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labwork [276]
2 years ago
12

Solve the equation a/a^2-9 +3/a-3=1/a+3

Mathematics
1 answer:
MAXImum [283]2 years ago
7 0
Answer is: a= -4
STEP
1
:

1
Simplify —————
a + 3
Equation at the end of step
1
:

a 3 1
(————————+—————)-——— = 0
((a2)-9) (a-3) a+3
STEP
2
:

3
Simplify —————
a - 3
Equation at the end of step
2
:

a 3 1
(————————+———)-——— = 0
((a2)-9) a-3 a+3
STEP
3
:

a
Simplify ——————
a2 - 9
Equation at the end of step
3
:

a 3 1
(————————————————— + —————) - ————— = 0
(a + 3) • (a - 3) a - 3 a + 3

Equation at the end of step
4
:

(4a + 9) 1
————————————————— - ————— = 0
(a + 3) • (a - 3) a + 3
Pull out like factors :

3a + 12 = 3 • (a + 4)

Equation at the end of step
6
:

3 • (a + 4)
————————————————— = 0
(a + 3) • (a - 3)

3•(a+4)
——————————— • (a+3)•(a-3) = 0 • (a+3)•(a-3)
(a+3)•(a-3)

a+4 = 0

Subtract 4 from both sides of the equation :
a = -4
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Divide the two values (19 and 60) to get the fraction 19/60. We can't reduce from here so we leave it like that.
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3 years ago
Verify that 1.5, 5 is a solution to 2x-y=-1​
pav-90 [236]

Place the x (1.5) and y (5) values into the equation, and solve. If the statement you get is true, it is a solution.

2x - y = -1​

2(1.5) - 5 = -1​

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Since this is a false statement, negative 2 is not equal to -1, the ordered pair is NOT a solution. I hope this helps and have a great day!

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2 years ago
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Method:

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S = 1,500/50 = 30

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2 years ago
Identify the independent and dependent variables. Then use the information to determine how many gallons of gas are left after t
lesya692 [45]

Answer:

Independent: miles travelled

Dependent: gallons of gas

Gas remaining after 68 miles: 7.2 gallons

Step-by-step explanation:

Looking at the table, it appears that after every 17 miles of driving, 1 gallon of gas is used.

  • 68 miles would be the next 17 miles after driving 51 miles
  • this means another gallon of gas would be used, so 8.2 - 1 = 7.2 gallons left

The <u>dependent variable</u> is the variable that depends on that of another

  • In this case, the dependent variable is the gallons of gas, because in order for the car to drive, it needs gas

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3 years ago
Bighorn sheep are beautiful wild animals found throughout the western United States. Data for this problem are based on informat
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Answer:

The answer and explanation are below

Step-by-step explanation:

i followed the data that was given in the question.

∑x=15 ; ∑y=87.3;∑x2=55; ∑y2=1569.77; ∑xy=275

a.)  please refer to the attachment for the scatter diagram. Y was plotted against X.

b. The equation is given as:

Y = b₁ + b₀X

∑x=15 ; ∑y=87.3;∑x2=55; ∑y2=1569.77; ∑xy=275

b₁ = n∑xy - (∑x)(∑y)/n(∑x²) - (∑x)²

b₁ = 5 x 275 - 15 x 87.3/5 x 55 - (15²)

= 1375-1309.5/275-225

= 65.5/50

= 1.31

b₀ = 87.3/5 - 1.31(15/5)

= 87.3/5 - 1.31x3

= 13.53

the regression line is

Y = 13.53 + 1.31X

please refer to the attachment for the diagram for the regression line.

c. we are required to find r.

r = n∑XY - (∑X)(∑Y)/√n∑X²-(∑X)² × √n∑y²-(∑y)²

∑x=15 ; ∑y=87.3;∑x2=55; ∑y2=1569.77; ∑xy=275

inserting these values:

r = 5 x 275-(15)(87.3)/√275-225 x √7848.85 - 7621.29

= 65.5/106.69

= 0.6139

Coefficient of determination = r²

r = 0.6139

r² = 0.3769 = 37.69%

Therefore 37.69% variation in y is explained by variation in x and the least square model.

3 0
3 years ago
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