Write an equation system based on the problem
For an instance, e stands for the price of a carton of eggs, and b stands for the price of a loaf of bread
"Kate bought 3 cartons of eggs and 5 loaves of bread for $30.07" could be written as 3e + 5b = 30.07 (first equation)
"Melissa bought 2 cartons of eggs and 2 loaves of bread for $14.74" could be written as 2e + 2b = 14.74 (second equation)
Solve the equation system using elimination method
Eliminate b to find e. To eliminate b, we should equalize the coefficient of b.
3e + 5b = 30.07 (multiplied by 2)
2e + 2b = 14.74 (multiplied by 5)
-------------------------------------------
6e + 10b = 60.14
10e + 10b = 73.70
------------------------- - (substract)
-4e = -13.56
e = -13.56/-4
e = 3.39
The price for a carton of eggs is $3.39
Answer:
x = (-5 ± 2√10) / 3
Step-by-step explanation:
5 − 10x − 3x² = 0
Write in standard form:
-3x² − 10x + 5 = 0
Solve with quadratic formula:
x = [ -b ± √(b² − 4ac) ] / 2a
x = [ -(-10) ± √((-10)² − 4(-3)(5)) ] / 2(-3)
x = [ 10 ± √(100 + 60) ] / -6
x = (10 ± 4√10) / -6
x = (-5 ± 2√10) / 3
I think it means to split a shape into common shapes. I.e. splitting a house shape into a triangle and a square
