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devlian [24]
2 years ago
9

C. The 100th term of 1, 3, 9, ... is

Mathematics
1 answer:
True [87]2 years ago
4 0

Answer:

Step-by-step explanation:

Remark

We really should have 1 more term in the sequence. There could be a lot of things that determine what the sequence is. I'm going to say that each term is multiplied by 3

Givens

a1 = 1

r = 3

Formula

tn = a1 * 3^(n-1)

t100 = 1 * 3^(100 - 1)

t_100 = 3^99

t_100 = 1.72 * 10^47

This really is a scientific calculator problem. If you don't own such a thing, but you have windows 10 on your computer, go to the calculator. Go to the scientific calculator and put in these key strokes.

3

x^y

99

=

This is what you get

1.7179250691067044367882037658854e+47

Naturally, I rounded it a bit.

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The parabola with equation $y=ax^2+bx+c$ is graphed below:
Mashutka [201]

Answer:

m-n=2

Step-by-step explanation:

Instead of using the standard form, we can use the vertex form of a quadratic equation:

f(x)=a(x-h)^2+k

Where a is the leading coefficient, and (h, k) is our vertex.

Our vertex point is at (2, -4). So, let’s substitute 2 for h and -4 for k:

f(x)=a(x-2)^2-4

Now, we need to determine a.

We know that it passes through the point (4, 12). So, when x is 4, y must be 12. In other words:

12=a((4)-2)^2-4

Solve for a. Subtract within the parentheses:

12=a(2)^2-4

Add 4 to both sides:

16=a(2)^2

Square:

16=4a

Solve:

a=4

Thererfore, the value of a is 4.

So, our function is:

f(x)=4(x-2)^2-4

Now, let’s find our roots. Set the equation to 0 and solve for x:

0=4(x-2)^2-4

4=4(x-2)^2\\1=(x-2)^2\\x-2=\pm1 \\ x=2\pm1 \\ x=3\text{ or } 1

So, our roots are 1 and 3.

The greater root is 3 and the lesser root is 1.

Therefore, m-n, where m>n, is 3-1 or 2.

Our final answer is 2.

4 0
2 years ago
Read 2 more answers
Factor Completely: 3x2 + 9x - 30
enyata [817]

Answer:

3(x-2)(x+5)

Step-by-step explanation:

1. Factor out common term 3

3(x^2 +3x-10)

2. Factor (x^2 +3x-10)

3(x-2)(x+5)

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3 years ago
Find the percent increase. From 32 teachers to 45 teachers.
qaws [65]

Answer:

71.1

Step-by-step explanation:

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Logan is going to invest $61,000 and leave it in an account for 20 years. Assuming
hodyreva [135]

Answer:

its 2.62

Step-by-step explanation:

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3 years ago
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Estimate the difference of 1.9 – 0.7 = ________ by rounding each number to the nearest whole number.
miss Akunina [59]
B 1 since you would round 1.9 to 2 and 0.7 to 1
7 0
3 years ago
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