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Zolol [24]
3 years ago
13

Use properties of operations to complete the equivalent expression. 5(y+9)=​___y+​___ 5(y+9)=nothingy+nothing

Mathematics
1 answer:
laiz [17]3 years ago
5 0

Answer:

5y+45

Step-by-step explanation:

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Find the solutions to the equation below.<br> Check all that apply.<br> 4x2 + 4x + 1 = 0
Verizon [17]

Answer:

The solution for the given polynomial 4x^2 + 4x+ 1 = 0 is x  = (\frac{-1}{2})

Step-by-step explanation:

Here, the given quadratic equation is : 4x^2 + 4x+ 1 = 0

Now, here solving the given equation by SPLITTING THE MIDDLE TERM:

4x^2 + 4x+ 1 = 0  = 4x^2 + 2x+ 2x +  1 = 0\\\implies 2x( 2x + 1) + 1(2x + 1) = 0\\\implies (2x +1)(2x +1)  = 0\\

⇒ either (2x+1) = 0, or ( 2x + 1) = 0

⇒ x = -1/2 or x  = -1/2

Here, in both the cases, the value of x is equal i.e x  =  -1/2

So, the given function has TWO IDENTICAL ROOTS.

Hence the solution for the given polynomial 4x^2 + 4x+ 1 = 0 is x  = (\frac{-1}{2})

4 0
3 years ago
The table shows the approximate area in square miles of the largest and smallest states in the United States.
alexandr402 [8]
Who’s tryna hop on cod tho
8 0
2 years ago
PLZ HELP ME !!!!!!!!!!!!!!<br> 2 questions
disa [49]

Answer: D

Step-by-step explanation: I think

6 0
2 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}}

or

\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

-\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
Find the nth term of the arithmetic sequences<br> a1=5,d=6,n=11
ki77a [65]

here's the solution,

  • n = 11
  • a = 5 ( a = first term )
  • d = 6 ( d = common difference )

we know,

=》

nth  \: \: term \:  = a   \: + (n - 1) \times d

=》

11th \:  \: term   = 5 + (11 - 1) \times 6

=》

11th \:  \: term = 5 + (10 \times 6)

=》

11th \:  \: term  = 5 + 60

=》

11th \:  \: term = 65

nth term ( 11th term ) = 65

3 0
3 years ago
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