A box contains 40 cards. Meg takes out 16 cards without looding 2 red. 2 yellow blue, and 4

The explicit rule for a sequence is given. an=4n−1 What is the recursive rule for the sequence?

Gnom [1K]

Answer:

$a_{n+1}=a_n+4$

Step-by-step explanation:

Have in mind the definition of the term $a_n=4\,n-1$ , and now work on what the term $a_{n+1}$ is based on the previous definition:

$a_{n+1} = 4\,(n+1)-1\\a_{n+1}=4\,n+4-1$

In the next step do NOT combine the numerical values, but try to identify the $a_n$ term ( $4\,n-1$ ) in the expression (notice the use of square brackets to group the relevant terms):

$a_{n+1}=4\,n+4-1\\a_{n+1}=[4\,n-1]+4\\a_{n+1}=a_n+4$

So now we have the term " $a_{n+1}$ " defined in a recursive manner based on the previous term " $a_n$ "

8 0

3 years ago

A science teacher has a supply of 5% hydrochloric acid and a supply of 65% hydrochloric acid(HC1). How much of each solution sho

Sphinxa [80]

Assume that the amount needed from the 5% solution is x and that the amount needed from the 65% solution is y.

We are given that, the final solution should be 42 ml, this means that:
x + y = 42 ...........> equation I
This can also be written as:
x = 42-y .......> equation II

We are also given that the final concentration should be 45%, this means that:
5% x + 65% y = 45% (x+y)
0.05x + 0.65y = 0.45(x+y)

We have x+y = 42 from equation I, therefore:
0.05x + 0.65y = 0.45(42)
0.05x + 0.65y = 18.9 .........> equation III

Substitute with equation II in equation III as follows:
0.05x + 0.65y = 18.9
0.05(42-y) + 0.65y = 18.9
2.1 - 0.05y + 0.65y = 18.9
0.6y = 18.9 - 2.1
0.6y = 16.8
y = 28 ml

Substitute with y in equation II to get x as follows:
x = 42-y
x = 42 - 28
x = 14 ml

Based on the above calculations:
amount of 5% solution = x = 14 ml
amount of 65% solution = y = 28 ml
The correct choice is:
The teacher will need 14 mL of the 5% solution and 28 mL of the 65% solution.

6 0

4 years ago

10x3 + 3x2 – 20x – 6

Helga [31]

-2
Because -2(10x+3) is (-20x-6) when you distribute

4 0

3 years ago

Solve the system of equations x – 2y = -19 and - 3x + 5y = 48 by combining<br> the equations.

mr_godi [17]

Answer:

x= -1

y = 9