Answer:
r=-16
Step-by-step explanation:
21=6r+5-7r
1) Combine alike terms on the right side (6r and -7r):
21=-r+5
2) Subtract a 5 from both sides:
16=-r
3) Divide both sides by -1:
r=-16
The slope of the given line is m = 8
You can think of m = 8 as m = 8/1. Flip the fraction to get 1/8 and then flip the sign to get -1/8
Answer: -1/8
Note: Multiplying the original slope (8) and the perpendicular slope (-1/8) will lead to the result of -1. This applies to any two perpendicular lines as long as one of the lines isn't vertical.
From the picture, we see that there are two congruent sides. Therefore, following the Isosceles Triangle Theorem, if two sides in a triangle are congruent, then the angles opposite those sides are congruent. So, we know that the angles opposite of the congruent sides have an angle measure of x°. We are given the measure of the angle at the top vertex of 100°. Following the Triangle Sum Theorem, the three interior angles in a triangle must sum up to 180°. Therefore, we can create an Algebraic equation to solve for the two base angles that measure x°.
x+100+x=180
x=the base angle measures since they are congruent.
100+x+x=180
Community Property of Addition
100+2x=180.
Added x+x as like terms to = 2x.
100-100+2x=180-100
Subtraction of 100 from both sides to cancel it out and move it.
2x=80
Subtraction operation
2x/2=80/2
Divided by 2 to cancel it out on both sides and move it.
x=40°.
Therefore, the two base angles (angles opposite of the two congruent sides) are 40°.
2(40)+100=80+100=180.
So x=40
Answer:
9 Pizzas.
Step-by-step explanation:
Since Sam has $150 in total, and already spent $40 on drinks, we need to deduct that from the total ($150 - $40), in turn leaving us with $110. Since we aren't sure of the amount of pizzas bought yet, lets use the variable x in its place. Since each pizza costs $12, we need to use $12(x) = $110, $110 again being the total after Sam bought the drinks. After dividing $110 by $12, we are left with 9 pizzas, with $2 extra. Therefore, he can buy 9 pizzas.