C is 6 because the absolute value of -19 -13 would be 19-13 which equals 6
Answer:
equation 1
y = -2x
equation 2
y = x-3
Solution to both
(1,-2)
Step-by-step explanation:
We need to get the equations of both lines
General form is;
y = mx + c
where m is slope and c is the y-intercept
Table 1
since we have a point 0,0; the y-intercept here is zero
Let us get the slope. We can do this by selecting any two points
m = (y2-y1)/(x2-x1)
m = (2-10)/(-1+5) = -8/4 = -2
So the equation of the first line is;
y = -2x
Table 2
we get the slope
m = (4+2)/(7-1) = 6/6 = 1
The partial equation is;
y = x + c
To get c, we select any two point and substitute
4 = 7 + c
c = 4-7
c = -3
So the equation is;
y = x-3
To get the solution to both systems, we equate the y
-2x = x - 3
-2x-x = -3
-3x = -3
x = -3/-3
x = 1
To get y, we substitute;
recall; y = -2x
y = -2(1)
y = -2
Solution to the system is;
(1,-2)
Answer:
Trampolinist will land on the trampoline after 0.9 seconds.
Step-by-step explanation:
The function h(t) = -16t² + 15 represents the relation between height 'h' above the ground and the time 't' of the trampolinist.
We have to find the time when trampolinist lands on the ground.
That means we have to find the value of 't' when h(t) = 15 - 13 = 2
[Since trampoline is 2 feet above the ground]
When we plug in the value h(t) = 2
2 = -16t² + 15
2 + 16t² = -16t² + 16t² + 15
16t² + 2 = 15
16t² + 2 - 2 = 15 - 2
16t² = 13


t = 
t ≈ 0.9 seconds
Therefore, trampolinist will land on the trampoline at 0.9 seconds.
Answer:

Step-by-step explanation:
<u>Mathematical Modeling</u>
To model a real-life situation, a mathematical model can be constructed in such a way it accurately represents the variables measured in the system.
This problem requires to build a model for the yearly cost of a small and successful business.
The first data is the fixed monthly cost or the money the owner must pay regardless of the number of employees he hires. This cost includes shipping supplies and products for $2,000. To operate for a full year, the fixed cost is 12*$2,000=$24,000.
The other component of the cost function is the variable cost of x employees. Given each employee costs $1,600 each month, having x employees cost 1,600x each month. For a full year, the variable cost will be
12*1,600x=19,200x.
We finally form the total cost function:

Answer:
y= -4x + 3
Step-by-step explanation:
Because the slope is -4/1 which is the same as 4 and 3 is the y-intercept.
Here's the work;
We can just use the first two coordinates which are (0,3) and (1,-1) to get from the x-value 0 to 1 we add 1. and to get from the y-value 3 to -1 we subtract 4. Therefore the slope is -4 and the y- intercept (when x is zero) is 3. Pop that into slope intercept form to get y=-4x +3
Hope that helps and have a great day!