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yan [13]
3 years ago
13

8q + 6 = 4q - 14 Please help

Mathematics
2 answers:
Kisachek [45]3 years ago
5 0

Answer:

q = - 5

Step-by-step explanation:

ICE Princess25 [194]3 years ago
3 0

Answer:

q=-5

Step-by-step explanation:

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What is the nth term rule of the quadratic sequence below?
Vladimir [108]

Answer:

3n² + 5n - 2

Step-by-step explanation:

<u>Given sequence</u>:

6, 20, 40, 66, 98, 136, ...

Calculate the <u>first differences</u> between the terms:

6 \underset{+14}{\longrightarrow} 20 \underset{+20}{\longrightarrow} 40 \underset{+26}{\longrightarrow} 66 \underset{+32}{\longrightarrow} 98 \underset{+38}{\longrightarrow} 136

As the first differences are not the same, calculate the <u>second differences:</u>

14 \underset{+6}{\longrightarrow} 20 \underset{+6}{\longrightarrow} 26 \underset{+6}{\longrightarrow} 32 \underset{+6}{\longrightarrow} 38

As the <u>second differences are the same</u>, the sequence is quadratic and will contain an n² term.

The <u>coefficient</u> of the n² term is <u>half of the second difference</u>.

Therefore, the n² term is:  3n²

Compare 3n² with the given sequence:

\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5} 3n^2 & 3 & 12 & 27 & 48 \\\cline{1-5} \sf operation & +3&+8 & +13 & +18 \\\cline{1-5} \sf sequence & 6 & 20 & 40 & 66\\\cline{1-5}\end{array}

The second operations are different, therefore calculate the differences <em>between</em> the second operations:

3 \underset{+5}{\longrightarrow} 8 \underset{+5}{\longrightarrow} 13\underset{+5}{\longrightarrow} 18

As the differences are the same, we need to add 5n as the second operation:

\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5} 3n^2  +5n & 8&22 & 42 & 68\\\cline{1-5}\sf operation & -2 &-2  &-2  & -2  \\\cline{1-5} \sf sequence & 6 & 20 & 40 & 66\\\cline{1-5}\end{array}

Finally, we can clearly see that the operation to get from 3n² + 5n to the given sequence is to subtract 2.

Therefore, the nth term of the quadratic sequence is:

3n² + 5n - 2

6 0
1 year ago
| 2x + 9 | = 15<br> Help pls
ikadub [295]

Answer:

x = 3 and x = -12

Step-by-step explanation:

To solve an absolute value equation, you create two equations, one where the right side is negated and one where the right side isn't:

| 2x + 9 | = 15 becomes:

2x + 9 = 15 and 2x + 9 = -15

2x = 6 and 2x = -24

x = 3 and x = -12

Why this works is that |-x| and |x| will both be equal to 0. Remember that absolute value is the distance a number is away from 0.

4 0
3 years ago
Help help help the choices are <br> A.).10<br> B.).55<br> C.)05
ahrayia [7]
.10 because 1.10 - 1.00 = .10
8 0
3 years ago
Read 2 more answers
Solve the system of equations algebraically. Verify your
xz_007 [3.2K]

Answer:

The solution is the point (0.5,-3)

Step-by-step explanation:

we have

y=4x-5 ----> equation A

y=-3 ----> equation B

Solve the system by substitution

Substitute equation B in equation A

-3=4x-5

Solve for x

Adds 5 both sides

-3+5=4x

2=4x

Divide by 4 both sides

x=0.5

therefore

The solution is the point (0.5,-3)

<em>Verify your  answer using the graph</em>

using a graphing tool

Remember that the solution of the system of equations is the intersection point both graphs

The intersection point is (0.5,-3)

therefore

The solution is the point (0.5,-3)

see the attached figure

8 0
3 years ago
Read 2 more answers
The function f(t) = 16 represents the distance (in feet) a dropped object falls in t seconds. The function g(t) = s, represents
Lady bird [3.3K]

Answer:

16

Step-by-step explanation:

3 0
3 years ago
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