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3 years ago

The coefficients of the expression 3x^4-6x^3+x^2 are ____.

Mathematics

1 answer:

Effectus [21]3 years ago

3 0

its a numerical or constant quantity placed before and multiplying the variable in an algebraic expression

so 3,6,1

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Find the slope Thxxxx

Helga [31]

Answer:

-The slope:

$m = \frac{3}{2}$

Step-by-step explanation:

-To find the slope, you need this trick:

$m= \frac{rise}{run}$

-So, according to the graph, start to the first doted point which is (0,1) to get to the second doted point, which is (2,4) on the graph, by counting how far up and how far across:

Rise: 3

Run: 2

$m= \frac{3}{2}$

So, therefore the slope is $\frac{3}{2}$ .

6 0

3 years ago

Here is the questions sorry

xxMikexx [17]

Answer:

I think the answer is about 10

Step-by-step explanation:

6 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

2 years ago

John earns $7.50 per hour at his job. Becky's earnings are given by the equation P = 8.25x, where P is her

hodyreva [135]

In 9 hours
john earns $67.5
becky earns $74.25
becky earns $6.75 more than john

4 0

3 years ago

7x + 2y=24 8x + 2y=30

Bumek [7]

Answer:

x=6 y=-9

Step-by-step explanation:

Layer the equations on each other as you would in a subtraction problem:

8x + 2y=30

7x + 2y=24

Subtract the equation just like you would normally. This should leave 1x=6 or x=6.
Now that you have your x value, plug it in as x for one of the equations. For the 2nd equation, this leaves:

42+2y=24 then

2y=-18 then

y=-9

Double check your y value by plugging x=6 into the first equation. This should also leave y=-9.

3 0

3 years ago