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spayn [35]
3 years ago
7

6.5x-10=4.5x+6 can someone give a step by step answer plz

Mathematics
2 answers:
scoundrel [369]3 years ago
8 0

Answer:

\huge{\bold{\boxed{\sf{x = 8 }}}}

Step-by-step explanation:

6.5x - 10 = 4.5x + 6

Move 4.5x to left hand side and change its sign.

Similarly, move 10 to right hand side and change its sign.

⇒6.5x - 4.5x = 6 + 10

Subtract 4.5x from 6.5x

⇒2x = 6 + 10

Add the numbers: 6 and 10

⇒2x = 16

Divide both sides by 2

⇒\frac{2x}{2} = \frac{16}{2}

Calculate

⇒\boxed{\sf{ x = 8 }}

Hope I helped!

Best regards!

~\sf{TheAnimeGirl}

Trava [24]3 years ago
7 0

Collect like terms
6.5x-4.5x = 6+10
2x = 6+10
Divide both sides
2x = 16
X= 8
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Find the slope of the line that passes through the given points (7, 3) and (13, 8)​
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4 0
3 years ago
What will be the value of
madreJ [45]

The expression as given doesn't make much sense. I think you're trying to describe an infinitely nested radical. We can express this recursively by

\begin{cases}a_1=\sqrt{42}\\a_n=\sqrt{42+a_{n-1}}\end{cases}

Then you want to know the value of

\displaystyle\lim_{n\to\infty}a_n

if it exists.

To show the limit exists and that a_n converges to some limit, we can try showing that the sequence is bounded and monotonic.

Boundedness: It's true that a_1=\sqrt{42}\le\sqrt{49}=7. Suppose a_k\le 7. Then a_{k+1}=\sqrt{42+a_k}\le\sqrt{42+7}=7. So by induction, a_n is bounded above by 7 for all n.

Monontonicity: We have a_1=\sqrt{42} and a_2=\sqrt{42+\sqrt{42}}. It should be quite clear that a_2>a_1. Suppose a_k>a_{k-1}. Then a_{k+1}=\sqrt{42+a_k}>\sqrt{42+a_{k-1}}=a_k. So by induction, a_n is monotonically increasing.

Then because a_n is bounded above and strictly increasing, the limit exists. Call it L. Now,

\displaystyle\lim_{n\to\infty}a_n=\lim_{n\to\infty}a_{n-1}=L

\displaystyle\lim_{n\to\infty}a_n=\lim_{n\to\infty}\sqrt{42+a_{n-1}}=\sqrt{42+\lim_{n\to\infty}a_{n-1}}

\implies L=\sqrt{42+L}

Solve for L:

L^2=42+L\implies L^2-L-42=(L-7)(L+6)=0\implies L=7

We omit L=-6 because our analysis above showed that L must be positive.

So the value of the infinitely nested radical is 7.

4 0
3 years ago
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