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Lerok [7]
3 years ago
8

A rectangular folder has a perimeter of 30 inches and an area of 54 square inches. What are the dimensions of the folder?

Mathematics
1 answer:
-Dominant- [34]3 years ago
3 0
We know, perimeter = 2(l + w)
So, 2(l + w) = 30
2l + 2w = 30
Divide the equation 2, 
l + w = 15

Now, Area = l * w
l * w = 54

Substitute the value of l from previous equation, 
(15-w) * w = 54
15w - w² = 54
w² - 15w + 54 = 0
w² - 6w - 9w + 54 = 0
w(w - 6) -9(w - 6) = 0
(w-6)(w-9) = 0
w = 6 or 9

In short, Your Dimensions would be: 6 × 9 in

Hope this helps!
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Find the missing side lengths. Leave your answers as radicals in simplest form.
sattari [20]

Answer:

see explanation

Step-by-step explanation:

To find x use the sine ratio in the right triangle and the exact value

sin60° = \frac{\sqrt{3} }{2} , then

sin60° = \frac{opposite}{hypotenuse} = \frac{14\sqrt{3} }{x} = \frac{\sqrt{3} }{2} ( cross- multiply )

x \sqrt{3} = 28\sqrt{3} ( divide both sides by \sqrt{3} )

x = 28

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

To find y use the tangent ratio in the right triangle and the exact value

tan60° = \sqrt{3} , then

tan60° = \frac{opposite}{adjacent} = \frac{14\sqrt{3} }{y} = \sqrt{3} ( multiply both sides by y )

14\sqrt{3} = y \sqrt{3} ( divide both sides by \sqrt{3} )

y = 14

3 0
3 years ago
Please help with this and explain how to do it, I'll give 15 points
MrRissso [65]

Answer:

Option (4).

Step-by-step explanation:

Outer diameter of the hollow metallic ball = 10 centimeters

Outer radius of this ball = \frac{10}{2} = 5 cm

Volume of the outer ball V_{1} = \frac{4}{3}\pi (r)^3

                                         = \frac{4}{3}\pi (5)^3

Inner radius of the hollow metallic ball = (5 - 1) = 4 cm

Volume of the inner hollow ball V_{2} = \frac{4}{3}\pi (4)^3

Volume of the metal used in the metallic ball = V_{1}-V_{2}

                                                                           = \frac{4}{3}\pi (5)^3-\frac{4}{3}\pi (4)^{3}

                                                                           = \frac{4}{3}\pi [(5)^3-(4)^3]

Therefore, expression given in option (4) will be used to measure the volume of the hollow metallic ball.

8 0
3 years ago
Please help!
Marat540 [252]

Answer:

y= 3(x+5)^2 -4

5 0
3 years ago
Can you explain how you got the answer as well please?
Vikki [24]

Answer:

A. 35

Step-by-step explanation:

The total amount of movies that the critic rates that we are given is 20. Now they want to figure us to figure it out with 100 movies. 20 times 5 is one hundred. We are supposed to look at the 3 star reviews, which is 7 movies. 7 times 5 is 35. Hope this helps!

5 0
2 years ago
Read 2 more answers
A restaurant earns $1073 on Friday and $1108 on Saturday. Write and solve an equation to find the amount xx (in dollars) the res
Brums [2.3K]
(1073 + 1108 + x) / 3 = 1000
(2181 + x) / 3 = 1000 ....multiply both sides by 3
2181 + x = 1000 * 3
2181 + x = 3000
x = 3000 - 2181
x = 819 <== they would need to earn $ 819 on Sunday
8 0
2 years ago
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