Answer:
The area of the shaded figure is:
Step-by-step explanation:
To obtain the area of the shaded figure, first, you must calculate this as a rectangle, with the measurements: wide (4 units), and long (6 units):
- Area of a rectangle = long * wide
- Area of a rectangle = 6 * 4
- Area of a rectangle = 24 units^2
How the figure isn't a rectangle, you must subtract the triangle on the top, so, now we calculate the area of that triangle with measurements: wide (4 units), and height (2 units):
- Area of a triangle =
![\frac{wide*height}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bwide%2Aheight%7D%7B2%7D)
- Area of a triangle =
![\frac{4*2}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B4%2A2%7D%7B2%7D)
- Area of a triangle =
![\frac{8}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B8%7D%7B2%7D)
- Area of a triangle = 4 units^2
In the end, you subtract the area of the triangle to the area of the rectangle, to obtain the area of the shaded figure:
- Area of the shaded figure = Area of the rectangle - Area of the triangle
- Area of the shaded figure = 24 units^2 - 4 units^2
- <u>Area of the shaded figure = 20 units^2</u>
I use the name "units" because the exercise doesn't say if they are feet, inches, or another, but you can replace this in case you need it.
The total surface area of the triangular prism that has a height of h and the side length of a is given below.
![\rm a(\dfrac{\sqrt3}{2} \ a + 3h)](https://tex.z-dn.net/?f=%5Crm%20a%28%5Cdfrac%7B%5Csqrt3%7D%7B2%7D%20%5C%20a%20%2B%203h%29)
<h3>What is a triangular prism?</h3>
A triangular prism is a closed solid that has two parallel triangular bases connected by a rectangle surface.
A box is in the shape of an equilateral triangular prism.
If the box is to be covered with paper on its lateral sides.
Let a be the side length of the equilateral triangle and h be the height of the prism.
Then the surface area of the triangular prism will be
Surface area = 2 × area of triangle + 3 × area of the rectangle
The area of the triangle will be
![\rm Area\ of\ triangle = \dfrac{\sqrt{3}a^2}{4}](https://tex.z-dn.net/?f=%5Crm%20Area%5C%20of%5C%20triangle%20%3D%20%5Cdfrac%7B%5Csqrt%7B3%7Da%5E2%7D%7B4%7D)
The area of the rectangle will be
![\rm Area \ of \ rectangle = a \ h](https://tex.z-dn.net/?f=%5Crm%20Area%20%5C%20of%20%5C%20rectangle%20%3D%20a%20%5C%20h)
Then the total surface area will be
![\rm Surface\ area = 2 \times \dfrac{\sqrt3 a^2 }{4} + 3 ah\\\\\\Surface\ area = a(\dfrac{\sqrt3}{2} \ a + 3h)](https://tex.z-dn.net/?f=%5Crm%20Surface%5C%20area%20%3D%20%202%20%5Ctimes%20%5Cdfrac%7B%5Csqrt3%20a%5E2%20%7D%7B4%7D%20%2B%203%20ah%5C%5C%5C%5C%5C%5CSurface%5C%20area%20%3D%20%20a%28%5Cdfrac%7B%5Csqrt3%7D%7B2%7D%20%5C%20a%20%2B%203h%29)
More about the triangular prism link is given below.
brainly.com/question/21308574
Answer:
D
Step-by-step explanation:
Brainliest?
Answer:
Step-by-step explanation:
Given
![6x_1-9x_2=8](https://tex.z-dn.net/?f=6x_1-9x_2%3D8)
![9x_1+kx_2=-1](https://tex.z-dn.net/?f=9x_1%2Bkx_2%3D-1)
The given system is
can be represented by
![\begin{bmatrix}6 &-9 \\ 9 & k\end{bmatrix}\begin{bmatrix}x_1\\ x_2\end{bmatrix}=\begin{bmatrix}8\\ -1\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D6%20%26-9%20%5C%5C%209%20%26%20k%5Cend%7Bbmatrix%7D%5Cbegin%7Bbmatrix%7Dx_1%5C%5C%20x_2%5Cend%7Bbmatrix%7D%3D%5Cbegin%7Bbmatrix%7D8%5C%5C%20-1%5Cend%7Bbmatrix%7D)
The given system is consistent when determinant of A is not equal to zero
![|A|](https://tex.z-dn.net/?f=%7CA%7C)
![|A|=6k-(-81)=6k+81](https://tex.z-dn.net/?f=%7CA%7C%3D6k-%28-81%29%3D6k%2B81)
![k\neq \frac{-27}{2}](https://tex.z-dn.net/?f=k%5Cneq%20%5Cfrac%7B-27%7D%7B2%7D)
i.e. system is consistent for all value of k except ![k=\frac{-27}{2}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B-27%7D%7B2%7D)
![R-\frac{-27}{2}](https://tex.z-dn.net/?f=R-%5Cfrac%7B-27%7D%7B2%7D)
If he goes there 4 times a week then $8 plus $2 equals $10 and times $10 by 4 times a week equals $40
So Elijah spends $40 a week at the restaurant