2-9 Weighted Averages
Mixture problems are...
Two or more parts are combined into a whole and solved using weighted averages.
Solve:
4x - 4y = 8
-8x + y = 19
(-3, -5)
Solve: 2x2 + 22x + 56
x = {-7, -4}
sqrt(a + 5) + 7 = 12
a = 20
Tasha ordered the 15¢ / ounce soup and 20¢ / ounce salad for lunch. If Tasha ordered 10 ounces of soup for lunch and the total cost was $3.30, how many ounces of salad did Tasha order?
9
Solve:
2x + 3y = -11
-8x - 5y = 9
(2, -5)
Solve: 3x2 + 17x + 10
x = {-5, -2/3}
Solve sqrt(k + 1) = k - 1.
k = 3
Solve the equation for w.
10.50(5)+35w=25(5+w)
w = 7.25
Solve:
3x + 4y = 11
2x + y = -1
(-3, 5)
Solve: 5x2 - 3x + 4
prime; no real solution
Solve: sqrt(1 - 2t) = 1 + t.
t = 0
Rosamaria is setting up a 20-gallon saltwater fish tank that needs to have a salt content of 3.5%. If Rosamaria has water that has 2.5% salt and water that has 3.7% salt, how many gallons of the water with 3.7% salt content should Rosamaria use?
approx. 16.67 gallons
Of the 17 species of penguins in the world, the largest species is the emperor penguin. One of the smallest is the Galapagos penguin. The total height of the two penguins is 169 centimeters. The emperor penguin is 22 centimeters more than twice the height of the Galapagos penguin. Find the height of each penguin.
The height of the emperor penguin is 120 centimeters, and the height of the Galapagos penguin is 49 centimeters.
Ben dives from a 36-foot platform. The equation h = -16t2 + 14t + 36 models the dive (t in seconds). How long will it take Ben to reach the water?
2 seconds
The surface area of a basketball is x square inches. What is the radius of the basketball if the formula for the surface area of a sphere is SA = 4pi(r2)?
r = (sqrt(x(pi))) / (2(pi))
A subway travels 60 miles per hour from Glendale to Midtown. Another subway, traveling at 45 miles per hour, takes 11 minutes longer for the same trip. How far apart are Glendale and Midtown?
approx. 0.53 miles
At a sale, Salazar bought 4 T-shirts and 3 pairs of jeans for $181. At the same store, Jenna bought 1 T-shirt and 2 pairs of jeans for $94. The T-shirts were all the same price, and the jeans were all the same price. What is the cost of a T-shirt and a pair of jeans?
T-shirt: $16
Jeans: $39
When Jerald shoots a free throw, the ball is 6 feet from the floor and has an initial upward velocity of 20 feet per second. The hoop is 10 feet from the floor. The equation h = -16t2 + 20t + 6 models this situation. How long is the basketball in the air before it reaches the hoop?
1 second
The formula for the slant height c of a cone is c = sqrt(h2 + r2), where h is the height of the cone and r is the radius of its base. Find the height of the cone if the slant height is 4 units and the radius is 2 units. Round to the nearest tenth.
approx. 3.5 units