Answer:
a = 2, b = - 5
Step-by-step explanation:
Given
y = ax² + bx
is the measure of the slope at x = a
Differentiate each term with respect to x using the power rule
(a
) = na
= 2ax + b, hence
2ax + b = 3 at (2, - 2)
Substitute x = 2 into
4a + b = 3 → (1) and substitute x = 2 into y
4a + 2b = - 2 → (2)
Subtract ( 1) from (2)
b = - 2 - 3 = - 5
Substitute b = - 5 into (1)
4a - 5 = 3 ( add 5 to both sides )
4a = 8 ( divide both sides by 4 )
a = 2
Answer:
-8x
Step-by-step explanation:
Answer:
8<em>x</em> + 25
Step-by-step explanation:
In the second photo.
Slope-intercept form: y = mx + b
(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)
For lines to be parallel, they have to have the same slope.
y = 6x + 6 The slope of this line is 6, so the parallel line's slope is also 6.
Now that you know m = 6, substitute/plug it into the equation:
y = mx + b Plug in 6 for "m" in the equation
y = 6x + b To find "b", plug in the point (20, 1) into the equation
1 = 6(20) + b
1 = 120 + b Subtract 120 on both sides to get "b" by itself
1 - 120 = 120 - 120 + b
-119 = b Now that you know b = -119, plug it into the equation
y = 6x - 119
Answer:
81 adult tickets
Step-by-step explanation:
Step 1:
Set up a system of equations
Since the adult tickets and student tickets add to 243, we can do

and the student tickets sold were 2x the adult tickets, we can do

We can replace s in the first equation adding to 243 with 2a

Step 2:
Solve for a. We can divide both sides by 3.

Therefore, there were 81 adult tickets sold.
Step 3:
We can check our work! Since we learned earlier the student tickets are 2x adult tickets, we can multiply 81 by 2 and add that to 81 to see if it equals 243!

And...

So, 81 must be the answer!