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svp [43]
2 years ago
7

Solve the system of equations

Mathematics
1 answer:
Kazeer [188]2 years ago
8 0

Answer:

(3,4)

Step-by-step explanation:

x+y=7, where y=4, so therefore make x the subject and substitute y=4

x=7-y

x=7-4

x=3

therefore x=3, y=4.

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What is the equation of the line x–3y=18 in slope-intercept form?
Minchanka [31]

Answer:

Simple...

you have: x-3y=18

You want to convert it into slope-intercept form or y=mx+b form-->>>

x-3y=18

Isolate the variable-->>

x-3y=18

-x      -x

-3y=-x+18

Now simply divide...

-3y/-3  = -x+18/-3

y=1/3x=6

Thus, your answer.

3 0
3 years ago
Read 2 more answers
G = x-c/x solve for x
Elan Coil [88]

Answer:

x=\frac{c}{1-g}

Step-by-step explanation:

Step 1: Multiply both sides by x,

 gx=−c+x

Step 2: Add -x to both sides.

gx+−x=−c+x+−x

gx−x=−c

Step 3: Factor out variable x.

x(g−1)=−c

Step 4: Divide both sides by g-1.

\frac{x(g-1)}{g-1} =\frac{-c}{g-1\\}

x=\frac{c}{1-g}

Hope this helps!

5 0
3 years ago
Read 2 more answers
What is the answer? 3(x-5)+2(x-1)
777dan777 [17]
3x-15+2x-2
=5x-17
use the distribution property
5 0
3 years ago
The number of failures of a testing instrument from contamination particles on the product is a Poisson random variable with a m
Mazyrski [523]

Answer:

The probability that the instrument does not fail in an 8-hour shift is P(X=0) \approx 0.8659

The probability of at least 1 failure in a 24-hour day is P(X\geq 1 )\approx 0.3508

Step-by-step explanation:

The probability distribution of a Poisson random variable X representing the number of successes occurring in a given time interval or a specified region of space is given by the formula:

P(X)=\frac{e^{-\mu}\mu^x}{x!}

Let X be the number of failures of a testing instrument.

We know that the mean \mu = 0.018 failures per hour.

(a) To find the probability that the instrument does not fail in an 8-hour shift, you need to:

For an 8-hour shift, the mean is \mu=8\cdot 0.018=0.144

P(X=0)=\frac{e^{-0.144}0.144^0}{0!}\\\\P(X=0) \approx 0.8659

(b) To find the probability of at least 1 failure in a 24-hour day, you need to:

For a 24-hour day, the mean is \mu=24\cdot 0.018=0.432

P(X\geq 1 )=1-P(X=0)\\\\P(X\geq 1 )=1-\frac{e^{-0.432}0.432^0}{0!}\\\\P(X\geq 1 )\approx 0.3508

3 0
3 years ago
Please help me with this​
denis23 [38]

Answer:

20) \displaystyle [4, 1]

19) \displaystyle [-5, 1]

18) \displaystyle [3, 2]

17) \displaystyle [-2, 1]

16) \displaystyle [7, 6]

15) \displaystyle [-3, 2]

14) \displaystyle [-3, -2]

13) \displaystyle NO\:SOLUTION

12) \displaystyle [-4, -1]

11) \displaystyle [7, -2]

Step-by-step explanation:

20) {−2x - y = −9

{5x - 2y = 18

⅖[5x - 2y = 18]

{−2x - y = −9

{2x - ⅘y = 7⅕ >> New Equation

__________

\displaystyle \frac{-1\frac{4}{5}y}{-1\frac{4}{5}} = \frac{-1\frac{4}{5}}{-1\frac{4}{5}}

\displaystyle y = 1[Plug this back into both equations above to get the x-coordinate of 4]; \displaystyle 4 = x

_______________________________________________

19) {−5x - 8y = 17

{2x - 7y = −17

−⅞[−5x - 8y = 17]

{4⅜x + 7y = −14⅞ >> New Equation

{2x - 7y = −17

_____________

\displaystyle \frac{6\frac{3}{8}x}{6\frac{3}{8}} = \frac{-31\frac{7}{8}}{6\frac{3}{8}}

\displaystyle x = -5[Plug this back into both equations above to get the y-coordinate of 1]; \displaystyle 1 = y

_______________________________________________

18) {−2x + 6y = 6

{−7x + 8y = −5

−¾[−7x + 8y = −5]

{−2x + 6y = 6

{5¼x - 6y = 3¾ >> New Equation

____________

\displaystyle \frac{3\frac{1}{4}x}{3\frac{1}{4}} = \frac{9\frac{3}{4}}{3\frac{1}{4}}

\displaystyle x = 3[Plug this back into both equations above to get the y-coordinate of 2]; \displaystyle 2 = y

_______________________________________________

17) {−3x - 4y = 2

{3x + 3y = −3

__________

\displaystyle \frac{-y}{-1} = \frac{-1}{-1}

\displaystyle y = 1[Plug this back into both equations above to get the x-coordinate of −2]; \displaystyle -2 = x

_______________________________________________

16) {2x + y = 20

{6x - 5y = 12

−⅓[6x - 5y = 12]

{2x + y = 20

{−2x + 1⅔y = −4 >> New Equation

____________

\displaystyle \frac{2\frac{2}{3}y}{2\frac{2}{3}} = \frac{16}{2\frac{2}{3}}

\displaystyle y = 6[Plug this back into both equations above to get the x-coordinate of 7]; \displaystyle 7 = x

_______________________________________________

15) {6x + 6y = −6

{5x + y = −13

−⅚[6x + 6y = −6]

{−5x - 5y = 5 >> New Equation

{5x + y = −13

_________

\displaystyle \frac{-4y}{-4} = \frac{-8}{-4}

\displaystyle y = 2[Plug this back into both equations above to get the x-coordinate of −3]; \displaystyle -3 = x

_______________________________________________

14) {−3x + 3y = 3

{−5x + y = 13

−⅓[−3x + 3y = 3]

{x - y = −1 >> New Equation

{−5x + y = 13

_________

\displaystyle \frac{-4x}{-4} = \frac{12}{-4}

\displaystyle x = -3[Plug this back into both equations above to get the y-coordinate of −2]; \displaystyle -2 = y

_______________________________________________

13) {−3x + 3y = 4

{−x + y = 3

−⅓[−3x + 3y = 4]

{x - y = −1⅓ >> New Equation

{−x + y = 3

________

\displaystyle 1\frac{2}{3} ≠ 0; NO\:SOLUTION

_______________________________________________

12) {−3x - 8y = 20

{−5x + y = 19

⅛[−3x - 8y = 20]

{−⅜x - y = 2½ >> New Equation

{−5x + y = 19

__________

\displaystyle \frac{-5\frac{3}{8}x}{-5\frac{3}{8}} = \frac{21\frac{1}{2}}{-5\frac{3}{8}}

\displaystyle x = -4[Plug this back into both equations above to get the y-coordinate of −1]; \displaystyle -1 = y

_______________________________________________

11) {x + 3y = 1

{−3x - 3y = −15

___________

\displaystyle \frac{-2x}{-2} = \frac{-14}{-2}

\displaystyle x = 7[Plug this back into both equations above to get the y-coordinate of −2]; \displaystyle -2 = y

I am delighted to assist you anytime my friend!

7 0
3 years ago
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