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SCORPION-xisa [38]

3 years ago

10

Write the prime factorization of 10. Use exponents when appropriate and order the factors from least to greatest (for example, 2

* 2*3*5)

1 answer:

earnstyle [38]3 years ago

5 0

The prime factorization of 10 is 2*5. No exponents required.

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BRAINLIEST AND 30 POINTS FOR WHOEVER CAN EXPLAIN HOW TO GET THESE ANSWERS...

Dvinal [7]

Step-by-step explanation:

Since m∠ACM = 90°, then by angle addition, m∠ACP + m∠PCM = 90°.
Since CP⊥ AM, then by definition of perpendicular, m∠APC = 90°. Since angles of a triangle add up to 180°, that means m∠PAC + m∠ACP = 90°.
By substitution, m∠PCM = m∠PAC.
Since m∠PCM + m∠CMP = 90°, then by substitution, m∠CMP = m∠PAC.
Therefore, by AAA, △ACP and △CMP are similar.

Having proven that the triangles are similar, we can write the proportion:

AP / CP = CP / MP

9 / CP = CP / 16

CP² = 144

CP = 12

Now, we can simply use Pythagorean theorem to find the other sides.

AC² = AP² + CP²

AC² = 9² + 12²

AC = 15

CM² = CP² + PM²

CM² = 12² + 16²

CM = 20

8 0

3 years ago

The perimeter of a college athletic field is 96 meters and the length is 16 m more than the width. Find the length and width.

Andre45 [30]

In order to figure this out, you are going to do the math backwards. If the perimeter of the entire field is 96 meters, you will want to remove 16, which will give you 80 meters. You will then divide this by 2, giving you 40 meters. The width of the field will be 40 meters. That means that the length of the field is going to be 56 meters.

3 0

3 years ago

Which is the answer

sukhopar [10]

Answer:

Inverse property

Step-by-step explanation:

The definition of the inverse property is to add to get a result of zero. Since we are adding the inverse of each term to get a result of zero each time, we are using the inverse property.

6 0

3 years ago

pls solve quickly!: It took a boat 2 hours to reach town A going upstream. The way back was 1h20 min. What is the speed of the b

goldenfox [79]

Answer:

15 mph

Step-by-step explanation:

Given: Boat took 2 hours to reach Town A going upstream.

Speed of stream= 3 mph

Time taken to reach back home= 1 hours 20 minutes

Lets assume distance covered one side be "d" and speed of boat in still water be "s".

∴ Speed of boat in upstream= $(s-3) \ mph$

Speed of boat in downstream= $(s+3)\ mph$

Also converting into fraction of time taken to reach back home.

Remember; 1 hour= 60 minutes

∴ Time taken to reach back home= $60+20= 80\ minutes$

Converting time given into fraction= $\frac{80\ minutes}{60\ minutes} = \frac{4}{3} \ hours$

hence, Time taken to reach back home is $\frac{4}{3} \ hours$

Now forming equation of boat travelling upstream and downstream, considering distance remain constant.

We know, $Distance= speed \times time$

⇒ $(s-3)\times 2= (s+3)\times \frac{4}{3}$

Using distributive property of multiplication

⇒ $2s-6= \frac{4}{3}s +4$

subtracting both side by $\frac{4}{3} s$

⇒ $2s-\frac{4}{3} s-6= 4$

Adding both side by 6

⇒ $2s-\frac{4}{3} s= 10$

taking LCD as 3

⇒ $\frac{2}{3} s= 10$

Multiplying both side by $\frac{3}{2}$

⇒ $s= \frac{3}{2} \times 10$

∴s= 15 mph

Hence, 15 mph is the speed of the boat in still water.

8 0

4 years ago

Rewrite sin^2 2xcos ^2 2x as an expression in terms of the first power of cosine

zavuch27 [327]

Answer:

Step-by-step explanation:

use the formula { a couple of times} cos 2 Θ = 2 cos ² Θ - 1 = 1 - 2 sin ² Θ....your answer will likely have a cos 2x , a cos 4x , and a cos 6x in it.....note : cos ² Θ - sin ²Φ = cos ( Θ + Φ) cos (Θ - Φ) will also be needed for appropriate choices of Θ & Φ in terms of x

8 0

3 years ago