Simplify the following:
((x^2 - 11 x + 30) (x^2 + 6 x + 5))/((x^2 - 25) (x - 5 x - 6))
The factors of 5 that sum to 6 are 5 and 1. So, x^2 + 6 x + 5 = (x + 5) (x + 1):
((x + 5) (x + 1) (x^2 - 11 x + 30))/((x^2 - 25) (x - 5 x - 6))
The factors of 30 that sum to -11 are -5 and -6. So, x^2 - 11 x + 30 = (x - 5) (x - 6):
((x - 5) (x - 6) (x + 5) (x + 1))/((x^2 - 25) (x - 5 x - 6))
x - 5 x = -4 x:
((x - 5) (x - 6) (x + 5) (x + 1))/((x^2 - 25) (-4 x - 6))
Factor -2 out of -4 x - 6:
((x - 5) (x - 6) (x + 5) (x + 1))/(-2 (2 x + 3) (x^2 - 25))
x^2 - 25 = x^2 - 5^2:
((x - 5) (x - 6) (x + 5) (x + 1))/(-2 (x^2 - 5^2) (2 x + 3))
Factor the difference of two squares. x^2 - 5^2 = (x - 5) (x + 5):
((x - 5) (x - 6) (x + 5) (x + 1))/(-2(x - 5) (x + 5) (2 x + 3))
((x - 5) (x - 6) (x + 5) (x + 1))/((x - 5) (x + 5) (-2) (2 x + 3)) = ((x - 5) (x + 5))/((x - 5) (x + 5))×((x - 6) (x + 1))/(-2 (2 x + 3)) = ((x - 6) (x + 1))/(-2 (2 x + 3)):
((x - 6) (x + 1))/(-2 (2 x + 3))
Multiply numerator and denominator of ((x - 6) (x + 1))/(-2 (2 x + 3)) by -1:
Answer: (-(x - 6) (x + 1))/(2 (2 x + 3))
Answer:
5 classes - 2 bass classes and 3 viola classes.
Step-by-step explanation:
Find the greatest common factor (GCF)
List the factors of 20 and 30:
20: 1, 2, 4, 5, 10, 20
30: 1, 2, 3, 5, 6, 10, 15, 30
The greatest factor that both numbers share is 10.
Therefore, there are 10 students in each class. So, she teaches 2 bass classes and 3 violas classes.
hope this helps! <3
Answer: The answer is 88
Step-by-step explanation: It is recursive because you can add 78+10=88
The algebraic expression, if broken down into each word would be :
X^2/3 + 4.
Answer:
9
Step-by-step explanation:
3/7 multiplied by 21 = 3/7 x 21 = 9 = 3/7 x 21/1 = 63/7 = 9
Or if you can't do the math - Think of a pizza with 21 slices . Now cut this pizza into 7 equal parts. You will find that each part contains exactly 3 slices. Now, eat 3 of these parts. With three slices in each part, you ate 9 slices - which is three sevenths of 21.
