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Leto [7]
3 years ago
15

QUESTION 4

Mathematics
1 answer:
makvit [3.9K]3 years ago
7 0

Answer:

4.1.1) x=1

4.1.2) I need more information

4.2)  y=2

Step-by-step explanation:

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There is black white pants in my room
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Here are some values of sequence Q. Write a recursive definition for the sequence.
Rashid [163]

Answer: Q(n) = Q(n - 1) + 2.5

Step-by-step explanation:

We have 3 values of the sequence Q(n)

These values are:

Q(1) = 3

Q(3) = 8

Q(7) = 18

I would think that this is a geometric sequence.

Remember that the equation for the n-th term of a geometric sequence is:

A(n) = A(1)*r^(n-1)

where r is a constant, and A(1) is the first term of the sequence.

If we rewrite the terms that we know of Q(n) in this way we get:

Q(3) = Q(1)*r^(3 - 1) = 3*r^2 = 8

Q(7) = Q(1)*r^(7 - 1) = 3*r^6 = 18

Then we have two equations:

3*r^2 = 8

3*r^6 = 18

We should see if r is the same for both equations:

in the first one we get:

r^2 = 8/3

r = (8/3)^(1/2) = 1.63

and in the other equation we get:

r^6 = 18/3

r = (18/3)^(1/6) = 1.34

Then this is not a geometric sequence.

Now let's see if this is an arithmetic sequence.

The n-th term of an arithmetic sequence is written as:

A(n) = A(1) + (n - 1)*d

where d is a constant.

If we write the terms of Q(n) that we know in this way we get:

Q(3) = Q(1) + (3 - 1)*d = 3 + 2*d = 8

Q(7) = Q(1) + (7 - 1)*d = 3 + 6*d = 18

We need to see if d is the same value for both equations.

in the first one we get:

3 + 2*d = 8

2*d = 8 - 3 = 5

d = 5/2 = 2.5

In the second equation we get:

3 + 6*d = 18

6*d = 18 - 3 = 15

d = 15/6 = 2.5

d is the same for both terms, then this is an arithmetic sequence.

An arithmetic sequence is a sequence where the difference between any two consecutive terms is always the same value (d)

Then the recursive relation is written as:

A(n) = A(n - 1) + d

Then the recursive relation for Q is:

Q(n) = Q(n - 1) + 2.5

4 0
3 years ago
Rearrange y =1/2x+1to make x the subject.
ella [17]

❤❤❤❤❤❤❤❤❤❤❤❤❤❤

y =  \frac{1}{2} x + 1 \\

Multiply sides by 2

2 \times y = 2 \times ( \frac{1}{2} x + 1) \\

2y =( 2 \times  \frac{1}{2} x) + (2 \times 1) \\

2y = x + 2

x + 2 = 2y

Subtract sides 2

x + 2 - 2 = 2y - 2

x = 2y - 2

Done...

❤❤❤❤❤❤❤❤❤❤❤❤❤

3 0
2 years ago
Read 2 more answers
Write a linear function f withe the values f (10) = 5 and f (2) = -3​
MakcuM [25]

Answer:

(a) f(x)=\frac{1}{2}x

(b)f(x)=-\frac{3}{2}x

Step-by-step explanation:

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2 years ago
Marshall uses 10 ounces of pineapple
garik1379 [7]

Answer:

20 ounces

Step-by-step explanation:

the ratio for 10 ounces of pineapple  juice to make 25 ounces of fruit punch is 2:5

so x:150

x = 20

3 0
2 years ago
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