Consider the two functions as
<span>y1(x) =3x^2 - 5x,
y2(x) = 2x^2 - x - c
The higher the value of c, father apart the two equations will be.
They will touch when the difference, i.e. y1(x)-y2(x)=x^2-4*x+c has a discriminant of 0.
This happens when D=((-4)^2-4c)=0, or when c=4.
(a)
So when c=4, the two equations will barely touch, giving a single solution, or coincident roots.
(b)
when c is greater than 4, the two curves are farther apart, thus there will be no (real) solution.
(c)
when c<4, then the two curves will cross at more than one location, giving two distinct solutions.
It will be more obvious if you plot the two curves in a graphics calculator using c=3,4, and 5.
</span>
Answer:
Integer = -40
Step-by-step explanation:
40 x -1
= -40
Therefore, -40 is the integer.
To solve this, you’ll first need to solve for their slopes.
The slope for line Q is y2-y1/x2-x1 = -8-(-2)/-8-(-10) = -3
We know that the lines are perpendicular so the negative reciprocal of -3 is 1/3
The equation you get it y = 1/3x + b.
Now you will need to solve for b by substituting in the first ordered pair of line R.
2 = 1/3(1) + b.
Once you solve for b, you should get 5/3 and y = 1/3x + 5/3
Now, to find a, you will need to substitute in 10 from the second ordered pair into x in your new equation.
y = 1/3(10) + 5/3.
Your solution should be 5.
So your answer is: a = 5
The probability that one of each color is selected is 
<h3>Probabilities</h3>
The probability of an event is the chances of the said event
The given parameters are:
- Total = 10
- Red = x
- Blue = 10 - x
<h3>Calculating the required probability</h3>
The probability that one of each color is selected is calculated as follows:
So, we have:
This gives
Take LCM
Simplify the above expression
Expand
Hence, the probability that one of each color is selected is
Read more about probabilities at:
brainly.com/question/7965468
Answer:
Step-by-step explanation:
![\sf \frac{3}{a} x - 4 = 20\\\\Add \ 4 \ to \ both \ sides\\\\\frac{3}{a} x = 20+4\\\\\frac{3}{a} x = 24\\\\Multiply \ both \ sides \ by \ a\\\\3x = 24 * a\\\\Divide \ 3 \ to \ both \ sides\\\\x = 24a / 3\\\\x = 8a\\\\\rule[225]{225}{2}](https://tex.z-dn.net/?f=%5Csf%20%5Cfrac%7B3%7D%7Ba%7D%20x%20-%204%20%3D%2020%5C%5C%5C%5CAdd%20%5C%204%20%5C%20to%20%5C%20both%20%5C%20sides%5C%5C%5C%5C%5Cfrac%7B3%7D%7Ba%7D%20x%20%3D%2020%2B4%5C%5C%5C%5C%5Cfrac%7B3%7D%7Ba%7D%20x%20%3D%2024%5C%5C%5C%5CMultiply%20%5C%20both%20%5C%20sides%20%5C%20by%20%5C%20a%5C%5C%5C%5C3x%20%3D%2024%20%2A%20a%5C%5C%5C%5CDivide%20%5C%203%20%5C%20to%20%5C%20both%20%5C%20sides%5C%5C%5C%5Cx%20%3D%2024a%20%2F%203%5C%5C%5C%5Cx%20%3D%208a%5C%5C%5C%5C%5Crule%5B225%5D%7B225%7D%7B2%7D)
Hope this helped!
<h3>~AH1807</h3>
