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snow_lady [41]
3 years ago
5

A ladder is leaning against a building and makes 42° angle with the ground. The top of the ladder reaches 30 feet up on the buil

ding. What is the length of the ladder?
Mathematics
2 answers:
Alex73 [517]3 years ago
4 0
Here we have a right triangle with hypotenuse h, which is to be found.  The top of the ladder is 30 feet above the ground, and that distance is opposite the 42 degree angle mentioned.   Use the sine function to determine the hypotenuse, h:

sin 42 deg = opp / hyp, or     hyp*sin 42 deg = 30 ft.  Then hyp = (30 ft)(sin 42), which in turn equals       hyp = (30 ft) / (0.669) = 44.8 feet (answer)
Ivanshal [37]3 years ago
3 0

Answer:

44.8

Step-by-step explanation:

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What is the solution for this inequality? 3(x-4)>5(x-2)-8
Marizza181 [45]

3x - 12 > 5x - 10 - 8 \\ 10 + 8 - 12 > 5x - 3x \\ 6 > 2x \\ x < 3
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3 years ago
What is an integer in math​
4vir4ik [10]

Answer:

An integer is any negative or positive number that’s not a fraction. Ex: 1, -3

Step-by-step explanation:

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2 years ago
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After 4,000 gallons of water were added to a large water tank that was already filled to 3/4 of its capacity, the tank was then
dangina [55]

Answer:  The correct option is

(E) 80,000.

Step-by-step explanation:  Given that after adding 4,000 gallons of water to a large tank that was already filled to \dfrac{3}{4} of its capacity, the tank was then at \drac{4}{5} of its capacity.

We are to find the number of gallons of water that the tank hold when filled to capacity.

Let the tank can hold x gallons of water when filled to capacity.

Then, according to the given information, we have

\dfrac{3}{4}x+4000=\dfrac{4}{5}x\\\\\\\Rightarrow \dfrac{4}{5}x-\dfrac{3}{4}x=4000\\\\\\\Rightarrow \dfrac{16-15}{20}x=4000\\\\\Rightarrow x=4000\times20\\\\\Rightarrow x=80000.

Thus, the required capacity of the tank is 80,000 gallons of water.

Option (E) is CORRECT.

4 0
3 years ago
The area A, in square meters, of a rectangle with a perimeter of 60 meters is given by the equation A = 30w − w2, where w is the
Delvig [45]

Answer:

Step-by-step explanation:

The area is given in two ways:  1) as a formula:  A = 30w - w^2, and 2) as a specific numerical value:  A = 200 m^2.

Equating these, we get:

A = 200 m^2 = A = 30w - w^2

Rewriting this equation in the standard form of a quadratic function:

-30w + w^2 + 200 m^2 = 0

or  w^2 - 30w + 200 = 0, which in factored form is (w - 10)(w - 20) = 0.

Then w = 10 and w = 20.

The perimeter of the rectangle is P = 60 m, and this equals 2w + 2l.  Therefore, 30 m = w + l, or l = 30 - w.  

We have already found that w could be either 10 or 20.

If w = 10, then l = 30 - 10 = 20, and the perimeter would thus be:

P = 2(10) + 2(20) = 20 + 40 = 60.

This satisfies the constraints on w.

The width of the rectangle is 10 meters.  The length is 20 meters.

5 0
3 years ago
Algebra help please?
Alika [10]

Ok, basically if you want to find when both equations are equal just make them equal to each other. 0.925x^2 - 4x + 20  = -1.125x^2 + 6x + 40.

From there use algebraic steps to find out what x is ( the break - even point ).

0.925x^2 - 4x + 20 = -1.125x^2 + 6x + 40

0.855625x - 4x + 20 = 1.265625x + 6x + 40

-0.41x - 4x + 20 = 6x + 40

-4.41x + 20 = 6x + 40

20 = 10.41x + 40

-20 = 10.41x

-1.92122958694 = x

Rounded to the nearest tenth it's -1.9 = x.

Tell me if I got something wrong :)

3 0
3 years ago
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