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The formula for f(t) as a sum of Heaviside functions is f(t) = tuc(t) - tuc(t-3) + (2t-3)uc(t-3) - (2t-3)uc(t-4) + 5uc(t-4).

To express f(t) as a sum of Heaviside functions, we break down the function into its respective intervals and use the unit step function or Heaviside function to represent the function in each interval.

f(t) = t, 0 ≤ t ≤ 3

f(t) = 2t - 3, 3 < t ≤ 4

f(t) = 5, 4 < t

Using the Heaviside function uc for the jump at c, we can represent each interval as follows:

f(t) = tuc(t) - tuc(t-3), 0 ≤ t ≤ 3

f(t) = (2t-3)uc(t-3) - (2t-3)uc(t-4), 3 < t ≤ 4

f(t) = 5uc(t-4), 4 < t

Therefore, the formula is f(t) = tuc(t) - tuc(t-3) + (2t-3)uc(t-3) - (2t-3)uc(t-4) + 5uc(t-4)

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Answer:

i have no idea try to use  m a t h w a y

Step-by-step explanation:

Answer:

4) (2)(4)(3.14) = 25.12 m

5) (12)(3.14) = 37.68 ft

6) (2)(2)(3.14) = 12.56 yd

In order to prove the triangles are similar, you have to use SAS, SSS and AA rule.

In triangle, the similarity theorem states that if they have the same ratio of corresponding sides and equal pair of corresponding angles.

Here we have to find the 3 shortcuts to prove the triangles are similar.

According to the similarity theorem, here we have triangle that is similar to other if two pairs of angles are congruent (AA) or if two pairs of sides are proportional and the included angles are congruent whereas if three pairs of sides are proportional (SSS).

Here we must know that the term similarity and congruent are similar terms.

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Well I can't be for sure but I know for a fact its not set IV it's not possible to make a triangle out of all right angles. Set II, well, that isn't right either. You can't make a triangle out of all obtuse angles. Like the right angle one, its not possible you can only use one obtuse or right angle in a triangle other wise it's not going to be a triangle. I'd say go try Set III since that would most likely make an equilateral triangle.

A parallelogram is a four-sided shape with two sets of parallel lines and two pairs of congruent sides. It is formed by combining two congruent trapezoids, which results in a quadrilateral with two pairs of opposite sides that are parallel and equal in length. All four angles of the parallelogram are also equal.

1. Draw the two congruent trapezoids.

2. Line up the two trapezoids, making sure that the corresponding sides are parallel and the same length.

3. Connect the two trapezoids with lines to form the parallelogram.

4. Check that the angles of the parallelogram are all equal, and that the two pairs of opposite sides are parallel and the same length.

A parallelogram is a four-sided shape with two sets of parallel lines and two pairs of congruent sides. To make a parallelogram, two congruent trapezoids are combined. This can be done by lining up the two trapezoids, making sure that the corresponding sides are parallel and the same length. Then, the two trapezoids can be connected with lines to form the parallelogram. It is important to check that the angles of the parallelogram are all equal, and that the two pairs of opposite sides are parallel and the same length. If these criteria are met, then the shape is a parallelogram.

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Answer: (x,y) ---> (-x,-y)

Step-by-step explanation: When rotating an image 180 degrees, you just need to flip your x and y to negatives. Just remember that 180 degrees is the complete opposite direction, and negative numbers are the opposite of positive numbers.

Hope this helps!

Answer:

Fencing = 95.03ft

Step-by-step explanation:

Since there is a path 3 ft wide around the garden, Ross needs to put a fence around the path.

To find that we need to find the circumference of the garden including the path.

Radius of garden =  diameter/2 = 2.5

path = 3ft

new radius =  5.5

circumference = π\(r^{2}\)

circumference = 95.03 ft  

Step-by-step explanation:

When we plug in the values we get

\(f(g(x)) = ({x}^{2} - 3x + 1) - 4 \\ = {x}^{2} - 3x - 3 \)

\(g(f(x)) = {(x - 4)}^{2} - 3(x - 4) + 1\)

\( {x}^{2} - 3x - 3 = {(x - 4)(x - 4)} - 3x + 12 + 1 \\ {x }^{2} - 3x - 3 = {x}^{2} - 8x + 16 - 3x + 13 \\ \\ {x}^{2} - {x}^{2} - 3x + 8x + 3x - 3 - 16 - 13 = 0 \\ 8x - 32 = 0 \\ 8x = 32 \\ \frac{8x}{8} = \frac{32}{8} \\ x = 4\)

The correct system of inequalities to represents this scenario are,

⇒ x² - 2y ≤ 5,000

⇒ 2x + 5y < 1000

A relation by which we can compare two or more mathematical expression is called an inequality.

We have to given that;

The value of a company’s stock is represented by the expression x²- 2y and the company’s purchases are modeled by 2x + 5y.

Here, The company’s goal is to maintain a stock value of at least $5,000.

Hence, We get;

⇒ x² - 2y ≤ 5000

And, keeping the purchases below $1,000.

Hence, We get;

⇒ 2x + 5y < 1,000

Thus, The correct system of inequalities to represents this scenario are,

⇒ x² - 2y ≤ 5,000

⇒ 2x + 5y < 1000

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Answer:

x2 – 2y ≥ 5000

2x + 5y < 1000

Step-by-step explanation:

I got it right on the test.

The maximum difference in radius for 295/75R22.5 trailer tires is 0.625 inches.

The tire size 295/75R22.5 represents certain measurements. The first number, 295, refers to the tire's width in millimeters. The second number, 75, represents the aspect ratio, which is the tire's sidewall height as a percentage of the width. The "R" stands for radial construction, and the number 22.5 denotes the diameter of the wheel in inches.

To calculate the maximum difference in radius, we need to determine the difference between the maximum and minimum radius values within the given tire size. The aspect ratio of 75 indicates that the sidewall height is 75% of the tire's width.

To find the maximum radius, we can calculate:

Maximum Radius = (Width in millimeters * Aspect Ratio / 100) + (Wheel Diameter in inches * 25.4 / 2)

For the given tire size, the maximum radius is:

Maximum Radius = (295 * 75 / 100) + (22.5 * 25.4 / 2) ≈ 388.98 mm

Similarly, we can find the minimum radius by considering the minimum aspect ratio value (in this case, 75) and calculate:

Minimum Radius = (295 * 75 / 100) + (22.5 * 25.4 / 2) ≈ 368.98 mm

The difference in radius between the maximum and minimum values is:

Difference in Radius = Maximum Radius - Minimum Radius ≈ 388.98 mm - 368.98 mm ≈ 20 mm

Converting this to inches, we have:

Difference in Radius ≈ 20 mm * 0.03937 ≈ 0.7874 inches

Therefore, the maximum difference in radius for 295/75R22.5 trailer tires is approximately 0.7874 inches, which can be rounded to 0.625 inches.

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L = k/f, where k is the variational constant, is the formula for the inverse variation.

A mathematical relationship between two variables in which they vary in opposing directions is referred to as an inverse proportion, also known as an inverse relationship. When one variable increases while the other decreases, this is known as having inverse proportions.

Using the variables length of violin 'l' and frequency of vibration 'f'

If the length of violin 'l' is inversely proportional to the frequency of vibration 'f', this is expressed as:

l α 1/f

l = k/f

Hence the formula for the inverse variation is l = k/f where k is the constant of variation.

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Answer:

2x4 - 50

STEP

2

:

STEP

3

:

Pulling out like terms

3.1 Pull out like factors :

2x4 - 50 = 2 • (x4 - 25)

Trying to factor as a Difference of Squares:

3.2 Factoring: x4 - 25

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 25 is the square of 5

Check : x4 is the square of x2

Factorization is : (x2 + 5) • (x2 - 5)

Gursoy's purchase level should be 0.3.

According to the given data, we have the following:

Mean demand, μ = 100

Standard deviation, σ = 30

Purchase price = $10

Selling price = $25

Hence, Cost of under-ordering, Cu = $25 - $10 =$15

Cost of over-ordering, Co = $10 + $25 =$35

Therefore, the calculation of optimal purchase level is calculated as follows:

purchase level = Cu / (Cu + Co)

purchase level = $15 / ($15 + $35)

purchase level = $15 / $50

purchase level = 0.3

The purchase level would be 0.3.

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Answer: \(y-2=3(x-4)\\y=3x-12+2\\-3x+y=-10\\3x-y=10\)

Step-by-step explanation:

I showed the steps to find the equation. In case you need to know, I used point-slope form, which involves using the formula y-y1=m(x-x1), in which you use a point like (4,2) and the slope, which we know is 3x since it's parallel to the original line. Simplifying and bringing it to standard form such as Ax+By=C. Ax has to be positive, which is why -3x went to positive, and y and -10 switched signs.

Answer:

126 blue marbles, 24 white marbles

Step-by-step explanation:

The ratio of blue marbles to white marbles is 21 to 4. From this, we have this equation:

\(21x + 4x = 150\)

\(25x = 150\)

\(x = 6\)

So we have 21 × 6 = 126 blue marbles and 4 × 6 = 24 blue marbles.

126/24 = 21/4

Answer:

Step-by-step explanation:

From a hot-air balloon, Violet measures a 24

∘

∘

 angle of depression to a landmark that’s 806 feet away, measuring horizontally. What’s the balloon’s vertical distance above the ground? Round your answer to the nearest tenth of a foot if necessary.

Answer:

Area = 200ft²

Step-by-step explanation:

Perimeter of a rectangle = 2(length+width)

Area of a rectangle = length * width

Then:

g = 2w           Eq. 1

60 = 2(g+w)   Eq. 2

g = length

w = width

From Eq. 2

60 = 2g + 2w

60 - 2g = 2w      Eq. 3

matching Eq. 1 and Eq. 3

g = 60 - 2g

g + 2g = 60

3g = 60

g = 60/3

g = 20 ft

From Eq. 1

g = 2w

20 = 2w

20/2 = w

w = 10 ft

Area

area = length * width

area = 20ft * 10 ft

area = 200ft²

Answer:

No solution

Step by Step Explaination:

Answer:

No solutions

Step-by-step explanation:

5(x - 3) = 7x - 2(x + 1)

5x - 15 = 7x - 2x - 2

5x - 15 = 5x - 2

-15 = -2 (not true so it’s no solution)

Hope this helps! Pls give brainliest!

Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

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Answer:

200

Step-by-step explanation:

I put the numbers in a cross multiply scenario:

So it looks like 25/100 and 50/?

So multiply 50 by 100.

Then divide that by 25!

Happy Halloween!

Answer:

watch the picture

Step-by-step explanation:

sum of all angles = 360°

c = 23° (opposite vertical angles so congruent)

b = (360° - 23 - 23) : 2    (opposite vertical angles so congruent)

b = 314 : 2

b = 157

----------------------

check

23 + 23 + 157 + 157 = 360°

the answer is good

the surface area of the regular pyramid is approximately  \(40sqrt(14) + 43.3 mm^2.\)To find the surface area of a regular pyramid, we need to find the area of each triangular face and add them together, then add the area of the base.

Let's start with finding the area of each triangular face. Since the pyramid is regular, all the triangular faces will be congruent, so we just need to find the area of one.

We know that the base of the triangle is 10 mm, and the height of the triangle is half the distance between the apex (the point at the top of the pyramid) and the base. Since the pyramid is regular, the apex is directly above the center of the base.

The height of the pyramid can be found using the Pythagorean theorem, where the height of the pyramid (h) is the hypotenuse of a right triangle with the base (b) and half the slant height (s) as the legs.

\(s^2 = hr^2 - (b/2)^2\)

We know the base is 10 mm and the height of the big triangle is 9 mm, so the half slant height is:

\(s = sqrt(h^2 - (b/2)^2) = sqrt(9^2 - (10/2)^2) = sqrt(81 - 25) = sqrt(56) = 2sqrt(14)\)

Now we can find the area of one triangular face using the formula:

Area = 1/2 x base x height

Area = 1/2 x 10 mm x 2sqrt(14) mm = \(10sqrt(14) mm^2\)

Since there are four triangular faces, the total area of the triangular faces is:

4 x 10sqrt(14) mm{power}2 = \(40sqrt(14) mm^2\)

Finally, we need to add the area of the base, which we know is 43.3 \(mm^2.\)

So the total surface area of the pyramid is:

\(Surface Area = 40sqrt(14) mm^2 + 43.3 mm^2 = 40sqrt(14) mm^2 + 43.3 mm^2 = 40sqrt(14) + 43.3 mm^2\)

Therefore, the surface area of the regular pyramid is approximately \(40sqrt(14) + 43.3 mm^2.\)

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The equation that can be used to solve for c in the given right triangle is the sine function: c = (3 meters) / sin(50°).

In the given right triangle ABC, we are given that angle ACB is a right angle (90°) and angle CBA is 50°. We also know the length of side AC, which is 3 meters. The length of side CB is denoted by "a," and the length of the hypotenuse AB is denoted by "c." To solve for c, we can use the trigonometric function sine (sin). In a right triangle, the sine of an acute angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, we can use the sine of angle CBA (50°) to find the ratio between side CB (a) and the hypotenuse AB (c).

The equation c = (3 meters) / sin(50°) represents this relationship. By dividing the length of side AC (3 meters) by the sine of angle CBA (50°), we can find the length of the hypotenuse AB (c) in meters. Using the given equation, we can calculate the value of c by evaluating the sine of 50° (approximately 0.766) and dividing 3 meters by this value. The resulting value will give us the length of the hypotenuse AB, completing the solution for the right triangle.

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When Tracey pours all the water from the smaller 5-inch cube container into the larger 7-inch cube container, the water will be approximately 7 inches deep in the larger container.

To find out how deep the water will be in the larger container, we need to consider the volume of water transferred from the smaller container. Since both containers are cube-shaped, the volume of each container is equal to the length of one side cubed.

The volume of the smaller container is 5 inches * 5 inches * 5 inches = 125 cubic inches.

When Tracey pours all the water from the smaller container into the larger container, the water completely fills the larger container. The volume of the larger container is 7 inches * 7 inches * 7 inches = 343 cubic inches.

Since the water fills the larger container completely, the depth of the water in the larger container will be equal to the height of the larger container. Since all sides of the larger container have the same length, the height of the larger container is 7 inches.

Therefore, the water will be approximately 7 inches deep in the larger container.

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23.4 is  8.125 percentage of 288.

Percentage is defined as "out of 100." Similar to fractions and decimals, percentages are used in mathematics to represent subsets of a whole. When expressing a sum as a percentage, 100 equal components are regarded to make up the whole. A percentage can be shown by the symbol % or, less frequently, by the abbreviation 'pct'.

1. Since 288 is the output value of the task, we assume that it is 100%.

2. We make the assumption that the value we are looking for is x.

3. If 100% = 288 then we can express that as 100% = 288.

4. Since we already know that the output result of x% equals 23.4, we can write it down as x%=23.4.

5. We now have two straightforward equations:

1) 100%=288

2) x%=23.4 where both of their right sides and left sides have the same units, allowing us to write something like this: 100%/x%=288/23.4

6. All that is left for us to do is solve the straightforward equation, and we will have our answer.

7. Calculate 23.4 as a percentage of 288.

100%/x%=288/23.4

We multiply both sides of the equation by x 100=12.307692307692 to get *x=(288/23.4)*x.

*x - we get x 100/12.307692307692=x 8.125=x by dividing both sides of the equation by (12.307692307692) to get x=8.125.

23.4 is  8.125 percentage of 288.

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The maximum purchase price per unit of the component that Ms. Alexander should negotiate with her supplier is $19.00, which is equal to the variable cost per unit to manufacture the part in-house.

In this scenario, Ms. Alexander needs to determine the maximum price per unit that she should be willing to pay the supplier for the component. She conducted a cost analysis and found that manufacturing the part in-house would require $450,000 in capital equipment and have a variable cost of $19.00 per unit.

Since there is no fixed cost associated with purchasing the component from the supplier, the maximum purchase price per unit should not exceed the variable cost per unit of manufacturing in-house. This ensures that the company does not incur additional costs by outsourcing the component.

Therefore, Ms. Alexander should negotiate a price with the supplier that is equal to or lower than the variable cost per unit, which is $19.00. By doing so, the company can avoid the initial capital investment and ongoing variable costs associated with in-house production, making it more cost-effective to purchase the component from the supplier.

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