We need to account for both x values on either side of the length, and width.
Thus, the length becomes 10 + x + x = 10 + 2x
and the width becomes 5 + x + x = 5 + 2x
For the second question, I'm assuming we don't account for the area that is covered by the garden.
Then we can say that the path is measured by: (5 + 2x)(10 + 2x) - 50, which is the area of the garden itself.
(5 + 2x)(10 + 2x) - 50 = 54
Expanding the brackets:






x = -9, or x = 3/2
Since x > 0, then x ≠ -9
Thus, the only x-value we can take is x = 3/2
Hi there!

There are 3 parts to this equation:
f(x)
f(x+1)
4f(x)
We must first determine these three parts separately.
<u>1) f(x)</u>
We're given that
:
⇒
:
<u>2) f(x+1)</u>
Now, we must find f(x+1). To do so, add 1 to x in the original function
:
⇒ 
<u>3) 4f(x)</u>
To find 4f(x), multiply the original function
by 4:
:
<u>4) Put it all together</u>
Now, plug each of the three parts into the equation
:


Factor the left side

Divide both sides by 3^x

Because this equation is true,
is therefore true.
I hope this helps!
True, it is a function because mainly the x and y values are the same;]
Answer:
a) 0.383
b) 0.375
Step-by-step explanation:
a) Calculate each z-score.
z = (x − μ) / σ
z₁ = (112 − 118) / 12 = -0.5
z₂ = (124 − 118) / 12 = 0.5
Use a calculator or z-score table to find the probability.
P(-0.5 < Z < 0.5) = 0.6915 − 0.3085 = 0.383
b) 0.383 × 16 ≈ 6. So the expected proportion would be 6/16 = 0.375.