Answer:
0
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
8x+4(4x+3)=4(6x+4)−4
8x+(4)(4x)+(4)(3)=(4)(6x)+(4)(4)+−4(Distribute)
8x+16x+12=24x+16+−4
(8x+16x)+(12)=(24x)+(16+−4)(Combine Like Terms)
24x+12=24x+12
24x+12=24x+12
Step 2: Subtract 24x from both sides.
24x+12−24x=24x+12−24x
12=12
Step 3: Subtract 12 from both sides.
12−12=12−12
0=0
Answer:
All real numbers are solutions.
Answer:
What are the dimensions of the garden?
Step-by-step explanation:
Answer:
Union of inqualities:
x<7 or x>8
(not sure if this helps or not sorry!)
A polar coordinate is that which can be written as (r, θ) where r is the radius and θ is the angle.
The radius, r, is also the hypotenuse of the right triangle that can be formed. Hence, it can be calculated through the equation,
r² = x² + y²
If we are to simplify this for the r alone, we have,
r = sqrt (x² + y²)
Substituting the known values,
r = sqrt ((4)² + (-4)²) = 4√2
The x and y can be related through the trigonometric function, tangent.
tan θ = y/x
To solve for θ
θ = tan⁻¹(y/x) = tan⁻¹(-4/4) = -45° = 315°
Hence, the polar coordinate is <em>(4√2, 315°)</em>
Answer:
$14.39
Step-by-step explanation:
The formula for continuous compounding of interest is:
A = Pe^(rt), were P is the initial dollar amount, A is the final amount, r is the interest rate as a decimal fraction, and t is the time in years.
Here we have $2109 = $500e^(10r) and need to solve for r.
To do this, take the natural log of both sides, obtaining:
ln 2109 = ln 500+ 10r.
Then 10r = ln 2109 - ln 500, and
ln 2109 - ln 500
r = --------------------------------------------
10
= .1439
The interest rate was 14.39%.
