Step-by-step explanation:
so 2/3 OF the class are boys...
***REMEMBER IN MATHEMATICS, ^OF^ IS USED TO SAY MULTPLICATION***
so 2/3 OF class(x) are boys and there are 12 boys...
so 2/3 * x = 12
12 / (2/3) = x
to solve use the Keep, Change, Flip method
Keep 12, change / to multiplication, flip 2/3 to 3/2
it becomes 12 * 3/2 and to solve easier 12 is same thing as 12/1
12/1 * 3/2
Multiply across (numerator by numerator and denominator by denominator)
(12*3) / (1*2) = 36 / 2
Simplify
18
So the class has 18 students, and 2/3 of boys (12 of the students)
we can solve for how many girls are in the class
Depending on how your teacher wants to see the work:
either 18 - 12 = 6
or 1/3 * 18 which we rewrite as 1/3 * 18/1 = (1*18)/(3*1) which is 18/3... simplified it is 6
There are 6 girls in the class.
Hope this helps! :)
Answer:
70 degrees
Step-by-step explanation:
Find the diagram attached
The sum of the angles is supplementary that is
45 + 2x- 5 = 180
2x + 40 = 180
2x = 180 - 40
2x = 140
x = 140/2
x = 70
Hence the value of x is 70 degrees
X=2h, y=3k
Substitute these values into equations.
y+2x = 4 ------> 3k+2*2h=4 -----> 3k +4h =4
2/y - 3/2x = 1-----> 2/3k -3/(2*2h) = 1 ------> 2/3k - 3/4h =1
We have a system of equations now.
3k +4h =4 ------> 3k = 4-4h ( Substitute 3k in the 2nd equation.)
2/3k - 3/4h =1
2/(4-4h) -3/4h = 1
2/(2(2-2h)) - 3/4h = 1
1/(2-2h) -3/4h - 1=0
4h/4h(2-2h) -3(2-2h)/4h(2-2h) - 4h(2-2h)/4h(2-2h) =0
(4h- 3(2-2h) - 4h(2-2h))/4h(2-2h) = 0
Numerator should be = 0
4h- 3(2-2h) - 4h(2-2h)=0
Denominator cannot be = 0
4h(2-2h)≠0
Solve equation for numerator=0
4h- 3(2-2h) - 4h(2-2h)=0
4h - 6+6h-8h+8h² =0
8h² +2h -6=0
4h² + h-3 =0
(4h-3)(h+1)=0
4h-3=0, h+1=0
h=3/4 or h=-1
Check which
4h(2-2h)≠0
1) h= 3/4 , 4*3/4(2-2*3/4)=3*(2-6)= -12 ≠0, so we can use h= 3/4
2)h=-1, 4(-1)(2-2*(-1)) =-4*4=-16 ≠0, so we can use h= -1, also.
h=3/4, then 3k = 4-4*3/4 =4 - 3=1 , 3k =1, k=1/3
h=-1, then 3k = 4-4*(-1) =8 , 3k=8, k=8/3
So,
if h=3/4, then k=1/3,
and if h=-1, then k=8/3 .
So we need to know what 23 1/2 + 9 5/8 + 6 1/4 is.
first, we need to make them into equivalent fraction.
so...
23 1/2 can be 23 4/8
9 5/8 and
6 1/4 can be 6 2/8
let's add the whole numbers.
23 + 9 + 6 = 38
4/8 + 5/8 + 2/8 = 11/8 = 1 3/8
so 38 + 1 3/8 is 39 3/8
the answer is 39 3/8 pounds
