Answer:
x = -1 ± √109
Step-by-step explanation:
2x • 3x + (2 • 3)x + 6x = 648
According to PEMDAS (parentheses/exponents | multiplication/division | addition/subtraction), we should solve the parentheses first.
(2 • 3) = 6
Now we have:
2x • 3x + (6)x + 6x = 648
Now let's multiply.
2x • 3x = 6x²
6 • x = 6x
Now we have.
6x² + 6x + 6x = 648
Combine like terms.
6x² + 12x = 648
Let's factor out a 6.
6(x² + 2x) = 648
Divide both sides by 6.
x² + 2x = 108
Let's use completing the square.
Our equation is in a² + bx = c form.
Divide b by 2.
2/2 = 1
Then square it.
1² = 1
Add 1 to both sides.
x² + 2x + 1 = 108 + 1
Simplify.
x² + 2x + 1 = 109
Now we want to factor the left side. A shortcut is just to use b/2.
(x + 1)² = 109
Take the square root of both sides.
x + 1 = ±√109
The square root is as simplified as possible.
Subtract 1 from both sides.
x = -1 ± √109
Hope this helps!
Answer:
y - 18 = -1.5(x - 12)
Step-by-step explanation:
A = (12, 18)
B=(1.25(12), 0.75(18)) = (15, 13.5)
Find slope: m = (13.5-18)/(15-12) = (-4.5)/3 = -1.5
Point slope form: y - y1 = m(x - x1)
Using point A as (x1, y1)
y - 18 = -1.5(x - 12)
A₁ = 9
a₂ = 9+2 → a₂ = a₁ + 2. Since it's an AP, d, the common difference is 2
1) Then the recursive formula is :
a(n) = a(n-1) + 2
2) Explicit formula:
It's an AP, with first term a₁, d= common difference and n = number of term, which is the number of rows in this problem.
the value of the nth term is given by the formula is:
value of nth term = a₁ + (n-1).d
3) Number of seats in the 12th row:
9 + (12-1).2 = 31 seats
3,162 x 10 = 31,620, you just add one zero
<h2>Answer</h2>
Janice convert a mixed number to the wrong improper fraction
<h2>Explanation</h2>
To convert a mixed number to an improper fraction, we multiply the whole number by the denominator of the fraction and add the result to the numerator of the fraction; while keeping the denominator of the fraction as the denominator of the improper fraction.
Let's convert our mixed numbers to improper fractions:
To convert 
we multiply the whole number 10 by the denominator of the fraction 6, and then we add the result to the numerator 5:
Now let's convert 
:
Notice that Janice converted as 
, which is incorrect.
Since 
, we can conclude that Janice convert a mixed number to the wrong improper fraction.
