The sum and product of two linear functions are shown. Which statements can be used to describe the original
functions f(x) and g(x)? Select two options.

The graph of g(x) will have the same shape as f(x), but every y-coordinate will be increased by 4 units,The graph of h(x) will have the same shape as f(x), but every x-coordinate will be decreased by 1 unit,The graph of k(x) is 20 and every y-coordinate is increased by 10 units and the graph of m(x) is horizontally squeezed.

To describe the graphs of the given functions, let's first analyze the effects of the transformations applied to the original function f(x) = 5 sin(x).

1. g(x) = 5 sin(x) + 4:

The function g(x) is obtained by vertically shifting the graph of f(x) by 4 units upward. This means that the graph of g(x) will have the same shape as f(x), but every y-coordinate will be increased by 4 units.

2. h(x) = 5 sin(x + 1):

The function h(x) is obtained by horizontally shifting the graph of f(x) to the left by 1 unit. This means that the graph of h(x) will have the same shape as f(x), but every x-coordinate will be decreased by 1 unit. The period of the function remains the same.

3. k(x) = 20 sin(x) + 10:

The function k(x) is obtained by vertically stretching the graph of f(x) by a factor of 20 and then shifting it 10 units upward. This means that the amplitude of the graph of k(x) is 20 (compared to the amplitude of 5 in f(x)), and every y-coordinate is increased by 10 units.

4. m(x) = 5 sin(4x - 1):

The function m(x) is obtained by compressing the graph of f(x) horizontally by a factor of 4, reflecting it across the y-axis, and shifting it 1 unit to the right. This means that the period of m(x) is 1/4 of the period of f(x), and the graph is horizontally squeezed. The reflection across the y-axis means that the graph of m(x) will be inverted compared to f(x). The amplitude remains the same.

Remember that the graph of the original function f(x) = 5 sin(x) represents a sine wave with an amplitude of 5 and a period of 2π. Applying the transformations described above will modify the position, scale, and shape of the graph, resulting in the respective graphs for each function g(x), h(x), k(x), and m(x).

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When Y is increased by 44%, X increases by 20%.

If X is proportional to the square root of Y, then we can express this relationship as X = k√Y, where k is the constant of proportionality. Now, let's consider the scenario where Y is increased by 44%.

Let's denote the initial value of Y as Y₀. When Y is increased by 44%, the new value of Y becomes Y₁ = Y₀ + 0.44Y₀ = 1.44Y₀.

Since X is proportional to the square root of Y, we can write the initial value of X as X₀ = k√Y₀, and the new value of X as X₁ = k√(1.44Y₀).

To find the percentage increase in X, we can calculate the difference between the new and initial values of X and express it as a percentage of the initial value:

Percentage increase in X = ((X₁ - X₀) / X₀) * 100

Substituting the values, we get:

Percentage increase in X = ((k√(1.44Y₀) - k√Y₀) / k√Y₀) * 100

Simplifying the expression, we find:

Percentage increase in X = ((√1.44 - √1) / √1) * 100

Percentage increase in X = (1.2 - 1) x 100

Percentage increase in X = 0.2 x 100

Percentage increase in X = 20%

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Answer:

C

Step-by-step explanation:

Both equations are the same

The quartiles of rainfall in April for the city are:

The quartiles refers to the e values that split sorted data into four parts each with an equal number of observations

To determine quartiles, we first need to sort the data in ascending order which are:

[tex]0.76, 1.08, 1.32, 1.55, 1.83, 2.09, 2.57, 2.83, 3.01, 3.25,\\3.63, 3.78, 4.09, 4.32, 4.64, 4.93, 5.23, 5.34, 5.44, 5.73[/tex]

There are 20 data points, so, median (Q2) will be the average of the 10th and 11th values.

Q2 = (3.25 + 3.63) / 2

Q2 = 3.44.

Q1 = (1.83 + 2.09) / 2

Q1 = 1.96.

Q3 = (4.64 + 4.93) / 2

Q3 = 4.79.

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Answer:

23x+250 and that would equal your total cost

The value of x is 45 in the provided assertion, and the Centerior angles do sum up to 180°, indicating that AD and BC are parallel.

We have,

Parallel in mathematics refers to two lines which never cross one another; picture an equal symbol. Three close pals' parallel lives could be depicted in a tale.

(a)

3x + x + 2x + 90 = 360

6x = 360 - 90

6x = 270

x = 45

(b) The answer will be yes, they would be parallel.

We can justify this using co-interior angles, which state that 2 angles subtended by parallel lines add up to 180°

We can check this with both angles 3x & x, or 2x & 90°.

If AD and BC are parallel, then 3x + x = 180, and since you already found the value of x we can substitute this in:

3(45) + (45) = 180

135 + 45 = 180

180 = 180

So the co-interior angles do add up to 180°, which means that AD and BC are parallel.

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The intervals on f(x) is increasing on (-∞, 0) and (8/3, ∞), and decreasing on (0, 8/3).

The intervals on which the function f(x) = x³ − 4x² + 10 is increasing or decreasing need to find its derivative and determine its sign.

f(x) = x³ − 4x² + 10

f'(x) = 3x² − 8x

The critical points we set f'(x) = 0 and solve for x:

3x² − 8x = 0

x(3x − 8) = 0

x = 0 or x = 8/3

These are the critical points of the function.

Now we can determine the sign of f'(x) in each interval:

Interval (-∞, 0):

Choose x = -1. f'(-1)

= 3(-1)² - 8(-1)

= 11 is positive.

So f(x) is increasing on (-∞, 0).

Interval (0, 8/3):

Choose x = 1. f'(1) = 3(1)² - 8(1)

= -5 is negative.

So f(x) is decreasing on (0, 8/3).

Interval (8/3, ∞):

Choose x = 3. f'(3) = 3(3)² - 8(3)

= 19 is positive.

So f(x) is increasing on (8/3, ∞).

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The area of the triangular figure is 16 m²

The area of a triangle is given by A = 1/2bh where

Given the figure below, we see that it is two triangles with height, h = 2 m and base, b = 8 m.

Since the area of each triangle is A = 1/2bh, and the area of both triangles are the same, then the area of both triangles is A" = A + A

= 2A

= 2(1/2bh)

= bh

Substituting the values of the variables into the equation, we have that

A" = bh

= 8 m × 2 m

= 16 m²

The area is 16 m²

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Answer:

f(x) = x^2 - 5x + 6

f'(x) = 2x - 5

Since the slope of h(x) is 1/3, the slope of the tangent line to f(x) will have slope -3.

2x - 5 = -3

2x = 2, so x = 1

Any options to pick from?

Most pens are about 13-14 cm or approx 5.5 inches.

Answer:

$17,320 after 12 months.

Step-by-step explanation:

f the Coach chooses the Three-Year Plan, the total amount he will spend after 12 months can be calculated as follows:

First, we need to calculate the total amount of monthly payments made in 12 months:

12 months x $610 per month = $7,320

Then, we need to add the down payment made at the time of purchase:

$7,320 + $10,000 = $17,320

Therefore, if the Coach chooses the Three-Year Plan, he will spend a total of $17,320 after 12 months.

Answer:

-14 = k

Step-by-step explanation:

44 = k+58

Subtract 58 from each side.

44-58 = k+58-58

-14 = k

Answer:

1/10

Step-by-step explanation:

2/5 * 1/4 = 2/20 = 1/10

2 right answers, 5 possible choices

Select one right choice = 2/5

After selecting one right choice, there are 4 possible choices with one more right choice left.
Select another right choice = 1/4

The letter "V" in the equation XXX × YV=••••+666=799Y is replaced by the number 89.

The equation can be simplified to XXX × YV=1335.

If both sides of the equation are divided by 3, X × YV = 445.

If now all the X's is replaced with 5's, 5 × YV = 445.

This gives the following equation:

5 × YV = 445

Now multiply both sides of the equation by Y, to get 5Y = 445.

This gives us the following equation:

5Y = 445

Finally, divide both sides of the equation by 5, to get Y=89.

Therefore, the letter "V" in the equation XXX × YV=••••+666=799Y is replaced by the number 89.

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Answer: 12.1

Step-by-step explanation: rounding 12.083 to the nearest tenth will leave you with- 12.1

hope this helps!

The graph of the functions f(x) and g(x) is given below.

Given that:

Function, f(x) = x³

Translated function, g(x) = (x + 6)³

If the function is translated by 'h' units horizontally and 'k' units vertically, then x and y are replaced with (x - h) and (y - k), respectively.

The curve of the function g(x) is translated left side by 6 units.

The graph of the functions is given below.

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There are three dots above the greatest height.

We have,

The greatest height is 75

The smallest height is 62

Now,

We can make a line plot as:

*                                       *

*         *         *        *         *

*         *         *        *         *    

62     66     68     72     75

Thus,

There are three dots above the greatest height.

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Answer:

x=3

Step-by-step explanation:

1.25/5.00=2/8=x/12=1/4

12=x×4

x=12÷4

x=3

The table can be filled as  Symmetry | Applies to the hexagon Reflective symmetry over AD | Yes Reflective symmetry over CE | No

We are given that;

The hexagon DEFCA

Now,

the hexagon has reflective symmetry over AD, because if we fold it along AD, the vertices B and F will match, as well as the vertices C and E. Therefore, the answer for reflective symmetry over AD is Yes.

However, the hexagon does not have reflective symmetry over CE, because if we fold it along CE, the vertices A and F will not match, nor will the vertices B and D. Therefore, the answer for reflective symmetry over CE is No.

Therefore, Symmetry | Applies to the hexagon Reflective symmetry over AD | Yes Reflective symmetry over CE | No.

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Answer:Set up a proportion, letting = the amount of cubic millimeters in 1,000 cubic centimeters. Solve for : 1,000,000 cubic millimeters are in 1,000 cubic centimeters.

Answer:

the answer is 10.63km/L.

The measure of the angles is c = 37. 5 degrees

d = 15 + 37.5 = 52. 5 degrees

To determine the value, we need to know what complementary angles are;

Complementary angles are defined as pair of angles whose sum is equal to 90 degrees

From the information given, we have that;

Angle c and d are both complementary angles

Also, the measure of angle d is 15 degrees greater than the measure of angle c

Then, we have;

d = 15 + c

Substitute the values

c + 15 +c = 90

collect like terms

2c = 90 - 15

2c = 75

Divide both sides by the coefficient

c = 37. 5 degrees

Substitute the value for angles d

d = 15 + 37.5 = 52. 5 degrees

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The solution is: Piece-wise function

f(x)=x+6 , x≤1

f(x) = x^2 + 3 , x>1, the following functions is graphed below.

Option C is correct.

Explanation:

We are given a graph of piece-wise function which break at x=1

We need to choose correct option for graph.

Function is break at x=1.

We will get two function

For x≤1 and x>1

As we can see x≤1, graph is linear and x>1 graph is parabolic.

Equation of linear graph, x≤1

Take two point of graph (0,6) and (-6,0)

Equation of line:

y-y1/y2-y1 = x-x1/x2-x1

y = x+1

f(x)=x+6 , x≤1

Equation of parabolic graph, x>1

f(x) = x^2 + 3

Piece-wise function

f(x)=x+6 , x≤1

f(x) = x^2 + 3 , x>1

Please see the attached figure.

Hence, The option C is correct.

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Answer:

A. Point estimates are used to make inferences about population parameters.