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4 years ago

Solve. Write your answer in interval notation.

Mathematics

1 answer:

lina2011 [118]4 years ago

3 0

Answer: x < 3 or x ≥ 11

(-∞, 3) or [11, ∞)

Step-by-step explanation:

subtract 4 from each side

2x < 6 . or . 3x ≥ 33

x < 3 or x ≥ 11

make sure you have an OPEN DOT at 3 pointing to negative infinity and a CLOSED DOT at 11 pointing to positive infinity.

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What is the equation of this line

yaroslaw [1]

The correct answer is D

6 0

3 years ago

Find missing variable and check: -3(x-6)+4(x+1)=7x-14

lana66690 [7]

We need to solve the equation to find x

$-3(x-6)+4(x+1)=7x-14$

We will simplify the left side by multiply each bracket by the number before it

-3(x - 6) = -3(x) + -3(-6) = -3x + 18

4(x + 1) = 4(x) + 4(1) = 4x + 4

Now put them on the left side

$-3x+18+4x+4=7x-14$

Add the like terms on the left side

$\begin{gathered} (-3x+4x)+(18+4)=7x-14 \\ x+22=7x-14 \end{gathered}$

Now we will collect x on the right side and the numbers on the left side

Subtract x from both sides

$\begin{gathered} x-x+22=7x-x-14 \\ 22=6x-14 \end{gathered}$

Add 14 to both sides

$\begin{gathered} 22+14=6x-14+14 \\ 36=6x \end{gathered}$

Divide both sides by 6 to find x

$\begin{gathered} \frac{36}{6}=\frac{6x}{6} \\ 6=x \end{gathered}$

The value of x is 6

3 0

1 year ago

Use DeMoivre's Theorem to find (4cis (pi/18))^3

DochEvi [55]

$\bf \qquad \textit{power of two complex numbers}
\\\\\
[\quad r[cos(\theta)+isin(\theta)]\quad ]^n\implies r^n[cos(n\cdot \theta)+isin(n\cdot \theta)]\\\\
-------------------------------$

$\bf 4\left[ cos\left( \frac{\pi }{18} \right)+i~sin\left( \frac{\pi }{18} \right) \right]^3\implies 4^3\left[ cos\left(3\cdot \frac{\pi }{18} \right)+i~sin\left( 3\cdot \frac{\pi }{18} \right) \right]
\\\\\\
64\left[ cos\left( \frac{\pi }{6} \right)+i~sin\left( \frac{\pi }{6} \right) \right]\implies 64\left[\frac{\sqrt{3}}{2}+i~\frac{1}{2} \right]
\\\\\\
32\sqrt{3}+32i$

8 0

3 years ago

I help me please I need these answers

Ivan

Answer:

G i think that is the answer

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

If 32 teams participate in a standard single elimination tournament, how many games must be played to decide a champion?

SCORPION-xisa [38]

<h3>Answer: 31 games</h3>

======================================================

Explanation:

32/2 = 16 games will happen in round 1. Afterward, 16 teams are left.
16/2 = 8 games will happen in round 2. Afterward, 8 teams are left.
8/2 = 4 games happen in round 3.
4/2 = 2 games in round 4.
2/2 = 1 game as the final championship.

Count the number of times you divide by two and we have five occurrences of this. So there five rounds overall.

To get the total number of games played, we add up the quotients

16+8+4+2+1 = 31

----------------

Or as a shortcut we can simply subtract off 1 since 1+2+4+...+2^n = 2^(n+1)-1

We can write that rule as

$\displaystyle \sum_{k=1}^{n}2^k = 2^{n+1}-1$

which is equivalent to

$\displaystyle \sum_{k=1}^{n}2^{k-1} = 2^n-1$

3 0

4 years ago