A ramp is used to move equipment off a loading dock and onto the ground. The loading dock floor is 6 feet above the ground.

The ramp measures 30 feet long.

What is the horizontal distance covered by the ramp?

Enter your answer, rounded to the nearest tenth of a foot, in the box.

ft

In order to graph the function, the slope will be 20 and the y-intercept will be at C=40, taking into account that the limit is x=50

to find the line join points (0,40) and the limit coordinate found through the equation

the other coordinate is (50,1040)

then, cross a line at x=25

Answer:

63

Step-by-step explanation:

Answer:

the area is 43cm²

Step-by-step explanation:

First, you find the area of the left side. 7cm - 3cm= 4cm

Secondly, you multiply 4cm x 4cm = 16cm

Then, you find the area of the bottom bit. 9cm x 3 cm = 27cm

Lastly, you add 27cm + 16cm, which brings your answer to...

43cm² :-)

(It's squared because you are finding the area)

Answer:

D. About 2700 in^2

Step-by-step explanation:

The area of a circle A = πd²/4 where d = diameter of circle.

A/d² = π/4 = k the proportionality constant.

So, A₁/d₁² = A₂/d₂² Now for circle A, Area = A₁ = 300 in² and diameter = d₁ = 20 inches. For circle B, Area = A₂ = unknown and diameter = d₂ = 60 inches.

So, we have

A₁/d₁² = A₂/d₂²

A₂ = A₁d₂²/d₁²

A₂ = A₁(d₂/d₁)²

substituting the values of the variables, we have

A₂ = 300 in²(60 in/20 in)²

A₂ = 300 in²(3)²

A₂ = 300 in²(9)

A₂ = 2700 in²

So, the area of circle B is about 2700 in²

Answer:

3895.38

Step-by-step explanation:

Multiply tax rate by income: 64923 x .06=3895.38

Answer:

ordered pair (2,-3); y-intercept-5

-3 2 and y intersection of 5 (3rd down)

Answer:

im pretty sure they are both 5. its a ratio of 5 to 1

Therefore, the approximate change in the function f(x, y) when x changes from 2 to 2.17 and y changes from 2 to 1.71 is approximately -0.24.

To find the approximate change of the function \(f(x, y) = 2x^2 + 2y^2 - 3xy + 1\), we will use the concept of total differentials.

The total differential of f(x, y) is given by:

df = (∂f/∂x)dx + (∂f/∂y)dy

Taking the partial derivatives of f(x, y) with respect to x and y:

∂f/∂x = 4x - 3y

∂f/∂y = 4y - 3x

Substituting the given values of x and y:

∂f/∂x (at x=2, y=2) = 4(2) - 3(2)

= 2

∂f/∂y (at x=2, y=2) = 4(2) - 3(2)

= 2

Now, we can calculate the approximate change using the formula:

Δf ≈ (∂f/∂x)Δx + (∂f/∂y)Δy

Substituting the values:

Δf ≈ (2)(2.17 - 2) + (2)(1.71 - 2)

Simplifying the expression:

Δf ≈ 0.34 + (-0.58)

Δf ≈ -0.24

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Explanation:

The blue rectangle has area of 4a^2*6a^2 = 24a^4

The red rectangle has area 4a^2*9a = 36a^3

The green rectangle has area 4a^2*3 = 12a^2

The total area is 24a^4 + 36a^3 + 12a^2

Answer:

1/3^7

Step-by-step explanation:

Negative exponents go to the denominator

The positive exponent for the given exponent is \(\frac{1}{3^7}\).

The given exponent is \(3^{-7}\).

The exponent of a number shows how many times the number is multiplied by itself.

A positive exponent tells us how many times to multiply a base number, and a negative exponent tells us how many times to divide a base number.

Now, \(3^{-7}=\frac{1}{3^7}\) (∵\(a^{-n}=\frac{1}{a^n}\))

Therefore, the positive exponent for the given exponent is \(\frac{1}{3^7}\).

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Based on the information represented by the boxplot ;

1.) The Lowest amount of sale made by Latasha in one month

2.) 50% of sales made by Kayla :

3.) Spread of the middle 50% of sales :

For Latasha :

For Kayla :

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Answer:

0.350

Step-by-step explanation:

Probability is defined as the chances that an event will occur or not occur. The entire idea of probability has to do with 'chance' events. Thus, the probability that an event will surely occur is 1, while the probability that an event will never occur is zero. Probabilities range between 0-1.

Probability of an event is obtained from

Probability= expected outcome/total number of outcomes

In this case,

Expected outcome= 35

Total number of outcomes = 100

Probability= 35/100= 0.350

There is a total of 15 yes/no questions on the test. Hence, 15 is the correct answer.

Let's assume the number of yes/no questions on the test is represented by 'x'. The number of multiple-choice questions would then be '20 - x' since the test consists of a total of 20 questions.

The points obtained from yes/no questions can be calculated as 3 times the number of yes/no questions, which is 3x.

Similarly, the points obtained from multiple-choice questions can be calculated as 11 times the number of multiple-choice questions, which is 11(20 - x).

Since the total points for the test are 100, we can set up the equation:

     \(3x + 11(20 - x) = 100\)

or, \(3x + 220 - 20x = 100\)

or, \(8x = 120\)

or, \(x = 15\)

Therefore, the total number of yes/no questions on the test is 15.

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The cost of ordering shirts for a club is 268 units.

Define Function.

A function, according to a technical definition, is a relationship between a set of inputs and a set of possible outputs, where each input is connected to precisely one output.

 This means that a function f will map an object x exactly to one object f(x) in the set of possible outputs if the object x is in the set of inputs (called the codomain).

The statement that f is a function from X to Y using the function notation f: X→Y

The function that represents the cost of the shirts(x) is f(x) = 8x+12

Now, for x = 32

 f(x) = 8x+12

f(32) = 8(32) + 12

        = 256 +12

f(32) = 268 units

.

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The true proportion of the side lengths of the quadrilaterals is A'B'/AB

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

Quadrilaterals ABCD and A'B'C'D

These quadrilaterals are similar

So, it means that the corresponding side lengths are proportional

So. we have

Side length = AB

Corresponding side length = A'B'

The true proportion is then represented as

k = Corresponding side length/Side length

Substitute the known values in the above equation, so, we have the following representation

k = A'B'/AB

Hence, the proportion is A'B'/AB

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Answer:

The origin is included in the shaded region and the shaded region is below the line.

Explanation:

First, let's graph the line that separates the region: y = 1/3 x + 4

So, to graph the line, we need to find two points in the line as follows:

If x = 0, then y is equal to:

y = 1/3 (0) + 4

y = 4

If x = 3, then y is equal to:

y = 1/3 (3) + 4

y = 1 + 4

y = 5

So, using the points (0, 4) and (3, 5), we get:

Now, we can determine whether the origin is included or not replacing x and y by the coordinates of the origin (0, 0) and determine if this point satisfies the inequality. So:

y < 1/3x + 4​

0 < 1/3(0) + 4

0 < 0 + 4

0 < 4

Since 0 is less than 4, the origin is included in the shaded region, so the shaded region is below the line.

Answer:

(f - g)(x) = -x² + 3x + 5

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

f(x) = 3x + 5

g(x) = x²

(f - g)(x) is f(x) - g(x)

Step 2: Find (f - g)(x)

Answer:

The Great Western Trail = 4,455 miles

Step-by-step explanation:

The Iditarod Trail = 1,025 miles long

The Great Western Trail is 355 miles longer than 4 times the length of the Iditarod Trail.

The Great Western Trail = (4 × 1,025) miles + 355 miles

= 4,100 miles + 355 miles

= 4,455 miles

The Great Western Trail = 4,455 miles

Answer:

-12√3n

Step-by-step explanation:

We want to write this in its simplest form

48 = 16 * 3

√(48) = √16*3

√48 = 4 √3

so we have

-3 * 4 √3n

=

-12√3n

Out of a whole population, a sample is a small part which is considered for any survey.  

The population in this case would be all the one-bedroom apartments available for rent near the college.

The sample would be the listings that Greg is looking at in the local newspaper and on the internet site.

Sample: listings in a local newspaper and on an Internet site              

Population: all available apartments near the college          

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Answer:

$2.25

Step-by-step explanation:

You have to set up a proportion to show how much the cost of milk is when discounted per gallon. 0% off, the milk would be $3.75. 40% off, the milk would be x. Now I flipped the percents because that is how much you are actually paying.

Proportion would look something like this:

3.75/100 = x/60

solve for x:

225 = 100x

x= 2.25

Answer:

\(51-m=n\)

Step-by-step explanation:

M - Number of cookies his family ate

N - The remaining number of cookies left

Answer:

Step-by-step explanation:

Then, the total time, which is 2 hours, is equal to x plus 7x, or 8x. So the amount of time he spends in the automobile is x=1/4 hour. The distance he travels in 1/4 hour at 28 mph is 7 miles.

pls mark brainliest

The correct internal moment expression in segment BC as a function of x with the origin at A is D) 5x - 25.

To determine the internal moment expression in segment BC, we need to consider the external forces acting on the segment. Based on the given information of 5 kN and 15 kN, the net external moment at any point x on segment BC can be calculated as the sum of the moments due to these forces.

Since the origin is at A, the expression for the internal moment can be derived by integrating the net external moment equation from the origin (A) to point x on segment BC. Solving this integration will lead to the correct expression of 5x - 25 for the internal moment in segment BC. So d is correct option.

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The number of different spanning trees for each graph is: a) K3: 1, b) K4: 4, c) K2,2: 2 and d) C5: 5.

a) The complete graph K3 consists of 3 vertices, and in a spanning tree, we need to have exactly 3 vertices connected without forming any cycles. Therefore, K3 has only one possible spanning tree.

b) The complete graph K4 has 4 vertices. To form a spanning tree, we need to connect all 4 vertices without creating any cycles. K4 can be thought of as a tree with 4 branches extending from a central vertex. Each branch can be connected to any of the other vertices. Hence, there are 4 possible spanning trees for K4.

c) The complete bipartite graph K2,2 consists of 4 vertices divided into two sets, each containing 2 vertices. To form a spanning tree, we need to connect all 4 vertices without creating any cycles. Since there are only two possible edges between the two sets, there are only two possible spanning trees for K2,2.

d) The cycle graph C5 consists of 5 vertices arranged in a circular shape. To form a spanning tree, we need to connect all 5 vertices without creating any cycles. Removing any one of the edges from the cycle will result in a tree. Therefore, C5 has 5 different spanning trees.

Therefore, the number of different spanning trees for each graph is:

a) K3: 1

b) K4: 4

c) K2,2: 2

d) C5: 5  

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Answer: w=8/3

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

20 /3 =2(w+ ( 2 /3 )

20 /3 =(2)(w)+(2)( 2 /3 )(Distribute)

20 /3 =2w+ 4 /3

Step 2: Flip the equation.

2w+ 4 /3 = 20 /3

Subtract 4/3 from each side: 2w+ 4 /3 − 4 /3 = 20 /3 − 4 /3

Divide both sides by 2: 2w/ 2 =16  3 /2

Answer w=8/3

Answer:

w=8/3

Step-by-step explanation:

Answer:

d=69, e=32, f=79

Step-by-step explanation:

e=32

d=69

f=180-69-32=79

The measure of each of the missing angles include the following:

d = 69.

e = 32.

f = 79.

In Geometry, the vertical angles theorem is also referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other.

By applying the vertical angles theorem to the geometric figure, we have the following:

m∠e = 32°

m∠d = 69°

From the linear postulate theorem, we have:

m∠e + m∠d + m∠f = 180°

32° + 69° + m∠f = 180°

m∠f = 180° - (32° + 69°)

m∠f = 79°

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Answer:

4

Step-by-step explanation:

2 16 12 48

2 8 6 24

4 3 12

2×2= 4

Answer:

The answer is 1050 ft^2

Hope I helped!

Answer:

It will take 50 seconds for the pebble to reach the height

Step-by-step explanation:

To calculate the time, simple substitute h(t) for 32,500

So we have

32,500 = 20,000 + 5t^2

5t^2 = 32,500-20,000

5t^2 = 12500

t^2 = 12500/5

t^2 = 2500

t = square root of 2500

t = 50 seconds