Answer:
1
7 ✔️
15
21
Only 7 is a prime number in this question.
To solve for p, square both sides and move the equation to one side is equal to zero. Then factor. I chose -2 and -5 because -2 x -5 = 10 and -2 + -5 = -7. After factoring, solve p-5=0 and p-2=0. When one of those equals zero then the equation (p-5)(p-2)=0 is true.
Find an equation of the plane that contains the points p(5,−1,1),q(9,1,5),and r(8,−6,0)p(5,−1,1),q(9,1,5),and r(8,−6,0).
topjm [15]
Given plane passes through:
p(5,-1,1), q(9,1,5), r(8,-6,0)
We need to find a plane that is parallel to the plane through all three points, we form the vectors of any two sides of the triangle pqr:
pq=p-q=<5-9,-1-1,1-5>=<-4,-2,-4>
pr=p-r=<5-8,-1-6,1-0>=<-3,5,1>
The vector product pq x pr gives a vector perpendicular to both pq and pr. This vector is the normal vector of a plane passing through all three points
pq x pr
=
i j k
-4 -2 -4
-3 5 1
=<-2+20,12+4,-20-6>
=<18,16,-26>
Since the length of the normal vector does not change the direction, we simplify the normal vector as
N = <9,8,-13>
The required plane must pass through all three points.
We know that the normal vector is perpendicular to the plane through the three points, so we just need to make sure the plane passes through one of the three points, say q(9,1,5).
The equation of the required plane is therefore
Π : 9(x-9)+8(y-1)-13(z-5)=0
expand and simplify, we get the equation
Π : 9x+8y-13z=24
Check to see that the plane passes through all three points:
at p: 9(5)+8(-1)-13(1)=45-8-13=24
at q: 9(9)+8(1)-13(5)=81+9-65=24
at r: 9(8)+8(-6)-13(0)=72-48-0=24
So plane passes through all three points, as required.
The answer is d. All you have to do is divide the reaction value by the product value. Sometimes they give you the answer is fraction form, and sometimes they give it in decimal form, which can be tricky.
Answer:
You would have to make and sell 600 video games.
Step-by-step explanation:
Step 1: Subtract the total cost of a game from the sell value to get the overall income from each game.
$20 - $2.65 = $17.35
Step 2: Divide the investment price in equipment by the overall income from each game.
$10,410 ÷ $17.35 = 600
Therefore, you would need to make and sell 600 video games before your business breaks even.