Answer:
|-13| = 13, so the opposite is -13
|14| = 14, the opposite is -14
-|42| = -42, the opposite is 42
A right triangle's longest side is the hypotenuse
let x=longest, y=middle, and z=shortest
x=y+2
y=2z-1
therefore x=(2z-1)+2=2z+1
find z
z^2+y^2=x^2 by Pythagorean theorem
plug in x and y in terms of z
z^2+(2z-1)^2=(2z+1)^2
z^2+4z^2-4z+1=4z^2+4z+1
subtract the right-hand side's value from the left-hand side's
z^2-8z=0
z(z-8)=0
z=0, 8
z cannot be zero as the sides must have some value to it.
Therefore the shortest side is equal to 8
Answer:
A. Plane B because it was 9.33 miles away
B. 48 units
Step-by-step explanation:
A. Since the airplanes fly at an angle to the runway, their direction forms a triangle with the runway with their height above the ground as the opposite of the angle and their distance from the airport as the hypotenuse.
So for airplane A with 44° angle of departure,
sin44° = y/h where y = height above the ground and h = distance from airport
So h = y/sin44° = 6/sin44° = 8.64 miles
So for airplane B with 40° angle of departure,
sin40° = y/H where y = height above the ground and H = distance from airport
So H = y/sin40° = 6/sin40° = 9.33 miles
Since airplane B is at 9.33 miles away from the airport whereas airplane A is 8.64 miles from the airport, airplane B is farther away.
B. We know that scale factor = new size/original size
Our scale factor = 4 and original size = 12 units. So,
new size = scale factor original size = 4 × 12 = 48 units.
Answer:
half dollar, quarter, dime and nickel
Step-by-step explanation:
When you sum it up it will give you 90 cents.
