Mary Catherine makes 2 gallons of punch for her party. How many quarts of punch did she make?

Match each function to its corresponding sequence.

givi [52]

The sequence and their functions are:

f(n) = f(n - 1) + 7 ⇒ 3, 10, 17, 24, 31.....
f(n) = f(n - 1) + 4n - 2 ⇒ 3, 9, 19, 33, 51.....
f(n) = 2[f(n - 1)] ⇒ 3, 6, 12, 24, 48.....

<h3>How to match the functions?</h3>

To do this, we simply set values for n and calculate the function values using the current value of n.

So, we have:

Function 1: f(n) = f(n - 1) + 6n - 5 where f(1) = 3

Let n = 2

f(2) = f(1) + 6(2) - 5 = 3 + 12 - 5 = 10

Let n = 3

f(3) = f(2) + 6(3) - 5 = 10 + 18 - 5 = 23

None of the sequence follows the pattern 3, 10, 23....

Function 2: f(n) = f(n - 1) + 2n - 1 where f(1) = 3

Let n = 2

f(2) = f(1) + 2(2) - 1 = 3 + 4 - 1 = 6

Let n = 3

f(3) = f(2) + 2(3) - 1 = 6 + 6 - 1 = 11

None of the sequence follows the pattern 3, 6, 11....

Function 3: f(n) = f(n - 1) + 6 where f(1) = 3

Let n = 2

f(2) = f(1) + 6 = 3 + 6 = 9

Let n = 3

f(3) = f(2) + 6 = 9 + 6 = 15

None of the sequence follows the pattern 3, 9, 15....

Function 4: f(n) = f(n - 1) + 7 where f(1) = 3

Let n = 2

f(2) = f(1) + 7 = 3 + 7 = 10

Let n = 3, 4 and 5

f(3) = f(2) + 7 = 10 + 7 = 17

f(4) = f(3) + 7 = 17 + 7 = 24

f(5) = f(4) + 7 = 24 + 7 = 31

So, we have:

f(n) = f(n - 1) + 7 ⇒ 3, 10, 17, 24, 31.....

Function 5: f(n) = f(n - 1) + 4n - 2 where f(1) = 3

Let n = 2

f(2) = f(1) + 4(2) - 2 = 3 + 8 - 2 = 9

Let n = 3, 4 and 5

f(3) = f(2) + 4(3) - 2 = 9 + 12 - 2 = 19

f(4) = f(3) + 4(4) - 2 = 19 + 16 - 2 = 33

f(5) = f(4) + 4(5) - 2 = 33 + 20 - 2 = 51

So, we have:

f(n) = f(n - 1) + 4n - 2 ⇒ 3, 9, 19, 33, 51.....

Function 6: f(n) = 2[f(n - 1)] where f(1) = 3

Let n = 2

f(2) = 2 * f(1) = 2 * 3 = 6

Let n = 3, 4 and 5

f(3) = 2 * f(2) = 2 * 6 = 12

f(4) = 2 * f(3) = 2 * 12 = 24

f(5) = 2 * f(4) = 2 * 24 = 48

So, we have:

f(n) = 2[f(n - 1)] ⇒ 3, 6, 12, 24, 48.....

Read more about sequence at:

brainly.com/question/6561461

#SPJ1

7 0

2 years ago

What is the length of the diagonal of the triangle?

Setler79 [48]

Answer:

21.25

Step-by-step explanation:

use the Pythagorean theorem, it is given that the shape is a rectangle so all opposite sides are congruent and all angles are right, since we know that the diagonal forms a right triangle we can use the pythagorean theorem

the Pythagorean theorm is a^2+b^2=c^2 where a and b are the legs (in this case the side of the triangle) and c is the hypotenuse which is the longest side in a right triangle

17^2+12.75^2=x^2

x^2=7225/16

now take the square root of both sides and you get -21.25 and 21.25

distance CAN NOT be negative so -21.25 isn't an option

7 0

3 years ago

A map using a scale inch of 1 to 5 miles shows a section of land with an area of 3.2 in.² what is the actual area of the section

Karolina [17]

Answer:

The actual area of land is 80 mi² .

Step-by-step explanation:

Given that we have to find the actual area so first we have to square the ratio(scale factor) :

1 in : 5 mi

(1 in)² : (5 mi)²

1 in² : 25 mi²

Next, the actual area will be :

1 in² = 25 mi²

(1 × 3.2) in² = (25 × 3.2) mi²

3.2 in² = 80 mi²

6 0

3 years ago

What are the solutions of the quadratic equation?

ANEK [815]

In this proble, we are asked to determine the roots of the quadratic equation x^2 + 11 x = -24. The standard form is x^2 + 11 x + 24 = 0. the second term is the negative sum of the roots and the third terms is the equal to the product of the roots.Hence the roots should be -3 and -8.

8 0

3 years ago

Read 2 more answers

Is this polyhedron a prism, a pyramid, or neither? Explain how you know.

serious [3.7K]

Answer:

Prism

Step-by-step explanation:

Pls give Brainliest.

4 0

1 year ago

Read 2 more answers