LCM stands for least common multiple. We are being asked to find the lowest multiple that 6 and 15 have in common.
Multiples of a number (n) are integers that are the product of n and another number. Let's list the multiples of both 6 and 15:
6: 6, 12, 18, 24, 30, 36
15: 15, 30, 45, 60, 75, 90
The LCM of 6 and 15 is 30.
Answer:
see explanation
Step-by-step explanation:
(1)
CD = CE - DE = 8 - 2 = 6
CB = CD = 6 ( given as congruent ) , thus
AC = AB + CB = 4 + 6 = 10
(2)
∠ 2 + ∠ BCD + ∠ DCF = 180° ( sum of angles on a straight line )
∠ 2 + 60° + 70° = 180°
∠ 2 + 130° = 180° ( subtract 130° from both sides )
∠ 2 = 50°
Answer:
14/45
Step-by-step explanation:
So we have the fraction:

We can do this algebraically. Follow to following steps:
Let's let this number equal to n. Thus:

Since there is only 1 digit repeating, let's multiply everything by 10. So:

Now, subtract n from both sides:

On the left, substitute the number for n. On the right, combine like terms:

All of the 1s will cancel. So:

Subtract:

Divide both sides by 9:

Remove the decimal by multiplying both sides by 10:

Reduce:

And we're done!
Use a calculator to check:

Answer:
see explanation
Step-by-step explanation:
Parallel lines have equal slopes.
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
L₁ is y = 5x + 1 ← in slope- intercept form
with slope m = 5
L₂ is 2y - 10x + 3 = 0 ( subtract - 10x + 3 from both sides )
2y = 10x - 3 ( divide all terms by 2 )
y = 5x -
← in slope- intercept form
with slope m = 5
Since L₁ and L₂ have equal slopes then they are parallel lines
Given Fig.is a triangle
Perimeter is simply sum of the all sides of a triangle
1/3x + 7/x^2 + (x+2)/x
=[ x+ 21 + 3x(x+2)]/3x^2
= (x+ 21 + 3x^2 + 6x)/3x^2
= (3x^2 + 7x +21)/3x^2