Answer:
120 degrees.
Step-by-step explanation:
All the angles in a triangle add up to 180. You have two of the angles given:
50 degrees and 70 degrees
To find the third angle of the triangle (BAC), use the expression:
180 - (50 + 70)
180 - 120
60
So, the third angle in the triangle is 60 degrees. Looking at angle DAB, you can see that it forms a straight line with angle BAC. A straight line is 180 degrees. Since we know BAC is 60, and BAC + DAB = 180, by doing 180 - 60, you can see that angle DAB is 120 degrees.
The total weight of candies is unknown. Let x = the total weight of candies.
"One student ate 3/20 of all candies and another 1.2 lb":
The first student ate (3/20)x plus 1.2 lb which is 0.15x + 1.2.
"The second student ate 3/5 of the candies and the remaining 0.3 lb."
The second student ate (3/5)x and 0.3 lb which is 0.6x + 0.3.
Altogether the 2 students ate 0.15x + 1.2 + 0.6x + 0.3.
That was all the amount of candies, so that sum equals x.
0.15x + 1.2 + 0.6x + 0.3 = x
Now we solve the equation for x to find what the total amount of candies was.
0.75x + 1.5 = x
-0.25x = -1.5
x = 6
The total amount of candies was 6 lb.
The first student ate 0.15x + 1.2 = 0.15(6) + 1.2 = 0.9 + 1.2 = 2.1, or 2.1 lb of candies.
The second student ate 0.6x + 0.3 = 0.6(6) + 0.3 = 3.6 + 0.3 = 3.9, or 3.9 lb of candies.
Answer: The first student ate 2.1 lb of candies, and the second student ate 3.9 lb of candies.
= (a-5).(a+3)
= a²+3a-5a-15
= a²-2a-15
N=number of nickels
d=number of dimes
q=number of quarters
example
if n:d=3:8
lets say n=3 and d=8
3*8=8*3
so
8n=3d
slightly confusing but go with it, it migh make sense or it might not
n:d=3:8
8n=3d
d:q=4:5
5d=4q
solve for one of them
solve for nickels in first and quarters in second
8n=3d, n=(3/8)d
5d=4q, (4/5)d=q
5n+10d+25q=690
divide by 5 to make it easeir
n+2d+4q=138
sub (3/8)d for n
sub (4/5)d for q
(3/8)d+2d+5(5/4)d=138
(3/8)d+2d+25/4d=138
3/8+2+25/4=
3/8+16/2+50/8=
69/8
(69/8)d=138
times both sides by 8
69d=1104
divide both sides by 69
d=16
16 dimes
sub back
(5/4)d=q
(5/4)16=q
80/4=q
20=q
(3/8)d=n
(3/8)16=n
48/8=n
6=n
6 nickles
16 dimes
20 quarters
yah
