1 modulo 9 is the set of numbers as follows:
(0(9) + 1), (1(9) + 1, ....)
which is:
1, 10, 19
All we have to do is divide 1000 by 9, and round down.
1000/9 = 111.111......
There are 111 numbers.
Now let us check our work.
the set is as follows:
(1,10,19, ....... (111)9 +1)
(1, 10, 19 ........ 1000)
We are within 1000.
Therefore, 111 of the 1000 smallest positive integers are congruent to 1 modulo 9.
Answer:
64°; no
Step-by-step explanation:
Since XW bisects angle X, we have ...
angle YXZ = 2(angle WXY)
(4x +6) = 2(3x -5)
4x +6 = 6x -10 . . . eliminate parentheses
16 = 2x . . . . . . . . add 10-4x
8 = x
Then angle XZY = 8x° = 8·8° = 64°. The angle WXZ is (3x-5)° = (3·8-5)° = 19°, an angle that is not complementary to 64°. XW cannot form a right angle with YZ, so it is not an altitude.
Angle XZY is 64°, and XW is not an altitude.
Answer: The salon charges $16 for a manicure and $25 for a pedicure.
Step-by-step explanation:
Let x represent the amount charged by the salon for a manicure.
Let y represent the amount charged by the salon for a pedicure.
Over the weekend, they performed 49 manicures and 16 pedicures, bringing in a total of $1,184 in receipts. It means that
49x + 16y = 1184- - - - - - - - - - 1
So far this week, they have administered 31 manicures and 33 pedicures, with receipts totalling $1,321. It means that
31x + 33y = 1321- - - - - - - - - - 2
Multiplying equation 1 by 31 and equation 2 by 49, it becomes
1519x + 496y = 36704
1519x + 1617y = 64729
Subtracting, it becomes
- 1121y = - 28025
y = - 28025/- 1121
y = $25
Substituting y = 25 into equation 1, it becomes
49x + 16 × 25 = 1184
49x + 400 = 1184
49x = 1184 - 400
49x = 784
x = 784/49
x = $16
Answer:
Function A
Step-by-step explanation:
Function B is not a linear function because it curves and is not a straight line. So you look at Function A and take any two points and subtract the y's and the x's and in conclusion, I found Function A to be the answer.
