Which expression can be used to find the area of the composite figure? o 4x O 2x+ 2x2 O x2 + 2x O 32​

Answer:

  18.8 m²

Step-by-step explanation:

The area of a sector is given by the formula ...

  A = (1/2)r²θ . . . . . . . r is radius, θ is the central angle in radians

To convert an angle in degrees to one in radians, multiply by π/180°.

Your 135° sector has an area of ...

  A = (1/2)(4 m)²(135°)(π/180°) = 6π m²

  A ≈ 18.8 m²

Using the perimeter of a rectangle, it is found that she can make a deck of 122 ft wide.

The perimeter of a rectangle of length l and width w is given by:

\(P = 2(l + w)\)

In this problem:

Then:

\(P = 2(l + w)\)

\(280 = 2(10 + 8 + w)\)

\(36 + 2w = 280\)

\(2w = 244\)

\(w = \frac{144}{2}\)

\(w = 122\)

She can make a deck of 122 ft wide.

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Answer:

75%

Step-by-step explanation:

Madison got 18 problems right and there's 24 problems in total. The question asks for the percentage of the problems that she answered correctly. So, put the number of questions that she got right and the total number of questions into a fraction and simplify.

18/24=3/4

3/4ths= 75%

Answer:

Pine would be 108.5 Redwood would be 116.5.

Step-by-step explanation:

Since they both grow the same amount, we just add their original number by 73.5.

The dimensions of the rectangle is D. 7 units by 6 units

Go 2 units to the right, and then 3 units up

5(d + 1) = 5d + 5 .

A vertex (plural: vertices) is a point where two or more lines, edges, or curves meet in a geometric shape. In graph theory, a vertex refers to a node in a graph, which can be connected to other vertices by edges.

For example, in a triangle, each of the three points where the sides of the triangle meet is a vertex. In a cube, each of the eight points where the edges of the cube meet is a vertex. In a graph, each point representing a person or object would be a vertex, and the connections between them would be edges.

The term vertex is commonly used in mathematics, geometry, computer science, and other fields where shapes or networks are analyzed and studied.

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Answer:

The set of probabilities associated with the values in a random variable's sample space is called the probability distribution. It provides the probability of each possible outcome or value that the random variable can take.

Step-by-step explanation:

The probability distribution can be represented in various forms, depending on the type of random variable. For discrete random variables, the probability distribution is often presented as a probability mass function (PMF), which assigns a probability to each possible value. For continuous random variables, the probability distribution is typically described by a probability density function (PDF), which specifies the likelihood of the variable falling within a certain range of values.

For example, let's consider a random variable X that represents the outcome of rolling a fair six-sided die. The sample space of X consists of the values {1, 2, 3, 4, 5, 6}. The probability distribution or PMF for X would assign a probability to each of these values.

Assuming the die is fair, each outcome has an equal probability of occurring, so the PMF for X would be:

P(X = 1) = 1/6

P(X = 2) = 1/6

P(X = 3) = 1/6

P(X = 4) = 1/6

P(X = 5) = 1/6

P(X = 6) = 1/6

These probabilities sum up to 1, indicating that the probabilities assigned to all possible values of X cover the entire sample space.

Answer: 390

Step-by-step explanation:

32 ÷ 6 = 5 1/3

2080 ÷ 5 1/3 = 390

Charles spent 60 hours picking up litter if each student spent the same amount of time.

According to the question,

We have the following details:

Charles and 7 other students spent a total of 480 hours picking up litter last year.

So, the total number of students including Charles are 8.

8 persons = 480 hours

So, we have to find time spent in hours for 1 person:

1 person = 480/8 hours

1 person = 60 hours

So, this one person can be any eight of them including Charles.

Hence, Charles spent 60 hours picking up litter last year with other 7 students.

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Answer:

247.7 cm³

Step-by-step explanation:

V = πr²h

V = 3.14159 × (3.2 cm)² × 7.7 cm

V = 247.70808 cm³

Answer: 247.7 cm³

Answer:

See the picture down below

Step-by-step explanation:

When you are drawing a line you should first mark the y-intercept, which in this case it's (0,-3) because the the b in the equation is -3. Then we will go 2 units up then 1 unit right. Keep going until you've run out of room. Then draw the line going through all the points.

The graph of  y = 2x - 3 is attached and slope of the given graph is 2.

A line is an infinitely long object with no width, depth, or curvature.

y=mx+b is the standard form of a line, where m is slope and b is the y intercept.

When a line passes through (x₁, y₁) and (x₂, y₂) then slope

m=y₂-y₁/x₂-x₁

The given equation is  y = 2x - 3

When we compare this with standard form

m is 2 which is slope.

To draw graph we have to find few values of x and y.

If x=0,

then y=-3

(0, -3) is one point in the line.

If x=1

then y=-1

(1, -1) is second point in the line.

if x=2

y=1

if x=3

then y=3

if x=4

then y=5

Hence, the graph of  y = 2x - 3 is attached and slope of the given graph is 2.

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Answer:

What are the numbers?

Step-by-step explanation:

Connor borrowed a principal amount of $4,500. To determine the principal amount Connor borrowed, we can use the formula for simple interest: Interest = Principal × Rate × Time.

Given that the interest is $180, the rate is 4%, and the time is 3 years, we can rearrange the formula to solve for the principal.

Let P represent the principal amount. Substituting the given values into the formula, we have:

$180 = P × 0.04 × 3.

Simplifying the equation, we get:

$180 = P × 0.12.

To isolate P, we divide both sides of the equation by 0.12:

P = $180 ÷ 0.12 = $1,500 ÷ 0.01 = $4,500.

Therefore, Connor borrowed a principal amount of $4,500 to purchase the car.

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Step-by-step explanation:

3x - 5 = 2x - 25

3x - 2x = -25 + 5

x = -20

The value of x from the given figure is 42°.

The given angles are (3x-5)° and (2x-25)°.

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.

from the given figure,

y+(2x-25)°=180° (Adjacent angles adds up to 180°)

⇒ y=180°-2x+25°

⇒ y=205°-2x

Here, (3x-5)°=y (Corresponding angles are congruent)

⇒ (3x-5)°=205°-2x

⇒ 3x+2x=205+5

⇒ 5x=210

⇒ x=42°

Hence, the value of x from the given figure is 42°.

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Answer:

(1,-1)

Step-by-step explanation:

-2x-1 = x+2

-3x = 3

x = -1

substitute

y = (-1) + 2

y = 1

point: (1,-1)

Answer:

-18/7

Step-by-step explanation:

When subtracting a negative, the sign becomes positive, so now the equation would be -3 2/7 + 5/7.

By turning -3 2/7 into an improper fraction, you would get -23/7 + 5/7.

-23 +5 = -18 so -18 would be the numerator over the denominator (7) equals -18/7

Answer:

v=20π ft/s

Step-by-step explanation:

Given:

Distance from the security car to the movie theater, D=25 ft

Distance of the reflection from the car, d=30 ft

Speed of rotation of the strobe lights, 2 rev/s

To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.

We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.

ω=2πf

=> ω=2π(2)

=> ω=4π rad/s

The distance between the security car and the reflection on the wall of the theater is...

r=30-25= 5 ft

The speed of reflection is given as (this is the linear velocity)...

v=ωr

Plug our know values into the equation.

v=ωr

=> v=(4π)(5)

∴ v=20π ft/s

Thus, the problem is solved.

The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.

To solve this problem, we can use the concept of related rates. Let's consider the following variables:

x: Distance between the security car and the movie theater wall

y: Distance between the reflection of the security strobe lights and the security car

θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights

We are given:

x = 25 ft (constant)

y = 30 ft (changing)

θ = 2 revolutions per second (constant)

We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.

Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:

x^2 + y^2 = z^2

Differentiating both sides of the equation with respect to time (t), we get:

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.

Plugging in the known values, we have:

2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)

Simplifying the equation, we find:

60(dy/dt) = 120π

Dividing both sides by 60, we get:

dy/dt = 2π ft/s

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Applying the, Intersecting Chords Theorem, the value of x is calculated as: x = 16.

The Intersecting Chords Theorem is a geometric principle that states that when two chords intersect within a circle, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

Thus, we would apply this theorem to find the value of x in the image given as explained below:

(x - 6)(8) = (x)(5)

8x - 48 = 5x

8x - 5x = 48

3x = 48

Divide both sides by 3

3x/3 = 48/3

x = 16

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Answer:  5 pieces

===================================================

Explanation:

Note how

(number of pieces)*(length per piece) = 5*(3/5) = 15/5 = 3

which is the total length of the original rope.

So that's why the answer is 5.

We can get this answer through either guess and check, or we can divide 3 over 3/5 like so

3 divide 3/5 = (3/1) divide by (3/5) = (3/1)*(5/3) = 15/3 = 5

The second fraction 3/5 flips when we divide by it. Also the division changes to a multiplication when we flip the second fraction.

The domain of \( g(x) \) can be expressed in interval notation as \( (3, \infty) \).

To determine the domain of the function \( g(x) = \log_6(x-3) \), we need to consider the restrictions on the input values of \( x \) that make the function well-defined.

In this case, the logarithm function \( \log_6(x-3) \) is defined only for positive values inside the logarithm. Therefore, the expression \( x-3 \) must be greater than 0 for the function to be defined.

Solving the inequality \( x-3 > 0 \), we find that \( x > 3 \). This means that the function \( g(x) \) is defined for all values of \( x \) greater than 3.

Therefore, the domain of \( g(x) \) can be expressed in interval notation as \( (3, \infty) \).

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Answer: Devon, Tasha, Liza, Effon

Step-by-step explanation:

From the question, we are informed that four friends race their bikes down the street and that Evan finishes in 6.2 seconds, Devon in 6.0999 seconds, Liza in 6.188 seconds, and Tasha in 6.168 seconds.

The order that shows the friends' times from fastest to slowest is:

• Devon

• Tasha

• Liza

• Effon

Devon used 6.0999 seconds which is the fastest time, after then Tasha comes next with 6.168 seconds, then Liza with 6.188 seconds and lastly Effon with 6.2 seconds

Answer:

D

Step-by-step explanation:

The Y-intercept is 2 so basically every other answer is eliminated

Answer:

• 7

• 7

Explanation:

The absolute function is a function that always returns a positive value.

In general, the absolute value of any number is the positive of that number.

103-7 = 96 then 96/2 = 48 so we can say that Sydney is 48 and devaughn is 48+7 = 55 years old.

Therefore, Sydney is 48 years of age.

The equation that relates the number of jars of jelly bean candies and the number of containers of caramel candies is 8/16 J + 40/16 c = 10.

The given parameters:

Weight of jelly bean can = 8 ounces

Weight of caramel candies, = 40 ounces

Amount of Jelly bean and caramel candies bought  = 10 pounds

Number of ounces in one pound = 16 ounces.

Therefore, the equation that relates the number of jars of jelly bean candies and the number of containers of caramel candies is 8/16 J + 40/16 c = 10.

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Answer:

A=30

Step-by-step explanation:

A=a+b

   ------- x h

     2

3+7

-------  x 6

2

10/2=5

5 x 6 = 30

The sum of first five or twelve term in the A.P given the value 60.

The term AP refers a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value.

Here we have given that  A. P. 16,14,12,.

And we need to find the number of term to get the value of 60.

While we looking into the given question we have identified that the  common difference d of the A.P. is − 2

Here we also know that the terms of the A.P. are in descending order.

Now, we have to take n = 5  then then first 5 terms are 16,14,12,10,8.

Here we have identified that the sum is 60.

Similarly, here by taking n = 12 , then the last 7 terms ( 12 − 5 ) (12-5) are 6 , 4 , 2 , 0 , − 2 , − 4 , − 5 6,4,2,0,-2,-4,-5

Here we have identified that the sum of these seven terms is 0.

Therefore, sum of first 12 terms is also 60.

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Answer:

Step-by-step explanation:

image_2 is the image of image_1 by the translation (drawn in red)

image_4 is the image of image_3 by the rotation (135° drawn in red)

No, Brianna is not correct.

The distance around the pool is 131.4 ft

The perimeter of a semicircle is the sum of half of the circumference of the circle and its diameter. As the perimeter of a circle is 2πr or πd. So, the perimeter of a semicircle is 1/2 (πd) + d or πr + 2r, where r is the radius, and, 2r=d is diameter.

P=(πr + 2r)

here, we have,

1) Semi circle with a diameter equal to the side opposite it, 20 ft.

Find the length of half the circle:

Circumference of semi-circle = (1/2)(πd)

Where:

π = 3.14

d = 20 ft.

Circumference of semi-circle = (1/2)(3.14)(20 ft) = 31.4 ft.

2) Vertical lengths from the endpoint of semi-circle to the endpoints of horizontal lengths, 40 ft each ⇒ 2 × 40 ft. = 80 ft.

3.) Horizontal length at 20 ft.

Add the semi-circle, vertical, and horizontal lengths:

Distance around the pool = 31.4 ft + 80 ft. + 20 ft.

Distance around the pool = 131.4 ft.

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