Answer:
The price where the manufacture sells the maximum number of toys is $20
Step-by-step explanation:
The given equation for that represents the number of toys the manufacturer can sell is given as follows;
T = -4·p² + 160·p - 305
Where;
p = The price of the toys in dollars
At the point where the manufacture sells the maxim number of toys on the graph of the equation T = -4·p² + 160·p - 305, which is the top of the graph, the slope = 0
Therefore, at the maximum point;
The slope = 0 = dT/dp = d(-4·p² + 160·p - 305)/dp = -8·p + 160
∴ -8·p + 160 = 0
160 = 8·p
8·p = 160
p = 160/8 = 20
The price where the manufacture sells the maximum number of toys is = p = 20 dollars
The factored expression is: 3(5n-6)
The GCF between 15 and 18 is 3. So you would divide both numbers by 3. That would leave you with 5 taking the place of 15 and 6 taking the place of 18. Then you would fill in the blanks. Three multiplied by the expression 5n-6 would give you your original expression of 15n-18.
Start with your exponetial growth formula: y = a(1 + r)^t.
Now, a is going to be your initial amount, r is the rate, and t is the time.
So we have y = $4,000(1 + .02)^7.
Now simplify inside the parenthses first.
So we have y = $4,000(1.02)^7.
Simplifying further gives us y = $4,000(1.14868).
Now use a calculator to get y = $4,594.72
<h2>The length of each side of the equilateral traingle is 1/24 unit.</h2>
<u>Step-by-step explanation:</u>
Given that the perimeter of an equilateral triangle is 1/8 unit. With this information, we are asked to find the length of each side of yhe equilateral traingle.
The perimeter of equilateral traingle is defined as the three times of the length of edge. Mathematically;
→ Perimeter = 3a
By substituting the given values in the formula, we get the following results:
→ 1/8 = 3a
→ a = 1/24
Hence, the length of each side of the equilateral traingle is 1/24 unit.
<u>Additional information:</u>
- A triangle has three sides or edges.
- A triangle has three angles.
- A triangle has three vertices or corners.
- The sum of all internal angles of a triangle is always equal to 180 degrees. This is known as the angle sum property of a triangle.
- The sum of the length of any two sides of a triangle is greater than the length of the third side.
- There are three types of triangle, Scalene Triangle, Isosceles Triangle, Equilateral Triangle.
- Area of triangle = 1/2 * b * h.
- Perimeter of triangle = sum of all sides.
