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3 years ago

Find the first five terms of the geometric sequence whose constant ratio is -5 and whose first term is 6.

Mathematics

2 answers:

Molodets [167]3 years ago

6 0

Answer: 6, -30, 150, -750 and 3750.

Step-by-step explanation:

First term= 6

Second term= ar = 6×(-5)= -30

Third term= ar^2 = 6×(-5)(-5) = 150

Forth term= ar^3 = 6×(-5)^3 = -750

Fifth term= ar^4 = 6×(-5)^4 = 3750

saw5 [17]3 years ago

5 0

Answer: 6,-30,150,-750,3750

Step-by-step explanation:

Geometric progression formula is

An=a1r^(n-1)

An= nth term

A1= first term

R= common ratio

N= nth position

A1=6

R=-5

We already know the first term,looking for 2nd 3rd 4th & 5th

A2=a1r^(n-1)

A2=6×(-5^(2-1))

A2=6×(-5^1)

A2=6×-5

A2= -30

A3=a1r^(n-1)

A3=6×(-5^(3-1))

A3=6×(-5^(2))

A3=6×(25)

A3= 150

A4=a1r^(n-1)

A4=6×(-5^(4-1))

A4=6×(-5^3)

A4=6×-125

A4= -750

A5=a1r^(n-1)

A5=6×(-5^(5-1))

A5=6×(-5^(4))

A5=6×(625)

A5=3750

The first 5 numbers are

6,-30,150,-750,3750

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Write the standard form of the equation through: (-5, 4), parallel to y=-6/5x + 2

Yakvenalex [24]

Answer:

y = -6/5x - 2

Step-by-step explanation:

Parallel lines have the same slopes. Given the point, (-5, 4), and the linear equation, y = -6/5x + 2 (where the slope, m = -6/5), we can assume that the other line will have the same slope = -6/5. All we need to do at this point is determine the y-intercept, b, of the other line.

The y-coordinate (b) of the point, (0, b) is the y-intercept of the line where the graph of the linear equation crosses the y-axis. The y-intercept is also the value of y when x = 0.

Using the slope, m = -6/5, and the given point, (-5, 4), substitute these values into the slope-intercept form to solve for b:

y = mx + b

4 = -6/5(-5) + b

4 = 6 + b

Subtract 6 from both sides to isolate b:

4 - 6 = 6 - 6 + b

-2 = b

Therefore, the y-coordinate value of the y-intercept, (0, -2) is b = -2.

The linear equation of the line parallel to y = -6/5x + 2 is:

y = -6/5x - 2 (please take note of the negative value of the y-intercept in the final answer. It is different from the given equation).

Attached is a screenshot of the graphed equations, where it shows the parallel lines with different y-intercepts.

Please mark my answers as the Brainliest, if you find this helpful :)

8 0

3 years ago

A concession stand sell hot dogs and hamburgers. At a football game, 84 hot dogs and 36 hamburgers were sold for $276. At anothe

ICE Princess25 [194]

Answer:

The concession stand sold 46 hot dogs and 32 hamburgers.

Step-by-step explanation:

The first thing to do in algebraic problems is assign variables to things we don't know, so let's start there:

We don't know how many hot dogs the concession stand sold, so we will call that number d.

We don't know how many hamburgers the concession stand sold, so we will call that number h.

Now we translate the statements into algebraic equations:

The number of hot dogs and hamburgers that were sold is 78, so d+h=78.

If each hot dog is sold for 1.25, then the total revenue from hot dogs is given by 1.25d. In the same way, the total revenue from hamburgers is 1.50h. The total revenue from both hot dogs and hamburgers should be the sum of these, and since we are told the total revenue is 105.50, we can say 1.25d+1.5h=105.5.

We now have a system of two linear equations:

d+h=78

1.25d+1.5h=105.5

We can solve it using several methods, though I'm going to go with substitution. Use the first equation to solve for d:

d+h=78

→d=78−h

Now plug this in for d in the second equation:

1.25d+1.5h=105.5

→1.25(78−h)+1.5h=105.5

Solving for h, we have:

97.5−1.25h+1.5h=105.5

0.25h=8