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Tomtit [17]
3 years ago
7

The quadratic function f(x) has a vertex at (9, 8) and opens upward. If g(x) = 4(x − 8)2 + 9, which statement is true?

Mathematics
1 answer:
Colt1911 [192]3 years ago
6 0
ANSWER

D.
The minimum value of g(x) is greater than the minimum value of f(x).

EXPLANATION

It was given that;

f(x)
has a vertex at

(9,8)

and opens upwards.

This means that f(x) is a minimum graph and hence have a minimum value of 8.

Also ,

g(x) = 4 {(x - 8)}^{2} + 9

When we compare this function to

y = a {(x - h)}^{2} + k

We can see that,a=4, h=8 and y=9.

The vertex is

(8,9)

Since a>0, the graph opens upwards.

The graph has a minimum point which is (8,9) and hence the minimum value is 9.

We can see that, the minimum value of g(x) is greater than the minimum value of f(x).

Therefore the correct answer is D.
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The first one

Step-by-step explanation:

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30 points!!<br> What is the sum of the first six terms of the series?<br> 48 - 12 + 3 - 0.75 +...
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The sum of the first six terms is 38.39

Step-by-step explanation:

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To find the sum of first six terms, we need to find the fifth and sixth term of the sequence.

To find the fifth term:

The general form of geometric sequence is a_{n}=a_{1} \cdot r^{n-1}

To find the fifth term, substitute n=5 in a_{n}=a_{1} \cdot r^{n-1}

\begin{aligned}a_{5} &=(48) \cdot\left(-\frac{1}{4}\right)^{5-1} \\&=(48) \cdot\left(-\frac{1}{4}\right)^{4} \\&=(48)\left(\frac{1}{256}\right) \\a_{5} &=0.1875\end{aligned}

To find the sixth term, substitute n=6 in a_{n}=a_{1} \cdot r^{n-1}

\begin{aligned}a_{6} &=(48) \cdot\left(-\frac{1}{4}\right)^{6-1} \\&=(48) \cdot\left(-\frac{1}{4}\right)^{5} \\&=(48)\left(-\frac{1}{1024}\right) \\a_{5} &=-0.046875\end{aligned}

To find the sum of the first six terms:

The general formula to find Sn for |r| is S_{n}=\frac{a\left(1-r^{n}\right)}{1-r}

\begin{aligned}S_{6} &=\frac{48\left(1-\left(-\frac{1}{4}\right)^{6}\right)}{1-\left(-\frac{1}{4}\right)} \\&=\frac{48\left(1-\frac{1}{4096}\right)}{1+\frac{1}{4096}} \\&=\frac{48(0.95)}{5} \\&=\frac{48(0.9998)}{5} \\&=\frac{48(0.9998)}{5} \\&=\frac{47.9904}{5} \\&=38.39\end{aligned}

Thus, the sum of first six terms is 38.39

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