Use the pattern below for questions 6 - 8.

Mathematics

1 answer:

Yuliya22 [10]2 years ago

4 0

Answer:

See below

Step-by-step explanation:

The sequence given

6, 19, 58, 175

We see the pattern: triple the previous term plus 1

2) 19 = 6*3 + 1
3) 58 = 19*3 + 1
4) 175 = 58*3 + 1

Next two terms

5) 175*3 + 1 = 526
6) 526*3 + 1 = 1579

Following two terms

7) 1579*3 + 1 = 4738
8) 4738*3 + 1 = 14215

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What value of b will cause the system to have an infinite

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Hi there!

The way that an infinite number of solutions is achieved is when the two equations, when solved together, get an answer which is just a number equal to the same number. To do this, first substitute 6x-b in for y in the second equation.

$-3x+\frac{1}{2}(6x-b)=-3$

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Now, we see that b needs to be equal to -3 when multiplied by -1/2. When both sides are divided by -1/2, b becomes equal to 6. Thus, b must be 6.

Check work:

$6x-6=y$