Congruent triangle are the same shape and same size exactly
Answer:
No, natural numbers are positive whole numbers.
So, numbers such as 1, 10, 100, 1000 etc.
Numbers that cannot be a type of natural number is decimals like 3.5, or negative numbers.
Answer: Third option.
Step-by-step explanation:
Calculate the area of the gate (including the glass panel) which has the shape of a trapezoid.
The formula for calculate the area of a trapezoid is:
![A=\frac{h}{2}(B+b)](https://tex.z-dn.net/?f=A%3D%5Cfrac%7Bh%7D%7B2%7D%28B%2Bb%29)
Where h is the height, B is the larger base and b is the smaller base.
In this case:
![B=10ft\\b=7ft\\h=5ft](https://tex.z-dn.net/?f=B%3D10ft%5C%5Cb%3D7ft%5C%5Ch%3D5ft)
Substituting, you get:
![A_{gate}=\frac{5ft}{2}(10ft+7ft)=42.5ft^2](https://tex.z-dn.net/?f=A_%7Bgate%7D%3D%5Cfrac%7B5ft%7D%7B2%7D%2810ft%2B7ft%29%3D42.5ft%5E2)
Calculate the area of the rectangular glass panel, with the formula:
![A_{panel}=l*w](https://tex.z-dn.net/?f=A_%7Bpanel%7D%3Dl%2Aw)
Where the lenght is
and the width is ![w=0.71ft](https://tex.z-dn.net/?f=w%3D0.71ft)
Then:
The area he needs to paint is:
![A=A_{gate}-A_{panel}\\A=42.5ft^2-1.01ft^2\\A=41.49ft^2](https://tex.z-dn.net/?f=A%3DA_%7Bgate%7D-A_%7Bpanel%7D%5C%5CA%3D42.5ft%5E2-1.01ft%5E2%5C%5CA%3D41.49ft%5E2)
If painting the gate costs $2.50 per ft², for 41.49 ft² he will have to spend:
![=(41.49)(\$2.50)\\=\$103.725](https://tex.z-dn.net/?f=%3D%2841.49%29%28%5C%242.50%29%5C%5C%3D%5C%24103.725)
Therefore the answer is the third option.
Answer:
Both expressions equal 5 when substituting 2 for x because both expressions are equivalent
Step-by-step explanation:
Given
- Expression 1
-- - Expression 2
Required
Find the result of both expressions when ![x = 2](https://tex.z-dn.net/?f=x%20%3D%202)
<em>Expression 1</em>
![\frac{1}{2}x + 4](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7Dx%20%2B%204)
Substitute ![x = 2](https://tex.z-dn.net/?f=x%20%3D%202)
![\frac{1}{2} * 2 + 4](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20%2A%202%20%2B%204)
![1 + 4](https://tex.z-dn.net/?f=1%20%2B%204)
![Result = 5](https://tex.z-dn.net/?f=Result%20%3D%205)
<em>Expression 2</em>
![x + 6 - \frac{1}{2}x - 2](https://tex.z-dn.net/?f=x%20%2B%206%20-%20%5Cfrac%7B1%7D%7B2%7Dx%20-%202)
Substitute ![x = 2](https://tex.z-dn.net/?f=x%20%3D%202)
![2 + 6 - \frac{1}{2} * 2 - 2](https://tex.z-dn.net/?f=2%20%2B%206%20-%20%5Cfrac%7B1%7D%7B2%7D%20%2A%202%20-%202)
![2 + 6 -1 -2](https://tex.z-dn.net/?f=2%20%2B%206%20-1%20-2)
![Result = 5](https://tex.z-dn.net/?f=Result%20%3D%205)