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djverab [1.8K]
3 years ago
9

3. A children's slide is 10 feet long and inclines 64° from the ground. The

Mathematics
1 answer:
Nata [24]3 years ago
3 0

Answer:

  87.0°

Step-by-step explanation:

The law of sines can be used to solve this. We have two sides of a triangle and the angle opposite one of them. We want to find the angle opposite the other known side.

In the attached, the triangle is ΔACS. We have side "a" = 9, and side "c" = 10. Angle A is given as 64°. The law of sines tells us ...

  sin(C)/c = sin(A)/a

  sin(C) = (c/a)sin(A)

  C = arcsin((c/a)sin(A)) = arcsin(10/9·sin(64°)) ≈ 87.03°

The ladder makes an angle of about 87° with the ground.

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Find the area of rectangle ABCD
satela [25.4K]

9514 1404 393

Answer:

  D. 12

Step-by-step explanation:

There are a number of ways to find the area of this rectangle. Perhaps the most straightforward is to find the lengths of the sides and multiply those. The distance formula is useful.

  d = √((x2 -x1)^2 +(y2 -y1)^2)

Using the two upper-left points, we find the length of that side to be ...

  d = √((3 -0)^2 +(3 -0)^2) = √(9 +9) = √18 = 3√2

Similarly, the length of the lower-left side is ...

  d = √((-2 -0)^2 +(-2 -0)^2) = √(4+4) = √8 = 2√2

Then the area of the rectangle is ...

  A = LW

  A = (3√2)(2√2) = 3·2·(√2)^2 = 3·2·2 = 12

The area of rectangle ABCD is 12.

_____

Other methods include subtracting the area of the corner triangles from the area of the bounding square:

  5^2 -2(1/2)(3·3) -2(1/2)(2·2) = 25 -9 -4 = 12

4 0
3 years ago
Please help figure this out with the correct words
mr Goodwill [35]

Answer:

pyramids only have one base.

Step-by-step explanation:

polygon base

5 0
2 years ago
Fiona has a box with 5 red buttons and 9 blue buttons.She randomly selected one button, took it out of the box, then selected an
leonid [27]

Answer:

B. 10/91

Step-by-step explanation:

Box has 5 red buttons and 9 blue buttons.

We add 5 and 9 to get the total buttons.

5 + 9 = 14

Then, we find the probability for a red button.

5/14 = .35

Now, that we've taken out 1 button.

The amount of buttons available changes.

14 - 1 = 13

There are 4 red buttons remaining.

The probability for a red button changes to 4/13.

4/13 = .30

Then, we multiply both probabilities.

.30 x .35 = .111

Convert to a fraction.

.111 = 10/91

Thus it would be B.

7 0
3 years ago
(6m^3 -16m^2 + 15m - 40) / (2m^2 + 5)
Helen [10]
        6m3 - 16m2 + 15m - 40<span> Simplify ————————————————————— 2m2 + 5 </span>Checking for a perfect cube :

<span> 4.1 </span>  <span> 6m3 - 16m2 + 15m - 40</span>  is not a perfect cube 

Trying to factor by pulling out :

<span> 4.2 </span>     Factoring: <span> 6m3 - 16m2 + 15m - 40</span> 

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  15m - 40 
Group 2: <span> -16m2 + 6m3</span> 

Pull out from each group separately :

Group 1:   (3m - 8) • (5)
Group 2: <span>  (3m - 8) • (2m2)</span>
               -------------------
Add up the two groups :
              <span> (3m - 8)  • </span><span> (2m2 + 5)</span> 
<span>Which is the desired factorization</span>

<span>3m-8 is the answer</span>

4 0
3 years ago
Find the value of x. ​
Zinaida [17]

Answer:

x = 12

Step-by-step explanation:

3 0
3 years ago
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