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Lisa [10]
2 years ago
8

If f(1) = 7 and f(n) = 5f (n − 1) then find the value of f(5).

Mathematics
2 answers:
VLD [36.1K]2 years ago
5 0

<u>Answer: </u>

f(5) = 4375

<u>Step-by-step explanation: </u>

f(2) = 5f(1) = 5 × 7 = 35

f(3) = 5f(2) = 5 × 35 = 175

f(4) = 5f(3) = 5 × 175 = 875

f(5) = 5f(4) = 5 × 875 = 4375

nevsk [136]2 years ago
3 0

Answer:

f(5) = 4375

Step-by-step explanation:

Given f(n) = 5f(n - 1) and f(1) = 7

This allows us to find the next term in the sequence from the previous term

f(2) = 5f(1) = 5 × 7 = 35

f(3) = 5f(2) = 5 × 35 = 175

f(4) = 5f(3) = 5 × 175 = 875

f(5) = 5f(4) = 5 × 875 = 4375

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Jim baked 31 cookies. His family ate m of them. Using m, write an expression for the number of cookies that remained.
Serggg [28]

Answer:

31-m

Step-by-step explanation:

Hope this helps!

4 0
3 years ago
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8. The sum of two numbers is 8 less than twice the first number. Their difference is 4 less than twice
Delicious77 [7]

Answer:

14 and 6

Step-by-step explanation:

Let's start by naming the first number x.

We can name the second number y.

We can set up equations to model our situation.

x+y=2x-8

x-y=2y-4

Let's simplify the equations.

x+y=2x-8

Subtract 2x from both sides

-x+y=-8

__________

x-y=2y-4

Subtract 2y from both sides.

x-3y=-4

Add the two equations together to eliminate x.

x-3y=-4

-x+y=-8

________

0x-2y=-12

-2y=-12

Divide both sides by -2.

y=6

The second number is 6.

Plug that back in.

x+6=2x-8

Subtract x from both sides

6=x-8

Add 8 to both sides

x=14

The first number is 14

7 0
3 years ago
Helppppppppppppppppp​
Darina [25.2K]

Answer:

3)

Step-by-step explanation:

An equation is linear if equal changes in x produce equal changes in y.

Let's look at each choice.

1)

A decrease of 10% per year. That means each year, the value of the car is 0.9 times the value of the previous year.

For example, if the original value was $10,000, after 1 year, it is worth 0.9 * $10,000 = $9,000. In 1 year it lost $1,000. In the next year, its value is now 0.9 * $9,000. The value at the end of the 2nd year is $8,100. In the second year, it lost $900 in value. In one period of 1 year it lost $1000 in value. In another equal period of 1 year, it lost $900 in value. A change of 1 year in time produces different changes in loss of value, so it is not linear.

2)

Here, the number doubles every year. Let's say it starts with 100 fish. After 5 years, it has 200 fish. In a change of 5 years in x, the change in y is 100. In the next 5 years, it goes from 200 fish to 400 fish. The change in the second period of 5 years is 200. We see that a change of 5 years can produce a change of 100 fish, but another change of 5 years can produce a change is 100 fish. Since for equal changes in x, the changes in y are not all equal, this is not linear.

3)

Here for every change of 1 day in x, the change in y is 2 liters. Each change of 1 in x always produces a change of 2 in y. This is linear.

4)

Each 2 hours, the amount of caffeine is 2/3 of what it was before. This is similar to the choice 1), and it is not linear.

Answer: 3)

7 0
3 years ago
Sylvia earns $7 per hour at her after school job. After working one week, she received a paycheck for $91.
makvit [3.9K]

Answer:

a.) hours=13

b.) h\leq 15

c.) $$105

Step-by-step explanation:

a.) If she earns $7 'per' hour, this multiplication. After a week, we need to see how many hours she worked to earn $91, so this goes behind the equal sign. Let <em>h</em> be the unknown number of hours:

7h=91

Solve for h. Divide both sides by 7:

\frac{7h}{7}=\frac{91}{7}\\\\h=13

Sylvia worked 13 hours at a rate of $7 an hour.

b.) She can work at most 15 hours a week. At 'most' can also mean less than or equal to. Let <em>h</em> be hours:

h\leq 15

Sylvia can work less than or equal to 15 hours per week.

c.) If Sylvia can work 15 hours, plug in this value for <em>h</em> into an equation when she earns $7 per hour. Let the product of the hours and money equal <em>t</em> for total:

t=7(15)\\t=105

The most money Sylvia can earn in a week is $105.

<em>Finito.</em>

6 0
2 years ago
A fence completely surrounds a pool,that is 30 feet by 10 feet.what is the approximate length,in feet,of the fence
tamaranim1 [39]
Because the fence's dimensions is 30 feet by 10 feet, you can assume that one side of the pool is 30 feet while the other, non-congruent side, is 10 feet. The formula for perimeter, which you are trying to find,  is 2L+2W=P. In this problem, 30 will be your L and 10 will be your W. Therefore, 2(30) +2(10)=80.

So 80 feet will be your answer.
4 0
3 years ago
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