The formula representing this scenario is
The answer to this formula is
Initially, you need to formulate the equation.
Next, simplify the expressions.
Afterwards, subtract 5.7 from both sides.
Lastly, divide both sides by 5
Eric spent $21.85, including sales tax, on 2 jerseys and 3 pairs of socks. The jerseys cost $6.75 each and the total sales tax w
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Given:
It is stated that
PQ ⊥ PS and
∠QPR = 7x-9
∠RPS = 4x+22
To find the measure of ∠QPR.
Formula
According to the problem PR sits between PQ and PS,
Consequently,
∠QPR+∠RPS = 90°
Now,
Inserting the values for ∠RPS and ∠QPR yields
or,
or,
or,
or,
Substituting the value of into ∠QPR gives us
∠QPR =
or, ∠QPR =
So,
The measure of ∠QPR is 40°.
Answer:
The variable x lies within the interval of all positive real numbers less than 5 cm.
Detailed solution:
Problem statement:
Determine the volume of the open-topped box as a function of the side length x (in centimeters) of the square cutouts.
Refer to the provided diagram for clarity.
Define:
x → length in centimeters of each square cutout side
The volume of the box with open top can be written as:
Given this, we have:
By substitution:
Determine the domain of x:
Because:
Therefore:
Domain is the interval (0,5)
That means all real numbers strictly greater than zero and less than 5 cm are valid for x.
Hence, the volume V as a function of x is:
