Answer:
-(-5) ± √13 5 ± √13
x = ----------------------- = ---------------
2(3) 6
Step-by-step explanation:
This is a quadratic equation, with coefficients 3, -5 and 1.
The discriminant, b² - 4ac, turns out to be (-5)² - 4(3)(1), or 25 - 12 = 13
Thus, the roots are:
-(-5) ± √13 5 ± √13
x = ----------------------- = ---------------
2(3) 6
Answer:
<h2><em><u>n</u></em><em><u> </u></em><em><u>=</u></em><em><u> </u></em><em><u>7</u></em></h2>
Step-by-step explanation:
4(n-1)+2 = -23 +7n
=> 4n - 4 + 2 = - 23 + 7n
=> 23 - 4 + 2 = 7n - 4n
=> 21 = 3n
=> <em><u>n</u></em><em><u> </u></em><em><u>=</u></em><em><u> </u></em><em><u>7</u></em><em><u> </u></em><em><u>(</u></em><em><u>Ans</u></em><em><u>)</u></em>
Answer: rental cost for each movie $1.50
Rental cost for each video game $6.25
Explanation:
m = rental cost of each movie
g = rental cost of each game
Set up:
8m + 4g = 37
3m + 2g = 17
Modify for elimination:
3 (8m + 4g = 37) ———> 24m + 12g = 111
8 (3m + 2g = 17) ———> 24m + 16g = 136
Subtract:
24m + 16g = 136
- 24m - 12g = -111
——————————
4g = 25
Divide:
4g = 25
g = 25/4
g = 6.25
So each game is $6.25
Now plug in “g” to one of the original equations and solve for “m” to find the rental cost for each movie
3m + 2 (6.25) = 17 (multiply 2 & 6.25)
3m + 12.50 = 17 (subtract 12.50 from sides)
3m = 4.50 (divide both sides by 3)
m = 1.50
So each movie rental is $1.50
198=-4x+2(-6x+3), 198=-4x-12x+6, 198=-16x+6, collect the like terms, 198-6=-16x, 192=-16x, divide both sides by -16, 192/-16=-16x/-16, x=-12
54.85 grams of Alfredo sauce are in 2.5 cups
