Answer:
Length of smaller side = 15 inches
Length of bigger side = 36 inches
Length of hypotenuse = 39 inches
Step-by-step explanation:
Given:
Length of smaller side = a
Length of bigger side = (a + 21) inches
Length of hypotenuse = (a + 24) inches
Find:
Length of all side
Computation:
Using Pythagorean theorem
Hypotenuse² = Base² + Perpendicular²
(a+24)² = a² + (a+21)²
a² + 576 + 48a = a² + a² + 441 + 42a
a² - 6a - 135 = 0
(a-15)(a+7)
So
a = 15 inches a = -7 inches
So,
Length of smaller side = a = 15 inches
Length of bigger side = (a + 21) inches = 15 + 21 = 36 inches
Length of hypotenuse = (a + 24) inches = 15 + 24 = 39 inches
Answer:
The second base of the trapezoid b2 is 2.5 inches
Step-by-step explanation:
Here, we want to calculate the second base of the trapezoid.
Mathematically, the area of a trapezoid can be given as;
A = 1/2(a + b) h
where a and b represents the parallel bases and h is the height of the trapezoid
so this, we have from the question
1/2(4.5 + b2) * 6 = 21
3(4.5 + b2) = 21
divide both sides by 3
4.5 + b2 = 7
b2 = 7-4.5
b2 = 2.5 inches
Im guessing how many inches are 22 because it makes sense
First, remove the parentheses
-7+2x+7=-7
Cancel the equal terms.
2x+7=0
Subtract 7
2x= -7
Divide both sides by 2
Final answer is:
X= -3.5
Answer:
Vertex = (12,64)
The meaning of this pair of values is that the y-coordinate is the maximum profit obtainable, and the x-coordinate is how many cups sold will make the maximum profit.
X-intercepts: 4 and 20
The meaning of theses values is that these amounts of cups sold (4 and 20) will make zero profit.
Step-by-step explanation:
To find the vertex we can use the formula for the x-coordinate of the vertex:
x_v = -b/2a
Where a and b are coefficients of the quadratic equation (in this case, a = -1 and b = 24)
So we have that:
x_v = -24 / (-2) = 12
The vertex is 12 cups of coffee. Now we apply this value to find the y-coordinate of the vertex:
f(x) = -12^2 + 24*12 - 80 = 64
So the vertex is (12,64). The meaning of this pair of values is that the y-coordinate is the maximum profit obtainable, and the x-coordinate is how many cups sold will make the maximum profit.
To find the x-intercepts, we need to make f(x) = 0 and find the values of x:
-x2 + 24x - 80 = 0
Delta = 24^2 - 80*4 = 256
sqrt(Delta) = 16
x1 = (-24 + 16)/(-2) = 4
x2 = (-24 - 16)/(-2) = 20
The x-intercepts are 4 and 20. The meaning of theses values is that these amounts of cups sold (4 and 20) will make zero profit.
