Answer:
The area that was not painted is ![(2x^{2}-6x+6)\ units^{2}](https://tex.z-dn.net/?f=%282x%5E%7B2%7D-6x%2B6%29%5C%20units%5E%7B2%7D)
Step-by-step explanation:
step 1
Find the area of the rectangle
we know that
The area of a rectangle is equal to
![A=LW](https://tex.z-dn.net/?f=A%3DLW)
In this problem we have
![L=2x-3](https://tex.z-dn.net/?f=L%3D2x-3)
![W=x](https://tex.z-dn.net/?f=W%3Dx)
substitute
![A=(2x-3)x\\A=(2x^{2}-3x)\ units^{2}](https://tex.z-dn.net/?f=A%3D%282x-3%29x%5C%5CA%3D%282x%5E%7B2%7D-3x%29%5C%20units%5E%7B2%7D)
step 2
Find the area that was painted
![A=(3)(x-2)\\A=(3x-6)\ units^{2}](https://tex.z-dn.net/?f=A%3D%283%29%28x-2%29%5C%5CA%3D%283x-6%29%5C%20units%5E%7B2%7D)
step 3
Find the area that was not painted
Subtract the area that was painted from the total area of rectangle
so
![A=(2x^{2}-3x)-(3x-6)=(2x^{2}-6x+6)\ units^{2}](https://tex.z-dn.net/?f=A%3D%282x%5E%7B2%7D-3x%29-%283x-6%29%3D%282x%5E%7B2%7D-6x%2B6%29%5C%20units%5E%7B2%7D)
Answer:
C 111
Step-by-step explanation:
This problem can be completed in 2 ways. Both are acceptable.
Option 1:This is an isosceles trapezoid that can be divided into a rectangle and two congruent triangles.
The area of the rectangle is the base times the height.
![9 \times 4=36](https://tex.z-dn.net/?f=9%20%5Ctimes%204%3D36)
The area of one of the triangles is half the base times the height.
![\dfrac{1}{2} \times 5 \times 4 = 10](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B2%7D%20%5Ctimes%205%20%5Ctimes%204%20%3D%2010)
The other triangle must have that area too.
![36+10+10=56](https://tex.z-dn.net/?f=36%2B10%2B10%3D56)
The area is 56 square centimeters.
Option 2:We can use the area formula for the trapezoid.
![A=\dfrac{b_1+b_2}{2} \times h](https://tex.z-dn.net/?f=A%3D%5Cdfrac%7Bb_1%2Bb_2%7D%7B2%7D%20%5Ctimes%20h)
Where
![b_1](https://tex.z-dn.net/?f=b_1)
is the length of the shorter base
and
![b_2](https://tex.z-dn.net/?f=b_2)
is the length of the longer base
and
![h](https://tex.z-dn.net/?f=h)
is the height.
The length of the shorter base is 9.
The length of the longer base is 9+5+5, or 19.
The height is 4.
![A=\dfrac{9+19}{2} \times 4](https://tex.z-dn.net/?f=A%3D%5Cdfrac%7B9%2B19%7D%7B2%7D%20%5Ctimes%204)
![=56](https://tex.z-dn.net/?f=%3D56)
Same answer. The area is 56 square centimeters.
Both options are two acceptable ways the problem can be tackled.
Answer:
easy
Step-by-step explanation:
subtract 3x both side
Answer:
the students that brought a lunch box is 28
Step-by-step explanation:
The computation of the students that brought a lunch box is shown below:
= Entire school students × students that carry a lunch box ÷ entering students
= 84 students × 8 ÷ 24 students
= 28 students
Hence, the students that brought a lunch box is 28