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aliya0001 [1]
3 years ago
14

The number 48 can be written in the form 2n x 3. find the value of n!

Mathematics
2 answers:
stich3 [128]3 years ago
7 0

Answer:

n=22.5

Step-by-step explanation:

2*22.5=45, 45+3=48.

kolezko [41]3 years ago
4 0

Answer: n =8

Step-by-step explanation:

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A- 14 points per game
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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}.

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3 years ago
After getting 5 new rocks, George gave half of his rock collection to Susan. If George gave Susan 36 rocks, which equation could
White raven [17]

Answer:

1/2 (x+5) = 36  should be the equation that is used to determine how many rocks George started with.

Step-by-step explanation:

Let 'x' be the number of rocks George had.

As George gave, after getting 5 new rocks, half of his rock collection to Susan which is = 36 rocks

It means after getting 5 new rocks George's total rocks = 72

Given that he gave half collection to Susan = 36

Thus, before inducting 5 new rocks Georg's total rocks were = 67

Thus,

1/2 (x+5) = 36 should be the correct equation.

solving

1/2 (x+5) = 36

Multiplying both sides by 2

1/2 (x+5) × 2 = 36 × 2

x+5 = 72

x = 72 - 5

x = 67

Thus, before getting 5 new rocks, the number of rocks George had = 67

Therefore,

1/2 (x+5) = 36  should be the equation that is used to determine how many rocks George started with.

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L y l = 256<br> List 2 values of y
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Answer:

256, -256

Step-by-step explanation:

Absolute value simply removes the negative and does nothing to positive numbers

I think those were absolute value bars. not sure.

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I think it’s either 8 or negative 8
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