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3 years ago

Find the solution of the system of equations 5x=-2+7y x-7y=-34

1 answer:

6 0

(1) 5x=-2+7y
(2) x-7y=-34

Using the method of substitution:
Isolating x from the equation (2):
(2) x-7y=-34
x-7y+7y=-34+7y
x=7y-34 (3)

Replacing x by 7y-34 in the first equation:
(1) 5x=-2+7y
5(7y-34)=-2+7y
Solving for y:
35y-170=-2+7y
35y-170+170-7y=-2+7y+170-7y
28y=168
28y/28=168/28
y=6

Replacing y by 6 in equation (3)
(3) x=7y-34
x=7(6)-34
x=42-34
x=8

Answer: The solution of the system of equations is: x=8 and y=6

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What is the answer to -2a-9=6a+15

timurjin [86]

Answer:

$a=-3$

Step-by-step explanation:

$-2a-9=6a+15$

Add 9 to both sides:

$-2a-9+9=6a+15+9$

$-2a=6a+24$

Subtract 6a from both sides:

$-2a-6a=6a+24-6a$

$-8a=24$

Divide both sides by -8:

$\frac{-8a}{-8}=\frac{24}{-8}$

$a=-3$

4 0

3 years ago

Read 2 more answers

You roll two fair dice, a green one and a red one. (a) What is the probability of getting a sum of 7? (Enter your answer as a fr

Lera25 [3.4K]

Answer:

a) 0.167 b)0.056 c)0.023

Step-by-step explanation:

We are given the following information:

Sample space = {(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)

(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)

(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)

(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)

(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)

(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}

Total number of outcomes = 36

Formula:

$\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$

a) P(sum is 7)

Sum 7 possible outcomes = {(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)}

$= P = \displaystyle\frac{6}{36} = \displaystyle\frac{1}{6} = 0.167$

b) P(sum is 11)

Sum 11 possible outcomes = {(5,6), (6,5)}

$= P = \displaystyle\frac{2}{36} = \displaystyle\frac{1}{18} = 0.056$

c) P( sum is 7 or sum is 11)

$= P(\text{sum is 7}) + P(\text{sum is 11}) - (P(\text{sum is 7}\cap \text{sum is 11})) \\= \displaystyle\frac{6}{36} + \displaystyle\frac{2}{36} + 0\\\\= \displaystyle\frac{8}{36} = \displaystyle\frac{2}{9} = 0.223$

7 0

3 years ago

In an investment account what if $2000 is invested. What is the value after 3 years if compounded monthly by 6% ?

OleMash [197]

Compound interest formula A = P(1 +r/100)^n
A = Amount
r = rate = 6
n = number of compounding time.
P = Principal = $2000.
Since we are compounding monthly, r = 6% p.a = (6/12)% per month.
n= 3 years = 3*12 = 36 months.
Note that since we are compounding monthly, our time would be in months.
A = P(1 +r/100)^n
A = 2000 * (1 + (6/12)/100 )^36
A = 2000 * (1 + 6/1200)^36
A = 2000 * (1 + 0.005)^36 Use your calculator
 A = 2000 * (1 .005)^36 = 2393.36
Amount = $2 393.36
That's it. Cheers.

3 0

4 years ago

Please can someone help me answer these questions? Would be really grateful if it was done by the 12th of January. Thank you :)

FrozenT [24]

1. 4g= 37-5
⇒ 4g= 32
⇒ g= 32/4
⇒ g= 8

2. c= 5*6
⇒ c= 30

3. f+4= 3*5
⇒f+4= 15
⇒ f= 15-4
⇒ f= 11.

4. b+6= 30/5
⇒ b+6= 6
⇒ b= 6-6
⇒ b=0

5. a-5= 60/5
⇒ a-5= 12
⇒ a= 12+5
⇒ a= 17

6. e+2= 45/5
⇒ e+2= 9
⇒ e= 9-2
⇒ e= 7

7. d-5= 12/3
⇒ d-5= 4
⇒ d= 4+5
⇒ d= 9

8. m-4= 16/4
⇒ m-4= 4
⇒ m= 4+4
⇒ m= 8

9. q+6= 30/5
⇒ q+6= 6
⇒ q= 6-6
⇒ q= 0

10. h/3= 3+5
⇒ h/3= 8
⇒ h= 8*3
⇒ h= 24

11. 3c= 3-5
⇒ 3c= -2
⇒ c= -2/3

12. x/3= 6-7
⇒ x/3= -1
⇒ x= -1*3
⇒ x= -3

13. 6p= 2+1
⇒ 6p= 3
⇒ p= 3/6
⇒ p= 1/2

14. 2d-7= 27/3
⇒ 2d-7= 9
⇒ 2d= 9+7
⇒ 2d= 16
⇒ d= 16/2
⇒ d=8

15. b-3= 5/2
⇒ b-3= 2.5
⇒ b= 2.5+3
⇒ b= 5.5

16. y-1= 1/3
⇒ y= 1/3+1
⇒ y= 1 1/3

17. 5v= 9-3
⇒ 5v= 6
⇒ v= 6/5
⇒ v= 1.2

18. n-3 = 3*6
⇒ n-3= 18
⇒ n= 18+3
⇒ n= 21

19. t+10= 1*4
⇒ t+10= 4
⇒ t= 4-10
⇒ t= -6

20. 3c+4= 3*5
⇒ 3c+4= 15
⇒ 3c= 15-4
⇒ 3c= 11
⇒ c= 11/3
⇒ c= 3 2/3

Hope this helps~

6 0

4 years ago

Read 2 more answers

Select the correct answer.

coldgirl [10]

Answer:

B.(X - 6)^2 = 14 TNX ME LATER

8 0

3 years ago

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