Hi there Mary Dominguez, So what a vertical line test down is to find out if a particular graph is a function or not. What you do is take a vertical strait line and move it right to left or left to right, depending on your preference, along the X axis. The reason this works is a function can not have an x that has 2 different y values. If we use the vertical line test on a graph with say a graph that has (2,3) and (2,4) we can use the vertical line test and see that the line hits 2 points at once which means its not a function :)
Answer:
I am going to show you the first steps to complete squares for the given equation: 1) Starting equation: 3x^2 + 9x -4 = 0 2) Add 4 to both sides => 3x^2 + 9x - 4 + 4 = 4 => 3x^2 + 9x = 4 3) Extract common factor 3 in the left side => 3 (x^2 + 3x). Now, compare with a(x^2 + 3x) and you get a = 3. Answer: a = 3.
Answer:
h + s = 15
2h + s = 20
Step-by-step explanation:
Let the number of hats Chevy made = h
Let the number of scarves made by Chevy = s
From the statement of the question, " Chevy made a total number of 15 items"
Equation will be h + s = 15
Amount of yarn used to make one hat = 0.2 kilograms
So amount of yarn used to make "h"hats = 0.2h kilograms
Similarly Amount of yarn used to make one scarf = 0.1 kilograms
So amount of yarn used to make "h" scarves = 0.1s kilograms
Another statement states " Chevy wants to use 2 kilograms of yarn to make these items".
Equation for this statement will be,
0.2h + 0.1s = 2
OR 2h + s = 20 [By multiplying the equation by 10]
Therefore, system of the equations will be
h + s = 15
2h + s = 20
Part a:
x + y = 55
y = x + 25
part b:
jackie runs 15 minutes every day.
part c:
it is not possible for jackie to spend 45 minutes a day dancing, since the time she spends dancing and running is 55 minutes, and we know that it takes 15 minutes to run
step-by-step explanation:
let's call and while jackie is dancing
let's call x while jackie is running
then we know that jackie runs and dances for a total of 55 minutes every day
this means that:
x + y = 55
we also know that jackie dances 25 minutes more than she runs.
this meant that:
y = x + 25
now we substitute the second equation in the first and solve for the variable x
x + x + 25 = 552x = 55-252x = 30x = 15
jackie runs 15 minutes every day.
now we find the value of the variable -y
15 + y = 55y = 55-15y = 40
note that it is not possible for jackie to spend 45 minutes a day dancing, since the time she spends dancing and running is 55 minutes, and we know that it takes 15 minutes to run
