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3 years ago

A + b = 4a please help

Mathematics

1 answer:

LuckyWell [14K]3 years ago

4 0

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There is 12/15 of a pizza left. How many 3/10 pieces can be made from the leftover pizza? Show work please!

Katyanochek1 [597]

How many 1/3 pieces can be made from 2 pizzas, we know it is 6 and it is arrived by dividing 2 by 1/3 or multiplying by its reciprocal 3/1.

Hence to find how many 3/10 pieces can be made from 12/15 pizza, we have to divide 12/15 by 3/10 or multiplying by its reciprocal 10/3, i.e.

12/15 times 10/3= 8/3 or 2 2/3

What does that mean? This means that while 2 three-tenths pieces can be made, 2/3of 3/10 i.e. 2/3×3/10=2/10=1/5 or one-fifth of pizza will be left out.

So the answer is 2 three-tenths pieces can be made, and one-fifth pizza will be left out.

5 0

3 years ago

Solve the following recurrence relation: <img src="https://tex.z-dn.net/?f=A_%7Bn%7D%3Da_%7Bn-1%7D%2Bn%3B%20a_%7B1%7D%20%3D

-Dominant- [34]

By iteratively substituting, we have

$a_n = a_{n-1} + n$

$a_{n-1} = a_{n-2} + (n - 1) \implies a_n = a_{n-2} + n + (n - 1)$

$a_{n-2} = a_{n-3} + (n - 2) \implies a_n = a_{n-3} + n + (n - 1) + (n - 2)$

and the pattern continues down to the first term $a_1=0$ ,

$a_n = a_{n - (n - 1)} + n + (n - 1) + (n - 2) + \cdots + (n - (n - 2))$

$\implies a_n = a_1 + \displaystyle \sum_{k=0}^{n-2} (n - k)$

$\implies a_n = \displaystyle n \sum_{k=0}^{n-2} 1 - \sum_{k=0}^{n-2} k$

Recall the formulas

$\displaystyle \sum_{n=1}^N 1 = N$

$\displaystyle \sum_{n=1}^N n = \frac{N(N+1)}2$

It follows that

$a_n = n (n - 2) - \dfrac{(n-2)(n-1)}2$

$\implies a_n = \dfrac12 n^2 + \dfrac12 n - 1$

$\implies \boxed{a_n = \dfrac{(n+2)(n-1)}2}$

4 0

2 years ago

What is the GCF of 6 and 15? 3 5 6 2

larisa [96]

The answer is three I believe

5 0

3 years ago

Read 2 more answers

Which of the following is equivalent to the complex number i24?

Alika [10]

Answer: 1

Step-by-step explanation:

Rewrite as (i^4)^6

Rewrite i^4 as 1

Rewrite i^4 as (i^2) ^2

((i^2)) ^2)6

Rewrite i^2 as -1

((-1) ^2) 6

Raise -1 to the power of 2

1^6

One to any power is 1.

5 0

2 years ago

The Ruler below shows 7-inches segment divided into 2 equal parts. What is the length of one of those parts. Fill in the blanks

ella [17]

Answer:

$3\frac{1}{2}$

Step-by-step explanation:

If the ruler is divided into 2 equal parts, divide 7 inches by 2

7/2 = 3.5 or 3 $\frac{1}{2}$

8 0

3 years ago