Answer:
a) m<F = 70
b) AB = 6
Step-by-step explanation:
a)
Since this is an isoceles triangle, the base angles are equal so:
2x + 40 = 180
2x = 140
x = 70
b)
Since all of the angles are equal, this is an equilateral triangle. This also makes all of the sides equal and the same.
Answer:
x = 1 and y = 2
Step-by-step explanation:
Let apples are represented by x
and let oranges are represented by y
You purchase 5 pounds of apples and 2 pounds of oranges for $9. This line in equation format can be written as:
5x + 2y = 9
Your friend purchases 5 pounds of apples and 6 pounds of oranges for $17.
This line in equation format can be written as:
5x + 6y = 17
Now we have two equations:
5x + 2y = 9 -> eq (i)
5x + 6y = 17 -> eq(ii)
We can solve these equations to find the value of x and y.
Subtracting eq(i) from eq(ii)
5x + 6y = 17
5x + 2y = 9
- - -
_________
0+4y= 8
=> 4y = 8
y= 8/4
y = 2
Now, putting value of y in eq (i)
5x + 2y = 9
5x +2(2) = 9
5x +4 = 9
5x = 9-4
5x = 5
x = 1
so, x = 1 and y = 2
The average speed for the trip is 11 miles per hour, or mph. 99 miles divided by 9 is 11
x = r sin θ cos Ф
x² = r² sin² θ cos² Ф
y = r sin θ sin Ф
y² = r² sin² θ sin² Ф
z = r cos θ
z² = r² cos² θ
x² + y² + z²
= r² sin² θ cos² Ф + r² sin² θ sin² Ф + r² cos² θ
= r² sin² θ (cos² Ф + sin² Ф) + r² cos² θ
= r² sin² θ + r² cos² θ
= r² (sin² θ + cos² θ)
= r² √
9514 1404 393
Answer:
- Josh: 32 mph, 64 mi
- Greg: 64 mph, 320 mi
Step-by-step explanation:
Let x represent Josh's rate of travel in miles per hour. After 2 hours, his distance is ...
distance = speed · time
distance = x · 2 = 2x
Then 2x is Greg's rate of travel After 5 hours, his distance is ...
distance = speed · time
distance = (2x) · 5 = 10x
The distance they are apart is ...
10x -2x = 256
8x = 256
x = 32
__
Josh's rate: 32 miles per hour; Josh's distance = (2 h)(32 mi/h) = 64 miles.
Greg's rate: (32 mi/h)·2 = 64 mi/h; Greg's distance = (5 h)(64 mi/h) = 320 miles.
<em>__</em>
<em>Check</em>: 320 miles - 64 miles = 256 miles . . . . correct separation
