Answer:
1. a= 7, one solution
2. x=x, infinitely solutions
3. y=3, one solution
4. x=6, one solution
5. no solution
6. k = 2, one solution
Step-by-step explanation:
1.
7a - 6 = 43
7a = 49
one solution
a = 7
2.
3x + 4 = 3x + 4
3x = 3x
x = x
infinitely solutions
3.
4(2y - 4) = 5y + 2
8y - 16 = 5y + 2
3y -16 = 2
3y = 18
one solution
y= 6
4.
multiply 2 on both sides
5x + 6 = x + 30
4x = 24
one solution
x = 6
5.
4e - 19 = 4(e-4)
4e - 19 = 4e -16
-19 ≠ -16
no solution
6.
10k - 2(k+3) = 10
10k -2k - 6 = 10
8k - 6 = 10
8k = 16
one solution
k = 2
Answer:
51
Step-by-step explanation:
The possible components to sum up to 101 can only be divided into 2 groups, 1 is larger than 50 and the other is less than or equals to 50
For example
50 + 51 = 101
52 + 49 = 101
60 + 41 = 101
...
99 + 2 = 101
100 + 1 = 101
Therefore, the worst case scenario is to pick all numbers from only 1 group, either all number less than or equal to 50, which there are 50 of them from 1 to 50, or greater than 50, which there are 50 of them from 51 to 100.
So k has to be at least 51 to guarantee that at least one pair of the selected integers will sum to 101
Answer: 1.106 s
Step-by-step explanation:
This situation is related to projectile motion and one the equation that models the height of the blueberry pie in time is:

Where:
is the blueberry pie final height (when it hits the ground)
is the blueberry pie initial height
is the blueberry pie initial velocity
is the angle, assuming the pie was shot horizontally
is the time
is the acceleration due gravity
Rewriting the equation:

Isolating
:


Finally:

The height of the cone is 8.59
That would be choice 2. One acute angle is the complement of the other
eg in a 90-60-30 triangle sine 30 = cos 60