Answer:
x = -7 or x = 1
Step-by-step explanation:
Given expression:
(x + 3)² = -16
Problem;
Solve for x;
Solution:
To solve for x; we use the factorization method;
Take -16 to the left of the equation;
(x + 3)² = -16
(x + 3)² + 16 = 0
(x+ 3)² + 4² = 0
if x² + y² = (x + y)(x - y)
So;
(x + 3 + 4) (x + 3 - 4) = 0
(x + 7)(x - 1) = 0
x + 7 = 0 or x - 1 = 0
x = -7 or x = 1
Answer:
16.9 m
Step-by-step explanation:
Start with a half a circle. The central angle of a semicircle is 180 deg.
Now subtract 21 deg on each side.
180 - 21 - 21 = 138
The central angle is 138 deg.
The radius is 7 m.
Now we use the formula for the length of an arc of a circle given the radius of the circle and the central angle of the arc.



Answer:
29. 15.87%
30. 4.75%
31. 0.62%
32. probability cannot be calculated (0%)
Step-by-step explanation:
We have that the formula of the normal distribution is:
z = (x - m) / sd
where x is the value we are going to evaluate, m is the mean and sd is the standard deviation
x = 16 and m = 16.5
when sd = 0.5
z = (16 - 16.5) /0.5
z = -1
Now when looking in the z table, we have that the corresponding value is 0.1587, that is, the probability is 15.87%
when sd = 0.3
z = (16 - 16.5) /0.3
z = -1.67
Now when looking in the z table, we have that the corresponding value is 0.0475, that is, the probability is 4.75%
when sd = 0.2
z = (16 - 16.5) /0.2
z = -2.5
Now when looking in the z table, we have that the corresponding value is 0.0062, that is, the probability is 0.62%
when sd = 0
z = (16 - 16.5) / 0
z = infinity
probability cannot be calculated