Ask question

Ask question

All categories

3 years ago

12

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

y 2, the fraction becomes 3/4. What is the original fraction?
Which of the following systems of equations can be used to solve the problem?

1 answer:

fiasKO [112]3 years ago

5 0

The clues translate to

n/d = 2/3
(n+2)/(d+2) = 3/4

Solving this by cross multiplying both:

3n = 2d
3(d+2) = 4(n+2) => 3d + 6 = 4n + 8

then substituting d = 3/2 n in the second:

9/2n - 4n = 2 => 1/2 n = 2 => n = 4

if n=4 then d = 3/2*4 = 6.

So the original fraction was 4/6

You might be interested in

A Lua reflete parte da luz solar que nela incide. Admite que: a luz refletida pela Lua demora 1,28 segundos a chegar à Terra; en

Anuta_ua [19.1K]

Answer:

3.84 * 10^8 meters

Step-by-step explanation:

As the speed of light is 300,000,000 meters/second and the time that the light takes to go from the moon to the Earth is 1.28 seconds, we can find the distance using the formula:

Distance = speed * time

So we have that:

Distance = 300,000,000 * 1.28 = 384,000,000 meters

In cientific notation, we need the first number to be in the interval from 1 to 10, so we have 3.84, and we have to multiply by 10^8 to reach our result, so we have:

Distance = 3.84 * 10^8 meters

4 0

3 years ago

A regular polygon

olga55 [171]

Answer:

3.6° = ext. angle

Step-by-step explanation:

For the shape to be a regular polygon, all interior angles must be congruent.

We can find every interior angle by using the formula:

$\frac{180(n-2)}{n}$

$\frac{180(100-2)}{100}$

$\frac{180(98)}{100}$

$\frac{17640}{100}$

176.4 = each int. angle

We also know that int. and ext. angles are supplementary!

180 = 176.4 - x

3.6° = ext. angle

5 0

3 years ago

Which ordered pairs are solutions to the inequality 2y-x≤-6 ?

Ray Of Light [21]

Answer:

C

Step-by-step explanation:

3 0

3 years ago

8. Is the following statement true or false? Justify your conclusion. If a and b are nonnegative real numbers and a + b =0, then

atroni [7]

Answer:

If $a + b = 0$ then $a = 0$ and $b =0$

a | b | a + b (answer)

0 | 0 | 0

0 | 1 | 1

0 | 2 | 2

1 | 0 | 1

2 | 0 | 2

1 | 1 | 2

2 | 1 | 3

Step-by-step explanation:

Considering the following conditions for the real numbers:

$a\geq 0\\b\geq 0$

Following the rules of these in-equations, it is possible to deduce:

$a + b \geq 0$

Then, if the proposed statement is:

$a + b = 0$

The conditions above shall comply the requirements established, but first, analyzing the statement:

If $a \geq 0$ and $b \geq 0$ then $a + b \geq a$ , $a + b \geq b$ and $a + b \geq 0$ .

If $a = 0$ and b a non negative real number, then $a + b \geq b$ , but because to $a = 0$ , then $a + b = b$ . Due to the commutative property of sums, the same behavior will be presented if $b = 0$ and a a non negative real number.

According to that, if $a + b = 0$ , then $a = 0$ and $b = 0$ .

7 0

3 years ago

PLEASE SOMEONE HELP I TRULY DO NOT UNDERSTAND

IceJOKER [234]

Hi there!

$\large\boxed{f^{-1}(x) = \sqrt[3]{\frac{x+4}{9} } }$

$f(x) = 9x^{3} - 4$

Find the inverse by replacing f(x) with y and swapping the x and y variables:

$x = 9y^{3} - 4$

Isolate y by adding 4 to both sides:

$x + 4 = 9y^{3}$

Divide both sides by 9:

$\frac{x+4}{9}= y^{3}$

Take the cube root of both sides:

$y = \sqrt[3]{\frac{x+4}{9} }\\\\f^{-1}(x) = \sqrt[3]{\frac{x+4}{9} }$

7 0

3 years ago