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ExtremeBDS [4]
2 years ago
5

A 30−60−90 triangle has a longer leg with length 53√4 and a hypotenuse with length 5/2 . What is the length of the shorter leg?

Mathematics
1 answer:
Vlad1618 [11]2 years ago
8 0

The length of the shorter leg is √2

<h3>Pythagoras theroem</h3>

To get the length of the shorter leg, we will use the Pythagoras theorem. According to the theorem:

hyp^2 = opp^2 + adj^2

Given the following

Hyp = √4

Opposite = √2

Required

Adjacent side

Substitute into the formula

(√4 )^2 = 2 + adj^2

4 - 2  = adj^2

adj^2 = 2

adj = √2

Hence the length of the shorter leg is √2

Learn more on Pythagoras theorem here: brainly.com/question/343682

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It takes a hose 2 minutes to fill a rectangular aquarium 8 inches long, 9 inches wide, and 13 inches tall. How long will it take
nirvana33 [79]
To make it easier, you calculate the volume of the first aquarium.

1st aquarium:
V = L x W x H
V = 8 x 9 x 13
V = 72 x 13
V = 936 in.
Rate: 936 in./2 min.

Now that you've got the volume and rate of the first aquarium, you can find how many inches of the aquarium is filled within a minute, which is also known as the unit rate. To do that, you have to divide both the numerator and denominator by their least common multiple, which is 2. 936 divided by 2 is 468 and 2 divided by 2 is 1.
So the unit rate is 468 in./1 min. Now that you've got the unit rate, you can find out how long it'll take to fill the second aquarium up by finding its volume first.

2nd aquarium:
V = L x W x H
V = 21 x 29 x 30
V = 609 x 30
V 18,270 inches

Calculations:
Now, you divide 18,270 by 468 to find how many minutes it will take to fill up the second aquarium. 18,270 divided by 468 is about 39 (the answer wasn't exact, so I said "about").
 
2nd aquarium's rate:
18,270 in./39 min.

As a result, it'll take about 39 minutes to fill up an aquarium measuring 21 inches by 29 inches by 30 inches using the same hose. I really hope I helped and that you understood my explanation! :) If I didn't, I'm sorry. I tried. :(
7 0
3 years ago
315% is what of 82.53
Aloiza [94]
315% is roughly 0.0382 of 82.53.
On the other hand, 315% of 82.53 is 259.9695 .
8 0
3 years ago
Read 2 more answers
2. Write the equation of the circle in general form
Anon25 [30]
(-1,-2) and (-1,4)
so these have same x values, but different y values, so these are on differnt sidef of circle

distanc between them is 6
6/2=3
radius=3

so move 3 units up from (-1,-2)
(-1,1)
so

if center is (h,k) and radius is r then
(x-h)^2+(y-k)^2=r^2

(-1,1) is center and r=3

(x-(-1))^2+(y-1)^2=3^2
(x+1)^2+(y-1)^2=9
5 0
3 years ago
Point D is between Points E and F. DE = 3x + 9, DF = 12x - 1<br> and EF = 38. Find DE and DF.
jarptica [38.1K]

Answer:

DE = 15

DF = 23

Step-by-step explanation:

E___D___F

EF = DE + DF

38 = (3x +9) + (12x-1)

38 = 15x + 8

15x = 38 - 8

15x = 30

x = 30/15

x = 2

DE = 3x + 9 = 3(2) + 9 = 6 + 9 = 15

DF = 12x - 1 = 12(2) - 1 = 24 - 1 = 23

I hope I helped you^_^

7 0
3 years ago
What will be the result if the y-intercept of the line shown is changed to an 8,
nataly862011 [7]

I’m on the same question rn and I need help.

4 0
3 years ago
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