Given that <span>Line m is parallel to line n.
We prove that 1 is supplementary to 3 as follows:
![\begin{tabular} {|c|c|} Statement&Reason\\[1ex] Line m is parallel to line n&Given\\ \angle1\cong\angle2&Corresponding angles\\ m\angle1=m\angle2&Deifinition of Congruent angles\\ \angle2\ and\ \angle3\ form\ a\ linear\ pair&Adjacent angles on a straight line\\ \angle2\ is\ supplementary\ to\ \angle3&Deifinition of linear pair\\ m\angle2+m\angle3=180^o&Deifinition of supplementary \angle s\\ m\angle1+m\angle3=180^o&Substitution Property \end{tabular}](https://tex.z-dn.net/?f=%5Cbegin%7Btabular%7D%0A%7B%7Cc%7Cc%7C%7D%0AStatement%26Reason%5C%5C%5B1ex%5D%0ALine%20m%20is%20parallel%20to%20line%20n%26Given%5C%5C%0A%5Cangle1%5Ccong%5Cangle2%26Corresponding%20angles%5C%5C%0Am%5Cangle1%3Dm%5Cangle2%26Deifinition%20of%20Congruent%20angles%5C%5C%0A%5Cangle2%5C%20and%5C%20%5Cangle3%5C%20form%5C%20a%5C%20linear%5C%20pair%26Adjacent%20angles%20on%20a%20straight%20line%5C%5C%0A%5Cangle2%5C%20is%5C%20supplementary%5C%20to%5C%20%5Cangle3%26Deifinition%20of%20linear%20pair%5C%5C%0Am%5Cangle2%2Bm%5Cangle3%3D180%5Eo%26Deifinition%20of%20supplementary%20%5Cangle%20s%5C%5C%0Am%5Cangle1%2Bm%5Cangle3%3D180%5Eo%26Substitution%20Property%0A%5Cend%7Btabular%7D)
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<span>(5x^7 y^2)(-4x^4 y^5) =-20x^a y^b
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solve this:
(5x^7 y^2)(-4x^4 y^5)
= -20 x^(7 + 4) y^(2 + 5)
= -20 x^11 y^7
answer
</span>A) a=11, b=7
The average is found by adding the numbers and dividing by 2.
Since the average is 17, the total of the two numbers must equal 17 x 2 = 34.
One number is given as 11, so subtract 11 from 34:
34 - 11 = 23
The other number is 23.
Too check: add 11 and 23 and then divide by 2:
11 + 23 = 34
34/2 = 17.
Answer: The other no. is 5
Step-by-step explanation: Let the other no. be x
x = LCM/First no.
x = 120/24 = 5
The other no. is 5
Answer:
Using proportions, the pizza parlor should expect 20 breadsticks and 25 calzone orders if there were 100 total orders.
Step-by-step explanation:
Orders:
Salads 3
Pizzas 8
Sides of breadsticks 4
Pepperoni calzones 5
Total orders: 20
Proportion of sides breadsticks=4/20=0.2
Proportion of pepperoni calzones=5/20=0.25
For 100 total orders:
Sides of breadsticks=0.2(100)=20
Pepperoni calzones=0.25(100)=25
