Answer:
See explanation
Step-by-step explanation:
16. Two parallel lines are cut by transversal. Angles with measures 
and 
are alternate exterior angles. By alternate exterior angles, the measures of alternate exterior angles are the same:
Then
17. Two parallel lines are cut by transversal. Angles with measures 
and 
are alternate interior angles. By alternate interior angles, the measures of alternate interior angles are the same:
Then
18. Two parallel lines are cut by transversal. Angles with measures 
and 
are alternate exterior angles. By alternate interior angles, the measures of alternate exterior angles are the same:
Then
19. The diagram shows two complementary angles with measures 
and 
. The measures of complementary angles add up to 
then
Hence,
Check:
20. Angles 
and 
are vertical angles. By vertical angles theorem, vertical angles are congruent, so
Hence,
21. 
and 
are supplementary. The measures of supplementary angles add up to 
so
Therefore,
Answer:
17
Step-by-step explanation:
2c + d^3 - 3e +4f
=2(3) + (5^2) - 3(6) + 4(1)
=6+25-18+4
=17
Answer:
(5,-1) or x=5 y=-1
Step-by-step explanation:
I used the substitution method to solve this!
<em>1. Pick one of your equations and solve for one of the variables. I chose the first equation and solved for x.</em>
x-2y=7
(Move the -2y to the other side of the equation in order to get the x by itself. You do the opposite, so it becomes +2y.)
x=2y+7
<em>2. Now take your second equation and plug in what you got for x into the x variable.</em>
2(2y+7)+5y=5
(Multiple 2 by everything inside of the parentheses.)
4y+14+5y=5
(We want to get the y by itself, so move the 14 to the other side.)
4y+5y=-14+5
(Combine all the like terms.)
9y=-9
(Divide the 9 from the y. What you do to one side you must do to the other.)
y=-1
<em>3. Since you have one variable solved for. Now take the first equation and plug in your y.</em>
x-2(-1)=7
(Multiple -2 by -1)
x+2=7
(Move the 2 to the other side in order to get the x by itself.)
x=5
<em>4. If needed, plug in your x and y values into the equations in order to check your answer.</em>
Hope this could help!
Answer:
6x^3 - 2x^2 -11x +4
Step-by-step explanation:
(3x-4)(2x^2+2x-1)
Multiply 3x by the second term
3x* (2x^2+2x-1)
6x^3 +6x^2 -3x
Multiply -4 by the second term
-4*(2x^2+2x-1)
-8x^2 -8x+4
Add these together, lining up the terms
6x^3 +6x^2 -3x
-8x^2 -8x+4
----------------------------------
6x^3 - 2x^2 -11x +4
6b + 6p = 33.60 ; b=2.90
6(2.90) + 6p = 33.60
17.40 + 6p = 33.60
-17.40 -17.40
6p = 16.20
/6 /6
p = 2.70
ANSWER: each pendant costs $2.70
