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3 years ago

Two thirds of a number reduced by 11 is equal to 4 more than the numher. find the number

Mathematics

2 answers:

Anika [276]3 years ago

8 0

Answer:

- 45

Step-by-step explanation:

let n be the number , then

$\frac{2}{3}$ n - 11 = n + 4 ( add 11 to both sides )

$\frac{2}{3}$ n = n + 15 ( multiply through by 3 to clear the fraction

2n = 3n + 45 ( subtract 2n from both sides )

0 = n + 45 ( subtract 45 from both sides )

- 45 = n

The number is - 45

Nezavi [6.7K]3 years ago

7 0

Answer:

x = -45

Step-by-step explanation:

let the number be 'x'

Equation:-

2/3(x) - 11 = 4 + x

=> 2x/3 - 11 = 4 + x

=> 2x/3 - x = 4 + 11

=> (2x - 3x)/3 = 15

=> -x = 45

=> x = -45

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Read 2 more answers

Show in each case that the series converges or diverges

Montano1993 [528]

I can't make out the summand in (d), and I addressed (c) in your other question.

(a) $\displaystyle\sum_{n\ge1}\frac{\cos n\pi}{n\sqrt n}$

We have for positive integers $n$ that $\cos n\pi=(-1)^n$ . We also are aware that the series

$\displaystyle\sum_{n\ge1}\frac1{n^{3/2}}$

converges, since it is a $p$ -series with $p=\dfrac32>1$ . Since the $p$ -series converges in absolute value, the alternating series must also converge by comparison.

- - -

(b) $\displaystyle\sum_{n\ge1}(-1)^n\frac{\ln n}n$

By the alternating series test, this series will converge if the absolute value of the summand is increasing for some large enough $N$ and approaches zero.

We have

$\left|(-1)^n\dfrac{\ln n}n\right|=\dfrac{\ln n}n>0$

for all $n\ge1$ , and we also have that

$\displaystyle\lim_{n\to\infty}\frac{\ln n}n=\lim_{m\to\infty}\frac m{e^m}=0$

(where we substituted $m=\ln n$ , so that $e^m=n$ ).

Therefore (b) also converges.

4 0

3 years ago

Hope this helps yall! Have an Amazing day!!

uranmaximum [27]

Thanks but this isn’t math

4 0

3 years ago

A line passes through the points (2, –2) and (–6, 2). The point (a, –4) is also on the line. What is the value of a?

leonid [27]

Answer:

The value of a=6[/tex]

Step-by-step explanation:

step 1:-

col linearity of three points :-

We know that slopes of two parallel lines are equal.If two lines having the same slope pass through a common point ,then two lines will coincide . Hence ,If A,B,C are three points in the X Y- plane, then they will lie on a line,

that is three points are col linear if and only if Slope of AB= slope of BC

step 2:-

Since the given three points are col-linear, we have

Slope of AB= slope of BC

given points are A(2,-2) ,B(-6,2) and C(a,-4)

Step 3 :-

Slope of AB= slope of BC

$\frac{2-(-2)}{-6-2} =\frac{-4-2}{a+6}$

$\frac{-1}{2} =\frac{-6}{a+6} by cross multiplication we get \\a+6=12\\Step 4:-The value of a=6$

5 0

3 years ago

Two thirds of a number reduced by 11 is equal to 4 more than the numher. find the number ​

Two thirds of a number reduced by 11 is equal to 4 more than the numher. find the number