One way to find the least common multiple of two numbers is to first list the prime factors of each number.
8 = 2 x 2 x 2
Then multiply each factor the greatest number of times it occurs in either number. If the same factor occurs more than once in both numbers, you multiply the factor the greatest number of times it occurs.
2: three occurrences
3: one occurrence
So, our LCM should be
2 x 2 x 2 x 3 = 24.
So, Marco can buy, at the very least, 24 beads of each color to have equal colors of beads.
1. We assume, that the number 128 is 100% - because it's the output value of the task.
<span>2. We assume, that x is the value we are looking for. </span>
<span>3. If 128 is 100%, so we can write it down as 128=100%. </span>
<span>4. We know, that x is 51% of the output value, so we can write it down as x=51%. </span>
5. Now we have two simple equations:
1) 128=100%
2) x=51%
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
128/x=100%/51%
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.
7. Solution for what is 51% of 128
128/x=100/51
<span>(128/x)*x=(100/51)*x - </span>we multiply both sides of the equation by x
<span>128=1.96078431373*x - </span>we divide both sides of the equation by (1.96078431373) to get x
<span>128/1.96078431373=x </span>
<span>65.28=x </span>
x=65.28
<span>now we have: </span>
<span>51% of 128=65.28</span>
Answer:
x = -0.2 and x = -3.5
Step-by-step explanation:
Combine like terms in the given equation, by subtracting 2x^2 from both sides:
6x^2 + 15x + 3 = 2x^2
-2x^2 = -2x^2
----------------------------------
4x^2 + 15x + 3 = 0
This is a quadratic equation. We'll find the two solutions using the quadratic equation
-b ± √(b^2 - 4ac)
x = ---------------------------
2a
Here the coefficients of the quadratic are a = 4, b = 15 and c = 3.
Thus, the discriminant b^2 - 4ac is 15^2 - 4(4)(3), or +177
and from that we know we'll find two real, unequal roots.
-15 ± √177
The roots are: x = ------------------- , or x = -0.2 and x = -3.5
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