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3 years ago

Please help asap I need it

Mathematics

1 answer:

Ad libitum [116K]3 years ago

8 0

triangle B. because congruent is supposed to be the same shape same size but triangle b is same shape but a different size

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What number would you add to both sides of x2 + 7x = 4 to complete the square?

Nata [24]

Answer:

12.5

Step-by-step explanation:

(7/2) = 3.5

(3.5)^2 = 12.5

8 0

3 years ago

Prove that $5^{3^n} + 1$ is divisible by $3^{n + 1}$ for all nonnegative integers $n.$

Viktor [21]

When $n=0$ , we have

$5^{3^0} + 1 = 5^1 + 1 = 6$

$3^{0 + 1} = 3^1 = 3$

and of course 3 | 6. ("3 divides 6", in case the notation is unfamiliar.)

Suppose this is true for $n=k$ , that

$3^{k + 1} \mid 5^{3^k} + 1$

Now for $n=k+1$ , we have

$5^{3^{k+1}} + 1 = 5^{3^k \times 3} + 1 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k}\right)^3 + 1^3 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k} + 1\right) \left(\left(5^{3^k}\right)^2 - 5^{3^k} + 1\right)$

so we know the left side is at least divisible by $3^{k+1}$ by our assumption.

It remains to show that

$3 \mid \left(5^{3^k}\right)^2 - 5^{3^k} + 1$

which is easily done with Fermat's little theorem. It says

$a^p \equiv a \pmod p$

where $p$ is prime and $a$ is any integer. Then for any positive integer $x$ ,

$5^3 \equiv 5 \pmod 3 \implies (5^3)^x \equiv 5^x \pmod 3$

Furthermore,

$5^{3^k} \equiv 5^{3\times3^{k-1}} \equiv \left(5^{3^{k-1}}\right)^3 \equiv 5^{3^{k-1}} \pmod 3$

which goes all the way down to

$5^{3^k} \equiv 5 \pmod 3$

So, we find that

$\left(5^{3^k}\right)^2 - 5^{3^k} + 1 \equiv 5^2 - 5 + 1 \equiv 21 \equiv 0 \pmod3$

QED

5 0

1 year ago

the tigers won twice as many football games as thwy lost. They played 96 games. how many games did they win

emmainna [20.7K]

You do 96 divide by 2 which is 48
your answer is 48
<span>they win 48 times
hope i helped!!</span>

4 0

2 years ago

Read 2 more answers

All of the following expressions are equivalent except.___ 2+m m+2 m-(-2) -2-m

Pachacha [2.7K]

Answer:

$\Huge \boxed{-2-m}$

Step-by-step explanation:

2 + m

Rewrite with variable first.

m + 2

Can’t be simplified further.

m - (-2)

Distribute negative sign.

m + 2

-2-m

Rewrite with variable first.

-m - 2

The last expression is not equivalent to m+2.

4 0

2 years ago

15 Points!

Nezavi [6.7K]

Replace f(x) with 0 and swith the equation around to solve for x

x^4 - 32x^2 - 144 = 0

Factor the left side:

(x+6) (x-6) (x^2+4)

so far we have x+6 = 0, x = -6
x -6 = 0, x = 6

solve x^2 +4 = 0
x^2 = -4
x = sqrt(-4)
x = 2i, -21

The answer is B) 2i, 6, -6

8 0

2 years ago

Read 2 more answers