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Ugo [173]
3 years ago
8

Consider a sequence defined by the recursive rule f(1) = 15; f(n)=f(n - 1) - 6 for n 2. Choose True or

Mathematics
1 answer:
Shkiper50 [21]3 years ago
5 0

Answer:

The second term of the sequence is 8  False ⇒ B

The third term of the sequence is 3  True ⇒ A

The fourth term of the sequence is -3  True ⇒ A

Step-by-step explanation:

The form of the recursive rule is:

f(1) = first term; f(n) = f(n - 1) + d, where

  • f(1) is the first term
  • f(n) is the nth term
  • f(n - 1) is the term before the nth term
  • d is the common difference

∵ f(1) = 15, f(n) = f(n - 1) - 6 for n ≥ 2

∴ The first term = 15

∴ d = -6

let us find the 2nd, 3rd, and 4th terms

∵ n = 2

∴ f(2) = f(1) - 6

∵ f(1) = 15

∴ f(2) = 15 - 6 = 9

∴ The second term is 9

∴ The second term of the sequence is 8  False

∵ n = 3

∴ f(3) = f(2) - 6

∵ f(2) = 9

∴ f(3) = 9 - 6 = 3

∴ The third term is 3

∴ The third term of the sequence is 3 True

∵ n = 4

∴ f(4) = f(3) - 6

∵ f(3) = 3

∴ f(4) = 3 - 6 = -3

∴ The fourth term is -3

∴ The fourth term of the sequence is -3 True

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A chemical company makes two brands of antifreeze. The first brand is 20% pure antifreeze, and the second brand is 70% pure anti
andre [41]

Answer:

First brand of antifreeze: 21 gallons

Second brand of antifreeze: 9 gallons

Step-by-step explanation:

Let's call A the amount of  first brand of antifreeze. 20% pure antifreeze

Let's call B the amount of second brand of antifreeze. 70% pure antifreeze

The resulting mixture should have 35% pure antifreeze, and 30 gallons.

Then we know that the total amount of mixture will be:

A + B = 30

Then the total amount of pure antifreeze in the mixture will be:

0.2A + 0.7B = 0.35 * 30

0.2A + 0.7B = 10.5

Then we have two equations and two unknowns so we solve the system of equations. Multiply the first equation by -0.7 and add it to the second equation:

-0.7A -0.7B = -0.7*30

-0.7A -0.7B = -21

-0.7A -0.7B = -21

               +

0.2A + 0.7B = 10.5

--------------------------------------

-0.5A = -10.5

A = \frac{-10.5}{-0.5}

A = 21\ gallons

We substitute the value of A into one of the two equations and solve for B.

21 + B = 30

B = 9\ gallons

3 0
3 years ago
The length of a string is L inches. Samantha cuts it into two unequal pieces such that the length of the small piece is 35% of L
skelet666 [1.2K]

Answer:

The shorter piece   x  =  8.4 in

The longer one    y  =  15.6 in

Step-by-step explanation:

If we cut  a string length  L  in to unequal  pieces we get two pieces

first one with length  x  and the other one with length  y

Let call  x  the smaller piece,  then   y = L  -  x will be the longer one

If   x  =  35 %    then

x  =  0,35* L     and

y = L -  x  =  L - 0,35*L      ⇒  y  =  0,65 L     ⇒ y  =  0.65*24

Now if L  =  24  in

x  =  0,35*24          ⇒               x = 8.4 in

and

L  -  x  =  0.65*L      ⇒       L - x  =  0.65*24     y  =  L  -  x  =  15.6 in

as way of verification you can add the length of the two pieces and find:

8.4  +  15.6  = 24 in

4 0
3 years ago
Need help on this ASAP
vodomira [7]
76 granola bars
to solve this, you need to multiply 15 by 5 for the big boxes and 8 by 2 for the small boxes. 15 x 2 = 60 and 8 x 2 = 16, therefore adding them together gets you 76.
8 0
3 years ago
The temperature T of a refrigerator is at least 35°F and at most 41°F. Write a compound
s344n2d4d5 [400]

The compound inequality for the temperature T of a refrigerator that is at least 35°F and at most 41°F is 35  ≤  T ≤  41

A compound inequality has two inequality statements joined together

The the temperature of the inequality is represented by T

The temperature T of a refrigerator is at least 35°F and at most 41°F

This means that the temperature falls between 35°F and 41°F

Since the temperature, T, is at most 41°F

This can be mathematically interpreted as

T  ≤  41

The temperature, T, is at least 35°F

35  ≤  T

Combining the two inequality statements 35  ≤  T and T  ≤  41, the compound statement formed is:

35  ≤  T ≤  41

The compound inequality for the temperature T of a refrigerator that is at least 35°F and at most 41°F is 35  ≤  T ≤  41

Learn more here: brainly.com/question/11316045

8 0
3 years ago
Explain the difference between a square and a rectangle
uranmaximum [27]
So the difference of a square and a rectangle is that a square is a quadrilateral with all four right angles an all sides are same length. A rectangle has same length on opposite sides of the shape.
 
4 0
3 years ago
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