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2 years ago

6

Solve using the substitution method. Show steps please.

1 answer:

rusak2 [61]2 years ago

7 0

Answer:

X=1, Y=4

Step-by-step explanation:

IN THE ATTACHED FILE

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Which of the following formulas would find the lateral area of a right cylinder

zmey [24]

Answer:

2πrh unit^2.

Step-by-step explanation:

The lateral area is the circumference of the base * the height = 2πrh.

6 0

2 years ago

I need help on this 2 please help

Dovator [93]

Answer:

If we are working in a coordinate plane where the endpoints has the coordinates (x1,y1) and (x2,y2) then the midpoint coordinates is found by using the following formula:

midpoint=(x1+x22,y1+y22)

Step-by-step explanation:

6 0

2 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

Please answer if you think you are kind and beautiful of world

tia_tia [17]

Answer:

y = 0

Step-by-step explanation:

Given (-5, 0) and (0, 0),

Find the slope (m):

$slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 0}{0 - (-5)} = \frac{0}{5} = 0$

Slope (m) = 0.

Find the y-intercept (b):

y-intercept (b) = 0. This is the value of y, when x = 0.

To write the equation of the line, substitute m = 0, and b = 0 into y = mx + b

y = (0)(x) + 0

y = 0 + 0

y = 0

6 0

3 years ago

Ricardo has agreed to tutor for the school. He owes his older brother $59 and would like to end the summer with at least $400 in

Dvinal [7]

Answer:

44 or 45

Step-by-step explanation:

400 divided by nine

5 0

2 years ago

Read 2 more answers