A system of linear equations is shown below.
5X = 3y - 2
y = X + 4
What is the x -coordinate of the solution?
a.) 2
b.) 4
c.) 5
d.) 1 *****
Jean needs to graph the function below.
y = 7x ^2 + 8x -6
How many times should the graph of this function intersect the x-axis?
a.) 3 ******
b.) 2
c.) 1
d.) 0
nope. nope.
? ? ? ? ? ? ? ?
A system of linear equations is shown below.
5X = 3y - 2
y = X + 4
What is the x -coordinate of the solution?
a.) 2
b.) 4 *****
c.) 5
d.) 1
Jean needs to graph the function below.
y = 7x ^2 + 8x -6
How many times should the graph of this function intersect the x-axis?
a.) 3
b.) 2 ******
c.) 1
d.) 0
Are you just guessing?
Your second one happens to be correct, do you know why it is 2 ?
To find the x-coordinate of the solution to the system of linear equations, we need to solve the equations simultaneously.
First, we can substitute the value of y from the second equation into the first equation:
5X = 3(X + 4) - 2
Simplifying the equation:
5X = 3X + 12 - 2
Combining like terms:
5X = 3X + 10
Next, we want to isolate the variable X. We can subtract 3X from both sides of the equation:
5X - 3X = 10
2X = 10
Finally, divide both sides of the equation by 2:
X = 10 / 2
X = 5
Therefore, the x-coordinate of the solution is 5. Thus, the correct answer is option c.) 5.
To determine the number of times the graph of the function intersects the x-axis, we need to examine the discriminant of the quadratic equation.
The discriminant of a quadratic equation in the form ax^2 + bx + c = 0 is given by Δ = b^2 - 4ac.
In this case, the quadratic equation is y = 7x^2 + 8x - 6. Comparing it to the standard form, we have a = 7, b = 8, and c = -6.
Calculating the discriminant:
Δ = (8)^2 - 4(7)(-6)
= 64 + 168
= 232
The discriminant is 232.
If the discriminant is greater than zero (Δ > 0), the quadratic equation has two distinct real roots, meaning the graph intersects the x-axis twice. If the discriminant is equal to zero (Δ = 0), the quadratic equation has one real root, resulting in the graph touching the x-axis once. If the discriminant is less than zero (Δ < 0), the quadratic equation has no real roots, and the graph does not intersect the x-axis.
In this case, since Δ = 232, which is greater than zero, the graph of the function intersects the x-axis two times. Therefore, the correct answer is option a.) 3.