Let x = number of adult tickets sold
Let x-53 = number of student tickets sold
x + x -53 = 697
2x - 53 = 697.
Add 53 to both sides to get:
2x = 750
Divide both sides by 2 to get:
x = 375
375 adult tickets were sold.
47 -14i
You can work this out in the straight-forward way, or you can recognize that (6-i) is a common factor. In the latter case, you have ...
... = (6-i)(5 + 3-i)
... = (6 -i)(8 -i)
This product of binomials is found in the usual way. Each term of one factor is multiplied by each term of the other factor and the results summed. Of course, i = √-1, so i² = -1.
... = 6·8 -6i -8i +i²
... = 48 -14i -1
... =
_____
A suitable graphing calculator will work these complex number problems easily.
See the image below, hope it helps!
9514 1404 393
Answer:
48 ft
Step-by-step explanation:
For the quadratic ax^2 +bx +c, the axis of symmetry is x = -b/(2a). For the given quadratic, which defines a parabola opening downward, the axis of symmetry defines the time at which the maximum height is reached.
t = -48/(2(-16)) = 1.5
Then the maximum height is ...
f(1.5) = (-16·1.5 +48)1.5 +12 = (24·1.5) +12
f(1.5) = 48
The maximum height the object will reach is 48 feet.
Answer:
y = 2x +1
Step-by-step explanation:
The given line is in "slope-intercept" form, where the slope is the coefficient of x, 2, and the intercept is the added constant, 3. The parallel line will have the same slope, but its constant will be different. We can find the constant by putting the given point into an equation with the constant as the unknown:
y = 2x + b
-1 = 2(-1) +b . . . substitute for x and y
2 -1 = b . . . . . . add 2
1 = b
So the equation for the parallel line is ...
y = 2x + 1