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3 years ago

In Exercise 13, solve y=f(x) for x. Then find the input when the output is 2.

Mathematics

1 answer:

andrezito [222]3 years ago

6 0

Answer:

x = ±(√y)/3

x = ±(√2)/3

Step-by-step explanation:

Put the given information in the given equation and solve for x:

f(x) = 2

2 = 9x^2 . . . . . use 2 in place of f(x)

2/9 = x^2 . . . . divide by 9

±√(2/9) = x . . . take the square root

x = ±(√2)/3 . . . simplify

_____

Using this as an example, we can solve f(x) = y in the same way:

y = 9x^2 . . . . use y for f(x)

y/9 = x^2 . . . divide by the coefficient of x^2

±√(y/9) = x . . . take the square root; next, simplify

x = ±(√y)/3 . . . . the equation solved for x. Note this matches the above when y=2.

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The total number of gallons of water in a tank, w, after t minutes is given in this table and the plot.

Katyanochek1 [597]

The equation showing the relationship between w and t is $w = 4t$

From the table, we have the following points:

(0,0) and (1,4)

Start by calculating the slope (m)

$m = \frac{y_2 -y_1}{x_2 -x_1}$

So, we have:

$m = \frac{4 -0}{1 -0}$

Simplify the numerator and the denominator

$m = \frac{4}{1}$

Divide 4 by 1

$m = 4$

The equation is then calculated as:

$w = m(t - t_1) + w_1$

This gives

$w = 4(t - 0) + 0$

Simplify

$w = 4t$

Hence, the equation is $w = 4t$

Read more about linear equations at:

brainly.com/question/14323743

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3 years ago

An angle that measures 89 degrees is called?

mafiozo [28]

An acute angle is any angle that is below 90 degrees, so 89 degrees is an ancute angle

5 0

3 years ago

10. 10x + 5y = 15<br> y=2x-3

Ivan

Answer:

(i think) 1.5

Step-by-step explanation:

If you replace y with the equation y=2x-3, you get 5(2x - 3)

if you distribute this, it equals 10x - 15

combining like terms 10x + 10x - 15=15 will turn into 20x - 15 = 15

if you add 15 to both sides, -15 will cancel and 15 will turn into 30

20x = 30

divide both sides by 20 which will lead to x=1.5

6 0

3 years ago

Given that z is a standard normal random variable, find z for each situation. The area between 0 and z is .4750. Answer The area

algol13

Answer:

$P(0$

And solving for z we have

$P(Z$

And we can find the value for z with the following excel code:

"=NORM.INV(0.975,0,1)"

And we got z =1.96

$P(Z>z)= 0.1314$

And we can use the complement rule and we got:

$P(Z>z) = 1-P(Z$

$P(Z$

And we can find the value for z with the following excel code:

"=NORM.INV(0.8686,0,1)"

And we got z =1.120

$P(Z$

And we can find the value for z with the following excel code:

"=NORM.INV(0.67,0,1)"

And we got z =0.440

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

We want this probability:

$P(0$

And solving for z we have

$P(Z$

And we can find the value for z with the following excel code:

"=NORM.INV(0.975,0,1)"

And we got z =1.96

For the next part we want to calculate:

$P(Z>z)= 0.1314$

And we can use the complement rule and we got:

$P(Z>z) = 1-P(Z$

$P(Z$

And we can find the value for z with the following excel code:

"=NORM.INV(0.8686,0,1)"

And we got z =1.120

For the next part we want to calculate:

$P(Z$

And we can find the value for z with the following excel code:

"=NORM.INV(0.67,0,1)"

And we got z =0.440

6 0

3 years ago

Find the slope of the line passing through the points (7, 8) and (-7, 1). Show your work.

anygoal [31]

Answer:

The slope is $\frac{1}{2}$

Step-by-step explanation:

∵ The rule of the slope passing through 2 points is:

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

∵ The points are (7 , 8) and (-7 , 1)

∴ m = $\frac{1-8}{-7-7}=\frac{-7}{-14}=\frac{1}{2}$

4 0

3 years ago