Evaluate f(x) = 1/4x
for x = -5.

A. 20
B. -1/20
C. -1 1/4
D. -4/5

Answer:

True

Step-by-step explanation:

Complementary means they should sum to 90 degrees

34+56=90

Answer:

True

Step-by-step explanation:

Complementary angles are angles that add to 90 degrees, or a right angle.

If the two angles are complementary, then they will add to 90 degrees.

One angle is 34°, and it's complement is 56°.

Add the angles.

34°+56°

90°

Since they add to 90 degrees, they are complementary angles. Therefore, the statement is true.

Answer: b = 11.62

Step-by-step explanation:

We can use this formula to solve for b:

\(b^{2} =\) \(\sqrt{c^{2}-a^{2} }\)

\(b^{2} =\) \(\sqrt{12^{2}-3^2 }\)

\(b^2= \sqrt{144-9}\)

= 11.61895004

We can round that to 11.62.

Hope this helped!

The graph of h(x) = (x-1)^2 - 9 is a U-shaped parabola that opens upwards, with the vertex at (1, -9), and it extends indefinitely in both directions.

The function h(x) = (x-1)^2 - 9 represents a quadratic equation. Let's analyze the different components of the equation to understand the behavior of the graph.

The term (x-1)^2 represents a quadratic term. It indicates that the graph will have a parabolic shape. The coefficient in front of the quadratic term (1) implies that the parabola opens upwards.

The constant term -9 shifts the graph downward by 9 units. This means the vertex of the parabola will be at the point (1, -9).

Based on this information, we can draw the following conclusions:

The graph will be a U-shaped curve with the vertex at (1, -9).

The vertex represents the minimum point of the parabola since it opens upward.

The parabola will be symmetric with respect to the vertical line x = 1 since the coefficient of the quadratic term is positive.

The graph will extend indefinitely in both directions.

To accurately plot the graph, you can choose several x-values, substitute them into the equation to find the corresponding y-values, and then plot the points on the graph. Alternatively, you can use graphing software or calculators that can plot the graph of the equation for you.

Remember to label the axes and indicate the vertex at (1, -9) to provide a complete representation of the graph of h(x) = (x-1)^2 - 9.

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Answer:y=3/8+/7/8x

Step-by-step explanation:

The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

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Answer:

6x2-10x-4

Step-by-step explanation:

hx=(2x-4)(3x+1)

hx=2x(3x+1)-4(3x+1)

hx=6x2+2x-12x-4

hx=6x2-10x-4

Answer:

-3/7

Step-by-step explanation:

It is asking to find the slope of the secant line going through points (2,f(2)) and (9,f(9)).

We must find f(2) by looking at the curve at x=2. We should see that y=2 there so f(2)=2.

We must find f(9) by looking at the curve at x=9. We should see that y=-1 there so f(9)=-1.

The slope of a line is calculated by finding the ratio of the change of y to the change of x.

(-1-2)/(9-2)

(-3)/(7)

-3/7

Answer: 5(3n+4r)

Step-by-step explanation:You need to find the gcf/factor .So the gcf of 15 and 20 is 5.So know that you know the gcf ,you divide 15n by 5 which gives you 3n and divide 20r by5 which gives you 4r.Now the last thing you do is,take the GCF which is 5 and place a Parentheses and take 3n and 4r and add them together.

So you get 5(3n+4r) as your expression that  is equivalent to  15n + 20r .

Hope it helps . :)

The total number of rabbits bought by Doña Rose for your farm is 4 times the Number of given rabbits.

The number of rabbits bought by Doña Rose for your farm, we need to consider that the given rabbits represent only a quarter of the total number.

the total number of rabbits as 'x'. According to the information, the given rabbits represent a quarter of 'x', which can be expressed as:

Given rabbits = (1/4) * x

To find the value of 'x', we can multiply both sides of the equation by 4

4 * Given rabbits = x

Therefore, the total number of rabbits bought by Doña Rose for your farm is 4 times the number of given rabbits.

the exact value of 'x'. However, we can state that the total number of rabbits bought is four times the number of the given rabbits.

So, if the given rabbits represent 'n' in quantity, the total number of rabbits bought would be 4n.

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The given differential equation:

y''' − 2y'' + y' = 2 − 24ex + 40e5x,

y(0) = 1/2, y'(0) = 5/2, y''(0) = −11/2

Therefore, the next solution is 13/2

Differential Equation:

In mathematics, a differential equation is an equation relating one or more unknown functions to their derivatives. In applications, functions usually represent physical quantities, derivatives represent rates of change, and differential equations define the relationship between them. These relationships are common.

Now,

Given differential equation is

y''' - 2y'' +y' = 2- 24eˣ +40e⁵ˣ                 ------------ (1)

Auxiliary equation is m³ - 2m² +2m = 0

Now,

   m(m² - 2m +2) = 0

⇒ m(m-1)² = 0

Therefore, m = 0,1,1

Therefore,

\(y_{c} = c_{1}+ c_{2} e^{x} + c_{2}x e^{x}\)

Now, we have to find the particular solution by method of undetermined coefficient.

   \(y'_{y} = a + b(x^{2} e^{x} +2xe^{x} ) +5ce^{x}\)

⇒ \(y''_{p} = a + bx^{2} e^{x} +2bxe^{x} +5ce^{x}\)

⇒ \(y''_{p} = b(x^{2} e^{x} +2xe^{x}) + 2b(ex^{x}+ e^{x} +25ce^{x}\)

⇒ \(y'''_{p} = bx^{2} e^{x} +6bxe^{x} +6be^{x} +125ce^{5x}\)

Putting these values in differential equation (1), we get:

y'''(0) = 13/2

Complete Question:

Solve the given initial-value problem. y''' ? 2y'' + y' = 2 ? 24ex + 40e5x, y(0) = 1 2 , y'(0) = 5/ 2 , y''(0) = ? 13/ 2

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Answer:

\(18x^{2} + 24x+8\)

Step-by-step explanation:

To find the height of the shuttle, we can use trigonometry and the concept of similar triangles. The height of the shuttle is approximately 468.675 meters.

Let's assume that the height of the shuttle is represented by 'h' meters. From the information given, we know that the distance between the camera and the launch pad is 750 meters, and the angle of elevation from the camera to the shuttle is 32 degrees.

Using trigonometry, we can set up the following equation:

tan(32°) = h / 750

To find the value of h, we can rearrange the equation:

h = tan(32°) * 750

Using a calculator, we can find the value of tan(32°) ≈ 0.6249.

Now we can calculate the height of the shuttle:

h ≈ 0.6249 * 750

h ≈ 468.675 meters

Therefore, the height of the shuttle is approximately 468.675 meters.

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Answer:

Step-by-step explanation:

Slope of the line:

\(m = \frac{y-y1}{x-x1} \\\)

Given:

slope = -3/4

point (x1,y1) = (2, -1)

Substitute and solve

\(m = \frac{y-y1}{x-x1} \\-\frac{3}{4} = \frac{y-(-1))}{x-2} \\-3(x-2) = 4(y+1)\\-3x + 6 = 4y + 4 \\Transpose\\4y = -3x + 6 - 4\\4y = -3x + 2 \\y = -3/4x + 2/4\\y = -3/4x + 1/2\\OR\\4y +3x - 2 = 0\)

1/2 is the y-intercept

(0,1/2)

Since we have 2 points already, we can then graph the line.

(2, -1) and (0, 1/2)

The sprinkler waters an area of 225π square feet.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called as the area of the circle.

The area is defined as the space covered in a two-dimensional plane by any object.

If the sprinkler rotates 90°, it will cover one-fourth of a full circle.

The area of a full circle with a radius of 30 feet is:

πr² = π(30 feet)²= 900π square feet

So, the area of one-fourth of a circle with a radius of 30 feet is:

(1/4)πr² = (1/4)π(30 feet)² = (1/4)900π = 225π square feet

Therefore, the sprinkler waters an area of 225π square feet.

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Answer: The number is 14

Step-by-step explanation:

A number is increased by 20:  (X + 20)

Then doubled: 2(X + 20)

5 times the number: 5X

2 less than 5 times the number: 5X - 2

Setting the bold statements equal: 2(X+20) = 5X - 2

Distribute left side: 2X + 40 = 5X - 2

Move X's: 40 = 3X - 2

Move numbers: 42 = 3X

Divide both sides by 3: X = 14

Answer:

Step-by-step explanation:

Answer: y times y 8 times

Apply Exponent Rule

Simplified Form y^8

To write without exponents is basically just writing out y times itself 8 times.

Answer:

5 yards

Step-by-step explanation:

15/3=5

Answer:

The 4th company should receive $100,000 for their part in the project.

Step-by-step explanation:

Let's denote the amount of work completed by the 4th company as x. Then, according to the problem statement:

The 3rd company will complete 4x amount of work.

The 1st company will complete 3 times the amount of work completed by the 3rd company, so it will complete 3(4x) = 12x amount of work.

The 2nd company will complete twice the amount of work completed by the 1st company, so it will complete 2(12x) = 24x amount of work.

Therefore, the total amount of work completed by all four companies is:

x + 4x + 12x + 24x = 41x

We know that the total cost of the project is $4,100,000, so we can set up the following equation based on the proportion of the work completed by each company to the total amount of work:

Cost for 4th company / x = Total cost of project / (41x)

Simplifying this equation, we can solve for the cost for the 4th company:

Cost for 4th company = (x / (41x)) * $4,100,000

= $100,000

Therefore, the 4th company should receive $100,000 for their part in the project.

The amount that the taxpayer is owing in taxes is $2,691.05.

We have,

Income tax payable refers to a business organization's tax liability to the government in the jurisdiction in which it operates. The amount of liability will be determined by the company's profitability over a given time period and the applicable tax rates. Tax payable is considered a current liability rather than a long-term liability because it must be settled within the next 12 months.

Based on the table, we are using the tax rate of 15% for the taxable income of $11,757.

The tax payable will equals to:

= 15%*$11,757 + $927.50

= $1,763.55 + $927.50

= $2,691.05

Hence, The amount that the taxpayer is owing in taxes is $2,691.05.

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complete question:

Based on this table, if someone had a taxable income of $11,757, how much would they owe in taxes?

Answer:

\(\displaystyle{\frac{d}{dx} \int \limits_{2x}^{x^2} t^2+1 \ \text{dt} \ = \ 2x^5-8x^2+2x-2\)

Step-by-step explanation:

\(\displaystyle{\frac{d}{dx} \int \limits_{2x}^{x^2} t^2+1 \ \text{dt} = \ ?\)

We can use Part I of the Fundamental Theorem of Calculus:

Since we have two functions as the limits of integration, we can use one of the properties of integrals; the additivity rule.

The Additivity Rule for Integrals states that:

We can use this backward and break the integral into two parts. We can use any number for "b", but I will use 0 since it tends to make calculations simpler.

We want the variable to be the top limit of integration, so we can use the Order of Integration Rule to rewrite this.

The Order of Integration Rule states that:

We can use this rule to our advantage by flipping the limits of integration on the first integral and adding a negative sign.

Now we can take the derivative of the integrals by using the Fundamental Theorem of Calculus.

When taking the derivative of an integral, we can follow this notation:

For the first term, replace \(\text{t}\) with \(2x\), and apply the chain rule to the function. Do the same for the second term; replace

Simplify the expression by distributing \(2\) and \(2x\) inside their respective parentheses.

Rearrange the terms to be in order from the highest degree to the lowest degree.

This is the derivative of the given integral, and thus the solution to the problem.

Answer:

Step-by-step explanation:

Here are your workings

4.87 x 7.23  simplify

Step 2

(4.87)(7.23)  Add brackets(Optional)

Then you multiply the two exponents to get 35.2101

Your answer would be 35.2101

The slope of a line given the table is equal to 0.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the slope formula, we have the following;

Slope (m) = (9 - 9)/(3 - 1)

Slope (m) = 0/2

Slope (m) = 0.

Based on the table, the slope is the change in y-axis with respect to the x-axis and it is equal to 0.

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Total amount after three years

=  $8.360  

Explanation:

Given -

Principal amount  

p  = $.8,000

Rate of interest  

r  =  1.5%

Duration  

n  =  3 years

Total amount after three years = Principal amount + Interest amount

Total amount after three years

=  p +  (pnr)  = 8000  +  (8000×1.5100×3)  =  8000  +  360  =  $8.360

Total amount after three years

=  $8.360

Answer:

$8.360

Step-by-step explanation:

Answer: 1.2 cups of flour

Step-by-step explanation:

3 cups: 2 batches

2 batches=30 rolls

required is 12 roles

3:30  then x:12

36=30x

x=6/5=1.2

Answer:

Step-by-step explanation:

For 12 people Laura needs 12 rolls:

Answer:

90 costermers

Step-by-step explanation:

2×10=20

9×10=90

The calculated measure of the angle D is (c) 32 degrees

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

The triangles ABC and DEF

The triangles are similar triangles

This means that the corresponding angles are equal

Given that

A = 32 degrees

And the corresponding angle is D

We have

D = 32 degrees

Hence, the measure of the angle is (c) 32 degrees

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