For which of the following operations must two rational functions first have a common denominator? Select all that apply.

addition
division
multiplication
subtraction

Answer: 1134.11

A=3.14*r^2

Step-by-step explanation:

Answer:

a ≈ 1134.11 cm2

Step-by-step explanation:

The formula:

[tex]a=\pi r^{2}[/tex]

[tex]a=\pi (19)^{2} =361\pi[/tex]

[tex]a=1134.11cm^{2}[/tex]

Hope this helps

Answer:

N(0)=10000/(5+1245)

Step-by-step explanation:

substitute zero in for t. Anything to the zero power equals 1.

Answer:

8 people

Step-by-step explanation:

N(0)=10000/(5+1245e^-0.97(0))

N(0) = 10000/(5+1245e^0)

e^0 = 1

= 10000/5+1245(1)

= 10000/5+1245

= 10000/1250

= 8

substitute zero in for t. Anything to the zero power equals 1.

The total measurements of the roof in square feet as required to be determined in the task content is; 2649 ft².

It follows from the task content that the total area of the roof as given in the task content is to be determined.

On this note, the area of the roof is the total area of the 71ft by 39 ft rectangle minus the area of the shaded region with dimensions 15 ft by 8 ft.

Therefore;

Area = (71 × 39) - (15 × 8)

= 2649 ft².

Ultimately, the total area measure of the roof in square feet is; 2649 square feet.

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The dot plot where each dot represents a friend is given below

We are given that;

Number of siblings= 4,1,0,3,2, 2

Now,

To create a dot plot using this data, we need to follow these steps:

Draw a horizontal number line with the values from 0 to 4, which are the possible numbers of siblings that Sarah’s friends have. Label the number line as “Number of siblings”.

For each value in the data set, place a dot above the corresponding number on the number line. If there are more than one friend with the same number of siblings, stack the dots vertically.

Give the dot plot a title, such as “Number of Siblings of Sarah’s Friends”.

The dot plot should look something like this:

Therefore, by the dot plot is shown above.

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The amount of money that Theresa has left is equal to £2,740.

In order to write a linear equation to describe this situation, we would assign variables to the cost of flights for each of them and the cost of accommodation for each of them respectively, and then translate the word problem into a linear equation as follows:

Let the variable a represent cost of flights for each of them.

Let the variable f represent cost of accommodation for each of them.

Since Theresa paid for herself and 11 friends to go on holiday with a flight cost of £339 and accommodation cost of £266, a linear equation to describe this situation is given by;

y = 12(a + b)

y = 12(266 + 339)

y = £7,260

For the amount of money left, we have:

Amount of money left = £10,000 - £7,260

Amount of money left = £2,740.

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Answer: >$15

Step-by-step explanation: She needs at least $15, so, we use the greater then symbol, because she’ll be fine if she has more than $15(>15) but she won’t be able to buy the ticket if she has under $15(<15)

The two lengths of the chords of circle are solved and x = 5 units

Given data ,

Let the length of the two chords be represented as AB and CD

Now , AB = 21 and CD = 3x

where E is the extended point of the two chords which intersect at point E

Now , from the intersection of chords outside the circle ,

BE ( AE ) = DE ( CE )

On simplifying , we get

4 ( 25 ) = x ( 4x )

100 = 4x²

Divide by 4 on both sides , we get

x² = 25

Taking square roots on both sides , we get

x = 5 units

Hence , the chords are solved and x = 5 units

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Answer:

40°

Step-by-step explanation:

360-240=120

120÷3=40°

Answer

40°

Add of all angles would be 360° .

so equation would be

360° - 240° = 3x

360 - 240 is 120

so

120 = 3x

Dive the both sides of equation by 3 (*just to make it simple and clear. you cam just move 3 to other side of equation . since its multiplied in its side, it would change to division*)

120/3 = 3x/3

40° = x

all the X angle would be 40°

240 + 40 + 40 + 40 = 360°

Answer:

6-x-2x^2 - (-2x^2 +3x+2)=6-x-3x-2=-4x+4

Answer: D (t−3)(t−5)(t+4)

Step-by-step explanation:

Hope this helps! :)

The function f(x) = a(b^x) is an exponential function, where "a" is the initial value or y-intercept of the function, and "b" is the base of the exponent, which determines the rate of growth or decay.

When x = 0, we have:

f(0) = a(b^0)

Since any number raised to the power of 0 is 1, we can simplify the expression to:

f(0) = a(1) = a

Therefore, when x is equal to 0, the value of the function is just the initial value "a". This is true for any exponential function of the form f(x) = a(b^x).

In other words, the initial value of an exponential function is the value of the function when x = 0, and in this case, that value is just "a".

The equation of the hyperbola with center (-10, 5), a focus at (-10, 15),

and a co-vertex at (-18,5) is:

[(y - 5)² / 36] - [(x + 10)² / 64] = 1

From the question, we are to determine the equation of the hyperbola with the given center, focus and co-vertex.

The equation of a hyperbola with center (h, k), a focus at (h, k + c), and a co-vertex at (h + b, k) is given by

[(y - k)² / a²] - [(x - h)² / b²] = 1

Where a² = c² - b²

From the given information,

The center of the hyperbola is (-10, 5)

Thus,

h = -10, k = 5

The focus is at (-10, 15)

By comparison with (h, k + c)

k + c = 15

5 + c = 15

c = 15 - 5

c = 10

The co-vertex is at (-18, 5)

By comparing with (h + b, k)

h + b = -18

-10 + b = -18

b = -18 + 10

b = -8

From the formula a² = c² - b²

Then,

a² = c² - b²

a² = 10² - 8²

a² = 100 - 64

a² = 36

Now,

We can write the equation of the hyperbola

[(y - k)² / a²] - [(x - h)² / b²] = 1

Substitute the values

[(y - (5))² / (36)] - [(x - (-10))² / (-8)²] = 1

[(y - 5)² / 36] - [(x + 10)² / 64] = 1

Hence,

The equation of the hyperbola is:

[(y - 5)² / 36] - [(x + 10)² / 64] = 1

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the discount on the dog food is $0.27, and the discounted price is $1.08.

What is the percentage?

A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.

If the original price of the dog food is $1.35 and it is on sale for 20% off, the discount would be:

Discount = 20% of $1.35

Discount = 0.20 x $1.35

Discount = $0.27

Therefore, the discounted price of the dog food would be:

Discounted price = Original price - Discount

Discounted price = $1.35 - $0.27

Discounted price = $1.08

So the discount on the dog food is $0.27, and the discounted price is $1.08.

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Answer:

3 and 4

Step-by-step explanation:

- 2 < x < 5

has solutions x = - 1, 0, 1, 2, 3, 4

x > 2

has solutions

x = 3, 4, 5, 6, ...........

the integer values that satisfy both are x = 3, 4

Answer:

To find the inverse of the function f(x) = (x - 12)^2 on the domain [12, infinity), we can follow the steps below:

Step 1: Replace f(x) with y.

y = (x - 12)^2

Step 2: Swap the positions of x and y.

x = (y - 12)^2

Step 3: Solve for y.

Taking the square root of both sides, we get:

y - 12 = ±√x

Adding 12 to both sides, we get:

y = 12 ± √x

However, we are given that the domain of the inverse function is [12, infinity). Since the expression 12 - √x is negative for x > 144, we must choose the positive square root to satisfy the given domain. Therefore, the inverse function is:

f^-1(x) = 12 + √x, x ≥ 144

Note that we have restricted the domain of the inverse function to [144, infinity) to ensure that the function is one-to-one and has a unique inverse.

The value of collinear point mLP = 13x - 34.

Three or more points on the same line are referred to as collinear points. The Latin terms "col" and "linear," which signify together and in the same line, are the source of the English word "collinear."

Since L, M, and P are collinear points, we have:

mLM + mMP = mLP

Substituting the given values, we get:

(8x - 56) + mNP = mLP

(8x - 56) + (5x + 22) = mLP

13x - 34 = mLP

Therefore, mLP = 13x - 34.

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The complete question is:

If mLM = (8x - 56) and mNP = (5x + 22), find mLP.

The equation of the asymptotes for the given function y = 8/x are x = 0 and y = 0.

What is an asymptote?

an asymptote is a straight line or a curve that a function approaches but never touches as the independent variable (usually denoted by "x") approaches a certain value or becomes very large or small.

In the case of a straight line asymptote, the function approaches the line as x approaches positive or negative infinity. If the line is horizontal, then the function approaches a horizontal asymptote, and if the line is vertical, then the function approaches a vertical asymptote. For example, the function y = 1/x has a vertical asymptote at x = 0, because as x approaches 0, the function approaches infinity (or negative infinity) and never touches the vertical line x = 0.

The given equation y = 8/x represents a hyperbolic function. The graph of this function has two asymptotes, one in the x-axis (y = 0) and the other in the y-axis (x = 0).

To find the equation of the asymptotes, we can use the fact that as x becomes very large or very small, the function approaches the asymptotes. The equation of the vertical asymptote, which is x = 0, can be obtained by taking the limit of the function as x approaches 0 from both the positive and negative sides. We get:

lim x→0+ 8/x = +∞

lim x→0- 8/x = -∞

So the vertical asymptote is x = 0.

The equation of the horizontal asymptote, which is y = 0, can be obtained by taking the limit of the function as x becomes very large. We get:

lim x→±∞ 8/x = 0

So the horizontal asymptote is y = 0.

Therefore, the equation of the asymptotes for the given function y = 8/x are x = 0 and y = 0.

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The dot in the graph of the inequality, x > 5, will be opened

From the question, we are to determine if the dot in the graph of the given inequality will be opened or closed

The given inequality is x > 5

If the sign of an inequality has the equals sign included, that is greater than or equal to (≥) OR less than or equal to (≤), the dot in the graph will be closed.

But if the inequality is less than or greater than (< or >), the dot in the graph will be opened.

Hence,

The dot in the graph of x > 5 will be opened since the inequality sign is not greater than or equal to (≥) OR less than or equal to (≤).

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Answer:

A. 500 cm3

Step-by-step explanation:

The general inverse variation equation is

y = k/x, where y varies inverse as x and k is the constant of proportionality.

Thus, if we substitute V for y and P for x in the equation, we have

V = k / x

To find k, we can plug in 80 for V and 2000 for P and solve for k:

80 = k / 2000

160000 = k

Finally, to find V when P = 320 millimeters, we can plug in 160000 for k and 320 for P and solve for V:

V = 160000 / 320

V = 500 cm3

Answer:

Step-by-step explanation:

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Answer:

XY = 7.5 cm

Area = 105 cm²

Step-by-step explanation:

First, let us use the sin Θ to find the value of XY.

Sin Θ = Opposite ÷ Hypotenuse

Sin 43 = XY ÷ 11

0.6819 = XY ÷ 11

0.6819 × 11 = XY

7.5 cm = XY

The formula to find the area of the triangle is:

[tex]\sf Area=\frac{1}{2}*base*height\\\\\sf Area=\frac{1}{2}*28\:cm\:*7.5\\\\Area=105\:cm^2[/tex]

The critical value is Z = 2.331. The rejection region is Z > 2.33

What is meant by critical value?

A critical value is a value used in hypothesis testing to determine whether to reject or fail to reject the null hypothesis.

What is meant by rejection region?

The rejection region is the set of values that lead to the rejection of the null hypothesis in favor of the alternative hypothesis.

According to the given information

To find the critical value(s) and rejection region(s) for a right-tailed z-test with level of significance x = 0.01, we can use the following formula1:

Critical value: Z = Zα where α = x and Zα is the Z-score that corresponds to an area of α in the standard normal distribution table

Rejection region: Z > Zα

For a right-tailed test with α = 0.01, we can find the critical value using a standard normal distribution table1. The critical value is Z = 2.331. The rejection region is Z > 2.33

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Answer:

- The centers of the distributions should be similar

Step-by-step explanation: - The centers of the distributions should be similar

The minimum amount the student needs to earn per month to save enough money to pay the remaining cost is $500.

The total annual cost to attend community college is $5,000. The college offered a high school senior a scholarship for $1,800 and the student can get a loan for $1,200. To find the minimum amount the student needs to earn per month to save enough money to pay the remaining cost, follow these steps:

1. Subtract the scholarship and loan amounts from the total cost: $5,000 - $1,800 - $1,200 = $2,000.

2. Divide the remaining cost by the number of months (4) until the cost must be paid: $2,000 / 4 = $500.

Therefore, the minimum amount the student needs to earn per month to save enough money to pay the remaining cost is $500.

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This tetrahedron is known as a triangular pyramid and it has four triangular faces, four vertices, and six edges.

We can name the faces of the triangular prism as:

The edges would be:

The faces would be:

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Answer:

Let's say that the total cost of the classes is C and the number of classes is n. We can assume that each class costs the same amount, which we'll call p.

Then, the total cost of the classes can be expressed as:

C = np

However, Gregory charges a one-time processing fee of $3.00, so the total cost of the classes (including the processing fee) can be expressed as:

C = np + 3

Therefore, the equation that represents the relationship between the total cost of the classes (including the processing fee) and the number of classes is:

C = np + 3

Answer:

140° + 90° + 90° + k = 360°

320° + k = 360°

k = 40°

Therefore , the solution of the given problem of angles comes out to be k has a value of 40 degrees.

The largest and smallest walls of a skew are found at the intersection of the pathways connecting its ends. Two pathways could meet at a crossroads. Another result of two entities interacting is an angle. More than anything else, they resemble dihedral shapes. Two line beams can be arranged in a variety of ways between their endpoints to produce a two-dimensional curve.

Here,

According to the information provided, it seems that there is a 140° angle followed by an angle designated as "k". These two angles appear to be adjacent, and since the sum of all angles on a straight line is 180 degrees, we may construct the following equation:

=> 140° + k = 180°

We can now calculate the value of k as follows:

=> k = 180° - 140°

=> k = 40°

So, "k" has a value of 40 degrees.

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Answer: B: [tex]f(x) = x^2 - 4x-5[/tex]

Step-by-step explanation:

Lets write this first in vertex form:

We know the vertex of this function is at (2, -9)

this gives us h,k values. Since there is no stretch or compression, and no negative coefficient we can simply plug in:

f(x) = [tex](x-2)^2 - 9[/tex]

Expanding this, we get answer B.

Answer:

3 1/2 is located between 3 and 4 on the number line.