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KengaRu [80]
3 years ago
5

What is (6x+4) - (4x+2)

Mathematics
1 answer:
Nana76 [90]3 years ago
4 0

Answer:

x = -1

Step-by-step explanation:

1. Simplifying

6x + 4 = 4x + 2

2. Reorder the terms

4 + 6x = 4x + 2 to 4 + 6x = 2 + 4x

3. Solving

4 + 6x = 2 + 4x

4. Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right. Then add '-4x' to each side of the equation.

4 + 6x + -4x = 2 + 4x + -4x

5. Combine like terms: 6x + -4x = 2x

4 + 2x = 2 + 4x + -4x

6. Combine like terms: 4x + -4x = 0

4 + 2x = 2 + 0

4 + 2x = 2

7. Add '-4' to each side of the equation.

4 + -4 + 2x = 2 + -4

8. Combine like terms: 4 + -4 = 0

0 + 2x = 2 + -4

2x = 2 + -4

9. Combine like terms: 2 + -4 = -2

2x = -2

10. Divide each side by '2'.

x = -1

11. Simplifying

x = -1

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The first one
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For the following telescoping series, find a formula for the nth term of the sequence of partial sums
gtnhenbr [62]

I'm guessing the sum is supposed to be

\displaystyle\sum_{k=1}^\infty\frac{10}{(5k-1)(5k+4)}

Split the summand into partial fractions:

\dfrac1{(5k-1)(5k+4)}=\dfrac a{5k-1}+\dfrac b{5k+4}

1=a(5k+4)+b(5k-1)

If k=-\frac45, then

1=b(-4-1)\implies b=-\frac15

If k=\frac15, then

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This means

\dfrac{10}{(5k-1)(5k+4)}=\dfrac2{5k-1}-\dfrac2{5k+4}

Consider the nth partial sum of the series:

S_n=2\left(\dfrac14-\dfrac19\right)+2\left(\dfrac19-\dfrac1{14}\right)+2\left(\dfrac1{14}-\dfrac1{19}\right)+\cdots+2\left(\dfrac1{5n-1}-\dfrac1{5n+4}\right)

The sum telescopes so that

S_n=\dfrac2{14}-\dfrac2{5n+4}

and as n\to\infty, the second term vanishes and leaves us with

\displaystyle\sum_{k=1}^\infty\frac{10}{(5k-1)(5k+4)}=\lim_{n\to\infty}S_n=\frac17

7 0
3 years ago
Given ​ f(x)=x2+14x+40 ​.<br><br><br> Enter the quadratic function in vertex form in the box.
sammy [17]
Please indicate exponentiation using " ^ "   Thanks.

f(x)=x2+14x+40 => <span>f(x)=x^2+14x+40

Next, complete the square:

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Write this in the form y = (x+7)^2 - 9  or y + 9 = (x+7)^2
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In vertex form, the equation is y + 9 = (x+7)^2 and the vertex is at (-7, -9).
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4 years ago
Can somebody help me?
True [87]

Answer:

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Step-by-step explanation:

7-(-2)=9

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Hope this helps!

6 0
3 years ago
Integers between -1and -5​
egoroff_w [7]
-2, -3, -4.

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