What is -6 2/3

If the 9th term of an ap is 1/7 and the 7th term os 1/9 find the 63rd term

Mnenie [13.5K]

Answer:

$a_{63}$ = 1

Step-by-step explanation:

The n th term of an arithmetic progression is

$a_{n}$ = a + (n - 1)d

where a is the first term and d the common difference

use the 9 th term and 7 th term to find a and d

$a_{9}$ = a + 8d = $\frac{1}{7}$ → (1)

$a_{7}$ = a + 6d = $\frac{1}{9}$ → (2)

Subtract (2) from (1) term by term

2d = $\frac{2}{63}$ ⇒ d = $\frac{1}{63}$

Substitute this value into (2) and solve for a

a + $\frac{6}{63}$ = $\frac{1}{9}$

a = $\frac{1}{9}$ - $\frac{6}{63}$ = $\frac{1}{63}$

Hence

$a_{63}$ = $\frac{1}{63}$ + $\frac{62}{63}$ = 1

5 0

3 years ago

Which value is NOT a solution of 8x3 – 1 = 0?

Tpy6a [65]

Note: As you may have unintentionally missed to add the value choices. But, I would make sure to explain the concept so that you may improve your understanding in terms of solving these type of questions.

Answer:

Any value other than the values $x=\frac{1}{2},\:x=-\frac{1}{4}+i\frac{\sqrt{3}}{4},\:x=-\frac{1}{4}-i\frac{\sqrt{3}}{4}$ will not be a solution of $8x^3\:-\:1\:=\:0$ .

Step-by-step explanation:

Considering the equation

$8x^3\:-\:1\:=\:0$

Steps to solve the equation

$8x^3-1=0$

$\mathrm{Add\:}1\mathrm{\:to\:both\:sides}$

$8x^3-1+1=0+1$

$\mathrm{Simplify}$

$x^3=\frac{1}{8}$

$\mathrm{Divide\:both\:sides\:by\:}8$

$\frac{8x^3}{8}=\frac{1}{8}$

$\mathrm{Simplify}$

$x^3=\frac{1}{8}$

As

$\mathrm{For\:}x^3=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt[3]{f\left(a\right)},\:\sqrt[3]{f\left(a\right)}\frac{-1-\sqrt{3}i}{2},\:\sqrt[3]{f\left(a\right)}\frac{-1+\sqrt{3}i}{2}$

$x=\sqrt[3]{\frac{1}{8}},\:x=\sqrt[3]{\frac{1}{8}}\frac{-1+\sqrt{3}i}{2},\:x=\sqrt[3]{\frac{1}{8}}\frac{-1-\sqrt{3}i}{2}$

So,

$x=\frac{1}{2},\:x=-\frac{1}{4}+i\frac{\sqrt{3}}{4},\:x=-\frac{1}{4}-i\frac{\sqrt{3}}{4}$

Therefore,

Any value other than the values $x=\frac{1}{2},\:x=-\frac{1}{4}+i\frac{\sqrt{3}}{4},\:x=-\frac{1}{4}-i\frac{\sqrt{3}}{4}$ will not be a solution of $8x^3\:-\:1\:=\:0$ .

Keywords: solution, value

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7 0

3 years ago

In a test of a gender-selection technique, results consisted of 229 baby girls and 7 baby boys. Based on this result, what is

kirill115 [55]

Answer:

I'm pretty sure that the answer would be 229/236.

Step-by-step explanation:

Ok so. Since the results of the test is 229 for a girl and the results for a boy is 7. So i'm pretty sure what to do is combine both the results and keep that as the denominator. And then the numerator will be the result. So in this case the numerator would be 229 and the denominator would be 236.

I hope this helped, have a great day!!!

3 0

3 years ago

Mary is an years old. What expression represents her age 7 years from now? Two years ago?

Rudiy27

Answer

What expression represents her age 7 years from now?

y =x+7x

Two years ago?

z=y-2x

Step-by-step explanation:

7 0

3 years ago

Find two equivalent ratios for 3:4 using multiplication A. 6:8 B.9:12 C. 6:12

Alchen [17]

Answer:

A and B

Step-by-step explanation:

3:4 multiplied by 2 is 6:8

3x2=6 4x2=8

3:4 multiplied by 3 is 9:12

3x3=9 4x3=12

6 0

3 years ago

Read 2 more answers

What is -6 2/3 - 4 7/8