∠B = 77°, a = 7.42 and b = 12.61
Solution:
Given triangle ABC.
∠A = 35°, ∠C = 68°, c = 12
To find the measure of ∠B:
Sum of all the angles of the triangle = 180°
⇒ ∠A + ∠B + ∠C = 180°
⇒ 35° + ∠B + 68° = 180°
⇒ 103° + ∠B = 180°
⇒ ∠B = 180° – 103°
⇒ ∠B = 77°
To find the length of a and b:
The side opposite to angle A is a.
The side opposite to angle B is b.
Using law of sine,
Do cross multiplication, we get
Divide by 0.9271 on both sides, we get
⇒ a = 7.42
Again by law of sine,
Do cross multiplication, we get
Divide by 0.9271 on both sides, we get
⇒ b = 12.61
Hence ∠B = 77°, a = 7.42 and b = 12.61.
I'm assuming each grid square= 1 square mile.
To do this, you first need to find the total distance.
The first component of his walk takes him from an x-coordinate of 2 to a coordinate of -4 1/2. Since the y-value remains the same, you're not worried about that for this part of the problem. The difference between 2 and -4 1/2 is 6 1/2, so that is your horizontal distance.
Now he walks from the (-4 1/2, -1 3/4) to (-4 1/2, 5 1/4). This time, the x-value is constant, so you only need to worry about the y. As they are on opposite sides of the x-axis, you can add the y-values to get a result of 7, which is your vertical distance.
I just realized I did those distances in reverse order, but it should be ok because the total distance is the same.
To find the total distance, add vertical to horizontal.
6 1/2 + 7 = 13 1/2. This is your total distance.
Now that you have both his speed (given), and total distance, you can find the time it will take him. If he is moving at 4 1/2 mph and the distance is 13 1/2 miles, you can use s=d/t to find the time. 3 1/2 miles divided by the time = 4 1/2 mph. To solve for t, multiply both sides by t and divide that by s, so t= d/s. we know d= 13 1/2 and s= 4 1/2, so t= 13.5 divided by 4.5 = 3. As his speed is in mph, the unit is in hours. Therefore, the answer should be 3 hours.
WHat shape? Perimeter is all of the sides added together, so to find out. we would need to see the shape and its dimensions
When you rotate 90 degrees clockwise, (x,y) becomes (y,-x).
Therefore:
G = (3,1)
H = (0, 4)
I = (-2, -3)
Given function : 
We need to identify a " initial amount", b "growth factor", r " rate of growth".
We know, exponential growth formula
, where a is initial amount, b is growth factor. On comparing with given function let us find values of a and b.
⇔ .
We can see a= 1.05 and b = 1.46.
Now, b=1+r.
Therefore, 1+r =1.46.
Subtracting 1 from both sides, we get
1+r-1 =1.46-1
r = 0.46.
On converting 0.46 into percentage, we get
0.46 × 100 = 46.
Therefore, intial amount a = a= 1.05 , growth factor b = 1.46, and the rate of growth r= 46%.
