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.
Answer:
63 miles per hour
54 miles per hour
Step-by-step explanation:
Let the two buses be represented as bus A and bus B.
bus A and bus B leave a station at the same time and travel in opposite directions.
Let the speed of bus A be A miles per hour.
Let the speed of bus B be B miles per hour.
One bus travels 9 miles/hour slower than the other.
Let bus A be the faster bus.
This means that the speed of bus B is B = A - 9
If the two buses are 585 miles apart after 5hours, this means that after 5hours, the total distance travelled by bus A and bus B is 585 miles.
Distance travelled by bus A in 5 hours = speed × time = 5A
Distance travelled by bus B in 5 hours = speed × time = 5B
5A + 5B = 585 - - - - - -1
Substituting B = A - 9 in equation 1
5A + 5(A - 9) = 585
5A + 5A - 45 = 585
10A = 585 + 45 = 630
A = 630/10 = 63 miles per hour
B = A - 9 = 63 - 9 = 54 miles per hour
Hello from MrBillDoesMath!
Answer:
96 degrees
Discussion:
The base angles of an isosceles triangle are equal and a triangle has 180 degrees. In our case this means that
42 + 42 + (measure of vertex angle) = 180
84 + (measure of vertex angle) = 180 => (subtract 84 from both sides)
84 - 84 + (measure of vertex angle) = 180- 84 =>
(measure of vertex angle) = 180- 84 = 96
Thank you,
MrB
Jill put 10.3 gallons of gas into her car. She drove for 473.8 miles.
So we have to find how many miles per gallon she drove.
473.8 into 10.3 = 46
To make sure= 10.3 x 46 = 473.8
So Jill drove 46 miles per gallon.
Answer:
F(x)=8(x-3)
Step-by-step explanation:
Had to watch a video but I THINK this is the correct answer
