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KonstantinChe [14]
3 years ago
11

How does the graph of g(x) = (x + 2)3 − 7 compare to the parent function of f(x) = x3? g(x) is shifted 2 units to the right and

7 units down. g(x) is shifted 7 units to the right and 2 units up. g(x) is shifted 2 units to the left and 7 units down. g(x) is shifted 7 units to the left and 2 units down
Mathematics
1 answer:
Nitella [24]3 years ago
6 0

Answer: g(x) is shifted 2 units to the left and 7 units down.

Step-by-step explanation:

  • The original function f(x) becomes f(x+c), if it is shifted c units to the left.
  • The original function f(x) becomes f(x-c), if it is shifted c units to the right.
  • Also, if it is shifted d units down, then the function becomes f(x)-d.
  • If it is shifted d units up, then the function becomes f(x)+d.

Here, if we compare the graph of g(x) = (x + 2)^3 -7 compare to the parent function of f(x) = x^3.

We can observe that f(x) is shifted  2 units to the left and 7 units down.

So, the correct statement is "g(x) is shifted 2 units to the left and 7 units down".

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In a G.P the difference between the 1st and 5th term is 150, and the difference between the
liubo4ka [24]

Answer:

Either \displaystyle \frac{-1522}{\sqrt{41}} (approximately -238) or \displaystyle \frac{1522}{\sqrt{41}} (approximately 238.)

Step-by-step explanation:

Let a denote the first term of this geometric series, and let r denote the common ratio of this geometric series.

The first five terms of this series would be:

  • a,
  • a\cdot r,
  • a \cdot r^2,
  • a \cdot r^3,
  • a \cdot r^4.

First equation:

a\, r^4 - a = 150.

Second equation:

a\, r^3 - a\, r = 48.

Rewrite and simplify the first equation.

\begin{aligned}& a\, r^4 - a \\ &= a\, \left(r^4 - 1\right)\\ &= a\, \left(r^2 - 1\right) \, \left(r^2 + 1\right) \end{aligned}.

Therefore, the first equation becomes:

a\, \left(r^2 - 1\right) \, \left(r^2 + 1\right) = 150..

Similarly, rewrite and simplify the second equation:

\begin{aligned}&a\, r^3 - a\, r\\ &= a\, \left( r^3 - r\right) \\ &= a\, r\, \left(r^2 - 1\right) \end{aligned}.

Therefore, the second equation becomes:

a\, r\, \left(r^2 - 1\right) = 48.

Take the quotient between these two equations:

\begin{aligned}\frac{a\, \left(r^2 - 1\right) \, \left(r^2 + 1\right)}{a\cdot r\, \left(r^2 - 1\right)} = \frac{150}{48}\end{aligned}.

Simplify and solve for r:

\displaystyle \frac{r^2+ 1}{r} = \frac{25}{8}.

8\, r^2 - 25\, r + 8 = 0.

Either \displaystyle r = \frac{25 - 3\, \sqrt{41}}{16} or \displaystyle r = \frac{25 + 3\, \sqrt{41}}{16}.

Assume that \displaystyle r = \frac{25 - 3\, \sqrt{41}}{16}. Substitute back to either of the two original equations to show that \displaystyle a = -\frac{497\, \sqrt{41}}{41} - 75.

Calculate the sum of the first five terms:

\begin{aligned} &a + a\cdot r + a\cdot r^2 + a\cdot r^3 + a \cdot r^4\\ &= -\frac{1522\sqrt{41}}{41} \approx -238\end{aligned}.

Similarly, assume that \displaystyle r = \frac{25 + 3\, \sqrt{41}}{16}. Substitute back to either of the two original equations to show that \displaystyle a = \frac{497\, \sqrt{41}}{41} - 75.

Calculate the sum of the first five terms:

\begin{aligned} &a + a\cdot r + a\cdot r^2 + a\cdot r^3 + a \cdot r^4\\ &= \frac{1522\sqrt{41}}{41} \approx 238\end{aligned}.

4 0
3 years ago
What graph represents the solution set of this system of inequalities? {y≤2x 1} {y>−2x−3}
Genrish500 [490]
Already been answered||Vhttps://brainly.com/question/8240602


5 0
3 years ago
Find the equation of the line. HELPPPPP
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(4,-7) I’m sorry if you get it wrong hope it helpss
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Choose the correct simplification of (4x − 3)(3x2 − 4x − 3).
Korolek [52]

the expression simplified is:

12x^3 - 25x^2 + 9

<h3>How to simplify the given expression?</h3>

Here we have the expression:

(4x - 3)*(3x^2 - 4x - 3)

We just need to distribute the product, we will get:

(4x - 3)*(3x^2 - 4x - 3)\\\\(4x)*(3x^2 - 4x - 3)  - 3*(3x^2 - 4x - 3)\\\\12x^3 - 16x^2 - 12x - 9x^2 + 12x + 9

Now we just need to group terms with the same exponent of x:

12x^3 - 16x^2 - 12x - 9x^2 + 12x + 9\\\\12x^3 + (-16 - 9)x^2 + (-12 + 12)x + 9\\\\12x^3 - 25x^2 + 9

That is the expression simplified

If you want to learn more about simplification:

brainly.com/question/723406

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8 0
1 year ago
Can someone walk me through solving this? I have no idea how to start and I haven't done algebra in a long time so please be pat
professor190 [17]
First, square each side of the equation. It will then say (3x+4)=16. Now subtract 4 from each side, and finally, divide each side by 3. The solution will then stare up at you: x=4 .
5 0
3 years ago
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