Answers: ∠a = 30° ; ∠b = 60° ; ∠c = 105<span>°.
</span>_____________________________________________
1) The measure of Angle a is 30°. (m∠a = 30°).
Proof: All vertical angles are congruent, and we are shown in the diagram that angle A — AND the angle labeled with the measurement of 30°— are vertical angles.
2) The measure of Angle b is 60°. (m∠b = 60<span>°).
Proof: All three angles of a triangle add up to 90 degrees. In the diagram, we can examine the triangle formed by Angle A, Angle B, and a 90</span>° angle. This is a right triangle, and the angle with 90∠ degrees is indicated as such (with the "square" symbol). So we know that one angle is 90°. We also know that m∠a = 30°. If there are three angles in a triangle, and all three angles must add up to 180°, and we know the measurements of two of the three angles, we can solve for the unknown measurement of the remaining angle, which in this case is: m∠b.
90° + 30° + m∠b = 180<span>° ;
</span>180° - (<span>90° + 30°) = m∠b ;
</span>180° - (120°) = m∠b = 60<span>°
</span>___________________________
Now we need to solve for the measure of Angle c (<span>m∠c).
___________________________________________
All angles on a straight line (or straight "line segment") are called "supplementary angles" and must add up to 180</span>°. As shown, Angle c is on a "straight line". The measurement of the remaining angle represented ("supplementary angle" to Angle c is 75° (shown on diagram). As such, the measure of "Angle C" (m∠c) = m∠c = 180° - 75° = 105°.
The first penalty they received is three 15 yards so total yards is 3(15 yards)
the second penalty is one 5 yard
the last penalty is half the 34 yard line(34 yard)/2
total change = 3(15 yards) + 5 yrad + (34 yard)/2
= 45 yards + 5 yards + 17 yards= 67yards
Answer:
Victor should buy Legend because it has a better unit rate
<em></em>
Step-by-step explanation:
See attachment for complete question.
To determine which car has more gas efficiency, we have to calculate the slope of each car.
Vehicle 1: Legend
Take any two corresponding points from the table
The slope is then calculated using;
<em>This implies that this vehicle (legend) travels 18 miles per gallon of gas</em>
Vehicle 2: Supreme
Take any two corresponding points from the graph
The slope is then calculated using;
This implies that this vehicle (supreme) travels 16.7 miles per gallon of gas
<em>Base on the calculations above, Victor should buy Legend because it has a better unit rate</em>
2x+3(5-x)-12=4(x+2)
Distribution property:
2x+15-3x-12=4x+8
Add like terms:
-1x+3=4x+8
Add 1x to both sides:
3=5x+8
Subtract 8 from both sides:
-5=5x
Divide by 5 on both sides to get x by itself:
x= -1