Answer:
B = 34.2°
C = 58.2° or 121.8°
c= 10.6
Step-by-step explanation:
Step 1
Finding c
We calculate c using Pythagoras Theorem
c²= a² + b²
c = √a² + b²
a= 8, b = 7
c = √8² + 7²
c = √64 + 49
c = √(113)
c = 10.630145813
Approximately c = 10.6
Step 2
Find B
We solve this using Sine rule
a/sin A = b/sin B
A = 40°
a = 8
b = 7
Hence,
8/sin 40° = 7/sin B
8 × sin B = sin 40° × 7
sin B = sin 40° × 7/8
B = arc sin (sin 40° × 7/8)
B ≈34.22465°
Approximately = 34.2°
Step 3
We find C
Find B
We solve this using Sine rule
b/sin B = c/sin C
B = 34.2°
b = 7
c = 10.6
C = ?
Hence,
7/sin 34.2° = 10.6/sin C
7 × sin C = sin 34.2 × 10.6
sin C = sin 34.2° × 10.6/7
C = arc sin (sin 34.2° × 10.6/7)
C = arcsin(0.85)
C= 58.211669383
Approximately C = 58.2°
Or = 180 - 58.2
C = 121.8°
Answer:
Step-by-step explanation:
Let x represent the number of years it will take the two colleges to have the same enrollment.
In 2000, there were 12900 students at college A, with a projected enrollment increase of 900 students per year. This means that the expected number of students at college A in x years time is
12900 + 900x
In the same year, there were 25,000 students at college B, with a projected enrollment decline of 700 students per year. This means that the expected number of students at college B in x years time is
25000 - 700x
For both colleges to have the same enrollment,
12900 + 900x = 25000 - 700x
900x + 700x = 25000 - 12900
1600x = 12100
x = 12100/1600
x = 7.56
Approximately 8 years
The year would be 2000 + 8 = 2008
Answer:
sin(x) = 5/13
cos(y) = 5/12
Therefore, sin(x) = cos(y)
Step-by-step explanation:
Trig ratios:
where 
is the angle, O is the measure of the side opposite the angle, A is the measure of the side adjacent to the angle and H is the hypotenuse, of a right triangle
We have been given the measures of the two legs, so we can find the measure of the hypotenuse by using Pythagoras' Theorem 
(where a and b are the legs and c is the hypotenuse of a right triangle)
Now we can use the trig ratios:
Therefore, sin(x) = cos(y)
Answer:
The last equation x2 - 2x -4 = 0
has solution (x - 1)^2 - 5 = 0, x = 1 + root(5) or x = 1 - root(5)
Step-by-step explanation:
If a quadratic function has roots 1 and 5
f(x) = (x -1)(x- 5)
f(x) = x^2 - 6x + 5
Unless you meant. -4 and 6 ?
g(x) = (x + 4)(x - 6)
g(x) = x^2 -2x -24
-------------------------
Or did you mean x = 1 and x =4 ?...
x^2 + 2x + 4 = 0 : complete square x^2 + 2x + 1 + 3 = 0, (x+1)^2 + 3 = 0
x^2 - 2x + 4 = 0 : complete square: (x -1)^2 + 3 = 0
0x^2 + 2x - 4 = 0, 2x - 4 = 0, x = 2
x^2 - 2x - 4 = 0 becomes: x^2 - 2x + 1 - 1 -4 = 0 ; (x - 1)^2 - 5 = 0
