is given such as

y = 2/5x - 1

substitute x = 0

y = 2/5(0) - 1

y = 0 - 1

y = -1

so the ordered pair (0, -1) represents the y-intercept.

Thus, the y-intercept is: -1

<u>Determining the x-intercept:</u>

We know that the value of the x-intercept can be determined by setting x = y and determining the corresponding value of x.

As the equation is given such as

y = 2/5x - 1

substitute y = 0

0 = 2/5x - 1

2/5x = 1

x = 5/2

x = 2.5

so the ordered pair (2.5, 0) represents the x-intercept.

<u>Graph of the equation y = 2/5x - 1</u>

Please check the attached graph of the equation where:

The point (0, -1) represents the y-intercept, it is the point where the line crosses the y-axis.

The point (2.5, 0) represents the x-intercept, it is the point where the line crosses the x-axis.

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3 years ago

Ments

maw [93]

The sector area and the arc length are 34.92 square inches and 13.97 inches, respectively

<h3>How to find a sector area, and arc length?</h3>

For a sector that has a central angle of θ, and a radius of r;

The sector area, and the arc length are:

$A = \frac{\theta}{360} * \pi r^2$ --- sector area

$L = \frac{\theta}{360} * 2\pi r$ ---- arc length

<h3>How to find the given sector area, and arc length?</h3>

Here, the given parameters are:

Central angle, θ = 160

Radius, r = 5 inches

The sector area is

$A = \frac{\theta}{360} * \pi r^2$

So, we have:

$A = \frac{160}{360} * \frac{22}{7} * 5^2$

Evaluate

A = 34.92

The arc length is:

$L = \frac{\theta}{360} * 2\pi r$

So, we have:

$L = \frac{160}{360} * 2 * \frac{22}{7} * 5$

L = 13.97

Hence, the sector area and the arc length are 34.92 square inches and 13.97 inches, respectively

Read more about sector area and arc length at:

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2 years ago

3.30 Survey response rate. Pew Research reported in 2012 that the typical response rate to their surveys is only 9%. If for a pa

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Answer:

0% probability that at least 1,500 will agree to respond

Step-by-step explanation:

I am going to use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be 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.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .