What are the coordinates of the reflection of point R across the x-axis?





(-2, -3)


(-3, 2)


(-2, 3)


(2, -3)

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.

The equation that results from each transformation is given as follows:

a) reflect in the x-axis (vertical reflection): y = -7^x.

b) stretch vertically by a factor of 3: 3(7)^x.

c) stretch horizontally by a factor of 2.4: y = (7)^(x/2.4).

d) reflect in the y-axis and stretch vertically by a factor of 7: y = 7^(1 - x).

The parent function in the context of this problem is given as follows:

y = 7^x.

The reflection over the x-axis means that the sign of the entire function is exchanged, hence:

y = -7^x.

The vertical stretch by a factor of 3 means that the entire function is multiplied by 3, thus:

y = 3(7)^x.

The horizontal stretch by a factor of 2.4 means that x -> x/2.4, hence:

y = (7)^(x/2.4).

The reflection over the y-axis means that x -> -x, while the vertical stretch by a factor of 7 means that the function is multiplied by 7, hence the function for item d is given as follows:

y = 7(7)^(-x)

y = 7^(1 - x).

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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]

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:

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.

1+ X/4  Quotient= division also like fraction

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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Answer: C

Step-by-step explanation: -5,3,1 answer ;)

The area of the composite figure is A = 135 cm²

Given data ,

Let the figure consists of a rectangle and quarter circle

where the area of the rectangle is R and area of quarter circle is C

And , A = R + C

Area of rectangle A = 20 x 2 = 40 cm²

And , area of quarter circle C = ( 1/4 )π ( 11 )²

C = 95.033 cm²

So , A = 95 + 40

A = 135 cm²

Hence , the area of the figure is A = 135 cm²

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The complete question is attached below :

Determine the area of the composite figure to the nearest whole number.

135cm²

117cm²

173cm²

74cm²

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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We can use the given recursive formula to find the value of each term in the sequence.

Starting with a1 = 10, we can use the recursive formula to find a2:

a2 = a1 + 4 = 10 + 4 = 14

Similarly, we can find a3, a4, and a5:

a3 = a2 + 4 = 14 + 4 = 18

a4 = a3 + 4 = 18 + 4 = 22

a5 = a4 + 4 = 22 + 4 = 26

Therefore, the value of a5 is 26.

A recursive formula is what?

A formula which explains how to move from one word in a sequence to the next is known as a recursive rule for a sequence. The variable is typically used to represent the term "number."

What does a1 in the formula represent?

The first term of the formula, a1, and the nth term of the series, an, are both expressions containing the first term (the term preceding it), an-1.

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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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The expression sec θ / csc θ + 2sin θ / cos θ is equal to the expression 3tan θ is proven below.

Given that:

sec θ / csc θ + 2sin θ / cos θ = 3 tan θ

The properties are given as,

tan x = sin x / cos x

sec x = 1 / cos x

sin x = 1 / csc x

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

Take the left-hand side, then

LHS = sec θ / csc θ + 2sin θ / cos θ

LHS = sin θ / cos θ + 2tan θ

LHS = tan θ + 2 tan θ

LHS = 3 tan θ

LHS = RHS

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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:

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:

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:

Answer:

A. 60%

B. 40%

C. Math because Math has higher chance of being chosen.

D. 0%

Answer:

the ans is below

Step-by-step explanation:

499 or 501

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

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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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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Since the remainders are zero x³ - 1 is divisible by x - 1 and x³ -  8 is divisible by x - 2. The results can be used to find the slopes.

Polynomial long division is a method used to divide one polynomial by another polynomial. It is similar to the long division of integers.

The process involves dividing the highest degree term of the dividend by the highest degree term of the divisor to obtain the first term of the quotient, and then multiplying the entire divisor by this term and subtracting it from the dividend.

Here we have      

Show that x³ -1 is divisible by x - 1

Use polynomial long division to show that x³ - 1 is divisible by x - 1

        x² + x + 1

x - 1 | x³ + 0x² + 0x - 1

        x³ - x²  

               x² + 0x

                x² - x  

                  x - 1

                  x - 1  

                     0

Since the remainder is zero x³ - 1 is divisible by x - 1

Use polynomial long division to show that x³ - 8 is divisible by x - 2

           x² + 2x + 4

  x - 2 | x³ + 0x² + 0x - 8

            x³ - 2x²

                  2x² + 0x

                  2x² - 4x

                           4x - 8

                           4x - 8

                               0

Since the remainder is zero x³ -  8 is divisible by x - 2

These results can be useful in finding the slope of a certain curve.

Specifically, if we consider the curve y = x³, then we can use the fact that x³ - 1 is divisible by x - 1 and x³ - 8 is divisible by x - 2 to find the slope of the tangent line to the curve at the points (1,1) and (2,8), respectively.

Using the quotient rule of differentiation, find the derivative of y = x³ as:

=> dy/dx = 3x²

At x = 1, the slope of the tangent line is therefore 3.

At x = 2, the slope of the tangent line is also 3.

Therefore,

Since the remainders are zero x³ - 1 is divisible by x - 1 and x³ -  8 is divisible by x - 2. The results can be used to find the slopes.  

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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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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.

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:

Your answer will be B. A town's population grows at a rate of 7.2% every year.

Step-by-step explanation:

Pls give me brainliest thx

=The total surface area of the rectangular prism is 192 square inches.

You calculate the total surface area of the rectangular prism using the dimensions provided in the net. Since the net has 6 rectangular faces, we can find the area of each face and then sum them up to get the total surface area.

1. Top rectangle (8 inches by 3 inches): Area = length × width = 8 × 3 = 24 square inches.
Since the bottom rectangle is the same, its area is also 24 square inches.

2. Left rectangle (4 inches by 6 inches): Area = length × width = 4 × 6 = 24 square inches.
As the right rectangle is identical, its area is also 24 square inches.

3. Middle rectangle (8 inches by 6 inches): Area = length × width = 8 × 6 = 48 square inches.
The back rectangle is the same, so its area is 48 square inches as well.

Now, we'll sum up the areas of all 6 faces to get the total surface area:

Total Surface Area = (2 × 24) + (2 × 24) + (2 × 48) = 48 + 48 + 96 = 192 square inches.

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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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