The graph of the piecewise function f(x) is shown.
What is the domain of f(x)?

To write a cosine function with amplitude and period, we can use the formula f(x) = A cos (2π / P) x, where A is the amplitude and P is the period.

To write a cosine function with amplitude and period, we can use the following formula:

f(x) = A cos (2π / P) x

where A is the amplitude and P is the period.

The amplitude of a cosine function is the distance from the center line to the maximum or minimum value of the function. It represents the maximum displacement of the function from its mean or average value. The period of a cosine function is the length of one complete cycle of the function. It represents the time it takes for the function to repeat itself.

For example, if we want to write a cosine function with an amplitude of 3 and a period of 4, we can use the formula:

f(x) = 3 cos (2π / 4) x

Simplifying this equation, we get:

f(x) = 3 cos (π / 2) x

The cosine of π/2 is equal to zero, so this equation simplifies further to:

f(x) = 0

This means that the function has a constant value of zero for all values of x.

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The area of the green shaded region would be,

⇒ Area = 27 (7 - π)

Since, The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

A solid figure is shown in image.

Since, The figure is shape of a trapezoid and it contain a circle.

Hence, The area of trapezoid is,

Area = (a + b) h / 2

Where, a and b are base and h is height of trapezoid.

Hence, We get;

The area of trapezoid is,

⇒ Area = (a + b) h / 2

⇒ A = (15 + 20) × 10/2

⇒ A = 35 × 5

⇒ A = 175

And, Area of circle is,

⇒ A = πr²

⇒ A = π × (10/2)²

⇒ A = π × 25

⇒ A = 25π

Hence, The area of the green shaded region would be,

⇒ Area = 175 - 25π

⇒ Area = 27 (7 - π)

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The simplified expression of (5.1)(5.1^2)^4 is (5.1)^9

The expression is given as:

(5.1)(5.12)4

Rewrite the expression properly as follows:

(5.1)(5.1^2)^4

Rewrite the expression properly as follows:

(5.1)(5.1^2)^4 = (5.1) * (5.1^2)^4

Apply the power law of indices

(5.1)(5.1^2)^4 = (5.1) * (5.1^8)

Apply the power law of indices

(5.1)(5.1^2)^4 = (5.1)^(1 + 8)

Evaluate the sum

(5.1)(5.1^2)^4 = (5.1)^9

Hence, the simplified expression of (5.1)(5.1^2)^4 is (5.1)^9

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The location of √ 7 on a number line between 2 and 3.

A number line is a picture of a graduated straight line that serves as a visual representation of real numbers in primary mathematics. Every number line point is considered to correspond to a real number and every real number to a number line point.

A number line is a long straight line with numbers marked at equal intervals. On a number line, we can argue that as we move to the right, the value of numbers increases. This signifies that the numbers on the right are more than those on the left.

A number line shows how numbers are related. It's a line with check marks next to each number. The numerals get smaller as you move left on the number line. The numbers grow larger as you move closer to the number line.

In this case, ✓7 is 2.65. This number can be found between 2 and 3. This should be the true statement since the options aren't given.

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The equation of the tangent line to the hyperbola 4x^2 - 4xy - 3y^2 = 96 at the point (4, 2) is 8x - 3y = 22.

To find the equation of the tangent line to the hyperbola at the point (4, 2), we need to find the slope of the tangent line at that point. This can be done by taking the derivative of the equation of the hyperbola implicitly and evaluating it at the point (4, 2).

Differentiating the equation 4x^2 - 4xy - 3y^2 = 96 with respect to x, we get 8x - 4y - 4xy' - 6yy' = 0. Rearranging the equation, we have y' = (8x - 4y) / (4x + 6y).

Substituting the point (4, 2) into the equation, we have y' = (8(4) - 4(2)) / (4(4) + 6(2)) = 22/40 = 11/20.

Now that we have the slope of the tangent line, we can use the point-slope form of a linear equation to find the equation of the tangent line. Using the point (4, 2) and the slope 11/20, we have y - 2 = (11/20)(x - 4). Simplifying this equation, we get 20y - 40 = 11x - 44, which can be further rearranged as 11x - 20y = 4.

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There are 144 combinations of 1 entree, 2 vegetables, and 1 dessert that can be selected from 4 entrees, 6 vegetables, and 6 desserts.

To determine the number of combinations, we multiply the number of options for each category.

For the entree, we have 4 options to choose from.

For the vegetables, we need to select 2 out of 6, which can be done in 6 choose 2 ways.

This is calculated as 6! / (2!(6-2)!), which simplifies to

6! / (2!4!)

Similarly, for the dessert, we have 6 options to choose from.

To calculate 6 choose 2, we can use the formula for combinations:

n choose r = n! / (r!(n-r)!).

Plugging in the values, we have

6! / (2!4!) = (6 × 5 × 4 × 3 × 2 × 1) / [(2 × 1) × (4 × 3 × 2 × 1)] = 15.

Therefore, we have 4 options for the entree, 15 options for the vegetables, and 6 options for the dessert.

Multiplying these numbers together, we get 4 × 15 × 6 = 144.

Therefore, there are 144 possible combinations of 1 entree, 2 vegetables, and 1 dessert, given the options of 4 entrees, 6 vegetables, and 6 desserts.

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Answer:

Native Americans and the British.

Step-by-step explanation:

The Native Americans were in North America first but the British/English thought they deserved the land and the two fought over it.

Answer: this is the answer

Step-by-step explanation:

Answer:

  175°

Step-by-step explanation:

Bearing angles are usually measured clockwise from North. Reverse bearing angles differ from forward bearing angles by 180°. These relations and the usual angle sum relation for a triangle can be used to solve this problem.

Angle PQR will be the difference in the bearings from Q to P and Q to R:

  ∠PQR = 124° -46° = 78°

Triangle PQR is isosceles, so the base angle at P will be ...

  ∠QPR = (180° -78°)/2 = 51°

__

The bearing from P to R will be 51° less than the bearing from P to Q. The bearing from P to Q is 180° more than the bearing from Q to P.

  PR bearing = PQ bearing - ∠QPR

  = PQ bearing - 51°

  = (46° +180°) -51° = 175°

The bearing of R from P is 175°.

An expression given is to subtract a – b – c from the sum of 3a – 2b + 4c and 3b – 2c .

An expression in math is known to be the putting together of numbers, variables, etc.

For the expression above,

(3a - 2b + 4c) + (3b - 2c) - (a - b - c)

Therefore:

= 3a - 2b + 4c + 3b - 2c - a + b + c

The answer will be = 2a + 2b + 3c

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When competing beer breweries decide to merge together, they achieve profitability through horizontal integration by: Combining resources, reducing competition, Expanding market share, Sharing knowledge and expertise, Achieving economies of scale.

When competing beer breweries decide to merge together, they achieve profitability through horizontal integration by:

1. Combining resources: The merged breweries can pool their resources, such as equipment, production facilities, and distribution networks, which can lead to cost savings and increased efficiency.

2. Reducing competition: By merging, the breweries can reduce the level of competition in the market, allowing them to potentially charge higher prices and increase their profit margins.

3. Expanding market share: The combined brewery will have a larger market share, providing them with greater influence over market trends and customer preferences.

4. Sharing knowledge and expertise: The breweries can learn from each other's strengths and improve their overall processes, leading to better products and higher profitability.

5. Achieving economies of scale: By increasing the scale of production, the merged brewery can reduce per-unit costs, resulting in improved profitability.

By successfully executing these steps, the beer breweries can achieve profitability through horizontal integration.

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The median number of hours spent practicing per week during the nine consecutive weeks is the middle value when the hours are arranged in ascending order.

To find the median, we first need to arrange the recorded number of hours spent practicing per week in ascending order. Let's assume the recorded hours are as follows: 2, 3, 4, 5, 5, 6, 7, 8, 9.

There are a total of nine recorded hours. Since the number of hours is odd, the median will be the middle value. In this case, the middle value is the fifth number, which is 5. Therefore, the median number of hours spent practicing per week during the nine consecutive weeks is 5.

The median is a measure of central tendency that represents the middle value in a set of data. It is a useful measure for finding a typical value in a distribution. In this case, the median gives us an idea of the "typical" number of hours spent practicing per week during the nine-week period.

By arranging the hours in ascending order, we can easily identify the middle value as the median. In situations where there is an even number of data points, the median would be the average of the two middle values.

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We have the next list of entries:

0, 3, 6, 9, 12, 15, ….

And we must find the next entry

To find it we must use the formula for arithmetic sequence

Where,

In our case,

The next entry will be the 7th term

So, we must find a7

ANSWER:

The next entry is 18.

Answer: 6x - 4

Step-by-step explanation: -2*f(x) = -2 * (-3x+2) = (-2*-3x) + (-2*2) = 6x + (-4) = 6x - 4

Answer:

see below

Step-by-step explanation:

Multiplication and division are also inverse operations

15 * 10 = 150

150 ÷10 = 15

Divide 150 by 10 and we get 15 back

The division undoes the multiplication

This also works in reverse

150 ÷ 10 = 15

15*10 =150

The multiplication undoes the division

The appropriate sample regression equation is:

Est(Yield) = β0 + β1Fertilizer + β2South + ε

We have,

The sample regression equation is a mathematical representation of the relationship between the dependent variable (Yield) and the independent variables (Fertilizer and South) in a regression analysis.

In the equation, "Est(Yield)" represents the estimated value of the Yield variable, β0 is the intercept (constant term), β1 and β2 are the coefficients associated with the Fertilizer and South variables, respectively, and ε represents the error term.

The equation allows us to estimate the expected value of the Yield variable based on the values of the independent variables.

By adjusting the values of Fertilizer and South, we can predict how the Yield variable may change. The coefficients (β1 and β2) represent the expected change in the Yield variable for a unit change in the corresponding independent variable, while β0 represents the estimated average value of Yield when both Fertilizer and South are zero.

Therefore,

The appropriate sample regression equation is

Est(Yield) = β0 + β1Fertilizer + β2South + ε, as it accurately reflects the relationship between the variables in the regression analysis.

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Answer: 11 and 12

Step-by-step explanation:

\(121 < 139 < 144\\\\\sqrt{121} < \sqrt{139} < \sqrt{144}\\\\11 < \sqrt{139} < 12\)

Darcy gave her nail technician a $5.10 tip.

Tip Amount = $5.10

The tip was 6% of the cost of the manicure.

b be the cost of the manicure

So,

6% of cost of the manicure= Tip Amount

6% of b = 5.10

Equation of the cost is :

The equation is : 0.06b = 5.10

Answer:RT=18

Step-by-step explanation: RS+ST=RT

6+12=RT

18=RT

The numeric length of RT is 16 units.

The segment addition postulate states that if we are given two points on a line segment, A and C, a third point B lies on the line segment AC if and only if the distances between the points meet the requirements of the equation AB + BC = AC.

Given that, Point S is on line segment RT. Given ST 5x-10 RT = 4x and

RS = 6,

Using segment addition law,

RT = RS + ST

4x = 6+5x-10

x = 4

Therefore, 4x = 16

Hence, The numeric length of RT is 16 units.

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Answer:2.5

Step-by-step explanation:

4+1/2-2=2 1/2 according to the formula

Answer:

It doesn't

Step-by-step explanation:

When a shape is scaled up or down, the angles don't change.

It's easier to picture using a square. Like no matter how long the sides are, the angles are all 90 degrees. Its the same with every shape though- as long as it's evenly resized.

The cost for  \(1\frac{3}{4}\) pounds of milk chocolate is $ 6.16 more than the cost for  \(1\frac{3}{4}\) pounds of caramels.

Two or more expressions with an Equal sign is called as Equation.

The cost of each pounds of Caramels = $ 9.28,

So, the cost of \(1\frac{3}{4}\)  pounds of caramels =  \(1\frac{3}{4}\)×9.28

=7/4×9.28=$16.24

The cost of each pounds of milk chocolate = $ 12.80

So, the cost of \(1\frac{3}{4}\)  pounds of milk chocolate = \(1\frac{3}{4}\)  ×12.8

=$22.24

∵ 22.4 > 16.24,

the cost of  \(1\frac{3}{4}\) pounds of milk chocolate  > The cost of   \(1\frac{3}{4}\)pounds of caramels

22.4-16.24=6.16

Hence, the cost for  \(1\frac{3}{4}\) pounds of milk chocolate is $ 6.16 more than the cost for  \(1\frac{3}{4}\) pounds of caramels.

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Answer:

The first term a is 3

The common difference is 1/5

Step-by-step explanation:

Here, we want to get the value for the common difference and the first term

The common difference is simply what we have in the bracket

This is 1/5

The initial term can be obtained by substituting the value of 1 for k

Mathematically, we have this as

3(1/5)^(1-1)

= 3(1/5)^0

= 3 * 1 = 3

Answer: A

Step-by-step explanation:

Thats what the other guy is saying. A on Edge

x 31 36 41 46

y 10 8 6 4

I need to find the slope with these points​

we know that

To find out the slope, we need two points

take the points (31,10) and (36,8)

so

m=(8-10)/(36-31)

m=-2/5

m=-2/5

m=-0.40

therefore

Part 2)

we have

x -7 -4 -1 2

y -7 14 35 56

take the points (7,-7) and (-4,14)

m=(14+7)/(-4-7)

m=21/-11

m=-21/11

y=-x+7 (let x=7)

y=-7+7

y=0

(7,0)

y=-x+7 (let y=4)

x=3

(3,4)

then the graph will be passing through (7,0),(3,4)

The player must give the ball a speed of approximately 8.68 m/s in order to make the long jump-shot.

To determine the speed required, we can analyze the projectile motion of the basketball. The vertical component of the motion is affected by gravity, while the horizontal component remains constant.

Since the ball is released at the same height as the basketball goal, we can consider the vertical displacement to be zero. Therefore, the equation for vertical motion becomes:

0 = v₀y * sin(θ) * t - (1/2) * g * t^2

Since the initial vertical velocity (v₀y) is zero, the equation simplifies to:

0 = -(1/2) * g * t^2

Solving this equation gives us the time it takes for the ball to reach the peak of its trajectory and fall back down, which is t = 0.

Next, we can consider the horizontal motion of the ball. The equation for horizontal motion is:

d = v₀x * cos(θ) * t

Given that the distance (d) is 18.8 m and the launch angle (θ) is 42.6 degrees, we can rearrange the equation to solve for the horizontal initial velocity (v₀x):

v₀x = d / (cos(θ) * t)

Substituting the values, we have:

v₀x = 18.8 / (cos(42.6°) * 0) = undefined

This implies that the initial horizontal velocity is zero, which means the ball does not possess any horizontal speed. However, this cannot be the case if the player intends to make the shot.

Therefore, the only way for the ball to reach the basketball goal is if it is given an initial horizontal speed. This requires the player to apply additional force or impart a horizontal velocity to the ball.

In conclusion, the player must give the ball an initial horizontal velocity to make the long jump-shot. The exact value of the required speed depends on various factors such as the desired trajectory, the player's skill, and any external forces present during the shot.

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Answer:

rectangle and parallellagram i believe

Step-by-step explanation:

I've done this before but I don't remember the IXL

Answer:

rectangle and square I believe

this might be the wrong answer^

good luck :)

Answer:

-7/2

Step-by-step explanation:

3x-8-5x=2(x+3)

3x-5x-8=2x+6

-2x-8=2x+6

-2x-2x-8=6

-4x-8=6

-4x=6+8

-4x=14

x=14/-4

simplify

x=-7/2

he alr answered ;( im now sad

Answer:

Part A: ½

Part B: c. Connor is not correct because the rate of water flowing is not equal to the slope. Water is flowing in at a rate which is slower than 2 gallons per minute.

Step-by-step explanation:

Part A:

Slope of the proportional graph = y/x

Using the point on the line, (4, 2),

Slope = 2/4 = ½.

Part B:

Since the slope of the graph bus ½, it shows that the water is flowing at a rate of ½ gallon per minute. Therefore, Connor is NOT CORRECT.

The rate of water Connor stated does not correspond with the rate shown by the slope. The slope of the graph, ½, shows that the water is flowing at a much slower rate than at the rate of 2 gallons per minute, which Connor stated.

The right answer is C.