Answer:
see explanation
Step-by-step explanation:
Given
9n² - n - 
= 0 ← multiply through by 3 to clear the fraction
27n² - 3n - 2 = 0 ← factoring
Consider the factors of the product of the n² term and the constant term which sum to give the coefficient of the n- term
product = 27 × - 2 = - 54 and sum = - 3
The factors are - 9 and + 6
Use these factors to split the n- term
27n² - 9n + 6n - 2 = 0 ( factor the first/second and third/fourth terms )
9n(3n - 1) + 2(3n - 1) = 0 ← factor out (3n - 1) from each term
(3n - 1)(9n + 2) = 0
Equate each factor to zero and solve for n
3n - 1 = 0 ⇒ 3n = 1 ⇒ n = 
9n + 2 = 0 ⇒ 9n = - 2 ⇒ n = - 
Answer:
(-1, -1)
Step-by-step explanation:
Let's set these two equations equal to each other to solve the system:
x = 2x + 1
Solving for x, we get x = -1
Plug this value of x back into any of the two equations to get y: y = 2 * (-1) + 1 = -1.
Thus, the point of intersection is (-1, -1).
Hope this helps!
x+142 =3x+64
subtract x from each side
142 = 2x+64
subtract 64 from each side
142-64 = 2x
78=2x
divide by 2
78/2 = x
x=39
The number is 39
Hi there!
We can find the perimeter of a rectangle by using the following formula:
perimeter = 2 × width + 2 × length
In the question, we are given the following data: the length of the rectangle is 12 in and the perimeter is 56. Let's substitute this into our formula!
56 = 2 × width + 2 × 12
Multiply first.
56 = 2 × width + 24
Now subtract 24 from both sides.
32 = 2 × width
And finally, to find the width of the rectangle, divide both sides of the equation by 2.
16 = width
(we can eventually switch sides in the equation).
width = 16
~ Hope this helps you!
A multiplicative inverse of an integer a is an integer x such that the product ax is congruent to 1 with respect to the modulus m.
1. 
Check:
The multiplicative inverse of 5 in 
is 9.
2. 
Check:
The multiplicative inverse of 5 in 
is 5.
3. 
Check:
The multiplicative inverse of 5 in 
is 8.
