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lina2011 [118]
4 years ago
10

Simplify (4^3)^5 - - - - -

Mathematics
2 answers:
MissTica4 years ago
6 0

Answer:

\large\boxed{(4^3)^5=4^{15}}

Step-by-step explanation:

\text{Use}\ (a^n)^m=a^{nm}\\\\(4^3)^5=4^{(3)(5)}=4^{15}

Slav-nsk [51]4 years ago
5 0

Step-by-step explanation: Here we have the number  (4^3)^5.

We can use the relationship: (x^{a} )^{b} = x^{a*b}

so our number can be written as: (4^{3}) ^{5} = 4^{3*5} = 4^{15}.

But you can simplify it further!

we know that 4 = 2^{2}, then 4^{15} = (2^{2}) ^{15} = 2^{2*15} = 2^{30}

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The perimeter of an equilateral triangle is 12\/3 cm. Find the radius, apothem and area of the equilateral triangle.
Irina-Kira [14]

Answer:

<u><em>Radius -  </em></u>4

<u><em>Apothem -  </em></u>2

<u><em>Area - </em></u>12\sqrt{3} or 20.8

Step-by-step explanation:

Try to draw out my explanation so you know what this looks like.

~~~~

This is an equilateral triangle, so all sides are the same length. The perimeter can be divided by 3 to get each side length...

12\sqrt{3}  \div3 = 4\sqrt{3}

Now that we know the side lengths, we can get this started!

~~~~

Now, an equilateral triangle has angles that all equal 60 degrees. We can bisect this into TWO special case triangles of measures 90-60-30.

4 times the square root of 3 will be the hypotenuse, and the smallest leg is always half of that. The larger leg is represented as the small leg times the square root of 3.

Small=2\sqrt{3} \\Hypotenuse = 4\sqrt{3} \\Long =6

By the way, the formula for the area can be either of the two:

A= \frac{1}{2} bh\\or\\A = \frac{1}{2} NAS

we can easily find the area using the first formula.

A= \frac{1}{2} (4\sqrt{3} )(6)\\A=12\sqrt{3}

The radius is the distance from the center to the corners & the apothem is the distance from the center to a side...

So we can divide the big triangle into a mini triangle at the bottom left/right

The height (small leg) of that triangle would be the apothem

The hypotenuse of that triangle would be the radius.

I did the math really quick because this is getting long. Anyhow, the small leg is 2 so is the apothem, and the hypotenus is 4, so is the radius

<em>Happy April Fool's btw, lol.</em>

4 0
3 years ago
On a piece of paper, graph y=-3x-2
svet-max [94.6K]
Hope the answer helps!!!
:)

7 0
3 years ago
Whats the simplified expression for the area of one picture frame? (picture attatched)
dlinn [17]
11 / area / 24rcfrrfffrfrtgtggttccrgrfrc
6 0
3 years ago
If triangle ABC has the following
Free_Kalibri [48]

Answer:

Measure of side C is 7.14

Step-by-step explanation:

In this question, we are to find the length of the side C.

To get this, we are to employ the use of the cosine formula.

Mathematically, this is calculated as;

c^2 = a^2 +b^2 - 2ab*cos(C)

Where; a = 10 b = 3 and c = 15 degrees

Plugging these values into the equation, we have;

C^2 = 10^3 + 3^2 -2(3)(10)Cos 15

C^2 = 100 + 9 - 57.96

C^2 = 51.04

C = √(51.04)

C = 7.14

7 0
3 years ago
Read 2 more answers
Before the advance-purchase deadline, the cost of attending a particular event is $90. After that, the price goes up to $117. Wh
Bond [772]

Answer:

The percent increase in the advance-purchase deadline is 30% because if you divide $90 by 10 you get 9 and multiply that by 3 and you will get an 30% increase

word problem: 90 ÷ 10=  9 x 13 =1 17

3 0
3 years ago
Read 2 more answers
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