East common multiple is the smallest multiple both numbers can go into. (Example: the LCM of 10 and 4 is 20, because both 10 and 4 go into 20 and 20 is the smallest number both 10 and 4 can go into. You could just multiply them both, but you'd get 40 and since its a bigger number it would be harder to work with.)
<span>Least common denominator is just the least common multiple as a denominator. (Example: if you wanted to find the LCD of 5/7 and 1/10, you'd have to find the LCM of the demoniators (7 and 10) and then just use that as the denominator when adding fractions with unlikely denominators.) Sorry for such a long answer :P</span>
Answer:
x=5 and y=8
Step-by-step explanation:
Find x:
3x - 2 = x + 8
-x -x
2x - 2 = 8
+2 +2
2x = 10
---- ----
2 2
x = 5
Find y:
6y - 7 = y + 33
-y -y
5y - 7 = 33
+7 +7
5y = 40
---- -----
5 5
y = 8
We are given a right triangle that has angles of 45°-45°-90°. This would
indicate that the triangle is an isosceles type. We can use some
trigonemetric functions to solve for the other legs. We do as follows:
sin 45 = p / 10
p = 5√2
cos 45 = q /10
q = 5√2
<span>Hope this answers the question. Have a nice day.</span>
Answer:
15.6
Step-by-step explanation:
First, multiply the midpoint of each class by its frequency, as follows:
Class midpoint frequency midpoint*frequency
0-9 4.5 24 4.5*24 = 108
10-19 14.5 20 14.5*20 = 290
20-29 24.5 32 24.5*32 = 784
Total 76 1182
The mean is computed as the division between the addition of the "midpoint*frequency" column by the addition of "frequency" column.
mean = 1182/76 ≈ 15.6
Answer:
14. x=-2.5, y = -7
15. x=28 y = -20
Step-by-step explanation:
14. Let's solve this system by elimination. Multiply the first equation by -1.
-1*(4x-y)= -1*(- 3)
-4x +y = 3
Then add this to the second equation.
-4x+y = 3
6x-y= - 8
--------------
2x = -5
Divide each side by 2
x = -2.5
We still need to find y
-4x+y =3
-4(-2.5) + y =3
10 +y =3
Subtract 10 from each side.
y = 3-10
y = -7
15.I will again use elimination to solve this system, because using substitution will give me fractions which are harder to work with. I will elimiate the y variable. Multiply the first equation by 11
11(
5x+6y)= 11*20
55x+66y = 220
Multiply the second equation by -6
-6(9x+11y)=32*(-6)
-54x-66y = -192
Add the modified equations together.
55x+66y = 220
-54x-66y = -192
---------------------------
x = 28
We still need to solve for y
5x+6y = 20
5*28 + 6y =20
140 + 6y = 20
Subtract 140 from each side
6y = -120
Divide by 6
y = -20
