3. Point P(2, -1) is the image of point

Solve for x<br> (1/x) -2/3 = (4x)

Vadim26 [7]

The value of x is $x=\frac{-1+\sqrt{37}}{12}$ and $x=\frac{-1-\sqrt{37}}{12}$

Step-by-step explanation:

The equation is $\frac{1}{x}-\frac{2}{3}=4 x$

Subtracting by $4x$ on both sides,

$\frac{1}{x}-\frac{2}{3}-4 x=0$

Taking LCM,

$\frac{3-12 x^{2}-2 x}{3 x}=0$

Multiplying by 3x on both sides,

$-12 x^{2}-2 x+3=0$

Dividing by (-) on both sides,

$12 x^{2}+2 x-3=0$

Using quadratic formula, we can solve for x.

$\begin{aligned}x &=\frac{-2 \pm \sqrt{2^{2}-4 \cdot 12 \cdot(-3)}}{2 \cdot 12} \\&=\frac{-2 \pm \sqrt{4+144}}{2 \cdot 144} \\&=\frac{-2 \pm \sqrt{148}}{24} \\&=\frac{-2 \pm 2 \sqrt{37}}{24}\end{aligned}$

Taking out common term 2, we get,

$\begin{array}{l}{x=\frac{-2(1 \pm \sqrt{37})}{24}} \\{x=\frac{-1 \pm \sqrt{37}}{12}}\end{array}$

Thus, the value of x is $x=\frac{-1+\sqrt{37}}{12}$ and $x=\frac{-1-\sqrt{37}}{12}$

4 0

3 years ago

How many ways can 100 be written as the sum of distinct integers from the set {1, 2,..., 15}?

konstantin123 [22]

Answer:

48 ways

Step-by-step explanation:

Let me take a guess

S₁_₁₅ = (1+15)*7 + 8 = 120

There are 48 combinations of distinct digits from 1 to 15 to make 20

120-20=100

So every 20 has a corresponding 100

I wish I got it right, otherwise report it.

4 0

2 years ago

List 2 numbers between 5.2 and 5.03

Ann [662]

Answer:

5.1 and 5.05

Not really much to explain. Still, hope this helped!

P.S. (5.2 is more than 5.03, btw)

3 0

3 years ago

A woman had $200. She went to a meatshop,

alukav5142 [94]

Ok then after that what’s the question ?

6 0

3 years ago

The ratio of band students to choir students is 4:6. There are a total of 60 students in the band and choir. How many students a

xenn [34]

Answer:

24

Step-by-step explanation:

Given that:

The ratio of band students to choir students is 4 : 6.

Total number of students in the band and choir combined = 60

To find:

The number of students in the band = ?

Solution:

First of all, let us understand the meaning of the ratio given.

Ratio of 4 : 6 means there are 4 number of band students for every 6 number of choir students.

Also, number of band students will be in the multiples of 4 only and

number of choir students will be in the multiples of 6 only

Let the total number of band students = 4 $x$

Let the total number of choir students = 6 $x$

Total number of students = 60

As per question statement, we can write the following equation:

$\Rightarrow 4x+6x=60\\\Rightarrow 10x = 60\\\Rightarrow x =6$

Total number of band students = 4 $\times$ 6 = <em>24</em>

5 0

3 years ago