Answer:
8) The y coordinate of the solution: 4
9) Average of change from x = 2 to x = 4: 11
Step-by-step explanation:
8)
y = 2x + 2
y = x^2 + 3
So
x^2 + 3 = 2x + 2
x^2 - 2x + 3 - 2 = 0
x^2 - 2x + 1 = 0
(x - 1)^2 = 0
x - 1 = 0
x = 1
Plug in x = 1 into either those 2 equations to find y
y = 2(1) + 2 = 4
or
y = (1)^2 + 3 = 1 + 3 = 4
Answer:
The y coordinate of the solution is 4
9)
p(x) = x^2 + 5x - 2
p(2) = 2^2 + 5(2) - 2 = 4 + 10 - 2 = 12
p(4) = 4^2 + 5(4) - 2 = 16 + 20 - 2 = 34
Average of change from x = 2 to x = 4:
[p(4) - p(2)]/[(x(4) - x(2)] = (34 - 12)/(4-2) = 22 /2 = 11
Answer:
Average of change from x = 2 to x = 4 :11
Answer:
b. about 91.7 cm and 44.6 cm
Step-by-step explanation:
The lengths of the diagonals can be found using the Law of Cosines.
Consider the triangle(s) formed by a diagonal. The two given sides will form the other two sides of the triangle, and the corner angles of the parallelogram will be the measure of the angle between those sides (opposite the diagonal).
For diagonal "d" and sides "a" and "b" and corner angle D, we have ...
d² = a² +b² -2ab·cos(D)
The measure of angle D will either be the given 132°, or the supplement of that, 48°. We can use the fact that the cosines of an angle and its supplement are opposites. This means the diagonal measures will be ...
d² = 60² +40² -2·60·40·cos(D) ≈ 5200 ±4800(0.66913)
d² ≈ {1988.2, 8411.8}
d ≈ {44.6, 91.7} . . . . centimeters
The diagonals are about 91.7 cm and 44.6 cm.
Answer:
33 and 42
Step-by-step explanation:
Answer:
<u>Aaron played 4 games and went on 2 rides at the carnival.</u>
Step-by-step explanation:
1. Let's review the information provided to us to answer the question correctly:
Cost of each game = US$ 2.75
Cost of each ride = US$ 4.75
Total spent by Aaron at the carnival = US$ 20.50
Number of rides = x
Number of games = 2x (the number of games he played is twice the number of rides he went on)
2. Determine the number of games Aaron played and the number of rides Aaron went on.
For determine the number of games and the number of rides, we will use the following equation:
2.75 (2x) + 4.75x = 20.50
5.5x + 4.75x = 20.50
10.25x = 20.50
x = 20.50/10.25
x = 2 ⇒ 2x = 4
<u>Aaron played 4 games and went on 2 rides at the carnival.</u>
Answer:
$11,250
Step-by-step explanation:
Normally, when I work "mixture" problems, I like to choose the variable so it represents the amount of the largest contributor. Here, that would be the amount invested at 15%.
Unfortunately, the question asks for the amount invested at 7%. Using a variable to represent that amount means that there will be negative numbers involved. Care must be taken in the arithmetic.
Let x represent the amount invested at 7%. Then 16000-x is the amount invested at 15%. The total interest for one year is ...
0.07x + 0.15(16000 -x) = 1500 . . . . sum of interest amounts at each rate
-0.08x +2400 = 1500 . . simplify
-0.08x = -900 . . . . . . . . subtract 2400
x = 11250 . . . . . . . . . . . . divide by -0.08
The bank loaned $11,250 at 7%.
