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3 years ago

6-7(x+1)= -3(2-x) How do you solve this?

Mathematics

1 answer:

kicyunya [14]3 years ago

7 0

<h3><u>Explanation</u></h3>

Given the equation.

$6 - 7(x + 1) = - 3(2 - x)$

Distribute/Simplify

$6 - 7x - 7 = - 6 + 3x \\ - 1 - 7x = - 6 + 3x$

Solve the equation for x-term by making x as the subject.

$- 1 + 6 = 7x + 3x \\ 5 = 10x \\ \frac{5}{10} = x \\ \frac{1}{2} = x$

Answer Check by substituting the value of x in the equation.

$6 - 7( \frac{1}{2} ) - 7 = - 6 + 3( \frac{1}{2} ) \\ 6 - \frac{7}{2} - 7 = - 6 + \frac{3}{2} \Longrightarrow \sf{You \: \: can \: \: change \: \: sides \: \: to \: \: make \: \: it \: \: easier} \\ 6 - 7 + 6 = \frac{7}{2} + \frac{3}{2} \\ 5 = \frac{10}{2} \\ 5 = 5 \: \green{ \checkmark}$

The equation is true for x = 1/2.

<h3><u>Answer</u></h3>

<u> $\large \boxed{x = \frac{1}{2} } \: \: \: \: \green{ \checkmark}$ </u>

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Which is an outlier out of 45,47,71,50,49 and 52

Elis [28]

The outlier is 71.

An outlier in a set of data is the one that is significantly lower or higher than the average of the totals. Whichever number skews the average is the outlier.

In this case, it's 71.

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4 years ago

I need help with my math homework. The questions is: Find all solutions of the equation in the interval [0,2π).

Aleksandr-060686 [28]

Answer:

$\frac{7\pi}{24}$ and $\frac{31\pi}{24}$

Step-by-step explanation:

$\sqrt{3} \tan(x-\frac{\pi}{8})-1=0$

Let's first isolate the trig function.

Add 1 one on both sides:

$\sqrt{3} \tan(x-\frac{\pi}{8})=1$

Divide both sides by $\sqrt{3}$ :

$\tan(x-\frac{\pi}{8})=\frac{1}{\sqrt{3}}$

Now recall $\tan(u)=\frac{\sin(u)}{\cos(u)}$ .

$\frac{1}{\sqrt{3}}=\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}$

$\frac{1}{\sqrt{3}}=\frac{-\frac{1}{2}}{-\frac{\sqrt{3}}{2}}$

The first ratio I have can be found using $\frac{\pi}{6}$ in the first rotation of the unit circle.

The second ratio I have can be found using $\frac{7\pi}{6}$ you can see this is on the same line as the $\frac{\pi}{6}$ so you could write $\frac{7\pi}{6}$ as $\frac{\pi}{6}+\pi$ .

So this means the following:

$\tan(x-\frac{\pi}{8})=\frac{1}{\sqrt{3}}$

is true when $x-\frac{\pi}{8}=\frac{\pi}{6}+n \pi$

where $n$ is integer.

Integers are the set containing {..,-3,-2,-1,0,1,2,3,...}.

So now we have a linear equation to solve:

$x-\frac{\pi}{8}=\frac{\pi}{6}+n \pi$

Add $\frac{\pi}{8}$ on both sides:

$x=\frac{\pi}{6}+\frac{\pi}{8}+n \pi$

Find common denominator between the first two terms on the right.

That is 24.

$x=\frac{4\pi}{24}+\frac{3\pi}{24}+n \pi$

$x=\frac{7\pi}{24}+n \pi$ (So this is for all the solutions.)

Now I just notice that it said find all the solutions in the interval $[0,2\pi)$ .

So if $\sqrt{3} \tan(x-\frac{\pi}{8})-1=0$ and we let $u=x-\frac{\pi}{8}$ , then solving for $x$ gives us:

$u+\frac{\pi}{8}=x$ ( I just added $\frac{\pi}{8}$ on both sides.)

So recall $0\le x$ .

Then $0 \le u+\frac{\pi}{8}$ .

Subtract $\frac{\pi}{8}$ on both sides:

$-\frac{\pi}{8}\le u$

Simplify:

$-\frac{\pi}{8}\le u$

So we want to find solutions to:

$\tan(u)=\frac{1}{\sqrt{3}}$ with the condition:

$-\frac{\pi}{8}\le u$

That's just at $\frac{\pi}{6}$ and $\frac{7\pi}{6}$

So now adding $\frac{\pi}{8}$ to both gives us the solutions to:

$\tan(x-\frac{\pi}{8})=\frac{1}{\sqrt{3}}$ in the interval:

$0\le x$ .

The solutions we are looking for are:

$\frac{\pi}{6}+\frac{\pi}{8}$ and $\frac{7\pi}{6}+\frac{\pi}{8}$

Let's simplifying:

$(\frac{1}{6}+\frac{1}{8})\pi$ and $(\frac{7}{6}+\frac{1}{8})\pi$

$\frac{7}{24}\pi$ and $\frac{31}{24}\pi$

$\frac{7\pi}{24}$ and $\frac{31\pi}{24}$

5 0

3 years ago

In his boat, Sheldon can travel 45 mi downstream in the same time that it takes to travel 9 mi upstream. If the rate of the curr

Nataliya [291]

Answer:

9 mph

Step-by-step explanation:

-let x be the speed of current and t be time. The speed equation for both directions can then be represented as:

$Speed=\frac{Distance}{Time}\\\\\#Upstream\\(u-6)t=9\\\\\#Donwstream\\\\(u+6)t=45$

#Since t is equal in both, we can do away with t.

#We the divide the downstream equation by the upstream equation as:

$\frac{u+6}{u-6}=\frac{45}{9}\\\\(u+6)=5(u-6)\\\\u+6=5u-30\\\\4u=36\\\\u=9$

Hence, the boat's speed in still water is 9 mph

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3 years ago

2. What is the x-value to the solution for the system of equations y = -5x - 9 and y = 2x<br> + 5.

pav-90 [236]

Answer:

The x-value is -2

Step-by-step explanation:

U can substitute any of the equations for y

-5x + (-9) = 2x + 5

-9 = 7x + 5

-14 = 7x

-2 = x

x = 2

7 0

3 years ago

What is the measurement of 3/4 in simplest form

stepan [7]

Answer:

It is in simplest form

Step-by-step explanation:

6 0

3 years ago