Answer:
-1<b<7, or i suppose b.
Step-by-step explanation:
6b<42
b<7
4b+12>8
4b>-4
b>-1
<span>Angle 7 and 5 are vertical angles, so they're equal.
Angles 7 and 8 are supplementary, so they have to add up to 180.
2x + 15 + 3x = 180
Solve for x, then plug it into the expression for angle 7 to get you answer</span>
Answer:
The answer to your question is x² + y² - 8x - 6y = 0
Step-by-step explanation:
Data
P (1, 7)
Q (8, 6)
R (7, -1)
Use the general equation of the Circle
x² + y² + Dx + Ey + F = 0
Process
1.- Substitute each point in the general equation and simplify
For P
(1)² + (7)² + D + 7E + F = 0
1 + 49 + D + 7E + F = 0
50 + D + 7E + F = 0
D + 7E + F = -50 Equation l
For Q
(8)² + (6)² + 8D + 6E + F = 0
64 + 36 + 8D + 6E + F = 0
100 + 8D + 6E + F = 0
8D + 6E + F = -100 Equation ll
For R
(7)² + (-1)² + 7D - E + F = 0
49 + 1 + 7D - E + F = 0
50 + 7D - E + F = 0
7D - E + F = -50 Equation lll
Solve the system of equations, I do not include the process but the solutions are
D = -8 E = -6 F = 0
-Substitution
x² + y² - 8x - 6y = 0
Answer:
x = price of balcony tickets = $7
y = price of orchestra tickets = $21
Step-by-step explanation:
Let
x = price of balcony tickets
y = price of orchestra tickets
y = 3x (1)
148y + 76x = 3,640 (2)
Substitute y = 3x into (2)
148y + 76x = 3,640 (2)
148(3x) + 76x = 3,640
444x + 76x = 3,640
520x = 3,640
x = 3,640/520
x = 7
Substitute x = 7 into (1)
y = 3x (1)
y = 3(7)
y = 21
x = price of balcony tickets = $7
y = price of orchestra tickets = $21
<h3>
Answer: Choice B</h3>
With matrix subtraction, you simply subtract the corresponding values.
I like to think of it as if you had 2 buses. Each bus is a rectangle array of seats. Each seat would be a box where there's a number inside. Each seat is also labeled in a way so you can find it very quickly (eg: "seat C1" for row C, 1st seat on the very left). The rule is that you can only subtract values that are in the same seat between the two buses.
So in this case, we subtract the first upper left corner values 14 and 15 to get 14-15 = -1. The only answer that has this is choice B. So we can stop here if needed.
If we kept going then the other values would be...
row1,column2: P-R = -33-16 = -49
row1,column3: P-R = 28-(-24) = 52
row2,column1: P-R = 42-25 = 17
row2,column2: P-R = 35-(-30) = 65
row2,column3: P-R = -19-36 = -55
The values in bold correspond to the proper values shown in choice B.
As you can probably guess by now, matrix addition and subtraction is only possible if the two matrices are the same size (same number of rows, same number of columns). The matrices don't have to be square.
