Find the complete factored form of the<br> polynomial:<br> -24a^4

Blue whales eat an average of 5,000 pounds of fish daily, with a standard deviation of 850 pounds. Approximately what percentage

nikklg [1K]

15.87% is the answer

7 0

3 years ago

Lorena has two pieces of ribbons. One piece is 3 meter 14 centimeter long. The other piece is 8 meters 24 centimeters long. How

deff fn [24]

Lorena has
3 meters=300 cm
1st piece=314 cm
8 meters=800 cm
2nd piece=824 cm
together=824+314=1138 cm or 11 meters and 38 cm
1m=100 cm

4 0

3 years ago

Solve the following equations: (a) x^11=13 mod 35 (b) x^5=3 mod 64

tino4ka555 [31]

a.

$x^{11}=13\pmod{35}\implies\begin{cases}x^{11}\equiv13\equiv3\pmod5\\x^{11}\equiv13\equiv6\pmod7\end{cases}$

By Fermat's little theorem, we have

$x^{11}\equiv (x^5)^2x\equiv x^3\equiv3\pmod5$

$x^{11}\equiv x^7x^4\equiv x^5\equiv6\pmod 7$

5 and 7 are both prime, so $\varphi(5)=4$ and $\varphi(7)=6$ . By Euler's theorem, we get

$x^4\equiv1\pmod5\implies x\equiv3^{-1}\equiv2\pmod5$

$x^6\equiv1\pmod7\impleis x\equiv6^{-1}\equiv6\pmod7$

Now we can use the Chinese remainder theorem to solve for $x$ . Start with

$x=2\cdot7+5\cdot6$

Taken mod 5, the second term vanishes and $14\equiv4\pmod5$ . Multiply by the inverse of 4 mod 5 (4), then by 2.

$x=2\cdot7\cdot4\cdot2+5\cdot6$

Taken mod 7, the first term vanishes and $30\equiv2\pmod7$ . Multiply by the inverse of 2 mod 7 (4), then by 6.

$x=2\cdot7\cdot4\cdot2+5\cdot6\cdot4\cdot6$

$\implies x\equiv832\pmod{5\cdot7}\implies\boxed{x\equiv27\pmod{35}}$

b.

$x^5\equiv3\pmod{64}$

We have $\varphi(64)=32$ , so by Euler's theorem,

$x^{32}\equiv1\pmod{64}$

Now, raising both sides of the original congruence to the power of 6 gives

$x^{30}\equiv3^6\equiv729\equiv25\pmod{64}$

Then multiplying both sides by $x^2$ gives

$x^{32}\equiv25x^2\equiv1\pmod{64}$

so that $x^2$ is the inverse of 25 mod 64. To find this inverse, solve for $y$ in $25y\equiv1\pmod{64}$ . Using the Euclidean algorithm, we have

64 = 2*25 + 14

25 = 1*14 + 11

14 = 1*11 + 3

11 = 3*3 + 2

3 = 1*2 + 1

=> 1 = 9*64 - 23*25

so that $(-23)\cdot25\equiv1\pmod{64}\implies y=25^{-1}\equiv-23\equiv41\pmod{64}$ .

So we know

$25x^2\equiv1\pmod{64}\implies x^2\equiv41\pmod{64}$

Squaring both sides of this gives

$x^4\equiv1681\equiv17\pmod{64}$

and multiplying both sides by $x$ tells us

$x^5\equiv17x\equiv3\pmod{64}$

Use the Euclidean algorithm to solve for $x$ .

64 = 3*17 + 13

17 = 1*13 + 4

13 = 3*4 + 1

=> 1 = 4*64 - 15*17

so that $(-15)\cdot17\equiv1\pmod{64}\implies17^{-1}\equiv-15\equiv49\pmod{64}$ , and so $x\equiv147\pmod{64}\implies\boxed{x\equiv19\pmod{64}}$

5 0

3 years ago

Drag the expressions into the boxes to correctly complete the table. Polynomial Not a polynomial

uranmaximum [27]

The answer to the given question is as below:-

Polynomials:-

x³-7x²+9x-5x⁴-20

x⁵-5x⁴+4x³+2x-1

3x²-5x⁴+2x-12

Non-polynomial:-

x⁻5-5x⁻⁴+4x⁻³+2x⁻1-1

$\dfrac{4}{x^4}+ \dfrac{3}{x^3}-\dfrac{2}{x^4}-1$

$\sqrt[4]{x} -\sqrt[3]{x} 4+\sqrt{x}-8x+16$

<h3>What are polynomials?</h3>

A polynomial is a mathematical equation made up of indeterminates and coefficients and involves only addition, subtraction, multiplication, and non-negative integer exponentiation of variables. The exponents of the polynomials can not be irrational.

So the table will be formed as:-

Polynomials:- Non-polynomial:-

x³-7x²+9x-5x⁴-20 x⁻5-5x⁻⁴+4x⁻³+2x⁻1-1

x⁵-5x⁴+4x³+2x-1 $\dfrac{4}{x^4}+ \dfrac{3}{x^3}-\dfrac{2}{x^4}-1$

3x²-5x⁴+2x-12 $\sqrt[4]{x} -\sqrt[3]{x} 4+\sqrt{x}-8x+16$

Therefore the polynomials and non-polynomials are shown in the table above.

To know more about polynomials follow

brainly.com/question/2833285

#SPJ1

5 0

1 year ago

A company has six employees.The salary of five of the employees are P2200,P1300,P800,P940 and P560.When the sixth employee is in

Dafna1 [17]

Answer:

First answer is 1200

Second answer is 900 for each new employee

Step-by-step explanation:

First answer:

2200+1300+800+940+560+x = 7000

5800+x = 7000 subtract 5800 from both sides and you get your answer

x = 1200

Second answer:

x = 900. Each of the two employees made 900 a month or 1800 a month for both of them.

To find the average we take the total salaries and divide by the number of people to find the average salary. In this case, we know the average and we know all of the salaries, but two. We can figure this out.

(7000 + 2x)/8 = 1100 multiple both sides by 8 to clear the fraction/

7000 +2x = 8800 Subtract both sides by 7000

2x = 1800 Divide both sides by 2

x = 900

3 0

1 year ago

Find the complete factored form of the polynomial: -24a^4 – 20a^3