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ss7ja [257]
3 years ago
7

a ladder leans against the sufe of a house. the angle of elevation of the ladder is 70 degrees when the bottom of the ladder is

12 ft from the side of the house. find the length of the ladder. round your answer to the nearest tenth.
Mathematics
1 answer:
nekit [7.7K]3 years ago
4 0

Answer:

≈ 35.1 ft

Step-by-step explanation:

The model is a right triangle with ladder being the hypotenuse and the angle between the ground and the ladder is 70°

Using the cosine ratio, with l being the length of the ladder.

cos70° = \frac{adjacent}{hypotenuse} = \frac{12}{l} ( multiply both sides by l )

l × cos70° = 12 ( divide both sides by cos70° )

l = \frac{12}{cos70} ≈ 35.1 ( to the nearest tenth )

The ladder is approx 35.1 ft long

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Rewrite, using the distributive<br> property.<br> 5(2x – 3y) = [?]* - [ ]y
olchik [2.2K]

Answer:

10x-15y

Step-by-step explanation:

So, when they say use the distrubutive property, they basically mean turning this:

a(b+c)

Into this:

ab+ac

So in this case, it would be:

5(2x-3y)

And we will turn it into:

10x-15y

ANother way to think about it is we are multiplying 2x by 5, and -3y by 5. So:

2x*5

=

10x

And

-3y*5

=

-15y

Then we can combine these two:

10x-15y

Hope this helps!

7 0
3 years ago
Find the distance between the points (0,-2) and (-8,-8)
Ostrovityanka [42]

Answer:

Distance between the points = 10 units

Step-by-step explanation:

Given points:

(0,-2) and (-8,-8)

To find the distance between the two points.

Solution:

Applying distance formula to find the distance between the points.

For points (x_1,y_1) and (x_2,y_2) the distance is given as:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Plugging in the given points in the formula.

d=\sqrt{(-8-0)^2+(-8-(-2))^2}

d=\sqrt{(-8)^2+(-8+2))^2}

d=\sqrt{(-8)^2+(-6)^2}

d=\sqrt{64+36}

d=\sqrt{100}

d=\pm10

Since distance is always positive. So d=10 units.

3 0
3 years ago
On a certain​ route, an airline carries 8000 passengers per​ month, each paying ​$70.A market survey indicates that for each​ $1
son4ous [18]

Answer:

The maximum revenue is $661,250.

Step-by-step explanation:

The total revenue (R) is the product between the number of passengers (N) and the price of each ticket (P), so the inicial revenue is:

R = N * P = 8000 * 70 = $560,000

For each 1$ increase in the ticket, the airline loses 50 passengers, so if we call "x" the increase in the ticket price, we have that the revenue equation will be:

R = (8000-50*x) * (70+x) = 560000 + 8000*x - 50*70*x -50x2

R = -50*x2 + 4500*x + 560000

The value of x that gives the maximum value of a quadratic function is found using the formula:

x = -b/2a

where a and b are coefficients of the quadratic equation (in our case, a = -50 and b = 4500)

So the value of x that gives the maximum revenue is:

x = -4500 / (-100) = 45

Using this value in the revenue equation, we have that the maximum R is:

R = -50*45^2 + 4500*45 + 560000 = $661,250

(To get this revenue, the ticket will cost 70+45 = $115 and there will be 8000-50*45 = 5750 passengers)

3 0
3 years ago
The area of a rectangle is 60 square inches. The length is x – 3, and the width is x + 8. Find the value of x, and the dimension
Vikki [24]

Answer:

x = 7

Length = 4 inches , Width = 15 inches

Step-by-step explanation:

<em>PART</em><em> </em><em>1</em><em> </em><em>:</em>

Area of rectangle = Length × Width

A = L × W

L = x - 3

W = x + 8

Therefore:

A = L × W

60 = ( x - 3 ) ( x + 8 )

( x - 3 ) ( x + 8 ) - 60 = 0

x^2 + 8x - 3x - 24 - 60 = 0

x^2 + 5x - 84 = 0

x^2 + 12x - 7x - 84 = 0

x ( x + 12 ) - 7 ( x + 12 ) = 0

( x + 12 ) ( x - 7 ) = 0

THEREFORE:

x = - 12 , x = 7

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

<em>PART</em><em> </em><em>2</em><em> </em><em>:</em>

L = x - 3

L = ( - 12 ) - 3

L = - 15

OR

L = ( 7 ) - 3

L = 4

THEREFORE:

Length can not be a negative number. Hence, L can not equal to - 15.

L = 4 inches

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

W = x + 8

W = ( 7 ) + 8

THEREFORE:

W = 15 inches

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3 years ago
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11111nata11111 [884]
The volume of the triangular prism is 420
6 0
3 years ago
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