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IRISSAK [1]
4 years ago
7

Solve the system by substitution. -6x+8y=-18 3x=y

Mathematics
2 answers:
pickupchik [31]4 years ago
8 0

Answer:

x = —1, y = —3

Step-by-step explanation:

—6x + 8y = —18 (1)

3x = y (2)

From equation 2,

y = 3x

Now, substitute the value of y into equation 1 as shown below:

—6x + 8y = —18

—6x + 8(3x) = —18

—6x + 24x = —18

18x = —18

Divide both side by the coefficient of x i.e 18

x = —18/18

x = —1

Substitute the value of x into equation 2 as shown below:

y = 3x

y = 3(—1)

y = —3

Therefore, x = —1, y = —3

iren [92.7K]4 years ago
4 0

Answer:(-1,-3)

Step-by-step explanation:Solve for the first variable in one of the equations, then substitute the result into the other equation.

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Use the limit theorem and the properties of limits to find the horizontal asymptotes of the graph of the function g(x) = x2/x2-2
ElenaW [278]

Answer:

Option b is right.

Step-by-step explanation:

A function is given as

g(x) = \frac{x^2}{x^2-2x-1}

Limit is to be found out for x tends to infinity.

We find that numerator and denominator has the same degree.

HEnce a horizontal asymptote exists

COefficients of leading terms are 1 and 1 respectively

Asymtote would be y =1/11 = 1

Alternate method:

When x tends to infinity, 1/x tends to 0

g(x) =\frac{\frac{1}{x^2} }{1-\frac{2}{x} -\frac{1}{x^2} }

by dividing both numerator and denominator by square of x.

Now take limit as 1/x tends to 0

we get

limit is y tends to 1/1 =1

Hence horizontal asymptote is y =1

8 0
4 years ago
if I am taking a 1,747 mile road trip and gas price is at $3.50 per gallon how much money do I need for my trip?
IgorLugansk [536]

Answer:

$305.72

Step-by-step explanation:

If I did the math right that should be correct you might wanna check. 20miles/gallon 1747 / 20 = 87.35 × 3.50

8 0
4 years ago
A taxi company charges a $2.00 base fare plus an additional fare based on a per-mile rate and a per-minute rate. Ryan's first ta
Fed [463]

A $2.00 base fare charge, and per-mile, and per-minute rates related as follows; 3•x + 7•y = 6.5 and 7•x + 14•y = 14, give the distance traveled in the third ride as 4.5 miles

<h3>How can the length of the third ride be calculated?</h3>

The base fare = $2.00

Let <em>x </em>represent the per-mile rate, and let <em>y </em>represent the per-minute rate, we have;

The cost of Ryan's first taxi ride = $8.50

Distance traveled in the first ride = 3.0 miles

Time taken during the first ride = 7 minutes

Therefore;

2 + 3•x + 7•y = 8.5

Which gives;

3•x + 7•y = 8.5 - 2 = 6.5

  • 3•x + 7•y = 6.5...(1)

Distance traveled in the second ride = 7.0 miles

Duration of the second ride = 14 minutes

The second ride cost = $16.00

Therefore;

2 + 7•x + 14•y = 16

Which gives;

7•x + 14•y = 16 - 2 = 14

  • 7•x + 14•y = 14...(2)

Solving the above simultaneous equations by multiplying equation (1) by 2 then subtracting the result from equation (2) gives;

(7•x + 14•y) - 2 × (3•x + 7•y) = 14 - 2×6.5 = 1

x = 1

  • The per-mile rate, <em>x </em>= $1

3•x + 7•y = 6.5

7•y = 6.5 - 3•x

7•y = 6.5 - 3×1 = 3.5

y = 3.5/7 = 1/2 = 0.5

  • The per-minute rate, <em>y </em>= $0.5

Duration of the third taxi ride = 10 minutes

Cost of the third ride = $13.50

Therefore;

2 + 1×a + 10×y = $13.50

Where <em>a </em>is the distance traveled during the third ride, we have;

2 + 1×a + 10×0.5 = $13.50

2 + a + 5 = 13.5

a = 13.5 - 2 - 7 = 4.5

  • The third ride was, <em>a </em>= 4.5 miles

Learn more about simultaneous linear equations here:

brainly.com/question/24085666

#SPJ1

3 0
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Decide whether there is enough information to prove that r∥s. If so, state the theroem you would use.
Nonamiya [84]

Answer:

C

Step-by-step explanation:

if the two lines were parallel, then the alternate, on opposite side of the trasversal, exterior, or not inside the lines, angles would be congruent. sicne they are, the line are parallel

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PLA HURRY !! <br> ABCD is a rhombus. Find AB. Enter your answer as a fraction in simplest form.
rjkz [21]

Answer:

Step-by-step explanation:

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