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2 years ago

What is the y-intercept of the function f(x) = –4 • 2x? A. (0, –4) B. (0, –8) C. (0, 4) D. (0, 2)

1 answer:

5 0

_C because multiply 2X times f(x) Kansas X out to make it zero Sony multiply -4 times X it will leave you with a positive four instead since X times X

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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

If the area of a rectangle in terms of x is x2 + 15x + 26 / 6x2 and its width is x2 - 3x - 10 / 30x3 Find the length of the rect

Veseljchak [2.6K]

Answer:

The length of the rectangle is;

5x(x+13)/(x-5)

Step-by-step explanation:

Mathematically, we know that the area of a rectangle is the product of the length and width of the triangle

To find the length of the rectangle, we will have to divide the area by the width

we have this as;

(x^2 + 15x + 26)/6x^2 divided by (x^2-3x-10)/30x^3

thus, we have ;

(x^2 + 15x + 26)/6x^2 * 30x^3/(x^2-3x-10)

= (x^2+15x+ 26)/(x^2-3x-10) * 5x

But;

(x^2 + 15x + 26) = (x+ 2)(x+ 13)

(x^2-3x-10) = (x+2)(x-5)

Substituting the linear products in place of the trinomials, we have;

(x+2)(x+13)/(x+2)(x-5) * 5x

= 5x(x+13)/(x-5)

4 0

3 years ago

PLEASE HELP ITS DUE TODAY URGENT!

vlada-n [284]

Step-by-step explanation:

7. ∆ABC = ∆ILH by SSS

as, AB = IL , BC = LH , CA = HI

8. ∆DEF = ∆AMS by ASA

as , angle D = angle A, EF = MS , angle F = Angle S

9. ∆JKL = ∆HAT by SAS

as, JK = HA , KL = AT , angle L = angle T

10. ∆ABC = ∆KPG by ASA

as , CA = GK, Angle c = angle G and Angle B = angle P

11. ∆ABC = ∆YDE by ASA

as , angle A = angle Y, AB = YD , angle B = angle D

12. ∆MNO = ∆SAK by ASA

as , Angle M = angle S, NO = AK, angle O = angle K

hope this answer helps you dear...and may u have a great day ahead!

7 0

3 years ago

What is 5,000 + 5,000?

BaLLatris [955]

Answer:

5,000+5,000= 10000

Step-by-step explanation:

6 0

3 years ago

Is 4/3 greater than 4/8?

soldi70 [24.7K]

4/3 is greater than 4/8
This is because 4/3 is 1.33 in decimal from. Whereas 4/8 is 1/2 in decimal form
So, obviously 4/3 is greater ;)

3 0

3 years ago

Read 2 more answers