Answer:
Step-by-step explanation:
Given
Represent point A as thus;
Required
Determine the new position of A, when rotated counterclockwise
The new position will be denoted as A'
When a point is rotated counterclockwise, we start by switching the positions of x and y as follows:
Then, y is negated to give A'
Answer:
(3x-1)(x+5)
Step-by-step explanation:
Find two numbers that when they multiply, you get the third term,
which is -5 in this problem. And when they add up, you get the second term,
which is 14 in this problem.
Answer:
Step-by-step explanation:
If Samantha's earnings continue to increase at the same rate, this means that her earning is increasing arithmetically.
If she earned $550 in the first day, we can say the first term is $550
If she earned $750 on the third day, we can say the third term is $750
For us to know by how much her money is increasing, we need to find the common difference d formed by the sequence
550, x , 750
T1 = 550
T2 = x
T3 = 750
Common difference d = T2-T1 = T3-T2
x - 550 = 750 - x = d
Let's calculate the second term first i.e x
Since x - 550 = 750 - x = d
x - 550 = 750 - x
Collect like terms
x+x = 750+550
2x = 1300
x = 1300/2
x = 650
d = T2-T1
d = x - T1
d = 650-550
d = 100
Hence her money keeps increasing by $100 each day
-5/8c = 20....multiply both sides by -8/5 (this cancels out the -5/8 on the left
c = 20(-8/5)
c = -160/5
c = - 32
check..
-5/8(-32) = 20
160/8 = 20
20 = 20 (correct)
so c = -32
To answer this, you will write and equation in terms of the number of adult tickets sold and then solve for a, the number of adult tickets.
$5a + $3.50s = $2517.50
$5a + $3.50(a + 100) = $2517.50
5a + 3.50a + 350 = 2517.50
8.50a -350 -350
<u>8.5a</u> = <u>2167.50</u>
8.5 8.5
a = 255
The number of adult tickets sold was 255, and the number of student tickets sold was 355 (255 +100).