A 14 foot long ramp is being built to access a front door in a house. The door is 5 feet above the ground. How far away from the base of the house must the ramp be placed? What angle will the ramp make with the ground?

Answers

Answer 1

Answer:

The ramp must be placed 13.08 feet from the base of the house.

The angle the ramp will make with the ground is 20.92°.

Step-by-step explanation:

An illustrative diagram for the scenario is shown below.

In the diagram, d represents the distance of the door from the ground, r represents the length of the ramp and x represent the distance of the ramp from the base of the house.

To determine how far away from the base of the house the ramp must be placed, that is to determine x in the diagram.

The diagram is a right angle triangle and x can be determine using the Pythagorean theorem which states " the square of the hypotenuse equals sum of the squares of the other two sides"

In the diagram, the hypotenuse is r

∴ r² = d² + x²

r = 14 ft

d = 5 ft

∴ 14² = 5² + x²

196 = 25 + x²

Then, x² = 196 - 25

x² = 171

x = √171

x = 13.08

Hence, the ramp must be placed 13.08 feet from the base of the house.

Now, to determine what angle the ramp will make with the ground, that is θ in the diagram.

From the formula

Sinθ = Opposite / Hypotenuse

In the diagram, opposite = d = 5ft

and Hypotenuse = r = 14ft

∴ Sinθ = 5ft / 14ft

Sinθ = 0.3571

∴ θ = Sin⁻¹(0.3571)

θ = 20.92°

Hence, the angle the ramp will make with the ground is 20.92°.

A 14 Foot Long Ramp Is Being Built To Access A Front Door In A House. The Door Is 5 Feet Above The Ground.

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Answer:

1\2.

Step-by-step explanation:

change in y over change in x. so 13 - 11 over 6 - 2. 2/4 --.> 1\2.

Guys, I need help ASAP!!
The standard deviation of the following data set is 0.31. 95% of the data would fall in which range?
4.3, 5.1, 3.9, 4.5, 4.4, 4.9, 5.0, 4.7, 4.1, 4.6, 4.4, 4.3, 4.8, 4.4, 4.2, 4.5, 4.4
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Answer:

Step-by-step explanation:

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Answers

Product hints at multiplication so -5n is AT LEAST meaning that it is at or greater than 35....

-5n ≥ 35

Answer:

-5x≥35

Step-by-step explanation:

The word "product" means to multiply so I know that -5 times a number x is at least 35. The phrase "at least" means greater than or equal to so I know its a ≥ sign.

Hope this helps you

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Answer:

Step-by-step explanation:

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The product of the ages of two adults is 572. Find their ages.

Answers

Answer:

?

Step-by-step explanation:

If you divide 572 by 2 you get 286...

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Step-by-step explanation: thats a real big number but half of 572 is 286 and you can figure that out by diving by 2

Joseph deposits $950 every month into an account earning a monthly interest rate of 0.5%. How much would he have in the account after 19 months, to the nearest dollar?

Answers

Answer:

I think, 18,058 dollars.

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

Determine and state an equation of the line perpendicular to the line 4x – 5y = 10 and passing through the point (-4, -2).

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fortnite stroyline haja
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Colleen is searching online for airline to tickets. Two weeks ago, the cost to fly from denver to Boston was $250. Now the cost is $340. What is the percent increase? What would be the percent increase if the airline charges an additional $50 baggage fee with the new ticket price

Answers

Answer:

[tex]follow \: me \: please[/tex]

[tex]A sent telegram to b will you sell your car qoute lowest price B sent replay lowest price 50000 A sent second telegram ti B i agree to by car for 50000 B transfer refused to sell it there any contracy between A qnd B and can A Sue B for breach of contract give reason[/tex]

Step-by-step explanation:

A sent telegram to b will you sell your car qoute lowest price B sent replay lowest price 50000 A sent second telegram ti B i agree to by car for 50000 B transfer refused to sell it there any contracy between A qnd B and can A Sue B for breach of contract give reason

Answer:

Step-by-step explanation:

13%

help will give brainlyist and 5 star and heart​

Answers

The first answer is -3 !!

Use the interactive tool to graph the line given the following information:

coordinates (1,–3)

slope of –2

Based on your investigation, what is the value of b for the point (0,b)?

Answers

Answer:

b=  -1

Step-by-step explanation:

Graph the point and use the slope until you intercept the y-axis

Answer:

-1

Step-by-step explanation:

What are some reasons to live I could use them right now

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Answer:

mom will be sad

Step-by-step explanation:

YOU ARE A BEATIFUL AND AMAZING PERSON DONT DIE ON ME LIKE THIS

Please help!!!! ASAP!!! Thank you!!!

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Answer:

28

Step-by-step explanation:

There were 7 chairs in each row, now they add three more to each row so now there's 10 chairs per row. There were 56 chairs altogether previously but now they need 5 times more so 56 times 5 equals 280. so with ten chairs per row and 280 chairs in total: 280/10 = 28. You'll need 28 rows

In a survey of 1,500 people who owned a certain type of​ car, 300 said they would buy that type of car again. What percent of the people surveyed were satisfied with the​ car?

Answers

Answer:

20%

Step-by-step explanation:

Step one:

total number of people surveyed= 1500

we are told that 300 people would buy that car again,

this implies that they like the car and are satisfied with it

Step two:

the percent of people satisfied can be computed as

=300/1500*100

=3/15*100

=1/5*100

=0.2*100

=20%

The people surveyed were satisfied with the​ car are 20%

The radius of a circle is 8 in. Find its area in terms of \piπ.

Answers

Answer:

201.06 in

Step-by-step explanation:

I'm guessing you meant πr² because that's what you use to find the area of a circle.

Anyways, we know what the radius is, it's 8, so now we just need to plug it in.

π8² = 201.06

or you can do

3.14(8²) = 200.96

Using π just makes it more exact.

Answer:

201.1 in (approx.)

Explanation:

ok x so first I will multiply 8^2 by pi, that gives me an infinite decimal.. but after rounding it up to 1d.p, we get 201.1 inches which is your answer

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Answers

Answer:

Yes, they are equivalent, and the second question is B

Step-by-step explanation:

If you add x on both sides of equation A, then it comes up to 5x+2=6, which is equivalent to equation B. For the second question, you are just basically adding a variable to each side, so it is B.

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Answers

Answer:

.325

Step-by-step explanation:

Answer:

0.325 is a decimal

Step-by-step explanation:

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Answers

Hey there :,)

The answer is D. 9 5/24

Answer:

D

Step-by-step explanation:

twice the sum of k and 9 is 4

Answers

Answer:

2(k + 9) = 4

Step-by-step explanation:

Use distributive property.

2 x k = 2k

2 x 9 = 18

Equation:

2k + 18 = 4

Subtract 18 from both sides

2k = -14

Divide both sides by 2

k = -7

Answer:

-7

Step-by-step explanation:

First, we need to write this an equation

2(k+9)=4

2k+18=4

-18       -18

2k=-14

/2      /2

k=-7

A box contains 300 raffle tickets. Only 15 tickets are winning tickets. What is the
probability the first ticket drawn at random from the box is a winning ticket?

Answers

Answer:

5%

Step-by-step explanation:

15/300 = 0.05

5%

-2q– 32 = 0
q=
and
Som
One
Please
He
Lp
Ple
Ase

Answers

q= -16

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can someone help me with these questions I want to make sure I got them right ​

Answers

9514 1404 393

Answer:

14/9-3.65/411/2, 7/8, 5/18

Step-by-step explanation:

1. n = (11/6 -2/3)(4/3) = (7/6)(4/3) = 14/9

__

2. x = (9.82 -28.18)/5.1 = -3.6

__

3. y = 3/2 -1/4 = 5/4

__

4a. t = 2(3 -1/4) = 11/2

4b. y = (1/5 +1/2)(5/4) = ((2+5)/10)(5/4) = 7/8

4c. x = (11/3 -2)/6 = (5/3)(1/6) = 5/18

Justin and his children went into a grocery store and he bought $18 worth of bananas and mangos. Each banana costs $0.60 and each mango costs $1.50. He bought 2 more bananas than mangos. Graphically solve a system of equations to determine the number of bananas, x, and the number of mangos, y, that Justin bought.

Write an answer in y=mx+b form, please.
Two equations.

Answers

Answer:

x=10 and y= 8.

Step-by-step explanation:

Given that the cost of 1 banana = $0.60

Cost of 1 mango = $1.50.

Total cost= $ 18  

Here, x be the number of bananas and y be the numbers of mangos,

As the number of bananas is 2 more than the number of mangos,

So, x=y+2

[tex]\Rightarrow y=x-2 \cdots(i)[/tex]

Cost of x bananas [tex]=\$ 0.60 \times x[/tex]

Cost of y mangos [tex]=\$ 1.50 \times y[/tex]

Total cost = 0.6x+1.5y

[tex]\Rightarrow 18 = 0.6x+1.5y\\\\\Rightarrow 1.5y=18-0.6x\\\\\Rightarrow y= 12 - 0.4 x \cdots(ii).[/tex]

Solving both the equations (i) as well as (ii), graphically as shown in the figure by plotting both the graphs.

Both the graphs intersect at the point (10,8) as shown in the graph.

So, the solution of both the equations is, (x,y)=(10,8). i.e

The number of bananas = x= 10 and

the number of mangos = y = 8.

In the equation y = 2π^x, 2 is the ______ and π is the ______.

Answers

Answer:

pi(π) is the constant and x is the variable since pi is a numerical value and x can change according to the equation given.

Step-by-step explanation:

Help!!!
Find the total cost to the nearest cent. $18 breakfast; 7% tax

Answers

Answer:

19.26

Step-by-step explanation:

Jeremy find the cost by adding the percents. 25% off of $60 is equal to 15% off of $60, then subtracting 10% from that cost is equal to . The two total costs are

Answers

Answer:

a. 25% off of $60 is equal to $45.

b. 15% off of $60, then subtracting 10% from that cost is equal to $45.

c. The two total costs are $45 and $45, and their addition is equal to $90 (i.e. $45 + $45 = $90).

Step-by-step explanation:

These can be determined as follows:

a. Calculation of the first total cost, i.e. 25% off of $60

25% of 60 = 25% * $60 = 15

First total cost = 25% off of $60 = $60 - (25% of $60) = $60 - $15 = $45

Therefore, 25% off of $60 is equal to $45.

b. Calculation of the second total cost, i.e. 15% off of $60, then subtracting 10% from that cost

15% of $60 = $9

10% of $60 = $6

Cost = 15% off of $60 = $60 - (15% of $60) = $60 - $9 = $51

Second total cost = Cost - (10% of $60) = $51 - $6 = $45

Therefore, 15% off of $60, then subtracting 10% from that cost is equal to $45.

c. The two total costs

The two total costs are 25% off of $60 which is equal to $45 and 15% off of $60, then subtracting 10% from that cost which is also equal to $45. The addition of the two costs is $90 (i.e. $45 + $45 = $90).

Therefore, the two total costs are $45 and $45, and their addition is equal to $90 (i.e. $45 + $45 = $90).

The price P, in dollars, for a large pizza is P = 2n + 7, where n is the number of toppings on the pizza. How many toppings are on a pizza that costs $15?

Answers

Answer:

There are 4 toppings on a pizza that costs $15.

Step-by-step explanation:

To find the amount of toppings that are on a pizza that costs $15, you will need to consider that P=15, replace this value on the formula and then, solve for n that is the number of toppings on the pizza:

P=2n+7

15=2n+7

15-7=2n

n=8/2

n=4

According to this, the answer is that there are 4 toppings on a pizza that costs $15.

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