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
You are welcome :)
first no I get x = 5
5X = 3y - 2
3y = 3X + 12
----------------add
5 x + 3 y = 3 x + 3 y + 10
2 x = 10
x = 5
y = 7x ^2 + 8x -6
we need to make sure solution is real and not repeated
look at b^2-4ac
64 + 168
positive so sqrt of + number,
you are right, two real zeros
Psst
To find the x-coordinate of the solution to the system of linear equations, we need to solve the equations simultaneously.
Let's start by substituting the value of y from the second equation into the first equation.
Substituting y = x + 4 into 5x = 3y - 2:
5x = 3(x + 4) - 2
Now, distribute and simplify:
5x = 3x + 12 - 2
2x = 10
Divide both sides by 2:
x = 5
So, the x-coordinate of the solution is 5.
Therefore, the correct answer is (c) 5.
To determine the number of times the graph of the function y = 7x^2 + 8x - 6 intersects the x-axis, we need to find the number of x-intercepts.
The x-intercepts occur when the y-coordinate is equal to 0.
So, we need to solve the equation 7x^2 + 8x - 6 = 0.
To solve this quadratic equation, we can either factor it or use the quadratic formula.
Since the equation cannot be easily factored, let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In the given equation, a = 7, b = 8, and c = -6.
Plugging in these values, we get:
x = (-8 ± √(8^2 - 4*7*(-6))) / (2*7)
Simplifying further:
x = (-8 ± √(64 + 168)) / 14
x = (-8 ± √232) / 14
x = (-8 ± √(4*58)) / 14
x = (-8 ± 2√58) / 14
Now, since the discriminant (b^2 - 4ac) is positive, we have two distinct solutions.
Therefore, the graph of the function y = 7x^2 + 8x - 6 intersects the x-axis 2 times.
Hence, the correct answer is (b) 2.
Thanks Damon for checking my answers!
:-)