To divide two rational expressions, which fraction, if any, do you flip?
The second fraction
Neither fraction
Both fractions
The first fraction

Answer:

\(9\)

Step-by-step explanation:

1) Cancle x².

\(4 \times \frac{9}{4} \)

2) Cancle 4.

\(9\)

Therefor, the answer is 9.

Answer:

Step-by-step explanation:

\(\frac{4(9x^2)}{4x^2}\\ \\ \frac{36x^2}{4x^2}\\ \\ \text{Divide the numerator and denominator by }4x^2\\ \\ 9\)

The work done in each of the cases is:

B) W =  8,400 N*m

C) W = 17,500 N*m

The work can be defined by the product between the force and the distance translated.

W = Force*Distance

So, if there is a force of 120N and the vehicle moves 70 meters, the work done is:

W = 120N*70m = 8,400 N*m

C) Similar case to the above one, here the force is F = 3.5 KN = 3,500N

And the distance is d = 15m

Then in this case the work done is:

W = 3,500N*15m = 17,500 N*m

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Answer:

D. IT shows it is Exponential function i believe

Step-by-step explanation:

Answer:c

Step-by-step explanation:

The equation of the line would be y = (-3/4)x + 5.

What is the slope-point form of the line?

For the line having slope "m" and the point (x1, y1) the equation of the line passing through the point (x1, y1) having slope 'm' would be

                      y - y1 = m(x - x1)

The given equation is \(y=-\frac{3}{4}x-17\)

The required line is parallel to the given line.

and we know that the slopes of the parallel lines are equal so the slope of the required line would be m = -3/4

And the required line passes through (8, -1)

so by using slope - point form of the line,

      y - (-1) = (-3/4)(x - 8)

      y + 1 = (-3/4)x - (-3/4)8

       y + 1 = (-3/4)x + 24/4

       y = (-3/4)x + (12/2 - 1)

       y = (-3/4)x + 5

Hence, the equation of the line would be y = (-3/4)x + 5.

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The volume of the solid formed when the region R bounded by y=2x and y=x^2 is revolved about the x-axis is 64π/15. This can be found using the washer method, where the washer is formed by subtracting the area of a smaller cylinder from the area of a larger cylinder.

The radius of the smaller cylinder is given by y=x^2 and the radius of the larger cylinder is given by y=2x. The thickness of the washer is dx. Here is the explanation in more detail:

The washer method is a method for finding the volume of a solid of revolution that is created by rotating a region bounded by two curves about a line. The region R is bounded by the curves y=2x and y=x^2. The x-axis is the line of rotation. The washer is formed by subtracting the area of a smaller cylinder from the area of a larger cylinder. The radius of the smaller cylinder is given by y=x^2 and the radius of the larger cylinder is given by y=2x. The thickness of the washer is dx.

The volume of the washer is given by the following formula:

V = π[(r_1)^2 - (r_2)^2] * dx

where r_1 is the radius of the smaller cylinder, r_2 is the radius of the larger cylinder, and dx is the thickness of the washer. Plugging in the values of r_1 and r_2, we get the following formula for the volume of the solid of revolution:

V = π[(x^2)^2 - (2x)^2] * dx

Simplifying the expression, we get the following formula:

V = π(x^4 - 4x^2) * dx

Now, we need to integrate this expression with respect to x. The limits of integration are from x=0 to x=1.

V = π∫_0^1 (x^4 - 4x^2) * dx

Evaluating the integral, we get the following answer:

V = 64π/15

Therefore, the volume of the solid of revolution is 64π/15.

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Answer:

41%

Step-by-step explanation:

step one to determine what the fraction would be you just read the question: first you have to see what they want to calculate the percentage of. In this case it's students who like traveling out of state but don't like camping. 88 students like traveling out of state and 36 of those students don't like camping so the fraction you have to use is 36/88 step two next you multiply your fraction by 100 to calculate your percentage 36/88×100= 40.9% step three since you have to round to the nearest whole percent your answer would be 41%

(a) The number of students who were undergraduates, living off campus, or both is 38. (b) The number of students who were undergraduates living on campus is 30. (c) The number of graduate students living on campus cannot be determined from the given information.

Let's solve each part of the question step by step:

(a) To find the number of students who were undergraduates, living off campus, or both, we can use the principle of inclusion-exclusion. The total number of students surveyed is 60.

Number of undergraduates = 32

Number of students living off campus = 8

Number of undergraduates living off campus = 2

To find the number of students who were undergraduates, living off campus, or both, we can add the number of undergraduates and the number of students living off campus and then subtract the number of undergraduates living off campus to avoid double-counting:

Number of students who were undergraduates, living off campus, or both = Number of undergraduates + Number of students living off campus - Number of undergraduates living off campus = 32 + 8 - 2    = 38

Therefore, 38 students were undergraduates, living off campus, or both.

(b) To find the number of students who were undergraduates living on campus, we need to subtract the number of undergraduates living off campus from the total number of undergraduates:

Number of undergraduates living on campus = Number of undergraduates - Number of undergraduates living off campus = 32 - 2   = 30

Therefore, 30 students were undergraduates living on campus.

(c) The question doesn't provide the exact number of graduate students, so we cannot determine the number of graduate students living on campus from the given information.

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Step-by-step explanation:

if x is 7 ok so 2(7)+5

14+5

19

Answer:

\(x = 5 + \sqrt{17 } \\ 4\)

Answer:

{-2, -1, 1}

Step-by-step explanation:

Since we are given all the possible inputs {-8, -3, 7} we can use them one by one in the equation to find the outputs.

5y = x - 2 , if x is -8

5y = -8 - 2

5y = -10

y = -2

Next,

5y = x - 2, if x = -33

5y = -3 - 2

5y = -5

y = -1

Last,

5y = x - 2 when x =7

5y = 7 - 2

5y = 5

y = 1

So the set is {-2, -1, 1}

Answer:

(3,2)

Step-by-step explanation:

the other three ordered pairs do not lie in the shaded region

The function f(x) = 4x/(x-16) has vertical asymptotes at x = 16.

To see this, we can factor the denominator:

f(x) = 4x/(x-16) = 4x/x - 16

As x approaches 16 from the left or right, the denominator x-16 approaches 0, but the numerator 4x does not. This means that the function approaches infinity or negative infinity as x approaches 16, indicating a vertical asymptote at x = 16.

To find the end behavior of the function, we can look at the behavior of the function as x approaches positive or negative infinity. We can see that f(x) = 4x/(x-16)

As x increases without bound, x-16 increases without bound. This means that the denominator becomes larger and larger, making the function approach 0 as x approaches positive infinity.

As x decreases without bound, x-16 decreases without bound as well, this means that the denominator becomes smaller and smaller, making the function approach 0 as x approaches negative infinity.

Therefore, the function has a vertical asymptote at x = 16 and approaches 0 as x approaches positive and negative infinity.

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Answer:

f(x) =. 4x/(x-16)

4x= 0 =>x=

x-16= 0

=>x=16

Asymptotes(x) =16

Step-by-step explanation:

The key features of the quadratic equation y = - x² - 2x + 1 is  line of symmetry is x = -1; vertex = (h, k) = (-1, 2); y-intercept is (0, 1);  

the domain = -∞ ≤ x ≤ ∞ and the range = 2 ≥ y ≥ -∞.

What are the key features of a quadratic function?

Three properties that are universal to all quadratic functions:

1) The graph of a quadratic function is always a parabola that either opens upward or downward (end behavior);

2) The domain of a quadratic function is all real numbers; and

3) The vertex is the lowest point when the parabola opens upwards; while the vertex is the highest point when the parabola opens downward.

According to the given question:

The given equation is y = - x² - 2x + 1

The general vertex form is y = a·(x - h)² + k

h = -b/(2·a) = 2/(-2) = -1

k = f(h) = -(-1)² - 2×(-1) + 1 = 2

Therefore;

1) The line of symmetry goes through the vertex and the line of symmetry is x = -1

2) The vertex = (h, k) = (-1, 2)

3) The y-intercept is the coordinate of the point where x = 0 which is  

   (0, 1)

4) The domain are the possible x-values, therefore,

    the domain = -∞ ≤ x ≤ ∞

5) The range is the possible values y-values.

    On plotting the graph, we have the range = 2 ≥ y ≥ -∞

Complete question:

Identify the key features of the Quadratic Function y = - x² - 2x + 1

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The compound inequality for the given situation is $2.75x + $4.25y ≥ $65 and $2.75x + $4.25y ≤ $75, where x represents the number of daylight cameras and y represents the number of flash cameras.

To solve this compound inequality, we need to find the values of x and y that satisfy both conditions. The inequality $2.75x + $4.25y ≥ $65 represents the lower bound, ensuring that the total cost of the cameras is at least $65. The inequality $2.75x + $4.25y ≤ $75 represents the upper bound, making sure that the total cost does not exceed $75.

To list the solutions involving whole numbers of cameras, we need to consider integer values for x and y. We can start by finding the values of x and y that satisfy the lower bound inequality and then check if they also satisfy the upper bound inequality. By trying different combinations, we can determine the possible solutions that meet these criteria.

After solving the compound inequality, we find that the solutions involving whole numbers of cameras are as follows:

(x, y) = (10, 10), (11, 8), (12, 6), (13, 4), (14, 2), (15, 0), (16, 0), (17, 0), (18, 0), (19, 0), (20, 0).

These solutions represent the combinations of daylight and flash cameras that fulfill the requirements of buying exactly 20 cameras and spending between $65 and $75.

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Answer:

5

Step-by-step explanation:

Units = ones. For instance if the question was "5938, which number is in the units?" it would be 8.

Answer:

B 16 Bowls

Step-by-step explanation:

Turn 3 3/4 into a decimal

3.75 times 16 is 60

The volume of the box is 3,189,068 cubic centimeters. The length, width, and height of a large, custom-made shipping crate are 1.22 m, 3.22 m, and 0.83 m, respectively. What is the volume of the box (in cm)? The volume of a box is calculated by multiplying the length, width, and height of a box.

However, the dimensions are given in meters, not centimeters, so they must first be converted. The given dimensions are as follows: Length = 1.22 m, Width = 3.22 m, Height = 0.83 m.

To convert meters to centimeters, multiply each dimension by 100. As a result, the dimensions will be as follows:Length = 122 cmWidth = 322 cmHeight = 83 cm.

Now, using the formula, Volume = Length x Width x Height= 122 x 322 x 83= 3,189,068 cubic centimeters. Therefore, the volume of the box is 3,189,068 cubic centimeters.

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P(X = 7), λ = 6: The Poisson probability of X = 7, with a parameter (λ) value of 6, is 0.1446. P(X = 11), λ = 12: The Poisson probability of X = 11, with a parameter (λ) value of 12, is 0.0946. P(X = 6), λ = 8: The Poisson probability of X = 6, with a parameter (λ) value of 8, is 0.1206.

The Poisson probability is used to calculate the probability of a certain number of events occurring in a fixed interval of time or space, given the average rate of occurrence (parameter λ). The formula for Poisson probability is P(X = k) = (e^-λ * λ^k) / k!, where X is the random variable representing the number of events and k is the desired number of events.

To calculate the Poisson probabilities in this case, we substitute the given values of λ and k into the formula. For example, for the first case (a), we have λ = 6 and k = 7: P(X = 7) = (e^-6 * 6^7) / 7!

Using a calculator, we can evaluate this expression to find that the probability is approximately 0.1446. Similarly, for case (b) with λ = 12 and k = 11, and for case (c) with λ = 8 and k = 6, we can apply the same formula to find the respective Poisson probabilities.

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The interval of increase for the function f(x) = ex x8 is (0, ∞).

To determine the intervals of increase or decrease for the given function, we need to analyze the sign of the derivative.

Let's find the derivative of f(x) with respect to x:

f'(x) = (ex x8)' = ex x8 (8x7 + ex)

To determine the intervals of increase, we need to find where the derivative is positive (greater than zero).

Setting f'(x) > 0, we have:

ex x8 (8x7 + ex) > 0

The exponential term ex is always positive, so we can ignore it for determining the sign. Therefore, we have:

8x7 + ex > 0

Now, we solve for x:

8x7 > 0

Since 8 is positive, we can divide both sides by 8 without changing the inequality:

x7 > 0

The inequality x7 > 0 holds true for all positive values of x. Therefore, the interval of increase for the function is (0, ∞), which means the function increases for all positive values of x.

The function f(x) = ex x8 increases in the interval (0, ∞).

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Answer:  Pigs

Explanation:

For each animal type, divide the number who caught the disease over the total number of that particular animal.

Unfortunately the cows and chickens have percentages higher than 5.5%, so they are not healthier compared to the average.

Pigs on the other hand have a percentage less than 5.5%, so they seem to be slightly healthier than the county average.

The range is 6 and the interquartile range 2.

From the given box - and - whisker plot we get,

Least value is = 4

First quartile is = Q3 = 7

Median is = Q2 = 8

Third Quartile = Q3 = 9

Greatest value is = 10

We know that the range of the data set is = Greatest Value - Least Value = 10 - 4 = 6

Now, Interquartile Range = Third Quartile - First Quartile = 9 - 7 = 2.

Hence the range is given by 6 and interquartile range is given by 2.

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The formula for the exponential function that passes through the two given points is: f(x) = 4^x

Step-by-step explanation:

An exponential function has the form f(x) = a^x, where a is a constant base.

We can use the two points given to find the value of a.

Using the first point (0, 4), we get:

f(0) = a^0 = 1a = 4

So, a = 4.

Now, we can write the exponential function as:

f(x) = 4^x

To check if this function passes through the second point (3, 256), we substitute x = 3:

f(3) = 4^3 = 64 * 4 = 256

So, the function passes through both points (0, 4) and (3, 256).

Therefore, the formula for the exponential function that passes through the two given points is:

f(x) = 4^x

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The volume of the cylinder depends on its radius and height. The volume of the cylinder is 141.3 m3.

The volume of the cylinder is defined as the density of the cylinder which measures the amount of material contained by the cylinder.

Given that the height h of the cylinder is 5m and the diameter d of the base of the cylinder is 6m.

The radius of the cylinder is given below.

\(r = \dfrac {d}{2}\)

\(r= \dfrac {6}{2}\)

\(r = 3\;\rm m\)

The volume of the cylinder is calculated as given below.

\(V = \pi r^2 h\)

\(V = 3.14 \times 3^2 \times 5\)

\(V = 141.3 \;\rm m^3\)

Hence we can conclude that the volume of the cylinder is 141.3 m3.

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Complete question is;

Michael is making scale drawings of rectangular rooms using a scale of 1 inch: 11/5 feet. He wants to use paper that has a width of 8 1/2 inches and a length of 11 inches for the drawings. Determine whether the scale drawings for each of these rooms will fit on one piece of paper.

Choose Yes or No for each set of dimensions.

a. 16 feet by 16 feet Yes/ No

b. 10 feet by 15 feet Yes/ No

c. 15 feet by 20 feet Yes/ No

d. 12 feet by 16 feet Yes/ No

Answer:

A) Yes

B) Yes

C) Yes

D) Yes

Step-by-step explanation:

We are told that 1 inch: 11/5 feet

This means in decimal form, 1 Inch represents 2.2 feet

A) 16 ft width gives: 16/2.2 inches = 7.27 inches

Also, 16ft length gives; 16/2.2 inches = 7.27 inches

Length and width are both less than the ones given in the question respectively. Thus, it's sufficient.

B) 10 ft width gives; 10/2.2 inches = 4.55 inches

15 ft length gives; 15/2.2 inches = 6.82 inches

Length and width are both less than the ones given in the question respectively. Thus, it's sufficient.

C) 15 ft width gives; 15/2.2 inches = 6.82 inches

20 ft width gives; 20/2.2 inches = 9.09 inches

Length and width are both less than the ones given in the question respectively. Thus, it's sufficient.

D) 12 ft width gives: 12/2.2 inches = 5.45 inches

16ft length gives; 16/2.2 inches = 7.27 inches

Length and width are both less than the ones given in the question respectively. Thus, it's sufficient.

Thus, all the dimensions are sufficient to fit on one piece of paper

Answer:

£699 in London

£902.87 in Paris

£1505.63 in New York

The lowest price of the iPhone is £699 in London.

Answer:

cljbgahkbvjdnm

Step-by-step explanation:

The new coordinates after applying the transformation are:

E(-78, -4)

F(-78, -40)

G(102, -40).

To find the new coordinates after applying the given transformation of center (-6, -4) and a scale factor of 6, we need to multiply the distance between each point and the center by the scale factor and then add the result to the center coordinates.

Let's calculate the new coordinates for each point:

For point E(-18, -4):

New x-coordinate = (-18 - (-6)) * 6 + (-6) = -12 * 6 - 6 = -78

New y-coordinate = (-4 - (-4)) * 6 + (-4) = 0 * 6 - 4 = -4

Therefore, the new coordinates for point E are (-78, -4).

For point F(-18, -10):

New x-coordinate = (-18 - (-6)) * 6 + (-6) = -12 * 6 - 6 = -78

New y-coordinate = (-10 - (-4)) * 6 + (-4) = -6 * 6 - 4 = -40

Therefore, the new coordinates for point F are (-78, -40).

For point G(12, -10):

New x-coordinate = (12 - (-6)) * 6 + (-6) = 18 * 6 - 6 = 102

New y-coordinate = (-10 - (-4)) * 6 + (-4) = -6 * 6 - 4 = -40

Therefore, the new coordinates for point G are (102, -40).

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