Answer:
Fractions are equivalent if their simplest forms are the same. So, to make equivalent fractions, all you have to do is multiply the top number (the numerator) and the bottom number (the denominator) by the same number—and it can be any number, as long as you use the same one for both the top and bottom.
Step-by-step explanation:
Fractions are equivalent if their simplest forms are the same. So, to make equivalent fractions, all you have to do is multiply the top number (the numerator) and the bottom number (the denominator) by the same number—and it can be any number, as long as you use the same one for both the top and bottom.
Answer:
a₆ ≈ 25.284
Step-by-step explanation:
There is a common ratio between consecutive terms , that is
8 ÷ 6 = 
÷ 8 = 
This indicates the sequence is geometric with nth term
= a₁ 
where a₁ is the first term and r the common ratio
Here a₁ = 6 and r = , then
a₆ = 6 × 
= 6 × 
= 
≈ 25.284 ( to the nearest thousandth )
Given:
2x - 3y = -6 ⇒ identified as 1st equation
x + 2y = 8 ⇒ identified as 2nd equation
Let us first get the value of x using the 2nd equation.
x + 2y = 8
x = 8 - 2y
Substitute x in the 1st equation with its value and find the value of y.
2x - 3y = -6
2(8-2y) - 3y = -6
16 - 4y -3y = -6
-4y - 3y = -6 -16
-7y = - 22
y = -22/-7
y = 22/7 simplified to 3 1/7
Substitute the value of y in the 2nd equation.
x = 8 - 2y
x = 8 - 2(22/7)
x = 8 - 44/7
x = (8 * 7/7) - 44/7
x = 56/7 - 44/7
x = (56-44)/7
x = 12/7 simplified to 1 5/7
To check: x = 12/7 and y = 22/7 *we need to use the improper fractions.
2x - 3y = -6
2(12/7) - 3(22/7) = -6
24/7 - 66/7 = -6
(24-66)/7 = -6
-42/7 = -6
-6 = -6
x + 2y = 8
12/7 + 2(22/7) = 8
12/7 + 44/7 = 8
(12+44)/7 = 8
56/7 = 8
8 = 8
Answer:
They have the same rate of change.
Step-by-step explanation:
Well the graph of Function B is y = 1 / 3x + 2
So they have the same rate of change, since they have the same slope.
Let's start by grouping like terms so we can factor out the most
(4x^4+24x^3)+(12x^2+8x)
now let's factor out as much as possible. we see all coefficients are multiples of 4, we will also factor out as high a degree of x as we can
4x^3(x+6)+4x(3x+2)
now we see that we still have a common multiple of 4x that we can remove
4x(x^2(x+6)+(3x+2))
so we find 4x is the largest value we can factor out
