Condene the logarithms on the left side by applying the property, ln(<em>a</em>) - ln(<em>b</em>) = ln(<em>a</em> / <em>b</em>):
ln(<em>x</em> - 2) - ln(<em>x</em> - 3) = 1
→ ln((<em>x</em> - 2) / (<em>x</em> - 3)) = 1
Now take the exponential of both sides:
exp(ln((<em>x</em> - 2) / (<em>x</em> - 3))) = exp(1)
(<em>x</em> - 2) / (<em>x</em> - 3) = <em>e</em>
Solve for <em>x</em> :
<em>x</em> - 2 = <em>e</em> (<em>x</em> - 3)
<em>x</em> - 2 = <em>e x</em> - 3<em>e</em>
<em>x</em> - <em>e x</em> = 2 - 3<em>e</em>
(1 - <em>e</em>) <em>x</em> = 2 - 3<em>e</em>
<em>x</em> = (2 - 3<em>e</em>) / (1 - <em>e</em>) ≈ 3.582
Answer:
-2x^2 + 3x -1
Step-by-step explanation:
y = ax^2 + bx + c
(0,-1):
-1 = a(0)^2 + b(0) + c
-1 = 0 + 0 + c
-1 = c
(1,0):
0 = a(1)^2 + b(1) + c
0 = a + b + c
(2,-3):
-3 = a(2)^2 + b(2) + c
-3 = 4a + 2b + c
Replace c with -1
0 = a + b -1
1 = a + b
-3 = 4a + 2b -1
-2 = 4a + 2b
-1 = 2a + b
Solve:
2a + b = -1
-1a - b = -1
a = -2
2a + b = -1
-2a -2b = -2
-b = -3 divide both by -1: b = 3
a = -2; b = 3; c = -1
y = ax^2 + bx + c or y = -2x^2 +3x -1
Answer:
Distance is 6.7units to the nearest tenth.
Explanation:
To solve this problem, we the distance formula. And this is given as:
We were given the equation:
y = 2 x + 4
This can also be rewritten as:
y – 2 x – 4 = 0.
Therefore, a = -2, b = 1 and c = -4
Also, we were given the points:
(x, y) = (–4, 11)
Making use of the above formula for distance, we have:
D = 6.7units (to the nearest tenth)
Answer:
47 rows
Step-by-step explanation:
To find the amount of needed rows, we will use the math operation division. We will take the total and divide it by the amount in each row.
846/18=47
To seat 18 people in each row, you will need 47 rows.
