Answer:
$8.50
Step-by-step explanation:
let the price before tax be $x
given that the sales tax rate is 4%, hence the amount she paid in taxes
= 4% of x
= (4/100)x
= 0.04x
We can now build an equation for what she paid:
Amount Paid = price before tax + amount paid in taxes
8.84 = x + 0.04x
8.84 = 1.04x (divide both sides by 1.04 and rearranging)
x = 8.84 / 1.04
x = $8.50
The cell phone tower is 1260 feet tall
<em><u>Solution:</u></em>
Given that 10-ft vertical post casts a 12-in shadow
At the same time a nearby cell phone tower casts a 126-ft shadow
To find: height of cellphone tower
We can use proportion to solve the sum
Here,
Let "x" be the height of tower
height of post = 10 feet
shadow of tower = 126 feet
shadow of post = 12 inches
We know that,
1 inches = 0.0833333 foot
12 inches = 12 x 0.0833333 foot = 1 foot
shadow of post = 1 foot
Thus the proportion becomes,
Thus the cell phone tower is 1260 feet tall
i looks like it would be v
<u>We are given the equation:</u>
log₂(x-3) + log₂x - log₂(x+2) = 2
<u>When is it defined:</u>
in this equation, log₂(x-3) and log₂(x+2) can only be defined when
x-3 >0 and x+2 > 0
solving for the values of x, we get:
x > 3 and x > -2
which basically means x > 3
<em>Because we are looking for an inequality which is true for both x>-2 and x>3</em>
Hence, x will have a value greater than 3
<u>Solving for x:</u>
using the product rule <em>[logₐb + logₐc = logₐ(bc)]</em>
log₂[(x-3)(x)] - log₂(x+2) = 2
using the quotient rule <em>[logₐb - logₐc = logₐ(b/c)]</em>
log₂[(x-3)(x) / (x+2)] = 2
from the property <em>[ aˣ = b ⇒ logₐb = x]</em>
(x² - 3x) / (x+2) = 2²
x² - 3x = 4x + 8
x² - 7x - 8 = 0
x² + x - 8x - 8 = 0
x(x+1) - 8(x+1) = 0
(x-8)(x+1) = 0
(x-8) = 0 OR (x+1) = 0
x = 8 OR x = -1
We know that the equation is defined only for x > 3
We can see that x = 8 satisfies that inequality
Therefore, x = 8
