Answer:
(-5, 3)
Step-by-step explanation:
it translated left 2 units => x'= x-2
down 2 units=> y'= y-2
Answer:
+8
Step-by-step explanation:
Answer:
neither
Step-by-step explanation:
find the slopes of FG and HJ using the slope formula (y_2-y_1)/(x_2-x_1)
FG: (-1+3)/(-2-1)=2/-3=-2/3
HJ: (3-0)/(6-5)=3/1=3
perpendicular lines have slopes that are the negative reciprocal of each other. -2/3's negative reciprocal is 3/2 which isn't 3. the lines aren't parallel or perpendicular
Answer: The number is 26.
Step-by-step explanation:
We know that:
The nth term of a sequence is 3n²-1
The nth term of a different sequence is 30–n²
We want to find a number that belongs to both sequences (it is not necessarily for the same value of n) then we can use n in one term (first one), and m in the other (second one), such that n and m must be integer numbers.
we get:
3n²- 1 = 30–m²
Notice that as n increases, the terms of the first sequence also increase.
And as n increases, the terms of the second sequence decrease.
One way to solve this, is to give different values to m (m = 1, m = 2, etc) and see if we can find an integer value for n.
if m = 1, then:
3n²- 1 = 30–1²
3n²- 1 = 29
3n² = 30
n² = 30/3 = 10
n² = 10
There is no integer n such that n² = 10
now let's try with m = 2, then:
3n²- 1 = 30–2² = 30 - 4
3n²- 1 = 26
3n² = 26 + 1 = 27
n² = 27/3 = 9
n² = 9
n = √9 = 3
So here we have m = 2, and n = 3, both integers as we wanted, so we just found the term that belongs to both sequences.
the number is:
3*(3)² - 1 = 26
30 - 2² = 26
The number that belongs to both sequences is 26.
