Does the equation represent a linear or nonlinear function? y = x² +8​

The coordinates of C prime are (-4, -7).

The coordinates of the vertices of triangle ABC are

A(-1, 0)

B(-5, 2)

C(-1, 2)

To find the coordinates of C prime, we need to translate the triangle three units left and nine units down. This means we need to subtract 3 from the x-coordinates of each vertex and subtract 9 from the y-coordinates of each vertex.

So, the new coordinates for each vertex are:

A'(-1 - 3, 0 - 9) = (-4, -9)

B'(-5 - 3, 2 - 9) = (-8, -7)

C'(-1 - 3, 2 - 9) = (-4, -7)

Therefore, the coordinates of C prime are (-4, -7).

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Using the given information:

The value of AC is 3 cm

The value of CB is 15 cm

From the question, we are to determine the distance of AC and CB.

From the given information,

Point C is located on line AB

Also,

From the given information,

AB = 18 cm

and

Distance from C to A is 3 cm

That is,

AC = 3 cm

Since C is located on AB,

We can write that

AC + CB = AB

Substitute the values of AC and AB

3 cm + CB = 18 cm

Thus,

CB = 18 cm - 3 cm

CB = 15 cm

Hence,

AC = 3 cm

and

CB = 15 cm

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The coordinates of the y-intercept are (0, 3.5) and the coordinates of the x-intercepts are (-17.5, 0). Using these coordinates, the graph of the equation is shown below.

From the question, we are to graph the given linear equation.

To graph the equation,

We will determine the coordinates of the x-intercepts and y-intercepts.

When x = 0

y = 1/5x + 3.5

y = 1/5(0) + 3.5

y = 3.5

(0, 3.5)

When y = 0

y = 1/5x + 3.5

0 = 1/5x + 3.5

Multiply through by 5

0 = x + 17.5

x = -17.5

(-17.5, 0)

Using the coordinates of the x-axis and y-axis, the graph of the equation is shown below.

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Evaluating the exponential equation we can see that after 5 years, the account has 2559.02

Here we need to use the formula:

A=P(1+r/n)^nt

Where P is the initial amount.

r is the percentage in decimal form, in this case 0.06

n is how many times it is compounded, in this case 4

t is the variable, in this case years.

Replacing all that we get:

A = 1900*(1 + 0.06/4)^(4t)

Now we want to evaluate this in t = 5, we will get:

A = 1900*(1 + 0.06/4)^(4*5)

A = 2559.02

That is the amount.

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Answer:

Step-by-step explanation:

Each time you spin your odds are always the same.   Over time the odds may be predicted but each spin has the same odds

Answer:

1/4

Step-by-step explanation:

The probability of tossing tails on a fair coin is 1/2. The probability of rolling a multiple of 2 on a fair six-sided number cube is 1/2 (since there are three multiples of 2: 2, 4 and 6). Since these two events are independent, the probability of both events happening is the product of their individual probabilities: (1/2) * (1/2) = 1/4.

Answer:

[tex]y = 25[/tex]

Step-by-step explanation:

[tex]24y = 15 \times 40[/tex]

[tex]24y = 600[/tex]

[tex]y = \frac{600}{24} [/tex]

[tex]y = 25[/tex]

Answer:

30

Step-by-step explanation:

70

40

Take out the zero

Then 7 - 4 then add a o to get 30

1) The domain of the rational function: Any real number except x = - 3

2) The function is undefined at x = - 3.

3) The end behavior of the function is equal to 4.

4) x-Intercept: - 8, y-Intercept: 32 / 3.

In this problem we find the case of rational function, whose features must be analyzed. First, we need to determine the domain of the function:

m(x) = [4 · (x - 5) · (x + 8)] / (x² - 2 · x - 15)

m(x) = [4 · (x - 5) · (x + 8)] / [(x - 5) · (x + 3)]

m(x) = [4 · (x + 8)] / (x + 3)

The domain of the rational function is any real number except x = - 3.

Second, we analyze the function at x = - 3 by lateral limits:

[tex]4\cdot \lim_{x \to - 3^{-}}\frac{x+ 8}{x + 3}[/tex]

[(- 3 - e) + 8] / [(- 3 - e) + 3]

(5 - e) / e

5 / e - 1

[tex]4\cdot \lim_{x \to - 3^{+}}\frac{x+ 8}{x + 3}[/tex]

[(- 3 + e) + 8] / [(- 3 + e) + 3]

(5 + e) / e

5 / e + 1

Then, the function m(x) does not exist for x = - 3.

Third, determine the end behavior of the function by limits:

[tex]4\cdot \lim_{x \to + \infty}\frac{x+ 8}{x + 3}[/tex]

4

Fourth, find the intercepts of the function by algebra:

x-Intercept:

[4 · (x + 8)] / (x + 3) = 0

x + 8 = 0

x = - 8

y-Intercept:

m(0) = (4 · 8) / 3

m(0) = 32 / 3

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Answer:

the ans is below

Step-by-step explanation:

499 or 501

Using an equation, the number of computers Mr. Victor sold in the morning is 30.

An equation is an algebraic statement that shows the equality or equivalence of two or more mathematical expressions.

Unlike mathematical expressions, equations include the equal symbol (=).

The number of computers Mr. Victor has for sale = 100

Let the number of computers sold in the morning = w

Let the number of computers sold in the afternoon = (2w+3)

Let the number of computers left = 7

The total number of computers, 100 = w + (2w+3) + 7

100 = 3w + 10

3w = 90

w = 30

Thus, since Mr. Victor sold w computers in the morning, w is equal to 30.

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An equation for the transformed logarithm shown below, that passes through points (0, 0) and (-5, 2) is f(x) = 2log₆(x + 1).

By critically observing the logarithmic graph (see attachment) that models the logarithm function, we can logically deduce that it was reflected across the y-axis.

In Mathematics, the general form of a logarithm function is represented by the following mathematical equation:

f(x) = alog(±x + c)

Where:

Note: The vertical asymptote is at x = 1.

Next, we would determine the value of c and a by using the points (0, 0) and and (-5, 2):

0 = alog(0 + c)    .....equation 1.

2 = alog(-(-5) + c)    .....equation 2.

By solving equations 1 and 2 simultaneously, we have:

1 = 0 + c

c = 1.

For the value of a, we have:

2 = alog(5 + c)

2 = alog(5 + 1)

2 = alog(6)

a = 2/log(6)

In conclusion, the required logarithm function in compact form is given by:

f(x) = alog(±x + c)

f(x) = 2/log(6) × log(-x + 1)

f(x) = 2log₆(-x + 1)

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Answer:

9rs cannot be factored any further since 9 and r and s are all prime numbers.

14xy cannot be factored any further since 14, x, and y have no common factors.

5x^2 cannot be factored any further since 5 and x^2 are both prime.

32x^2 can be factored as 2^5 * x^2.

20x^2 can be factored as 2^2 * 5 * x^2.

30x^2 can be factored as 2 * 3 * 5 * x^2.

5x^3 cannot be factored any further since 5 and x^3 are both prime.

25y^3 can be factored as 5^2 * y^3.

9xy cannot be factored any further since 9, x, and y are all prime numbers.

12x^4 can be factored as 2^2 * 3 * x^4.

Step-by-step explanation:

We can say with 98% confidence that the true average CPU time of the teleprocessing transactions falls between 5751 and 6278 milliseconds.

What is average?

In mathematics, the average is a value that represents the typical or central value of a set of numbers. It is also known as the mean and is calculated by adding up all the values in a set and then dividing by the number of values in the set.

To find the 98% confidence interval for the average CPU time, we can use the formula:

CI = [tex]\bar{x}[/tex] ± t_(α/2,n-1) * (s/√n)

where:

[tex]\bar{x}[/tex] = sample mean

t_(α/2,n-1) = critical value from the t-distribution with n-1 degrees of freedom and a significance level of α/2

s = sample standard deviation

n = sample size

First, we need to calculate the sample mean, sample standard deviation, and the critical value. Using Excel, we can find:

[tex]\bar{x}[/tex] = 6014.9

s = 996.4

t_(α/2,n-1) = T.INV.2T(0.02, 69) ≈ 2.660

Plugging in these values into the formula, we get:

CI = 6014.9 ± 2.660 * (996.4/√70)

CI ≈ 6014.9 ± 263.5

Rounding to the nearest integer and putting the interval in ascending order, we get:

CI ≈ (5751, 6278)

Therefore, we can say with 98% confidence that the true average CPU time of the teleprocessing transactions falls between 5751 and 6278 milliseconds.

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Answer:  D

Step-by-step explanation:

So you have 60kg of air, and the specific heat per kilogram is 1505j/(kg°C), this means you need 1505j to increase 1°C to the temperature of a mass of 1kg of air.

So, if the change in temperature is from 24°C to 31°C, you are increasing 7°C to 60kg of air.

then, for each degree you need 60*1505 j= 90300j

and for 7°c you need 7*90300j = 632100j, wich is answer D.

1+ X/4  Quotient= division also like fraction

The hypothesis is an alternative hypothesis. And the p-value will be 0.25.

For the null hypothesis,

H0: μ = 70

For the alternative hypothesis,

Ha: μ > 70

The test statistic is calculated as:

t = (x - μ) / (s / √n)

t = (75 - 70) / (20 / √64)

t = 2.00

Using a significance level of 0.01 and a one-tailed test, the critical t-value is 2.390. Since the calculated t-value of 2.00 is less than the critical t-value of 2.390, we fail to reject the null hypothesis.

The p-value is calculated as,

p-value = (75 - 70)/20

p-value = 0.25

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A compound inequality that represent example 5 is -2 < x ≤ 5.

A compound inequality that represent example 6 is -4 < x < 0.

In Mathematics and Geometry, a number line simply refers to a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

Since the open circle and closed circle are located at -2 and 5 respectively, a compound inequality to represent this is given by;

x > -2

x ≤ 5

By combining, we have:

-2 < x ≤ 5.

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It will take the final worker 21 days to complete the task

If a task can be completed by three men in ten days, the total work is:

3 men * 10 days = 30 man-days.

Let's suppose that each man has the same rate of production, allowing them to finish the work in equal amounts.

One worker left after three days, leaving just two men to do the job. They put in three more days of effort, so they finished the following amount of work in the first six days:

3 men multiplied by 3 days = 9 man-days.

One worker was left to do the job after another man departed after six days. The entire amount of work left is:

30 man-days - 9 man-days = 21 man-days

One man will need to put in 21 man-days of labour, which will need him to:

A man's day is equal to 21 man-days.

Therefore, it will take the final worker 21 days to complete the task

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Answer:

Step-by-step explanation:

To find the amount needed or available, we need to calculate the total cash collections and the total cash payments for the month, as well as the ending cash balance.

Total cash collections:

- For June sales: 20% collected in August = $40,000 x 0.2 = $8,000

- For July sales: 20% collected in August + 50% collected in September = $65,000 x 0.2 + $65,000 x 0.5 = $19,500

- For August sales: 20% collected in August + 50% collected in September + 25% collected in October = $52,850 x 0.2 + $52,850 x 0.5 + $52,850 x 0.25 = $31,710

- Total cash collections: $8,000 + $19,500 + $31,710 = $59,210

Total cash payments:

- Cash payment: $24,653

- Ending cash balance required: $50,000

- Total cash payments: $24,653 + $50,000 = $74,653

Ending cash balance:

- Beginning cash balance: $14,670

- Total cash collections: $59,210

- Total cash payments: $74,653

- Ending cash balance: $14,670 + $59,210 - $74,653 = -$735

Since the ending cash balance is negative, the company needs additional funds to cover its cash requirements. The amount needed by the bank is the absolute value of the ending cash balance:

Amount needed by the bank = $|-735| = $735

Since the company needs funds, the amount available to repay a loan is $0 - $735 = -$735, meaning that the company needs to borrow $735 to cover its cash requirements.

Answer:

m = 3/2

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Points (-3,7) (-9,-2)

We see the y decrease by 9, and the x decrease by 6, so the slope is

m = -9 / -6 = 3/2

Answer: 44

Step-by-step explanation:

Sum of external is 360  So add all up and make equal to 360

3x+2+2x+x+5+2x+1 = 360

8x + 8 =360

8x=352

x=44

Using the tax credit we know that the net income of the person is $71,500.

Tax credits are financial incentives that let some taxpayers deduct their accumulated credits from the total amount they owe the state.

Additionally, it might be a "discount" offered by the state in some circumstances or a credit given in acknowledgment of prior tax payments.

A tax credit can also be compared to a rebate.

So, the income of the person would be:

Net income = 72,000 - 4500 - 2000 + 6000

Net income = 78,000 - 6,500

Net income = 71,500

Therefore, using the tax credit we know that the net income of the person is $71,500.

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Answer:

a.[tex]\bold{log_7(xz) = log_7(x * z) = log_7(x) + log_7(z)}[/tex]

b.[tex]\bold{log_7(\frac{x}{y}) = log_7(y) - log_7(x)}[/tex]

c.[tex]\bold{log_7(\sqrt[3]{7} ) = log_7(z^{\frac{1}{3}}) = \frac{1}{3}log_7(z)}[/tex]

Step-by-step explanation:

let me provide an explanation for each of the expressions.

[tex]\bold{log_7(xz) = log_7(x * z) = log_7(x) + log_7(z)}[/tex]

[tex]\bold{log_7(\frac{x}{y}) = log_7(y) - log_7(x)}[/tex]

[tex]\bold{log_7(\sqrt[3]{7} ) = log_7(z^{\frac{1}{3}}) = \frac{1}{3}log_7(z)}[/tex]

Therefore, we can express each of the given expressions in terms of logarithms of x, y, z, or w using the logarithmic properties mentioned above.

Answer:

[tex]\textsf{a.} \quad \log_7(x) + \log_7(z)[/tex]

[tex]\textsf{b.} \quad \log_7(y) - \log_7(x)[/tex]

[tex]\textsf{c.} \quad \dfrac{1}{3}\log_7(z)[/tex]

Step-by-step explanation:

We can express the given logarithmic expressions in terms of x, y, z or w by using the laws of logarithms.

[tex]\hrulefill[/tex]

[tex]\boxed{\begin{array}{c}\underline{\textsf{Product law}}\\\\ \log_a(bc)=\log_a(b) + \log_a(c)\\\end{array}}[/tex]

By using the log product law, we can express log₇(xz) as:

[tex]\log_7(xz) =\log_7(x) + \log_7(z)[/tex]

[tex]\hrulefill[/tex]

[tex]\boxed{\begin{array}{c}\underline{\textsf{Quotient law}}\\\\\log_a \left(\dfrac{b}{c}\right)=\log_a(b) - \log_a(c)\end{array}}[/tex]

By using the log quotient law, we can express log₇(y/x) as:

[tex]\log_7 \left(\dfrac{y}{x}\right)=\log_7(y) - \log_7(x)[/tex]

[tex]\hrulefill[/tex]

[tex]\boxed{\begin{array}{c}\underline{\textsf{Power law}}\\\\\log_ax^n=n\log_ax\end{array}}[/tex]

By using the log power law, we can express log₇(∛z) as:

[tex]\begin{aligned}\log_7 \left(\sqrt[3]{z}\right)&=\log_7 \left(z^{\frac{1}{3}\right) \\&=\dfrac{1}{3}\log_7(z)\end{aligned}[/tex]

The sentences that is written in subjunctive mood is C. I wish you'd turn the lights off when you leave the room.

The subjunctive mood  can be regarded as the hypothetical scenario  that is been used in English, it can can be considered as the one that is been used to express a wish.

In some cases be used in the process of making  that recommendation, or demand, in the option C it can be seen that it is used to express wishes and this is the reason why it is been considered as a  subjunctive mood.

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Answer: I wish you'd turn the lights off when you leave the room.

The algebraic representation of "sum of a number and five" can be written as

n + 5

Where n represents the "number".

In mathematics, an algebraic representation is a way of expressing a mathematical relationship or equation using symbols, letters, and mathematical operations. It is a symbolic representation of a mathematical expression or equation that allows us to work with abstract concepts and manipulate them according to certain rules.

For example, the equation y = 2x + 1 is an algebraic representation of a linear function, where y and x represent variables and 2x + 1 is an expression that relates them. Algebraic representations are often used in algebra, calculus, and other areas of mathematics to describe relationships between quantities, solve equations, and make predictions based on mathematical models.

Hence, the algebraic representation of "sum of a number and five" can be written as

n + 5

Where n represents the "number".

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to find the area of the shape we have to find the area of the rectangle first then subtract the area of the 2 semi circles from it. to find the area of the rectangle its 13*6=78. to find the area of a circle you have to do this: radius*radius*pi. the diametre of the circle is 6 so we know the radius is 3. then if we do 3*3*3.14 it will be 28.26. and since there are 2 equal semi circles it is equal to 1 full circle so the area of the 2 semi circles combined is 28.26. Then you just do 78-28.26=49.74 which can be rounded up to 50 cm squared. So the answer is 50 cm squared also pls mark as brainliest answer thx

To calculate the area of the shape, first calculate the area of the rectangle, then deduct the combined areas of the two semicircles. 13*6=78 is the answer to the rectangle's area. To determine a circle's area, follow these steps: radius*radius*pi. Since the circle's diameter is 6, its radius must be 3. therefore the result of 3*3*3.14 is 28.26. The area of the two semicircles combined is 28.26 since there are two equal semicircles, which equals one full circle. The next step is to simply calculate 78-28.26=49.74, which can be rounded up to 50 cm2. The response is 50 cm squared.