Answer:
(8,5)
Step-by-step explanation:
x=8
5*8-2y=30
40-2y=30 . subtract 40 from both sides
-2y=-10 . divide both sides by-2
y=5
Answer:
x = 3/4 + (3 sqrt(5))/4 or x = 3/4 - (3 sqrt(5))/4
Step-by-step explanation:
Solve for x over the real numbers:
8 x^2 - 12 x - 23 = -5
Divide both sides by 8:
x^2 - (3 x)/2 - 23/8 = -5/8
Add 23/8 to both sides:
x^2 - (3 x)/2 = 9/4
Add 9/16 to both sides:
x^2 - (3 x)/2 + 9/16 = 45/16
Write the left hand side as a square:
(x - 3/4)^2 = 45/16
Take the square root of both sides:
x - 3/4 = (3 sqrt(5))/4 or x - 3/4 = -(3 sqrt(5))/4
Add 3/4 to both sides:
x = 3/4 + (3 sqrt(5))/4 or x - 3/4 = -(3 sqrt(5))/4
Add 3/4 to both sides:
Answer: x = 3/4 + (3 sqrt(5))/4 or x = 3/4 - (3 sqrt(5))/4
Answer: 46
Explanation: If Mia is paid $55 for every bicycle, she would need to fix up/sell 46 bicycles. This is because 45 x 55 = 2475 and Mia wants over 2500 but 46 x 55 = 2530. Therefore, 46 is the minimum number of bicycles.
Answer:
1. C
2. D
Step-by-step explanation:
1.
Pattern A is adding by 2's (1 -> 3, 4 -> 6, 7 -> 9 and so on).
Pattern B is multiplying by 2's (2 -> 4, 3 -> 6, 4 -> 8 and so on).
2.
If 0.25 gallons of paint = 24 ft^2, then 1 gallon will equal?
Set up an equation:
Variable x = area of ft^2 for 1 gallon of paint
0.25/24 = 1/x
Cross multiply
0.25 × x = 24 × 1
0.25x = 24
To make calculations easier, you can convert the decimal into a fraction: 0.25 = 1/4
1/4x = 24
Multiply both sides by 4
1x = 96
x = 96 ft^2
Check your work:
0.25/24 = 1/96
0.25 × 96 = 24 × 1
24 = 24
Correct
