The converted fractions are 3/12 and 5/12 and the sum is 2/3
<h3>How to convert the fractions?</h3>
From the question, the fractions are given as
1/4 and 5/12
The denominators of these fractions are
4 and 12
So. we start by calculating the LCD of the denominators
So, we have
4 = 2* 2
12 = 2 * 2 * 3
This gives
LCD = 2 * 2 * 3
Evaluate
LCD = 12
This means that the common denominator must be 12
So, we have
1/4 and 5/12
Multiply 1/4 by 3/3
This gives
3/12 and 5/12
When the fractions are added, we have
3/12 + 5/12 = (3 + 5)/12
Evaluate
3/12 + 5/12 = 8/12
Reduce fraction
3/12 + 5/12 = 2/3
Hence, the sum of the fractions is 2/3
Read more about fractions at
brainly.com/question/1622425
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Answer:
1 And 3
Step-by-step explanation:
Answer:
x= 0 , 
, 
Step-by-step explanation:
Given, equation is ![\sqrt[3]{15x-1}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B15x-1%7D)
+ ![\sqrt[3]{13x+1}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B13x%2B1%7D)
= ![4\sqrt[3]{x}](https://tex.z-dn.net/?f=4%5Csqrt%5B3%5D%7Bx%7D)
. →→→ (1)
Now, by cubing the equation on both sides, we get
( + )³ = ()³
⇒ (15x-1) + (13x+1) + 3×× ( + ) = 64 x.
⇒ 28x + 3×× () = 64x.
(since from (1), + = )
⇒ 12× × (![\sqrt[3]{x}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%7D)
)= 36x.
⇒ 3x = ![\sqrt[3]{(15x-1)(13+1)(x)}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B%2815x-1%29%2813%2B1%29%28x%29%7D)
.
Now, once again cubing on both sides, we get
(3x)³ = ()³.
⇒ 27x³ = (15x-1)(13x+1)(x).
⇒ 27x³ = 195x³ + 2x² - x
⇒ 168x³ + 2x² - x = 0
⇒ x(168x² + 2x -1) = 0
⇒ by, solving the equation we get ,
x = 0 ; x = ; x =
therefore, solution is x= 0 , ,
Answer:
- train: 40 kph
- plane: 140 kph
Step-by-step explanation:
Let t represent the speed of the train in km/h. Then 4t-20 is the speed of the plane. Travel times are the same, so we can use the formula ...
time = distance/speed
and equate the travel times.
110/t = 385/(4t-20)
Cross multiplying gives ...
110(4t -20) = 385t
440t -2200 = 385t . . . . . eliminate parentheses
55t -2200 = 0 . . . . . . . . . subtract 385t
t -40 = 0 . . . . . . . . . divide by 55
t = 40 . . . . . . . . . . . add 40; train's speed is 40 kph
4t -20 = 140 . . . . . . find plane's speed; 140 kph
The train's speed is 40 km/h; the plane's speed is 140 km/h.
_____
<em>Check</em>
Train's travel time = 110 km/(40 km/h) = 2.75 h.
Plane's travel time = 385 km/(140 km/h) = 2.75 h.
