The function f(x) = 9x + 27 represents the distance in miles a drone flew. The function g(x) = x + 3 represents the time the drone flew in hours. Part A: Find f(4) and g(4). Show your work. (2 points) Part B: Find f divided by g of 4. Show your work. (2 points) Part C: What is the domain of f divided by g of x? (2 points)

The diagram's area at x is [tex]$$x=\sqrt{-y^2+36} \text { or } x=-\sqrt{-y^2+36}$$[/tex], and at y is [tex]$$y=\sqrt{-x^2+36} \text { or } y=-\sqrt{-x^2+36}$$[/tex].

Let's try to find x.

[tex]$$x^2+y^2=36$$[/tex]

Phase 1: Add [tex]$-y^{\wedge} 2$[/tex] to both parties.

[tex]$$\begin{aligned}& x^2+y^2+-y^2=36+-y^2 \\& x^2=-y^2+36\end{aligned}$$[/tex]

Take the square root in step two.

[tex]$$x=\sqrt{-y^2+36} \text { or } x=-\sqrt{-y^2+36}$$[/tex]

Solve for y now.

[tex]$$x^2+y^2=36$$[/tex]

Phase 1: Add [tex]$-x^{\wedge} 2$[/tex] to both parties.

[tex]$$\begin{aligned}& x^2+y^2+-x^2=36+-x^2 \\& y^2=-x^2+36\end{aligned}$$[/tex]

Take the square root in step two.

[tex]$$y=\sqrt{-x^2+36} \text { or } y=-\sqrt{-x^2+36}$$[/tex]

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The probability of blue marbles is 11/25.

Probability is a way to gauge how likely something is to happen. According to the probability formula, the likelihood that an event will occur is equal to the proportion of positive outcomes to all outcomes. The probability that an event will occur P(E) is equal to the ratio of favorable outcomes to total outcomes. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

Given red marbles in the bag = 28

blue marbles in bag = 22

total marbles = 50

probability = favorable outcome/total outcome

P(blue marbles) = 22/50

P(blue marbles) = 11/25

Hence the probability is 11/25.

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The total medical expenses for the five people in the car are $3,000 + $3*$500 + $62,000 = $3,000 + $1,500 + $62,000 = $66,500

What does a math word problem entail?

A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world." In order for kids to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.

Since Allen's personal injury protection policy covers each person up to $50,000, the insurance company must pay out $50,000*5 = $250,000 for the five people in the car.

Since the total medical expenses for the five people are $66,500, the insurance company will pay out the total medical expenses for the five people, which is $66,500.

Therefore, the insurance company must pay out $66,500 for these five people.

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Answer:

[tex]3(3x+7)[/tex]

Step-by-step explanation:

[tex]9x=3(3x), 21=3(7) \implies 9x+21=3(3x+7)[/tex]

Answer:

b [3x = 1]

Step-by-step explanation:

7x + 4 = 5 + 3x + 1x

Combine like terms:

7x + 4 = 5 + 4x

Subtract 4 from both sides:

7x = 1 + 4x

Subtract 4x from both sides:

[3x = 1]

Answer:

y= -5 - 4x

Step-by-step explanation:

4x + 2y = -10 - 4x

-4x                    -4x

2y = -10 - 8x

/2.         / 2

y= -5 - 4x

The slowest time of the 40 yard dash is given by the equation A = 3.41 sec

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the slowest time be represented as A

Now , the equation will be

Let the total length of the yard = 40 yard dash

Let the fastest time be represented as F

The value of F = 4.58 seconds

The difference between the fastest and the slowest time = 1.17 seconds

Substituting the values in the equation , we get

Fastest time - slowest time = 1.17 seconds

So ,

4.58 - A = 1.17

On simplifying the equation , we get

Adding A on both sides of the equation , we get

A + 1.17 = 4.58

Subtracting 1.17 on both sides of the equation , we get

A = 4.58 - 1.17

A = 3.41 seconds

Therefore , the value of A is 3.41 seconds

Hence , the equation is A = 3.41 seconds

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a. To express Julianne's pay for these x hours algebraically, you would use the equation: pay = 13x + tips

b. To express the amount Julianne received in tips algebraically, you would use the equation: tips = 0.18y

c. To express Julianne's total earnings for the day algebraically, you would add her pay (13x) to the amount of tips she received (0.18y) to get the equation: total earnings = 13x + 0.18y.

a. Julianne earns $13 per hour plus tips, so her pay for working x hours can be expressed algebraically as pay = 13x + tips. This equation means that her pay is equal to $13 multiplied by the number of hours she worked, plus any additional tips she received. The variable "x" represents the number of hours she worked, and "tips" represents the additional money she earned from tips.

b. Julianne received tips from serving 9 tables, and the total bill for these tables was y dollars. We can express the amount she received in tips algebraically as tips = 0.18y. This equation means that the amount of tips she received is equal to 18% of the total bill for the 9 tables, represented by the variable "y". The 0.18 represents 18% in decimal form.

c. To find Julianne's total earnings for the day, we need to add her pay (13x) to the amount of tips she received (0.18y). This can be expressed algebraically as total earnings = 13x + 0.18y. This equation means that her total earnings for the day is equal to her pay for working x hours plus the amount of tips she received. The variable "x" represents the number of hours she worked, the variable "y" represents the total bill for the nine tables, and the product of 0.18 * y represents the amount she received as tips.

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Answer:

24°

Step-by-step explanation:

For an n-sided regular polygon, the sum of internal angles = (n-2)×180°

Since all internal angles are equal, the internal angle can is given as:

Here, it is given that the polygon has 15 sides.

So n = 15

So each internal angle is 156°.

Internal and external angles are always supplementary. So the sum of the internal and external angles is 180°.

So external angle = 180° - 156° = 24°.

The measure of each external angle is 24°.

The 7 classes are provided in the frequency table.

What is a frequency table ?

A frequency table consists of the lists of items in a given data set and the number of times each item occurs in the data set and The number of times a particular data value occurs in a given data set is referred to as its frequency.

e.g.

A, A, A, B, B, B, B, C, C, D

Count the number of times each grade occurs in the above series. Yes, ‘A’ occurs thrice, ‘B+’ occurs four times, ‘C’ occurs twice, and ‘D’ occurs once. Now, according to the definition of frequency, we can note the frequency of each grade as follows:

Frequency of A = 3

Frequency of B = 4

Frequency of C = 2

Frequency of D = 1

Let us list the grades obtained by the students in the above example, in a frequency table. Table is in image.

Now,

Class width=94-20/7

=74/7

=10+4/7

class width=11

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The ballroom is 40m by 20m

just think of numbers that times together to get 800 and then check if the perimeter is right.

A rectangular ballroom has two dimensions: length and width,

The perimeter is the sum of all the sides of the rectangle,

P=L+LW+W=2L+2W

The area is the product of these two dimensions,

A=L,W

We know that the perimeter is 120m and the area is 800m². Replacing in the equations above, we have two equations with two variables L and W,

120=2L+2W

     =800LW

Solve the first equation for W. Subtract 2L from both sides,

120-2L=2L-2L+2W

120-2L=2W

And divide both sides by 2,

120-2L/2=2W/2

60-L=W

The next step is to replace W by this expression in the second equation,

800=L(60-L)

Now we have to solve this equation for L. Apply the distributive property on the right side of the equation,

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In temperatures between -4°F and 113°F, Layla should refrain from using her phone.

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The amount of chromium left after 4 months of decay is 380 grams.

The half-life of the element is defined as the time span in which the element grows or decays half of its whole composition of growth and decay.

Here,
Let y be the amount of decay for x months

y = 6080aˣ

Half-life
1 / 2 = a¹
a = 1/2 = 0.5

Now,
y = 6080[0.5]⁴
y = 380

Thus, the amount of chromium left after 4 months of decay is 380 grams.

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The answer for this question is Celsius for Fahrenheit.

To convert temperatures from degrees Fahrenheit to degrees Celsius, multiply the result by.5556 (or 5/9) after subtracting 32.

(50°F - 32) x.5556 = 10°C, for instance.

When converting from degrees Celsius to Fahrenheit, multiply the result by 1.8 (or 9/5) and then by 32.

For instance, (30°C x 1.8) + 32 = 86°F'

Here are two useful charts that translate between F and C as well as between C and F.

The temperature of f degrees Fahrenheit converted to degree Celsius.

(( f)=5/9 (f-32)

represent the temperature of f degrees Fahrenheit converted to degree Celsius.

The function C(F) will be "C of F" it will be converted Fahrenheit to Celsius.

So that means if the temperature is in Fahrenheit it will be converted to Celsius.

So that means the C(F) represents the Celsius temperature.

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Complete Question -

For one month diera calculated her home town's average high temperature in degrees Fahrenheit. She wants to convert that temperature from degrees FAhrenheit to degrees Celsius using the function C(F) = 5/9(F-32). What does C(F) represent?

The function that grows least quickly is

A. f(x)

Exponential function is a type of function of the form: f(x) = a(b)^x. It is made up of  3 main parts

a = the starting or initial value

b = the base function

x = the exponents

Considering the given problem, The base is what determines exponential growth or decay

The higher the base the more it will grow and the lesser the base the less quickly it grows

When the base is less than one we have exponential decay

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The distance between Sam's head and the helicopter is 28.36 m

Step 1: Find the vertical distance travelled by the helicopter in 10 seconds

The vertical distance travelled by the helicopter in 10 seconds = 5 m/sec x 10 sec = 50 m

Step 2: Find the horizontal distance between Sam and the helicopter

We can use the trigonometric relationship, tan 62° = Opposite/Adjacent

Therefore, the horizontal distance between Sam and the helicopter = 50 m/tan 62°

= 50 m/1.8813

= 26.56 m

Step 3: Find the distance between Sam's head and the helicopter

Since Sam is 1.8 m tall, the distance between Sam's head and the helicopter = 26.56 m + 1.8 m

= 28.36 m

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Answer:I need to know what the phrases are.

Step-by-step explanation:

I can't answer this unless you do so.

The ratio of their volumes is equal to: D. 27:125.

Mathematically, the volume of a sphere can be calculated by using this formula:

Volume = 4/3 × πr³

Where:

r represents the radius.

Based on the information provided about the two spheres, an expression which models their surface areas (S) with respect to volumes (V) is given by;

S₁/S₂ = V₁/V₂

S₁/S₂ = 9/25

(4πr₁²)/(4πr₂²) = 9/25

r₁²/r₂² = 9/25

Taking the square root of both sides of the expression, we have:

r₁/r₂ = 3/4

From the volume of a sphere formula, we have:

V₁/V₂ = (4/3 × πr₁³)/(4/3 × πr₂³)

V₁/V₂ = r₁³/r₂³

V₁/V₂ = 3³/4³

V₁/V₂ = 27/125.

Therefore, the required ratio is 27:125.

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The circumference of the larger pizza is 12.56 longer than the smaller pizza.

The length around the circle or the perimeter of the circle is called its circumference.

Given that, Anthony ordered two pizzas for a party. One was a small pepperoni pizza with a radius of 5 inches, and the other was a large cheese pizza with a 7 in. radius.

We need to find how much longer than the circumference of the smaller pizza,

We know that,  

Circumference of a circle = 2πr.

Therefore,

Circumference of the larger pizza = 2 × 3.14 × 7 = 43.96 in

Circumference of the smaller pizza = 2 × 3.14 × 5 = 31.4 in

Therefore,

Subtracting the circumference of smaller pizza from larger pizza to get the difference = 43.96 - 31.4 = 12.56 in

Hence, the circumference of the larger pizza is 12.56 longer than the smaller pizza.

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The annual interest rate on this loan is 4.8%.

Simple interest is defined as the interest obtained over the principal amount on a certain rate.

Given that,

Principal amount, P = $500,000

Loan term, t = 15 years

Loan payment = $4,778.26 per month

                        = $57339.12 per year

                        = $860,086.8 in 15 years

We know that final amount for simple interest is,

A = P(1 + r t)

860,086.8 = 500,000(1 + 15r)

1.7201736 = 1 + 15r

r = 0.04801

r = 4.8%

Hence the annual interest rate is 4.8%.

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Only table 1 represents the directly proportional relationship.

Given are the tables representing proportional relationship.

We can write the slope as -

{m} = (- 4 + 3)/(- 2 + 1) = 1

The equation will be -

y = x

Remaining tables does not show the direct variation.

Refer to the graph attached.

Therefore, only table 1 represents the directly proportional relationship.

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Answer: 2151 magazines

Step-by-step explanation: First subtract the whole number of books and magazines by the number of books and you'll find your answers.

The domain of the function f(x) = 1/4x + 3 is all real numbers except x = 0, since division by 0 is undefined.

The range of the function is all real numbers. For any real number x, f(x) = 1/4x + 3 will always produce a real number, so the range is (-infinity, +infinity).

Answer:

To solve this problem, we need to use the concept of distance, rate and time (D = R x T)

We know that the distance is 49 miles and the rate is 14 miles per hour.

We want to find the time T.

We can use the formula D = R x T, to find the time T:

T = D/R = 49 miles / 14 miles/hour = 3.5 hours

So it takes Nena 3.5 hours to ride from the city park to the nearby lake.

Now we know that she needs to arrive at the lake at 1:00 PM, so we have to work out what time she needs to leave the park. We can subtract the time T from the arrival time to find the departure time:

1:00 PM - 3.5 hours = 9:30 AM

Therefore, the latest Nena can leave the park in order to arrive at the lake at 1:00 PM is 9:30 AM

Step-by-step explanation:

opposite interior angles

Using the formula of area of a rectangle, the number of planks that will surface the court is approximately 55

The area of a rectangle is calculated by multiplying the length of the rectangle by its width. The formula is:

Area = length x width

In this problem, we can find the area of the court and the area of the plank and divide both to determine the number of plank that would suffice.

Area of court = length * width

length = 94 feet = 28.64m

width = 50 feet = 15.24m

Area of court = 28.64 * 15.24 = 436.47m²

Area of plank = length * width

Area of plank = 10 * 0.8

Area of plank = 8m²

The number of planks required = 436.47 / 8 =  54.55 ≅ 55 planks

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