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2 years ago

The graphs below have the same shape. What is the equation of the blue

Mathematics

1 answer:

Drupady [299]2 years ago

4 0

Answer:

Option C. $g(x)=(x+3)^2+1$

Step-by-step explanation:

The complete question in the attached figure

we know that

The equation of the function f(x) is

$f(x)=x^2$

Is a parabola open upward

The vertex is the point (0,0)

The function g(x) have the same shape

The vertex of the function g(x) is the point (-3,1)

The rule of the transformation of f(x) to g(x) is

(0,0) -----> (-3,1)

(x,y) -----> (x-3,y+1)

That means----> The translation is 3 units at left and 1 unit up

therefore

The equation of the function g(x) in vertex form is equal to

$g(x)=(x+3)^2+1$

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Find the oth term of the geometric sequence 7, 14, 28, ...

yaroslaw [1]

Answer:

The nth term of the geometric sequence 7, 14, 28, ... is:

$a_n=7\cdot \:2^{n-1}$

Step-by-step explanation:

Given the geometric sequence

7, 14, 28, ...

We know that a geometric sequence has a constant ratio 'r' and is defined by

$a_n=a_1\cdot r^{n-1}$

where a₁ is the first term and r is the common ratio

Computing the ratios of all the adjacent terms

$\frac{14}{7}=2,\:\quad \frac{28}{14}=2$

The ratio of all the adjacent terms is the same and equal to

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now substituting r = 2 and a₁ = 7 in the nth term

$a_n=a_1\cdot r^{n-1}$

$a_n=7\cdot \:2^{n-1}$

Therefore, the nth term of the geometric sequence 7, 14, 28, ... is:

$a_n=7\cdot \:2^{n-1}$

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Help on these precalc problems 14-20

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Answer:

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Step-by-step explanation:

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