Index laws for zeros. Can anyone help me?

The ratio of the numerator to the denominator of a fraction is 2 to 3. If both the numerator and the denominator are increased b

masha68 [24]

Answer:

The fraction is $\frac{4}{6}$

Option (B) is correct.

$3n-2d=0$ and $4n+8=3d+6$

Step-by-step explanation:

Let n denotes numerator and d denotes denominator of the fraction.

Given : The ratio of the numerator to the denominator of a fraction is 2 to 3.

That is $\frac{n}{d}=\frac{2}{3}$

Cross multiply , we get,

$3n=2d$

Or, $3n-2d=0$ ........(1)

Also, given : . If both the numerator and the denominator are increased by 2, the fraction becomes 3/4

That is $\frac{n+2}{d+2}=\frac{3}{4}$

Cross multiply , We get,

$4{n+2}={3}{d+2}$

$4n+8=3d+6$ .........(2)

$3d-4n=2$ .......(3)

Thus, from (1) and (2) , option (B) follows.

Solving equation (1) and (3) to get the original fraction using elimination method,

3n - 2d = 0 ............(1)

and 3d - 4n = 2 .........(3)

Multiply equation (1) by 3 , we get ,

9n - 6d = 0 ..........(4)

Multiply equation (3) by 2 , we get ,

-8n + 6d = 4 ..........(5)

Adding (4) and (5) , we get,

9n - 6d -8n + 6d = 4 + 0

⇒ n = 4

Put n = 4 in (1), we get

3n - 2d = 0 ⇒ 3(4) - 2d = 0 ⇒ 12 -2d = 0 ⇒ 12 = 2d ⇒ d = 6

so, the numerator is 4 and the denominator is 6.

Thus, the fraction is $\frac{4}{6}$

6 0

3 years ago

What is the quadratic. Formula?

balu736 [363]

Answer:

$x = \frac{ - b ± \sqrt{ {b }^{2} - 4ac } }{2a}$

Step-by-step explanation:

For example, we'll use this quadratic equation.

${x}^{2} + 5x + 6$

To understand how to plug it into the formula we need to know what each term represents.

$a {x}^{2} + bx + c$

So the equation above would be put into the formula like this.

$x = \frac{ - 5± \sqrt{ {5}^{2} - 4(1)(6) } }{2(1)}$

Then we would solve

$\frac{ - 5± \sqrt{25 - 24} }{2} \\ \\ = \frac{ -5±1}{2}$

Now, the equation will branch off into one that solves when addition and one when subtraction.

$\frac{ - 5 + 1}{2} = \frac{ - 4}{2} = - 2 \\ \\ \frac{ - 5 - 1}{2} = \frac{ - 6}{2} = - 3$

So x={-3, -2} (-3 and -2)

6 0

3 years ago

What is 1/4 equal to?

zysi [14]

There are many answer:
1/4 is equal to 25%, .25 , 2/8 on so on. Hope this helps

6 0

3 years ago

Read 2 more answers

NEED ASAP!!!!

Usimov [2.4K]

Answer: the answer is Triangles BCP and CDP are condruent

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

The outer angle at the top C of the ABC is 112 °. If the bisector of the side AB intersects the side AC at point Q and the segme

Arisa [49]

Step-by-step explanation:

The outer angle at the top C of the ABC is 112 °. If the bisector of the side AB intersects the side AC at point Q and the segment BQ is perpendicular to AC, find the magnitude of ABC

3 0

2 years ago