Brad is standing on a hill which places him at the same height as a nearby flagpole. The flagpole is 15 ft. high and Brad is 20 ft. horizontally from the top of the pole. Brad can see the bottom of the flag pole.


What is the length in feet of Brad's "line of sight" to the base of the flagpole?

Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value.

[tex]\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=17 \end{cases}\implies C=2\pi (17)\implies C=34\pi[/tex]

Making linear equations for given scores, Grace scored 51 marks, John scored 47 marks, and Julius scored 52 marks in the examination.

What is a linear equation, exactly?

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a variable, with the degree of each variable being 1. In other words, a linear equation is an equation of a straight line, which can be expressed in the form of y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept of the line. Linear equations are used to model relationships between variables that have a constant rate of change, such as distance traveled over time or cost per item.

Now,

Let's assume that Grace's score is x.

Then, John's score will be x-4.

And, Julius's score will be x-4+5 = x+1.

The sum of their scores is given as 150. So, we can write an equation as:

x + (x-4) + (x+1) = 150

Simplifying the equation, we get:

3x - 3 = 150

Adding 3 to both sides, we get:

3x = 153

Dividing by 3 on both sides, we get:

x = 51

So, Grace's score is x = 51.

John's score is x-4 = 47.

And, Julius's score is x+1 = 52.

Therefore,

                      Grace scored 51 marks, John scored 47 marks, and Julius scored 52 marks in the examination.

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The service's expected profit is $6,800.

What is the basic arithmetic operations?

The four basic mathematical operations are Addition, subtraction, multiplication, and division.

To find the service's expected profit, we need to calculate the total revenue and the total cost, and then subtract the cost from the revenue.

First, let's calculate the total revenue. The service sells maintenance agreements for $75 a year, so for every 100 customers, the revenue will be:

100 customers x $75/customer = $7,500

Now, let's calculate the total cost. We know that 2 in every 100 people who purchase maintenance agreements have air conditioners that need repair, and the average cost of repairing an air conditioner is $350. So for every 100 customers, the cost of repairs will be:

2 customers x $350/customer = $700

Finally, let's calculate the expected profit:

Expected profit = Total revenue - Total cost

Expected profit = $7,500 - $700

Expected profit = $6,800

Hence, the service's expected profit is $6,800.

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Answer: Your welcome!

Step-by-step explanation:

5n / (n + 3) = n - 8

5n = n(n + 3) - 8(n + 3)

5n = n^2 + 3n - 8n - 24

n^2 - 5n - 24 = 0

n = 4 or n = -6

The verbal sentence to represent 5n/n+3=n-8 is "When n is 4 or -6, 5n divided by n plus 3 is equal to n minus 8."

The value of the functions are,

⇒ f (- 10) = 20201

⇒ f (2) = 17

⇒ f (3) = 143

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The value of function is,

⇒ f (x) = 2x⁴ + x² - 10x + 1

Now, We can find all the values as;

At x = - 10;

⇒ f (x) = 2x⁴ + x² - 10x + 1

⇒ f (- 10) = 2 (- 10)⁴ + (- 10)² - 10 (- 10) + 1

⇒ f (- 10) = 20000 + 100 + 100 + 1

⇒ f (- 10) = 20201

At x = 2;

⇒ f (x) = 2x⁴ + x² - 10x + 1

⇒ f (2) = 2 (2)⁴ + (2)² - 10 (2) + 1

⇒ f (2) = 32 + 4 - 20 + 1

⇒ f (2) = 17

At x = 3;

⇒ f (x) = 2x⁴ + x² - 10x + 1

⇒ f (3) = 2 (3)⁴ + (3)² - 10 (3) + 1

⇒ f (3) = 162 + 9 - 30 + 1

⇒ f (3) = 143

Thus, The value of the functions are,

⇒ f (- 10) = 20201

⇒ f (2) = 17

⇒ f (3) = 143

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Using  Remainder Theorem and synthetic division, f(-10) = 191, f(2) = 1, f(3) = 34

What is synthetic division?

A polynomial's coefficients are split one by one in synthetic division.

The split polynomial's zero, which belongs in the box on the far left, has this value.

To use the Remainder Theorem and synthetic division to evaluate f(-10), f(2), and f(3) for the function[tex]f(x)=2x^2+x^2-10x+1[/tex], we can proceed as follows:

First, we need to perform synthetic division using -10, 2, and 3 as the divisors.

1) For f(-10):

The result of the division is 191, so f(-10) = 191.

2) For f(2):

The result of the division is 1, so f(2) = 1.

3) For f(3):

The result of the division is 34, so f(3) = 34.

Therefore, we have:

f(-10) = 191

f(2) = 1

f(3) = 34

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Answer:

- A state fair uses 32 pallets of lemons for lemonade

Step-by-step explanation:

Answer:

30 men

Step-by-step explanation:

7 men x 300 days = 2100 man-days  to build 1 house)

(2100 man-days/house) x (1 house/70 days) = 30 men

In linear equation, $28.75   is the unit price .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                     Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

The cost of 3 scarves is $86.25

   then,

     the unit price is  =    $86.25/3   = $28.75

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Answer:

Step-by-step explanation:

Let's call the number of large bags of popcorn sold "L" and the number of small bags of popcorn sold "S".

We can set up two equations based on the information given:

L + S = 290 (the total number of bags of popcorn sold)

4L + S = 566 (the total revenue from popcorn sales)

We can use substitution or elimination to solve for L and S.

Substitution:

From the first equation, we know that S = 290 - L. We can substitute this into the second equation:

4L + (290 - L) = 566

Simplifying, we get:

3L + 290 = 566

3L = 276

L = 92

Then we can use the first equation to find S:

L + S = 290

92 + S = 290

S = 198

So the movie theater sold 92 large bags of popcorn and 198 small bags of popcorn.

Elimination:

We can eliminate one variable by multiplying one of the equations by a constant to make the coefficients of one of the variables equal but with opposite signs.

In this case, we can multiply the first equation by 4 to make the coefficients of S equal but with opposite signs:

4L + 4S = 1160

4L + S = 566

Subtracting the second equation from the first, we eliminate L:

3S = 594

S = 198

Then we can use either of the original equations to find L:

L + S = 290

L + 198 = 290

L = 92

So the movie theater sold 92 large bags of popcorn and 198 small bags of popcorn.

Answer:

Step-by-step explanation:

[tex]\frac{17}{25}[/tex]

Answer:

The isosceles triangle has three acute angles, meaning that the angles are less than 90°. The sum of three angles of an isosceles triangle is always 180°.

Step-by-step explanation:

We can use the future value formula for an annuity to solve this problem:

FV = PMT * ((1 + r)^n - 1) / r

where:

FV is the future value of the annuity

PMT is the regular payment or deposit

r is the annual interest rate

n is the number of periods (in this case, the number of years)

We want to solve for PMT, so we can rearrange the formula to get:

PMT = FV * r / ((1 + r)^n - 1)

Plugging in the given values, we get:

FV = $80,000

r = 6% = 0.06

n = 15 years

So, the annual deposit required is:

PMT = $80,000 * 0.06 / ((1 + 0.06)^15 - 1) ≈ $3,782.58

Therefore, the man would need to deposit approximately $3,782.58 into the account each year in order to have $80,000 saved up for his granddaughter's college education in 15 years, assuming a 6% return.

Answer:

This type of study would be a comparative study, as it involves comparing the level of academic motivation between college students and their siblings.

Step-by-step explanation:

If a car travels at an average speed of 68 miles per hour, it takes it 5 hours 15 minutes to travel 357 miles.

The average speed is the unit rate.

The average speed is computed as the quotient of the total distance and the total time.

Conversely, the time is a function of the division of the total distance by the average speed.

The total distance traveled by the car = 357 miles

The average speed = 68 miles per hour (mph)

The time = Distance/Average speed = 357/68 = 5.25 hours

= 5 hours 15 minutes.

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It is true that the graph contains the point (0, 0).

The following three assertions regarding the function and its graph are true:

The function's graph resembles a parabola.

The graph begins at the bottom.

The point is shown in the graph (0,0).

Explanation:

A second-degree polynomial function, the quadratic function f(x) = x2 - 5x + 12 has a parabola as its graph.

The parabola widens downward because the coefficient of x2 is positive (1 in this instance).

When we replace x with -10 in the given function, we obtain the value of f(-10) as (-10)2 - 5(-10) + 12 = 82. Hence, "f(-10) = 82" is true.

We substitute x = 20 in the given function, resulting in f(20) = 202 - 5(20) + 12 = 212, to see if the point (20, -8) is on the function's graph. The claim "The graph contains the point (20, -8)" is untrue since the point's y-coordinate is -8, which is not equivalent to f(20).

We substitute x = 0 in the given function to get f(0) = 02 - 5(0) + 12 = 12 to determine if the point (0, 0) is on the function's graph. The assertion "The graph contains the point (0, 0)" is true because the y-coordinate of the point (0, 0) is 0, which is equivalent to f(0).

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Answer:

Step-by-step explanation:

Kelly bought a total of 1500 pencil boxes.

Some numeric values of the exponential function y = 9(3)^x are given as follows:

To obtain the numeric value of a function or of an expression, we substitute each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The function for this problem is given as follows:

y = 9(3)^x.

Hence some numeric values of the function are given as follows:

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Answer:

The answer you're looking for is 7000ml

Step-by-step explanation:

Since there are 1000 millimeters inside a liter we can use the equation
x = 7×1000.
We need to first simplify all terms giving us this equation
x = 7000
With that, we are finished and that's how you do this question.

I hope this was helpful!

Answer:Let's convert hours to minutes:

Now we have:

44 minutes to 300 minutes

We write the ratio as a fraction:

We can reduce both the numerator and denominator by 4, to get:

The correct answer is:

Step-by-step explanation:

The inverse of function is (x + 3)^(1/3) + 2 and the graph is attached below

a) To find the inverse of the function f(x) = (x - 2)^3 - 3, we can follow these steps:

1. Replace f(x) with y: y = (x - 2)^3 - 3

Solve for x in terms of y:

a. Add 3 to both sides: y + 3 = (x - 2)^3

b. Take the cube root of both sides: (y + 3)^(1/3) = x - 2

c. Add 2 to both sides: x = (y + 3)^(1/3) + 2

Replace x with f^-1(x): f^-1(x) = (x + 3)^(1/3) + 2

b) To graph the inverse function f^-1(x), we can use the equation we found in part a) and plot some points:

So we have three points: (0, 3^(1/3) + 2), (1, 2^(1/3) + 2), and (3, 4).

To sketch the graph, we can also note that the function f(x) = (x - 2)^3 - 3 has a vertical asymptote at x = 2 and a local minimum at (2, -3). Therefore, the inverse function f^-1(x) will have a horizontal asymptote at y = 2 and a local maximum at (4, 2).

Combining all of this information, we can sketch the graph of f^-1(x) as shown below:

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Answer: We can use the formula for future value of an annuity to calculate how much will be saved for retirement:

FV = Pmt x (((1 + r)^n - 1) / r)

where:

FV is the future value of the annuity

Pmt is the payment made each period (in this case, the annual profit of $22,000)

r is the annual interest rate (9% or 0.09 as a decimal)

n is the number of periods (7 years)

Substituting the given values into the formula, we get:

FV = $22,000 x (((1 + 0.09)^7 - 1) / 0.09)

FV = $22,000 x (1.9904 / 0.09)

FV = $22,000 x 22.116

FV = $485,552

Therefore, the amount saved for retirement after 7 years will be $485,552.

Step-by-step explanation:

Answer:

x ≤ 6.8

Step-by-step explanation:

1.25x + 6.50 ≤ 15

1.25x ≤ 8.5

x ≤ 6.8

So, the answer is x ≤ 6.8

Answer:

Below

Step-by-step explanation:

1.25x + 6.50 <= 15     SUBTRACT 6.50 from both sides of the equation

  1.25x ≤ 8.50            DIVIDE both sides by 1.25

         x ≤ 6.8

As the temperature of the pan increases, the heat transfer from the butter to the pan increases, causing the butter to melt faster. Ultimately, this heat transfer is necessary for Luke to prepare his food. Without it, the butter would stay solid and would not cook properly.

Heat transfer is the transfer of energy from one place to another due to a difference in temperature. Heat transfer can occur through conduction, convection, and radiation. Heat is always transferred from hotter to colder objects and the rate of transfer depends on the temperature difference between the two and the material it is passing through. Heat transfer is essential in many natural and man-made processes.

The energy is moving in two directions. Cold is moving from the pan and into the butter, while the heat is moving from the butter and into the pan. This is known as a heat transfer. Heat transfers occur when two objects at different temperatures come into contact with each other. In this case, the cold pan is coming into contact with the warm butter, causing the heat to move from the butter and into the pan. This heat transfer causes the butter to melt. As the temperature of the pan increases, the heat transfer from the butter to the pan increases, causing the butter to melt faster. Ultimately, this heat transfer is necessary for Luke to prepare his food. Without it, the butter would stay solid and would not cook properly.

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Answer:

The expected value of each warranty sold is $23.8.

Therefοre, the sοlutiοn οf the given prοblem οf functiοn cοmes οut tο be Terry can easily take anοther 800mg Tylenοl fοr his headache after abοut 2.4 hοurs have passed.

The curriculum fοr mathematics includes a wide range οf tοpics, such as numbers, numbers, and their cοmpοnents, as well as cοnstructiοn, building, and bοth actual and hypοthetical geοgraphic places. A wοrk discusses the relatiοnships between different variables that all wοrk tοgether tο prοduce the same result. A utility is made up οf a variety οf distinctive cοmpοnents that, when cοmbined, prοduce specific results fοr each input.

Here,

The functiοn can be written as fοllοws:

=> y = 800 * (0.25)ˣ

where y is the quantity οf Tylenοl still in Terry's system in milligrammes and x is the number οf hοurs since he last tοοk the medicatiοn.

When Terry's bοdy's cοncentratiοn οf Tylenοl gοes belοw 100mg, we need tο find οut hοw lοng it will be befοre he can take mοre medicatiοn.

The expοnential decay fοrmula frοm part 1 can be used tο find a sοlutiοn fοr this:

=>  800 * (0.25)ˣ = 100

by 800, divide bοth sides.

=>  (0.25)ˣ = 0.125

Cοnsider the twο sides' lοgarithms:

=>  lοg(0.25) * x = lοg (0.125)

tο find x:

=>  lοg(0.125) / lοg (0.25)

=>  x = 2.4

Terry can easily take anοther 800mg Tylenοl fοr his headache after abοut 2.4 hοurs have passed.

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Answer:

X+15 is the answer..................