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3 years ago

Here are the first five terms of an arithmetic sequence.

Mathematics

1 answer:

qaws [65]3 years ago

6 0

9514 1404 393

Answer:

the difference of squares is 24(3n+2), so a multiple of 24

Step-by-step explanation:

The sequence has a first term of 7 and a common difference of 6, so the n-th term is ...

a[n] = a1 +d(n -1)

a[n] = 7 + 6(n -1)

a[n] = 6n +1

Then the (n+1)-th term is ...

a[n+1] = 6(n+1) +1 = 6n +7

The difference of the squares of these terms is ...

a[n+1]^2 -a[n]^2 = (6n+7)^2 -(6n+1)^2

= (36n^2 +84n +49) -(36n^2 +12n +1)

= 72n +48

= 24(3n +2) . . . . . always a multiple of 24

The difference of squares of terms n and n+1 is 24(3n+2), a multiple of 24.

_____

<em>Check</em>

The difference between squares for n=1 and n=2 is 13^2 -7^2 = 169 -49 = 120. The formula tells us the difference is 24(3·1 +2) = 24·5 = 120, in agreement.

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X^2 + 1/2x + = 2 + <br> Help please

Gennadij [26K]

Answer:

Step 2:

For Completing the square,

$(\frac{1}{2} coefficient\ x)^{2} =(\frac{1}{2}\times \frac{1}{2})^{2}=\frac{1}{16}$

Add half coefficient of x square on both the side we get

$x^{2}+\dfrac{x}{2}+\frac{1}{16}=2+\frac{1}{16}$

Step-by-step explanation:

Solve:

$2x^{2}+x-4=0$

$2x^{2}+x=4$

Solution:

Step 1:

Dividing both the side by two we get

$x^{2}+\dfrac{x}{2}=2$

Step 2:

For Completing the square,

$(\frac{1}{2} coefficient\ x)^{2} =(\frac{1}{2}\times \frac{1}{2})^{2}=\frac{1}{16}$

Add half coefficient of x square on both the side we get

$x^{2}+\dfrac{x}{2}+\frac{1}{16}=2+\frac{1}{16}$

Step 3:

We know $(a +b)^{2} = a^{2}+2ab +b^{2}$

$(x+\frac{1}{4})^{2}=\frac{33}{16} \\ \\(x+\dfrac{1}{4})=\pm \sqrt{\dfrac{33}{16}} \\\\x=-\dfrac{1}{4}\pm \sqrt{\dfrac{33}{16}}$

6 0

4 years ago

What is the radius of a circle with the equation x^2+y^2+6x-2y+3?

atroni [7]

Answer:

r = √13

Step-by-step explanation:

Starting with x^2+y^2+6x-2y+3, group like terms, first x terms and then y terms: x^2 + 6x + y^2 -2y = 3. Please note that there has to be an " = " sign in this equation, and that I have taken the liberty of replacing " +3" with " = 3 ."

We need to "complete the square" of x^2 + 6x. I'll just jump in and do it: Take half of the coefficient of the x term and square it; add, and then subtract, this square from x^2 + 6x: x^2 + 6x + 3^2 - 3^2. Then do the same for y^2 - 2y: y^2 - 2y + 1^2 - 1^2.

Now re-write the perfect square x^2 + 6x + 9 by (x + 3)^2. Then we have x^2 + 6x + 9 - 9; also y^2 - 1y + 1 - 1. Making these replacements:

(x + 3)^2 - 9 + (y - 1)^2 -1 = 3. Move the constants -9 and -1 to the other side of the equation: (x + 3)^2 + (y - 1)^2 = 3 + 9 + 1 = 13

Then the original equation now looks like (x + 3)^2 + (y - 1)^2 = 13, and this 13 is the square of the radius, r: r^2 = 13, so that the radius is r = √13.

8 0

3 years ago

Read 2 more answers

Please i really need help right now 25 points

Korolek [52]

Step-by-step explanation:

choice 2 ..............

8 0

2 years ago

A bag contains 6 brown, 8 white, and 4 black marbles. Each time you take a marble

marusya05 [52]

Answer:

4.44

Step-by-step explanation:

Total NM of ball=18,

black ball=4

p(black,black)=?

p(black,black)=p(b)+p(b)

4/18+4/18=4.44ans

3 0

3 years ago

Read 2 more answers

A group of 59 randomly selected students have a mean score of 29.5 with a standard deviation of 5.2 on a placement test. What is

BigorU [14]

Answer:

29.5+/-1.11

= ( 28.39, 30.61)

Therefore, the 90% confidence interval (a,b) =( 28.39, 30.61)

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = 29.5

Standard deviation r = 5.2

Number of samples n = 59

Confidence interval = 90%

z-value (at 90% confidence) = 1.645

Substituting the values we have;

29.5+/-1.645(5.2/√59)

29.5+/-1.645(0.676982337100)

29.5+/-1.113635944529

29.5+/-1.11

= ( 28.39, 30.61)

Therefore, the 90% confidence interval (a,b) =( 28.39, 30.61)

4 0

3 years ago