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Katena32 [7]
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?
Mathematics
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
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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
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