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valkas [14]
3 years ago
15

What is 3√20 - 3√45 + 5√12 in simplest radical form? Show all work.

Mathematics
1 answer:
lesya692 [45]3 years ago
8 0

Answer: -3√5 + 10√3

Step 1: Find the prime factorization of the number inside the radical.

Step 2: Determine the index of the radical. In this case, the index is two because it is a square root, which means we need two of a kind.

Step 3: Move each group of numbers or variables from inside the radical to outside the radical. In this case, the pair of 2’s and 3’s moved outside the radical.

Step 4: Simplify the expressions both inside and outside the radical by multiplying.


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Ms. Anguiano is enjoying a bicycle ride on a country road
GalinKa [24]

Answer:

The rate is 13 miles per hour

Step-by-step explanation:

* Lets explain how to solve the problem

- Jim lives three miles east of State College

- At noon, he leaves his house and begins to walk due east at a

constant speed of 2 miles per hour

- Annie lives four miles north of State College

- At noon, she leaves her house and begins to bicycle due north at a

constant speed of 8 miles per hour

- The east is perpendicular to the north

* Lets solve the problem

∵ At noon means 12 p.m

∵ They moved till 1 p.m

∵ Jim walked for 1 hour and Annie bicycled for 1 hour

∵ The rate of Jim is 2 miles per hour

∵ The rate of Annie is 8 miles per hour

- The distance = rate × time

∴ Jim walked = 2 × 1 = 2 miles

∴ Annie bicycled = 8 × 1 = 8 miles

- Lets calculate the distance of Jim from the State College till his

position at 1 p.m

∵ Jim lives three miles east of State College

∴ His distance at 1 p.m = 3 + 2 = 5 miles east

- Lats calculate the distance of Annie from the State College till her

position at 1 p.m

∵ Annie lives four miles north of State College

∴ Her distance at 1 p.m = 4 + 8 = 12 miles North

- Lets find the distance between them at 1 p.m

∵ The north ⊥ east

- Use Pythagoras Theorem to find the distance

∴ The distance = √(5² + 12)² = √(25 + 144) = √169 = 13 miles

- The rate = distance/time

∵ The distance between them is 13 miles in 1 hour

∴ The rate = 13/1 = 13 miles per hour

* The rate is 13 miles per hour

6 0
3 years ago
In a right triangle the leg opposite to the acute angle of 30° is 7 in. Find the hypotenuse and other leg.
Maksim231197 [3]
This is a 30-60-90 triangle. 
Therefore, 
7 is A
the other leg is A√3
And the hypotenuse is 2A
So the other leg is 7√3 and the hypotenuse is 14
5 0
3 years ago
Read 2 more answers
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xxMikexx [17]

Answer:14.70

Step-by-step explanation: 14.70

4 0
2 years ago
If x represents one of the equal sides of the triangle, then which equation can be used to solve the problem?
Maksim231197 [3]
X + 2(x + 4) = 32
3x + 8 = 32
3x = 24
x = 8

The lengths of the sides are  8, 12 and 12 (answer),
8 0
2 years ago
You earn $12.50 an hour at your job. How many hours do you need to work to<br> make more than $425?
Harman [31]
37 hours
$425/$12.50= 36.16
rounded= 37
4 0
2 years ago
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