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Kazeer [188]
2 years ago
10

While filling a pool 144centimeters deep, Fiona notices it has taken 2 hours to fill it up to a depth of 36 centimeters. 1a At w

hat rate, in meters per hour, is the pool being filled up? Leave your answer as a decimal.
Mathematics
1 answer:
Aneli [31]2 years ago
7 0

Answer:

Rate at which pool is getting filled 0.18 m/hr

Step-by-step explanation:

Given

Depth up to which the pool gets filled in two hours is equal to 36 centimeter

As we know

One meter = 100 centimeter

So 36 centimeter is equal to 0.36 meter

Rate at which pool is getting filled is equal to height up to which water is filled in 2 hours divided by time taken

Rate at which pool is getting filled \frac{0.36}{2} = 0.18 m/hr

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One month Ivanna rented 7 movies and 9 video games for a total of $80. The next month she rented 5 movies and 3 video games for
ZanzabumX [31]

Answer:

each movie costs $2.75, each video game costs $6.75

Step-by-step explanation:

x = movies, y = video games

7x + 9y = 80

5x + 3y = 34

simplified to

x = 11/4 , y = 27/4

5 0
2 years ago
A six-foot-tall person is standing next to a flagpole. The person is casting a shadow 1 1/2 feet in length, while the flagpole i
lara31 [8.8K]

Answer: 20 ft

This problem can be solved by the Thales’s theorem, which states:

<em>Two triangles are similar when they have equal angles and proportional sides  </em>

It should be noted that to apply Thales' Theorem, it is necessary to establish <u>the two triangles are similar</u>, that is, that t<u>hey have the corresponding angles equal or that their sides are proportional to each other.  </u>

<u />

Now, if we measure the shadow of the flagpole and the shadow of the person, <u>at the same moment</u>, we can use the first Thales' Theorem to calculate the height of the flagpole, knowing the height of the person.

In this case we have two similar triangles (Figure attached) where H is the height of the flagpole, h=6 ft is the height of the person, A=5 ft is the length of the shadow of the flagpole and a=1\frac{1}{2}=1.5 ft is the length of the shadow of the person.

Having this clear, we can write the following relation with both similar triangles:

\frac{H}{h}=\frac{A}{a}   (1)

We know all these lengths except H, which is the value we want to to find.  

So, in order to approach this problem we have to find H from equation (1):  

H=\frac{A}{a}h  

H=\frac{5 ft}{1.5 ft}(6 ft)  

Then:

H=20 ft >>>>>This is the height of the flagpole

4 0
3 years ago
PLEASE HELP!! find the value of x. attached image.
slamgirl [31]

Answer:

x     =   4.712145

Step-by-step explanation:

Given a=20 and b=28,

c = 4√74 = 34.409301068171

∠α = 35.538° = 35°32'16" = 0.62025 rad

∠β = 54.462° = 54°27'44" = 0.95055 rad

Area = 280

Perimeter = 82.409301068171

<h2><u>_____________________________________</u></h2>

Let's solve your equation step-by-step.

9x−8=34.409301

Step 1: Add 8 to both sides.

9x−8+8=34.409301+8

9x=42.409301

Step 2: Divide both sides by 9.

\frac{9x}{9} =\frac{42.409301}{9}

x=4.712145

<h2>Answer:</h2><h2>x=4.712145</h2>

4 0
2 years ago
Evaluate 7(m-11) if m =11
melamori03 [73]

Answer:

0

Step-by-step explanation:

Plug in 11 for m. Remember to follow PEMDAS. First solve the parenthesis, then multiply.

m = 11

7(m - 11) = 7(11 - 11) = 7(0) = 0

0 is your answer.

~

7 0
3 years ago
Read 2 more answers
If the smallest angle of a triangle is 20° and it is included between sides of 4 and 7, then (to the nearest tenth) the smallest
lawyer [7]

Answer:

3.5

Step-by-step explanation:

The smallest side of a triangle is formed by the smallest angle in the triangle.

To find the side opposite (formed by) the 20 degree angle, we can use the Law of Cosines. The Law of Cosines states that for any triangle, c^2=a^2+b^2-ab\cos \gamma, where a, b, and c are the three sides of the triangle and \gamma is the angle opposite to c.

Let c be the side opposite to the 20 degree angle.

Assign variables:

  • a\implies 4
  • b\implies 7
  • \gamma \implies 20^{\circ}

Substituting these variables, we get:

c^2=4^2+7^2-2(4)(7)\cos 20^{\circ},\\c^2=16+49-56\cos 20^{\circ},\\c^2=12.377213236,\\c=\sqrt{12.377213236}=3.51812638147\approx \boxed{3.5}

Therefore, the shortest side of this triangle is 3.5.

5 0
3 years ago
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