Answer:
5x -7y = 21
Step-by-step explanation:
A sketch can convince you that BC is a transversal perpendicular to parallel lines AB and CD. The question asks for an equation for CD, so we just need to write the equation of a line through D that is parallel to AB.
One way to do this is to equate the slopes of the parallel lines:
∆y/∆x for AB = ∆y/∆x for CD
(y2 -y1)/(x2 -x1) = (y -2)/(x -7) . . . . . . where (x1, y1) = A; (x2, y2) = B; (7, 2) = D
(4 -(-1))/(1 -(-6)) = (y -2)/(x -7)
5(x -7) = 7(y -2) . . . . . . . . . . . . . cross multiply
5x -7y = 21 . . . . . . . . . . . . . . . . add 35 -7y, simplify
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Note that the graph shows the line CD is named "b", and its equation is shown at upper left. Multiplying that equation by -1 gives the one shown here.
120 times because 300 divided by 25
Answer:
Alex will need 14 bags
Step-by-step explanation:
B= 4(2x+7)+3(2x+7)
and
2x+7=2
First, we should solve the second equation to obtain x:
2x+7=2
2x=2-7
x= -5/2
Then, we use this answer to calculate B:
B=4(2(-5/2)+7)+3(2)
B=4(-5+7)+6
B=4(2)+6
B=8+6
B=14
Alex will need 14 bags
Answer:
108 student tickets, and 176 adult tickets were sold
Step-by-step explanation:
Adult ticket $8 Call the number of adult tickets sold "a"
Student ticket $5 Call the number of student tickets sold "s"
Since we are talking about TWO consecutive days of sold out seats, the total number of seats sold were 2* 142 = 284
Then we create two different equations with the information given:
a + s = 284
8 * a + 5 * s = 1948
we can solve for s in the first equation as follows: s = 284 - a
and use it in the second equation
8 a + 5 (284 - a) = 1948
8 a + 1420 - 5 a = 1948
combining
3 a = 528
a = 528/3
a = 176
we find the number of student tickets using this answer in the substitution equation we used:
s - 284 - 176 = 108
Therefore 108 student tickets, and 176 adult tickets were sold.
