Answer:
x = sqrt(433/64) - 7/8 and x = -sqrt(433/64) - 7/8 So there are two. Let me know if there's something you don't understand.
Step-by-step explanation:
First you want to get them into the form where just y is on one side.
5-y=x^2+x
-y=x^2+x-5
y = -x^2 - x + 5
y+1 = 3/4x
y = 3/4x - 1
Let me know if you don't get how I did that.
To find where they intersect you just set them equal to each other and solve for x.
-x^2 - x + 5 = 3/4x - 1
Before you go solving you are going to want to avoid multiplying and dividing. Especially dividing here. if you divide something by (x-a) you make it so a cannot be used. take 1 for instance. graphing 1 is just a horizontal line at y=1. If you divide it by (x-a) in particular lets say (x-1) if you try and solve for x=1 you get 1/0 and you can't divide by 0. If you graph it on a calculator or computer you'll see the graph doesn't exist at x=1 either.
So yeah, no multiplying or dividing. So we turn this into a quadratic.
-x^2 - x + 5 = 3/4x - 1
-x + 5 = x^2 + 3/4x - 1
5 = x^2 + 7/4x - 1
0 = x^2 + 7/4x - 6
There are a few ways to solve but I am going to complete the square. If you don't understand how to solve it let me know and I will more specifically walk through it.
(x + 7/8)^2 - 433/64 = 0
(x + 7/8)^2 = 433/64
x + 7/8 = +/- sqrt(433/64)
x = +/- sqrt(433/64) - 7/8
So there are two answers here. Positive sqrt(433/64) - 7/8 and negative sqrt(433/64) - 7/8 Or approximately 1.726 and -3.476 respectively. To check try plugging these into the original two functions y = -x^2 - x + 5 and y = 3/4x-1 and make sure they give the same answer.
Let me know again if there's something you don't get. When oing intersections though you set the two equations equal to each other and solve for x however you can.
<u>The problem is as following:</u>
The graph shows the relationship between the total cost and the number of gift cards that Raj bought for raffle prizes. What would be the cost for 5 of the gift cards? $80, $90, $100 Or $110
===============================================================
<u>Solution</u>:
The points of the figure represents a straight line
The general form of the straight line is ⇒ y = mx + c
where m is the slope and c is constant
let x ⇒ The number of gifts cards , y ⇒ Total cost (in $)
we will find m and c using the points (1,20) , (2,40)
The slope = m =
∴ y = 20x + c
Substitute with the point (1,20) ⇒ y = 20 at x = 1
∴ 20 = 20 * 1 + c
∴ 20 = 20 + c
∴ c = 0
∴ The equation of the line ⇒⇒⇒ y = 20x
To find the cost for 5 of the gift cards substitute with x = 5
∴ y = 20 * 5 = 100
So, the cost for 5 of the gift cards = $100
<u>The correct answer is option 3 ⇒⇒⇒ $100</u>
Answer: 6(u-2)+2=6u-10
Step-by-step explanation:
Then, any value of u makes the equation true.
Answer:
-15x+27
Step-by-step explanation:
-3 * 5x = -15x
-3 * -9 = 27