How do I simplify this problem?

Mathematics

1 answer:

Norma-Jean [14]3 years ago

6 0

I think you would just have to find the square roots

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PROMISE to give brainiest but only if you get it right!!!

lilavasa [31]

900 because you have to add 24 squared + 18 squared

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3 years ago

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Show that 3 · 4^n + 51 is divisible by 3 and 9 for all positive integers n.

Leni [432]

Answer:

To prove that 3·4ⁿ + 51 is divisible by 3 and 9, we have;

3·4ⁿ is divisible by 3 and 51 is divisible by 3

Where we have;

$S_{(n)}$ = 3·4ⁿ + 51

$S_{(n+1)}$ = 3·4ⁿ⁺¹ + 51

$S_{(n+1)}$ - $S_{(n)}$ = 3·4ⁿ⁺¹ + 51 - (3·4ⁿ + 51) = 3·4ⁿ⁺¹ - 3·4ⁿ

$S_{(n+1)}$ - $S_{(n)}$ = 3( 4ⁿ⁺¹ - 4ⁿ) = 3×4ⁿ×(4 - 1) = 9×4ⁿ

∴ $S_{(n+1)}$ - $S_{(n)}$ is divisible by 9

Given that we have for S₀ = 3×4⁰ + 51 = 63 = 9×7

∴ S₀ is divisible by 9

Since $S_{(n+1)}$ - $S_{(n)}$ is divisible by 9, we have;

$S_{(0+1)}$ - $S_{(0)}$ = $S_{(1)}$ - $S_{(0)}$ is divisible by 9

Therefore $S_{(1)}$ is divisible by 9 and $S_{(n)}$ is divisible by 9 for all positive integers n

Step-by-step explanation:

5 0

3 years ago

A kite has a height of 36 inches and a width of 30 inches. Explain how to use the area formula for a triangle to find the area o

mote1985 [20]

Height of the kite is = 36 inches.

Width of the kite is = 30 inches

One of the ways to find the area is to draw a vertical line to break the kite into two equal triangles. Mark the base as 36 inches and height as 15 inches .

Now we will use the formula $area=\frac{1}{2}*base*height$ to find the area of each triangle. Then we will add both the areas to find the area of the kite.