Answer:
The answer to your question is 92.4 cm²
Step-by-step explanation:
Data
Side of a square = 6 units
Longest side of a rhombus = 10 units
Process
1.- Calculate the area of the square
Area = 6 x 6 = 36 u²
2.- Calculate the area of the rhombus
-Calculate the length of the short diagonal
6² = x² + x²
6² = 2x²
36 = 2x²
18 = x²
x = √18
-Short diagonal
x = 2√18
-Calculate the length of the long diagonal
10² = (√18)² + b²
b² = 100 - 18
b² = 82
b = √82
-Length of the long diagonal
d = √82 + √18
-Area of the rhombus
Area = (√82 + √18)(2√18) / 2
Area = (√82 + √18)(√18)
3.- Calculate the total area
Total area = (√82 + √18)(√18) + 36
-Simplification
Total area = (13.298)(4.243) + 36
Total area = 56.418 + 36
Total area = 92.4 cm²
Answer:
vertex = (0, -4)
equation of the parabola: ![y=3x^2-4](https://tex.z-dn.net/?f=y%3D3x%5E2-4)
Step-by-step explanation:
Given:
- y-intercept of parabola: -4
- parabola passes through points: (-2, 8) and (1, -1)
Vertex form of a parabola: ![y=a(x-h)^2+k](https://tex.z-dn.net/?f=y%3Da%28x-h%29%5E2%2Bk)
(where (h, k) is the vertex and
is some constant)
Substitute point (0, -4) into the equation:
![\begin{aligned}\textsf{At}\:(0,-4) \implies a(0-h)^2+k &=-4\\ah^2+k &=-4\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Ctextsf%7BAt%7D%5C%3A%280%2C-4%29%20%5Cimplies%20a%280-h%29%5E2%2Bk%20%26%3D-4%5C%5Cah%5E2%2Bk%20%26%3D-4%5Cend%7Baligned%7D)
Substitute point (-2, 8) and
into the equation:
![\begin{aligned}\textsf{At}\:(-2,8) \implies a(-2-h)^2+k &=8\\a(4+4h+h^2)+k &=8\\4a+4ah+ah^2+k &=8\\\implies 4a+4ah-4&=8\\4a(1+h)&=12\\a(1+h)&=3\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Ctextsf%7BAt%7D%5C%3A%28-2%2C8%29%20%5Cimplies%20a%28-2-h%29%5E2%2Bk%20%26%3D8%5C%5Ca%284%2B4h%2Bh%5E2%29%2Bk%20%26%3D8%5C%5C4a%2B4ah%2Bah%5E2%2Bk%20%26%3D8%5C%5C%5Cimplies%204a%2B4ah-4%26%3D8%5C%5C4a%281%2Bh%29%26%3D12%5C%5Ca%281%2Bh%29%26%3D3%5Cend%7Baligned%7D)
Substitute point (1, -1) and
into the equation:
![\begin{aligned}\textsf{At}\:(1.-1) \implies a(1-h)^2+k &=-1\\a(1-2h+h^2)+k &=-1\\a-2ah+ah^2+k &=-1\\\implies a-2ah-4&=-1\\a(1-2h)&=3\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Ctextsf%7BAt%7D%5C%3A%281.-1%29%20%5Cimplies%20a%281-h%29%5E2%2Bk%20%26%3D-1%5C%5Ca%281-2h%2Bh%5E2%29%2Bk%20%26%3D-1%5C%5Ca-2ah%2Bah%5E2%2Bk%20%26%3D-1%5C%5C%5Cimplies%20a-2ah-4%26%3D-1%5C%5Ca%281-2h%29%26%3D3%5Cend%7Baligned%7D)
Equate to find h:
![\begin{aligned}\implies a(1+h) &=a(1-2h)\\1+h &=1-2h\\3h &=0\\h &=0\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Cimplies%20a%281%2Bh%29%20%26%3Da%281-2h%29%5C%5C1%2Bh%20%26%3D1-2h%5C%5C3h%20%26%3D0%5C%5Ch%20%26%3D0%5Cend%7Baligned%7D)
Substitute found value of h into one of the equations to find a:
![\begin{aligned}\implies a(1+0) &=3\\a &=3\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Cimplies%20a%281%2B0%29%20%26%3D3%5C%5Ca%20%26%3D3%5Cend%7Baligned%7D)
Substitute found values of h and a to find k:
![\begin{aligned}\implies ah^2+k&=-4\\(3)(0)^2+k &=-4\\k &=-4\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Cimplies%20ah%5E2%2Bk%26%3D-4%5C%5C%283%29%280%29%5E2%2Bk%20%26%3D-4%5C%5Ck%20%26%3D-4%5Cend%7Baligned%7D)
Therefore, the equation of the parabola in vertex form is:
![\implies y=3(x-0)^2-4=3x^2-4](https://tex.z-dn.net/?f=%5Cimplies%20y%3D3%28x-0%29%5E2-4%3D3x%5E2-4)
So the vertex of the parabola is (0, -4)
Answer:
30
Step-by-step explanation:
discounting by 20% is the same as marking to 80% of the original cost. 80% = .8
set up equation and solve
.8x=24
x=30
You can use a protractor to solve for the angles
Answer:
y = 17.5
Step-by-step explanation:
Use the direct proportion equation, y = kx
Plug in the x and y values to solve for k
y = kx
35 = k(140)
0.25 = k
Then, plug in the k value and given x value into the equation, and solve for y
y = kx
y = 0.25(70)
y = 17.5