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3 years ago

5

What is 57 x 4? Enter your answers in the boxes to complete the area model.

1 answer:

Anarel [89]3 years ago

3 0

Answer:

200 + 28= 228

..................

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A roller coaster begins at 418 feet above sea level. Then it descends 384 feet. What is the height of the roller coaster after i

Ainat [17]

Answer:

34 feet

Step-by-step explanation:

418 - 384 = 34 feet above sea level

3 0

2 years ago

Their is no point for brainly if you need to sign in I don't wanna be mean tho

Nesterboy [21]

but it helps with homework and learning how to do stuff you dont know how to do

3 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

A square has a side length of 3x inches and an area of 324 in? What is the value of x

Firdavs [7]

So its a square with a side length of 3x so all sides are 3x so 3x x 3x is 9x 9x = 324 so 924/9 is your answer ;D

8 0

3 years ago

Please someone explain how to solve this piecewise function!!!! Im super confused

Xelga [282]

Answer:

From top to bottom:

$0, 1, 2, -8, -8$

Step-by-step explanation:

We are given the piecewise function:

$g(x) = \left\{ \begin{array}{ll} 0.5x+1 & \text{if } x \leq 2 \\ -8 & \text{if } x > 2 \end{array} \right.$

Row 1:

We want to find g(-2).

Since -2 is less than (or equal to) 2, we will use the first equation. Thus:

$g(-2)=0.5(-2)+1=-1+1=0$

Row 2:

Likewise, 0 is less than or equal to 2. We will continue to use the first equation:

$g(0)=0.5(0)+1=1$

Row 3:

2 is not less than 2 but it is equal to 2. So we will continue to use the first equation:

$g(2)=0.5(2)+1=1+1=2$

Row 4 and 5:

Both 4 and 6 are greater than 2. Thus, we will use the second equation. Therefore:

$g(4)=-8\text{ and } g(6)=-8$

7 0

3 years ago