Answer:
$6.65
Step-by-step explanation:
Total sales tax = Item cost 
sales tax rate
Item Price: $95
Sales tax rate: 7% = 0.07
Total sales tax = $6.65
I hope this helps! (✿◕‿◕✿)
Answer:
Orange juice that is 3 dollars per 1 jug
Step-by-step explanation:
A unit rate is per 1 of an item
The only 1 that is per 1 of an item is
Orange juice that is 3 dollars per 1 jug
Answer:
32m^4 + 12m^3 = 4m^3(8m + 3) ---------->correct
40m^6 - 4 = 4(10m^6 - 1) ---------->correct
Step-by-step explanation:
32m^4 + 12m^3 = 4m^3(8m + 3) ---------->correct
40m^6 - 4 = 4(10m^6 - 1) ---------->correct
15m^3 - 6m = 3m(5m^2 - 2) , so it's not correct if answer : 3m(5m^2 - 6m)
6m^2 + 18m = 6m(m + 3) , so it's not correct if answer : 6m^2(1 + 3)
Of the four x-coordinates to choose only 1/√(11) belongs can belong to the unit circle.
The other three x-coordinates are greater than 1, then they are out of the unit circle.
The unit circle formula is x^2 +y^2 = 1
Then to find the y-coordinate given the x-coordinate you can solve for y from that formula:
y^2 = 1 - x^2
y = (+/-)√(1-x^2)
Substitute the value of x
y = (+/-)√{1 - [1/√(11)]^2} = (+/-) √{(1 - 1/11} =(+/-) √ {(11 -1)/11 =(+/-)√(10/11) ≈ +/- 0.95
An interesting question!
Instead of solving each set of non-linear system of equations 6 times, I will try a simpler way, which is more adapted to multiple choice questions. However, please be warned that this method will not improve immensely math skills, but will help with reasoning, and possibly a broader understand in system of equations.
For simplicity, I will denote the sets of system of non-linear equations by S={A,B,C,D,E,F} from left to right.
1. given solutions {(-2,3),(7,-6)}
We first check each member of S, i.e. A,B,C,D,E,F for the linear conditions.
A: x+y=-2+3=1 ≠ 3 so no
B: x-y=-2-3=-5 ≠ 1 so no
C: 2x+y=-2(2)+3=-1 ≠ 1 so no
D: x+2y=-2+3(2)=4 ≠ 2 so no
E: -x+y=2+3=5 ≠ 1 so no
F: x+y=-2+3=1 ≠ 3 so YES now check the other solution 7-6=-1 OK
Now check the non-linear condition for F:
S1: (-2,3)
y-15=3-15=-12
-x^2+4x=-(-2)^2+4*(-2)=-12 good
S2:(7,-6)
y-15=-6-15=-21
-x^2+4x=-(7^2)+4(7)=-49+28=-21 also good,
So Solution set (1) matches tile F
(2) Given solutions {(-5,8),(3,0)}
We proceed in a similar way, to find that
-5+8=3 & 3+0=3 (matches A) and nothing else.
Check non-linear conditions (optionally, I transposed the terms to make comparison easier)
A. x^2+x-y=(-5)^2+(-5)-8=25-5-8=12 (looks good)
x^2+x-y=(3)^2+(3)-0=9+3=12 (looks even better)
So we determined that {(-5,8),(3,0)} is the solution for tile A.
(3) For solution set {(-2,5),(3,-5)}
Check linear conditions:
x+y=3 and -3, so does not satisfy A,& F.
x-y=-7 and 8, so does not satisfy B
2x+y=5 and 1 so satisfies C
x+2y=8 & -7 so does not satisfy D
-x+y=7 & -8 so does not satisfy E
Thus C is our only set. NOTE: if two distinct points satisfy one linear condition (say C), then both points cannot satisfy another non-equivalent linear condition, i.e. we didn't really have to check points D & E (which are not equivalent linear conditions as C) once we have found C.
Now check non-linear conditions:
x^2-3x-y=(-2)^2-3(-2)-5=5 ok
x^2-3x-y=(3)^2-3(3)-(-5)=5 ok
So solution set (3) matches tile C.
@officiallyqueenz, for your benefit, I will leave one for you as exercise. Please proceed to find the system for solution set (4). Post a your work as comments if you get stuck, or your answer for verification if you wish.
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