The graph of a function h (x) is shown.

What is the average rate of change of h(x) over the interval [4, 8]?
A)-6
B)-2
C)-32
D)-23

a)In a typical week, Maybelle will earn a total of: $600 + $250 = $850

b) Her total earnings for the week would be: $600 + $300 = $900

c)  Her paycheck will be reduced by $100.

d) Her wage earnings should remain the same assuming she still works at least 40 hours per week.

To calculate Maybelle's earnings in a typical week, we first need to determine the minimum number of hours she works. Since she earns $15 per hour for at least 40 hours per week, her minimum wage earnings are:

$15 x 40 = $600

In addition to her wage earnings, Maybelle earns a commission of 10% for each pair of shoes she sells. Since she is expected to sell $2,500 worth of shoes every week, her commission earnings are:

$2,500 x 0.10 = $250

b) If Maybelle sells $3,000 worth of shoes in one week, her commission earnings would be:

$3,000 x 0.10 = $300

On top of her wage earnings of $600 (based on working at least 40 hours at $15 per hour)

c) If customers return $1,000 worth of shoes the next week, Maybelle's commission earnings will not be affected. However, her wage earnings will be reduced by the amount of the returned shoes, which is $1,000 x 0.10 = $100.

d) With an economic downturn and sales slump, Maybelle's earnings from commission will likely decrease since she will sell fewer shoes. However, her total earnings will likely decrease due to the decrease in commission earnings.

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Answer:

-9(x+1) < 12x+9

if you need me to solve it here it is:

-9x - 9 < 12x + 9

     + 9           +9

-9x      < 12x + 18

-12x       -12x

-18x     <          18

(divide by -18 on both sides)

x < - 1

Therefore, any number is that is greater than -1 will work for this inequality.

Hope this helps!

The solution to the system of equations is x = 1 and y = -3.

To solve the system of equations using the substitution or elimination method, let's start with the substitution method.

Given equations:

y = 4x - 7

4x + 2y = -2

We'll solve equation 1) for y and substitute it into equation 2):

Substituting y from equation 1) into equation 2):

4x + 2(4x - 7) = -2

4x + 8x - 14 = -2

12x - 14 = -2

Now, we'll solve this equation for x:

12x = -2 + 14

12x = 12

x = 12/12

x = 1

Now that we have the value of x, we can substitute it back into equation 1) to find y:

y = 4(1) - 7

y = 4 - 7

y = -3

Therefore, the solution to the system of equations is x = 1 and y = -3.

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Answer:

Step-by-step explanation:

a) To solve the equation tan θ = 1/√3, we can find the angle whose tangent is 1/√3 by taking the inverse tangent (arctan) of 1/√3.

θ = arctan(1/√3)

θ ≈ 30.0°

Therefore, the angle in standard position that satisfies tan θ = 1/√3 is approximately 30.0°.

b) To solve the equation 2cos θ = √3, we can isolate the cosine term by dividing both sides of the equation by 2.

cos θ = √3 / 2

Now, we can find the angle whose cosine is √3/2 by taking the inverse cosine (arccos) of √3/2.

θ = arccos(√3/2)

θ ≈ 30.0°

Therefore, the angle in standard position that satisfies 2cos θ = √3 is approximately 30.0°.

The best measure of center of the data is (a) mean; because the data are close together

From the question, we have the following parameters that can be used in our computation:

The dataset of 10 values

Where we can see that there are no outliers present in the dataset

By definition, outliers are extreme values.

Since there are no outliers, it means that the mean is the best measure of center

This is because the mean is affected by the presence of outliers and since no outlier is present, we use the mean

From the list of options, we have the mean value to be 42.536

Hence, the true statement is (a)

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The true statement about the transformation is that the second trapezoid is a dilation of the first trapezoid with a scale factor of 2.

The given transformation involves two trapezoids with identical angle measures but different side lengths. Let's analyze the two trapezoids and determine the statement that is true about the transformation.

First Trapezoid:

Side lengths: 4, 2, 6, 2

Second Trapezoid:

Side lengths: 8, 4, 12, 4

To determine the relationship between the side lengths of the two trapezoids, we can compare the corresponding sides.

Comparing the corresponding sides:

4 / 8 = 2 / 4 = 6 / 12 = 2 / 4

We can observe that the corresponding sides of the two trapezoids have the same ratio. This indicates that the side lengths of the second trapezoid are twice the lengths of the corresponding sides of the first trapezoid. Therefore, the statement that is true about the transformation is:

The second trapezoid is a dilation of the first trapezoid with a scale factor of 2.

A dilation is a type of transformation that produces an image that is the same shape as the original figure but a different size. In this case, the second trapezoid is obtained by scaling up the first trapezoid by a factor of 2 in all directions.

This transformation preserves the shape and angle measures of the trapezoid but changes its size. The corresponding sides of the second trapezoid are twice as long as the corresponding sides of the first trapezoid.

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Step-by-step explanation:

To find a system with the same solution as the given system, we can multiply both sides of both equations by a nonzero constant, which will result in a system that is equivalent to the original one.

For example, let's multiply the first equation by 2 and the second equation by 3:

First equation (multiplied by 2):

6x + 4y = -10

Second equation (multiplied by 3):

6x + 9y = 15

The new system of equations is:

6x + 4y = -10

6x + 9y = 15

This system has the same solution as the original system because it's just a scalar multiple of the original system.

Answer:

x=8

Step-by-step explanation:

This is a triangle, all 3 angles should add up to 180 degrees. Since we already have an angle at 69 degrees (nice), and we know that this is an isosceles triangle, we can put it as 9y-3 = 69

9y = 72, y=8

Now, you know that two angles both have angles of 69, add it up and subtract it from 180. This gives a 42-degree angle of angle B. Make its equation equal to 42 degrees.

42 = 5x+2

40 = 5x

x=8

Hope this helps!

The functions y₁(t) = e^ãt cos(μt) and y₂(t) = e^ãt sin(μt) are a fundamental set of solutions because they are linearly independent and satisfy the given homogeneous linear differential equation, allowing for the formation of the general solution.

To show that y₁(t) = e^ãt cos(μt) and y₂(t) = e^ãt sin(μt) are a fundamental set of solutions, we need to demonstrate two things: linear independence and satisfaction of the given homogeneous linear differential equation.

First, let's consider linear independence. We can prove it by showing that there is no constant c₁ and c₂, not both zero, such that c₁y₁(t) + c₂y₂(t) = 0 for all t.

Now, let's verify that y₁(t) and y₂(t) satisfy the homogeneous linear differential equation. If the given differential equation is of the form ay''(t) + by'(t) + cy(t) = 0, we can substitute y₁(t) and y₂(t) into the equation and verify that it holds true.

Once we have established linear independence and satisfaction of the differential equation, we can state that the general solution to the homogeneous linear differential equation is given by y(t) = c₁y₁(t) + c₂y₂(t), where c₁ and c₂ are arbitrary constants. This general solution represents the linear combination of the fundamental set of solutions.

In summary, y₁(t) = e^ãt cos(μt) and y₂(t) = e^ãt sin(μt) form a fundamental set of solutions for the given differential equation, and the general solution is given by y(t) = c₁y₁(t) + c₂y₂(t).

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The calculated value of m in the triangular prism is 13

From the question, we have the following parameters that can be used in our computation:

The triangular prism

Where, we have

Volume = 1170

The volume of the triangular prism is calculated as

Volume = Base area * Height

So, we have

1/2 * m * 18 * 10 = 1170

Evaluate the products

This gives

90m = 1170

So, we have

m = 13

Hence, the value of m is 13

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The percentage of profit on a $1200 investment resulting in a $350 profit is 29.17%.

The percentage of profit on a $1200 investment that results in a $350 profit can be calculated using the formula:

Percentage of profit = (Profit / Investment) x 100

In this case, the profit is $350 and the investment is $1200. Plugging these values into the formula:

PercThe percentage of profit on a $1200 investment that results in a $350 profit can be calculated using the formula:

Percentage of profit = (Profit / Investment) x 100

In this case, the profit is $350 and the investment is $1200. Plugging these values into the formula:

Percentage of profit = (350 / 1200) x 100

Calculating this expression gives us:

Percentage of profit = 0.2917 x 100 = 29.17%

Therefore, the percentage of profit on a $1200 investment resulting in a $350 profit is 29.17%.

To calculate the percentage of profit, we divide the profit by the investment and then multiply by 100 to express it as a percentage. In this case, the profit is $350 and the investment is $1200. Dividing $350 by $1200 gives us 0.2917. Multiplying this by 100 gives us 29.17%. This means that the profit of $350 represents 29.17% of the initial investment of $1200.entage of profit = (350 / 1200) x 100

Calculating this expression gives us:

Percentage of profit = 0.2917 x 100 = 29.17%

Therefore, the percentage of profit on a $1200 investment resulting in a $350 profit is 29.17%.

To calculate the percentage of profit, we divide the profit by the investment and then multiply by 100 to express it as a percentage. In this case, the profit is $350 and the investment is $1200. Dividing $350 by $1200 gives us 0.2917.

Multiplying this by 100 gives us 29.17%. This means that the profit of $350 represents 29.17% of the initial investment of $1200.

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Answer:

It's A and B: Opposite sides are parallel and Corresponding parts of congruent triangles are congruent.

Step-by-step explanation:

El movimiento en línea recta se refiere al desplazamiento de un objeto en una trayectoria rectilínea, es decir, sin cambios de dirección.

En este tipo de movimiento, la velocidad y la aceleración del objeto pueden variar, pero su dirección se mantiene constante a lo largo del recorrido.

El movimiento en línea recta puede ser uniforme o no uniforme. En el caso del movimiento uniforme, la velocidad del objeto es constante, lo que implica que el desplazamiento realizado en intervalos iguales de tiempo es también constante.

Por otro lado, en el movimiento no uniforme, la velocidad cambia a lo largo del tiempo, resultando en diferentes desplazamientos en intervalos de tiempo iguales.

La descripción matemática del movimiento en línea recta se basa en conceptos como la posición, la velocidad y la aceleración. La posición se refiere a la ubicación del objeto en relación a un punto de referencia, la velocidad representa la tasa de cambio de la posición y la aceleración indica la tasa de cambio de la velocidad.

El estudio del movimiento en línea recta es fundamental en la física y tiene aplicaciones en diversas áreas, como la mecánica, la cinemática, la dinámica y la física de partículas.

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The equation is y = 7.75x, where x is the number of hours Steven babysits and y is the amount he charges.

To represent the relationship between the number of hours Steven babysits (x) and the amount he charges (y), we can use a linear equation in the form of y = mx + b, where m is the slope and b is the y-intercept.

From the given information, we can identify two data points:

(4, 31.00) and (8, 62.00)

Using these points, we can calculate the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)

m = (62.00 - 31.00) / (8 - 4)

m = 31.00 / 4

m = 7.75

Now, we can substitute one of the points and the slope into the equation to find the y-intercept (b).

Using the point (4, 31.00):

31.00 = 7.75(4) + b

31.00 = 31.00 + b

b = 0

Therefore, the equation that represents the relationship between the number of hours Steven babysits (x) and the amount he charges (y) is:

y = 7.75x

The equation is y = 7.75x, where x is the number of hours Steven babysits and y is the amount he charges.

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Step-by-step explanation:

a. f(g(0)) = f(0^2 - 2) = f(-2) = -2 + 3 = 1

b. g(f(0)) = g(0+3) = g(3) = 3^2 - 2 = 7

c. f(g(x)) = g(x) + 3 = x^2 - 2 + 3 = x^2 + 1

d. g(f(x)) = f(x)^2 - 2 = (x+3)^2 - 2 = x^2 + 6x + 7

e. f(f(-2)) = f(-2+3) = f(1) = 1+3 = 4

f. g(g(4)) = g(4^2 - 2) = g(14) = 14^2 - 2 = 194

g. f(f(x)) = f(x+3) = (x+3)+3 = x+6

h. g(g(x)) = g(x^2 - 2) = (x^2 - 2)^2 -2 = x^4 - 4x^2 + 2

The estimated population of the state in the year 2022 is 19,280,700 people.

The given equation represents the population of a certain state as a function of time, where p is the population in thousands of people and t is the number of years since 2010.

The equation is given as p = 80.7t + 18,312.3.

To estimate the population of the state, we substitute the value of t into the equation. For example, if we want to estimate the population in the year 2022 (12 years since 2010), we substitute t = 12 into the equation:

p = 80.7(12) + 18,312.3

= 968.4 + 18,312.3

= 19,280.7.

The estimated population of the state in the year 2022 is 19,280,700 people.

We can estimate the population for any given year by substituting the corresponding value of t into the equation.

It's important to note that the population is given in thousands of people, so we multiply the final result by 1,000 to obtain the population in actual numbers.

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The conditions that prove that the triangles ΔABC and ΔXYZ are similar, ΔABC ~ ΔXYZ, based on the order of the lettering are;

BA/YX = BC/YZ = AC/XZ

AC/XZ = BA/YX, ∠A ≅ ∠C

Similar triangles are triangles that have the same shape (the same two or all three interior angles in each triangle) but in which may have different sizes.

Triangles are similar if they equivalent ratio for their sides and and if the angles in each triangle are congruent to the angles in the other triangle

Therefore, the conditions that indicates that two triangles are that one triangle is a scaled image of the other triangle, therefore, the ratio of the corresponding sides of the triangles are equivalent, which indicates;

ΔABC is similar to ΔXYZ if we get;

A condition that indicates that two triangle are similar is the Side Angle Side, SAS, similarity postulate, which states that two triangles are congruent if the ratio of two corresponding sides are equivalent and the angle between the two sides in the two triangles are congruent, therefore;

ΔABC is similar to ΔXYZ if we get;

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The x-intercepts of the function y = (x-5)(x+3) are 5 and -3.

To find the x-intercepts of the function y = (x-5)(x+3), we need to set y equal to zero and solve for x.

The x-intercepts are the values of x where the graph of the function intersects or crosses the x-axis.

Set y = 0:

0 = (x-5)(x+3)

Apply the zero-product property:

The product of two factors is equal to zero if and only if at least one of the factors is equal to zero.

Therefore, we can set each factor equal to zero and solve for x.

Setting x-5 = 0:

x - 5 = 0

x = 5

Setting x+3 = 0:

x + 3 = 0

x = -3.

The x-intercepts of the function y = (x-5)(x+3) are x = 5 and x = -3.

These are the values of x where the graph of the function crosses the x-axis.

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If the graph of [tex]f(x) = 4e^{0.1x}[/tex] is blue, then the graph of [tex]f(x) = 4(1 + \frac{0.1}{0.5} )e^{0.5x}[/tex] is green.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

[tex]f(x)=a(b)^x[/tex]

Where:

Assuming x = 10, the output value of [tex]f(x) = 4e^{0.1x}[/tex] is given by;

[tex]f(x) = 4e^{0.1x}\\\\f(10) = 4e^{0.1\times 10}[/tex]

f(10) = 10.872

[tex]f(x) = 4(1 + \frac{0.1}{0.5} )e^{0.5x}\\\\f(10) = 4(1 + \frac{0.1}{0.5} )e^{0.5 \times 10}[/tex]

f(10) = 9.9533

Therefore, the green graph most likely represents [tex]f(x) = 4(1 + \frac{0.1}{0.5} )e^{0.5x}[/tex] .

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Answer:

Step-by-step explanation:

Answer:

We can construct only one triangle with the given description(this triangle is unique).

It is isosceles so the two sides are congruent(

4

4 cm) each. The angle they form is specified

80

°

80° so there is no way to construct one more with the same characteristics(we will have to change the angle or the length of the two sides).

Step-by-step explanation:

Answer:

One triangle

Step-by-step explanation:

By the Law of Cosines, given two side lengths of 3 inches and an included angle of 20°, then we are able to get the length of the third side using the formula [tex]a^2=b^2+c^2+2bc\cos(A)[/tex]

Hence, you can construct only one triangle because of SAS Theorem.

Answer:

Relative maximum at x=0; Relative minimum at x=8/3

Step-by-step explanation:

To find the relative maximums and the relative minimums, you must first find the first derivative of the function. The first derivative of this function is 6x^2-16x. Simply it and you get 2x(3x-8). X would be equal to 0 and 8/3. Next, make a number line where you put 0 and 8/3 have a value of zero.

        +                           -                                 +      

-------------------0----------------------------8/3-----------------------

Plug in a value of x<0 to get the region left of 0. Say we use -1, we get -2(-3-8), which is positive, meaning that it is increasing there. From 0 to 8/3, if we use 1, we get 2(3-8), which is decreasing. If we use 3, we get 6(9-8), which is increasing. From this, we can see that when x=0, the graph has a relative maximum. When x=8/3, the graph has a relative minimum.

Answer:

This is an equation of a parabola.

[tex](y+6)^2=4(x+1)[/tex]

Step-by-step explanation:

A conic section is a curve obtained by the intersection of a plane and a cone. The three major conic sections are parabola, hyperbola and ellipse (the circle is a special type of ellipse).

The standard equations for hyperbolas and ellipses all include x² and y² terms. The standard equation for a parabola includes the square of only one of the two variables.

Therefore, the equation y² - 4x + 12y + 32 = 0 represents a parabola, as there is no x² term.

As the y-variable is squared, the parabola is horizontal (sideways), and has an axis of symmetry parallel to the x-axis.

The conic form of a sideways parabola is:

[tex]\boxed{(y-k)^2=4p(x-h)}[/tex]

where:

To write the given equation in conic form, we need to complete the square for the y-variable.

Rearrange the equation so that the y-terms are on the left side:

[tex]y^2 + 12y = 4x - 32[/tex]

Add the square of half the coefficient of the y-term to both sides of the equation:

[tex]y^2 + 12y+\left(\dfrac{-12}{2}\right)^2 = 4x - 32+\left(\dfrac{-12}{2}\right)^2[/tex]

    [tex]y^2 + 12y+\left(-6\right)^2 = 4x - 32+\left(-6\right)^2[/tex]

         [tex]y^2 + 12y+36 = 4x - 32+36[/tex]

         [tex]y^2 + 12y+36 = 4x +4[/tex]

Factor the perfect square trinomial on the left side of the equation:

[tex](y+6)^2=4x+4[/tex]

Factor out the coefficient of the x-term from the right side of the equation:

[tex](y+6)^2=4(x+1)[/tex]

Therefore, the equation of the given conic section in conic form is:

[tex]\boxed{(y+6)^2=4(x+1)}[/tex]

where:

The conic section of the equation y² - 9x + 12y + 32 = 0 is a parabola

The given equation is

y² - 9x + 12y + 32 = 0

The above equation is an illustration of a parabola equation

The standard form of a parabola is

(x - h)² = 4a(y - k)²

Where

(h, k) is the center

While the general form of the equation is

Ax² + Dx + Ey + F = 0

In this case, the equation y² - 9x + 12y + 32 = 0 takes the general form

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HI Your answer is 42

I have calculated it you can trust me

Well you have marked right in the pic

PLEASE MARK AS BRAINLIEST

★ Apply Phythagoras Theorem:-

[tex] \sf \longrightarrow \: {(adjacent \: side)}^{2} + {(opposite \: side)}^{2} = {(hypotenuse)}^{2} [/tex]

[tex] \sf \longrightarrow \: {(9)}^{2} + {(opposite \: side)}^{2} = {(17)}^{2} [/tex]

[tex] \sf \longrightarrow \: 81 + {(opposite \: side)}^{2} = {(17)}^{2} [/tex]

[tex] \sf \longrightarrow \: 81 + {(opposite \: side)}^{2} = 289[/tex]

[tex] \sf \longrightarrow \: {(opposite \: side)}^{2} = 289 - 81[/tex]

[tex] \sf \longrightarrow \: {(opposite \: side)}^{2} = 208[/tex]

[tex] \sf \longrightarrow \: opposite \: side= \sqrt{ 208}[/tex]

[tex] \sf \longrightarrow \: opposite \: side=14.422[/tex]

Answer:

There are three main ways to prove that two triangles are congruent using transformations:

1. Congruence by translation: If there is a translation that maps one triangle onto the other, then the triangles are congruent.

2. Congruence by reflection: If there is a line of reflection that maps one triangle onto the other, then the triangles are congruent.

3. Congruence by rotation: If there is a rotation that maps one triangle onto the other, then the triangles are congruent.

In order to use these transformations to prove congruence, you need to show that all corresponding parts (angles and sides) are congruent after the transformation is applied. This can be done either algebraically, using coordinate geometry, or by providing a clear visual representation of the transformations that are applied.

For example, if you want to prove that two triangles, ABC and DEF, are congruent by translation, you need to show that there is a vector that, when added to the coordinates of any point on triangle ABC, produces the coordinates of the corresponding point on triangle DEF. Once you have shown that all three sides and angles are congruent after the translation, you can conclude that the triangles are congruent.

The nurse should administer 4 Lasix 20 mg tablets to the patient to achieve the prescribed dose of 80 mg.

To determine the number of Lasix 20 mg tablets that should be administered to the patient, we need to calculate how many tablets are equivalent to the prescribed dose of 80 mg.

Given that each Lasix tablet contains 20 mg of the medication, we can divide the prescribed dose (80 mg) by the dosage strength of each tablet (20 mg) to find the number of tablets needed.

Number of tablets = Prescribed dose / Dosage strength per tablet

Number of tablets = 80 mg / 20 mg

Number of tablets = 4 tablets

Therefore, the nurse should administer 4 Lasix 20 mg tablets to the patient to achieve the prescribed dose of 80 mg.

It is important to note that this calculation assumes that the Lasix tablets can be divided or split if necessary. However, it is crucial to follow the specific instructions provided by the prescribing physician or consult with a pharmacist if there are any concerns about the appropriate administration of the medication.

Additionally, it is important to consider any additional instructions, such as the frequency and timing of administration, as specified by the physician's order.

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Answer:

The slope of the graphed line is A. -5

Step-by-step explanation:

Since when we move one step in x direction, we move 5 steps downwards in y direction, so, the slope is,

m = y/x

m = -5/1

m = -5

Answer:

H= [4 -1

      4 0]

Step-by-step explanation: