Answer:
<h2>x = 14, z = 65</h2>
Step-by-step explanation:
The angles (5x - 5)° and (6x + 31)° are supplementary angles.
Supplementary Angles add up to 180°.
Therefore we have the equation:
5x - 5 + 6x + 31 = 180 <em>combine like terms</em>
(5x + 6x) + (-5 + 31) = 180
11x + 26 = 180 <em>subtract 26 from both sides</em>
11x = 154 <em>divide both sides by 11</em>
x = 14
The angles (5x - 5)° and z° are vertical angles.
Vertical angles are congruent.
Therefore we have the equation:
z = 5x - 5 <em>put x = 14 to the equation</em>
z = 5(14) - 5
z = 70 - 5
z = 65
Step-by-step explanation:
it is a simple addition and subtraction sequence :
10 + 0 + -21 + 14 = 3
since the result is positive, it is overall a gain.
if the result were negative, it would be an overall loss.
so, he had an overall gain of 3 yards.
Answer:
± 27.33 ft
Step-by-step explanation:
For the given problem, we can estimate the initial and final coordinates of the line of the ball path as (-40,-50) and (0,0). Therefore, the slope is:
(-50-0)/(-40-0) = 50/40 = 1.25
Similarly, we can estimate the slope of a perpendicular line to the line of the ball path as: -1*(1/1.25) = -0.8.
Therefore, using (0,0) and the slope -0.8, the equation of the perpendicular line is: -0.8 = (y-0)/(x-0);
-0.8 = y/x
y = -0.8x
Furthermore, we are given the circle radius as 35 ft and we can use the distance formula to find the two points 35 ft far from the origin:
35^2 = x^2 + y^2
y = -0.8x
35^2 = x^2 + (-0.8x)^2
1225 = (x^2 + 0.64x^2)
1225 = 1.64x^2
x^2 = 1225/1.64 = 746.95
x = sqrt(746.95) = ± 27.33 ft
Answer:0.2 gallons and 1.6 pints
Step-by-step explanation:
1 gallon = 8 pint
1 gallon / 5=0.2 gallon
8 pint / 5=1.6 pint
There are 63 cornstalks in total
