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Mnenie [13.5K]
3 years ago
5

A 12-foot cable attached to the top of the mast of a sailboat is fastened to a point on the deck 4 feet from the base of the mas

t. What is the height of the mast?

Mathematics
1 answer:
Vilka [71]3 years ago
8 0

Answer:

The height of the mast is 8√2 feet

Step-by-step explanation:

In this question, we are asked to calculate the height of the mast given the information in the question.

Please check the attachment for diagrammatic representation.

From the diagrammatic representation, we can conclude that we are asked to calculate the value of the third side of a right angled triangle, given the length of the two other sides.

Using the pythagoras’s theorem;

Square of hypotenuse = square of opposite + square of adjacent

From the diagram, we can see that the length of the cable represents the hypotenuse.

Hence;

AB^2= BC^2 + AC^2

12^2 = 4^2 + AC^2

144 = 16 + AC^2

AC^2 = 144 - 16

AC^2 = 128

AC = √128

AC = 8√2 feet

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nadezda [96]

Answer:

You should make 150 quarts of Creamy Vanilla and 50 quarts of Continental Mocha.

Step-by-step explanation:

This problem can be solved by a system of equations.

The largest profit is going to earned when all the eggs and cups of cream in stock are used.

I am going to call x the number of quarts of Creamy Vanilla and y the number of quarts of Continental Mocha.

The problem states that each quart of Creamy Vanilla uses 2 eggs and each quart of Continental Mocha uses 1 egg. There are 350 eggs in stock, so:

2x + y = 350

Each quart of Creamy Vanilla uses 3 cups of cream, as does each quart of Continental Mocha. There are 600 cups of cream in stock.

So:

3x + 3y = 600 Simplifying by 3.

x + y = 200

We have the following system

1)2x + y = 350

2)x + y = 200

I am going to multiply 2) by (-1) and then add with 1), so i can eliminate y

1)2x + y = 350

2)-x - y = -200

2x - x + y - y = 350 - 200

x = 150

x + y = 200

y = 200 - 150 = 50

You should make 150 quarts of Creamy Vanilla and 50 quarts of Continental Mocha.

3 0
3 years ago
5p/7 - 18 = -43<br> A: -50<br> B: -85 &amp; 2/5<br> C: -31<br> D: -35
Oliga [24]

I'm sorry I really don't know I'm not really good with math that's why I got them brainly for other people's help because I really not that cool math and I'm homeschooled

4 0
3 years ago
F(x)=(-3x+2) and g(x)=(2x^2-5x-1)
pashok25 [27]

Answer: -6x² + 15x + 5

Step-by-step explanation:

To solve this problem, you only need to substitute g(x)'s equation as the value of the x in f(x), then simplify.

Step 1: f(x) = -3(2x² - 5x - 1) + 2

Step 2: Apply the distributive property

-3(2x²) + -3(-5x) + -3(-1)

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Step 3: Simplify

f(x) = -6x² + 15x + 3 + 2

f(x) = -6x² + 15x + 5

6 0
3 years ago
A boat travels 438 km in 8 hours (with a constant speed). How far can it travel in 5 hours (with the same speed
Gre4nikov [31]
The distance that the boat can travel in one hour
=438km/8h
=54.75km/h
The boat can travel in 5 hours
=(54.75*5)km
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3 0
3 years ago
A company had an 8% increase in profits in July. If the July profits were
vovikov84 [41]

Answer:

A- $55k

Step-by-step explanation:

common sense if there was in increase by only 8% that the only logial answer that would be the A- : $4444 when you multiply 8% of 55,555

5 0
2 years ago
Read 2 more answers
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