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3 years ago

Solve the system of equations. 3x + 4y = -23 x = 3y + 1 y = X=

Mathematics

2 answers:

horrorfan [7]3 years ago

6 0

Answer:

(-5, -2)

Step-by-step explanation:

3x+4y=-23

x=3y+1

since we have what x is, we need to subsitute

3( 3y+1) + 4y= -23

no we need to multiply the number inside the parenthesis by 3

9y + 3 + 4y= -23

combine like terms ( add the numbers or variables that look alike)

9y+4y is 13y

13y+3= -23

since we need to get the y alone we need to subtract 3 on both sides since its the opposite of adding

13y+3-3=-23-3

13y= -26

now we divide 13 on both sides to get Y alone

13y/13= -26/13

y= -2

now since we have y we need to substitute it to find x

x= 3y+1

x= 3( -2) +1

now we mutliply 3 with -2

x= -6 +1

x=-5

those are ur answers

y= -2

x= -5

hope this helped:D

lianna [129]3 years ago

4 0

Answer:

x = -5

y = -2

Step-by-step explanation:

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

tino4ka555 [31]

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

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.

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

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

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

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

What is 7,776 ÷ 24? This is for 30 points.

baherus [9]

Answer:

324

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

ra1l [238]

It cost 5 per game , hope it helps

3 0

3 years ago

(x+2)(x+5) find the following products by using distributive property

nika2105 [10]

Answer:

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

(

)

(

)

becomes:

(

)

(

)

(

)

(

)

We can now combine like terms:

(

)

Step-by-step explanation:

7 0

3 years ago

Kayla and latasha work for a department store the amount of sales they made over the last year was collected monthly in the data

tresset_1 [31]

Based on the information represented by the boxplot ;

Latasha's lowest sale amount = 50

Kayla's median is between 200 and 300

Latasha has a greater spread due to higher IQR value

1.) The Lowest amount of sale made by Latasha in one month

The minimum value is denoted by the starting position of the lower whisker on a boxplot.

Lowest amount of sale made by Latasha = 50

2.) 50% of sales made by Kayla :

50% of sales made marks the median value in a boxplot, it is denoted by the vertical line in between the box.

50% of sales made by Kayla is between 200 and 300

With median sale value being 250

3.) Spread of the middle 50% of sales :

The measure of spread of the middle 50% of a distribution on a boxplot is the Interquartile range (IQR) of the distribution

IQR = Upper Quartile (Q3) - Lower quartile(Q1)

For Latasha :

Q3 = 450 (Endpoint of the box)
Q1 = 150 (starting point of the box)

IQR = 450 - 150 = 300

For Kayla :

Q3 = 375 (Endpoint of the box)
Q1 = 100 (starting point of the box)
IQR = 375 - 100 = 275

Since, Latasha's IQR is greater than Kayla's, then Latasha has a greater mid 50% spread than Kayla.

Learn more :brainly.com/question/24582786

4 0

2 years ago