In a parallelogram, opposite angles are congruent.
This means that the four angles of the parallelogram are:
![L = x+40,\quad M = 3x,\quad N = x+40,\quad O = 3x](https://tex.z-dn.net/?f=L%20%3D%20x%2B40%2C%5Cquad%20M%20%3D%203x%2C%5Cquad%20N%20%3D%20x%2B40%2C%5Cquad%20O%20%3D%203x)
Moreover, the sum of the interior angles of a polygon with n sides is 180(n-2). So, the sum of the interior angles of a parallelogram is 360.
This means
![L+M+N+O = 360 \iff 2(x+40)+2(3x) = 2x+80+6x = 360 \iff 8x = 280 \iff x = 35](https://tex.z-dn.net/?f=L%2BM%2BN%2BO%20%3D%20360%20%5Ciff%202%28x%2B40%29%2B2%283x%29%20%3D%202x%2B80%2B6x%20%3D%20360%20%5Ciff%208x%20%3D%20280%20%5Ciff%20x%20%3D%2035)
And since
, we have ![O=3\cdot 35=105](https://tex.z-dn.net/?f=O%3D3%5Ccdot%2035%3D105)
7/8+9/10=71/40=1 31/40
1/4+2/3=11/12
1/2+1/4 is different from 1/2+1/3 because
1/2+1/4= 2/4+1/4= 5/1 =1 1/4
1/2+1/3=3/6+2/6=5/6
Answer:
14 quarters and 28 nickels
Step-by-step explanation:
System of Equations where x = number of quarters and y = number of nickels
(1) equation with value of each coin
0.25(x)+0.05(y) = 4.90
(2) total number of coins
x + y = 42
Solve system of equations using either substitution or elimination
(elimination multiplying equation 2 by -0.5)
.25(x) + 0.05(y) = 4.90
-0.05(x) - 0.05(y) = 42 * (-0.05)
(3) Resulting equation
.20(x) = 2.8
x = 14
plug x into equation 2
14 + y = 42
y = 28
There are 14 quarters and 28 nickels in Mary's collection.
Answer:
(5,10)
(3,6)
Step-by-step explanation:
The equation y=2x means that 2 multiplied by the first value would equal the second value, so this means that the second value is twice as much as the first value. This is not true for the first option because 8 is not twice of 16, and this is the same for (4,6), (4,2), and (1,3). Therefore (5,10) and (3,6) work.
Answer:
6
Step-by-step explanation:
Straight line is 180
square = right angle=90
180-90=90
5x+(x+54)=90
6x+54=90
6x=36
x=6
Hope this helps :D