Answer: Interval Notation (0, 6)
Graph: 0 o--------------o 6
<u>Step-by-step explanation:</u>
![\dfrac{2}{x}>\dfrac{4}{12}\implies \dfrac{2}{x}>\dfrac{1}{3}\\\\\text{Restriction: Since the denominator cannot be zero, }x\neq 0\\\\\text{First, set the left side EQUAL to the right side and solve:}\\\dfrac{2}{x}=\dfrac{1}{3}\quad \text{cross multiply}\rightarrow 2(3)=x\quad \rightarrow \quad 6=x\\\\\\\text{Next, choose your test points}\\\bullet \text{to the left of 0: I choose -1}\\\bullet \text{between 0 and 6: I choose 1}\\\bullet \text{to the right of 6: I choose 8}](https://tex.z-dn.net/?f=%5Cdfrac%7B2%7D%7Bx%7D%3E%5Cdfrac%7B4%7D%7B12%7D%5Cimplies%20%5Cdfrac%7B2%7D%7Bx%7D%3E%5Cdfrac%7B1%7D%7B3%7D%5C%5C%5C%5C%5Ctext%7BRestriction%3A%20Since%20the%20denominator%20cannot%20be%20zero%2C%20%7Dx%5Cneq%200%5C%5C%5C%5C%5Ctext%7BFirst%2C%20set%20the%20left%20side%20EQUAL%20to%20the%20right%20side%20and%20solve%3A%7D%5C%5C%5Cdfrac%7B2%7D%7Bx%7D%3D%5Cdfrac%7B1%7D%7B3%7D%5Cquad%20%5Ctext%7Bcross%20multiply%7D%5Crightarrow%202%283%29%3Dx%5Cquad%20%5Crightarrow%20%5Cquad%206%3Dx%5C%5C%5C%5C%5C%5C%5Ctext%7BNext%2C%20choose%20your%20test%20points%7D%5C%5C%5Cbullet%20%5Ctext%7Bto%20the%20left%20of%200%3A%20I%20choose%20-1%7D%5C%5C%5Cbullet%20%5Ctext%7Bbetween%200%20and%206%3A%20I%20choose%201%7D%5C%5C%5Cbullet%20%5Ctext%7Bto%20the%20right%20of%206%3A%20I%20choose%208%7D)
![\text{Now, plug each of the test points into the inequality to see which one(s)}\\\text{make a true statement.}\\\\\dfrac{2}{-1}>\dfrac{1}{3}\implies -2>\dfrac{1}{3}\quad FALSE\\\\\\\dfrac{2}{1}>\dfrac{1}{3}\implies 2>\dfrac{1}{3}\quad \boxed{TRUE!}\\\\\\\dfrac{2}{8}>\dfrac{1}{3}\implies -2>\dfrac{1}{3}\quad FALSE](https://tex.z-dn.net/?f=%5Ctext%7BNow%2C%20plug%20each%20of%20the%20test%20points%20into%20the%20inequality%20to%20see%20which%20one%28s%29%7D%5C%5C%5Ctext%7Bmake%20a%20true%20statement.%7D%5C%5C%5C%5C%5Cdfrac%7B2%7D%7B-1%7D%3E%5Cdfrac%7B1%7D%7B3%7D%5Cimplies%20-2%3E%5Cdfrac%7B1%7D%7B3%7D%5Cquad%20FALSE%5C%5C%5C%5C%5C%5C%5Cdfrac%7B2%7D%7B1%7D%3E%5Cdfrac%7B1%7D%7B3%7D%5Cimplies%202%3E%5Cdfrac%7B1%7D%7B3%7D%5Cquad%20%5Cboxed%7BTRUE%21%7D%5C%5C%5C%5C%5C%5C%5Cdfrac%7B2%7D%7B8%7D%3E%5Cdfrac%7B1%7D%7B3%7D%5Cimplies%20-2%3E%5Cdfrac%7B1%7D%7B3%7D%5Cquad%20FALSE)
So, the solution is: every value between 0 and 6
The value of the scale factor is 3. Then the height and area of the triangle ΔABC will be 9 ft and 54 square ft.
<h3>What is dilation?</h3>
Dilation means the changing of the size of the object without changing the shape. The size of the object may be increased or decreased based on the scale factor.
The area of the triangle ΔDEF is 6 square ft. And the base length of the triangle ΔDEF is 4 ft.
The area of the triangle is given as
![\rm Area = \dfrac{1}{2} \times bh\\\\](https://tex.z-dn.net/?f=%5Crm%20Area%20%3D%20%5Cdfrac%7B1%7D%7B2%7D%20%5Ctimes%20bh%5C%5C%5C%5C)
Then the height of the triangle ΔDEF will be
![\rm 6 = \dfrac{1}{2} \times 4 \times h\\\\h = \dfrac{12}{4}\\\\h = 3](https://tex.z-dn.net/?f=%5Crm%206%20%3D%20%5Cdfrac%7B1%7D%7B2%7D%20%5Ctimes%204%20%5Ctimes%20h%5C%5C%5C%5Ch%20%3D%20%5Cdfrac%7B12%7D%7B4%7D%5C%5C%5C%5Ch%20%20%3D%203)
Then the scale factor will be
![\rm SF = \dfrac{12}{4} = 3](https://tex.z-dn.net/?f=%5Crm%20SF%20%3D%20%5Cdfrac%7B12%7D%7B4%7D%20%3D%203)
Then the height of the triangle ΔABC will be
![\rm \dfrac{H}{3} = 3\\\\H \ = 9](https://tex.z-dn.net/?f=%5Crm%20%5Cdfrac%7BH%7D%7B3%7D%20%3D%203%5C%5C%5C%5CH%20%5C%20%3D%209)
Then the area of the dilated triangle ΔABC will be
![\rm Dilated \ Area = \dfrac{1}{2} \times 12 \times 9\\\\Dilated \ Area = 54 \ ft^2](https://tex.z-dn.net/?f=%5Crm%20Dilated%20%5C%20Area%20%3D%20%5Cdfrac%7B1%7D%7B2%7D%20%5Ctimes%2012%20%5Ctimes%209%5C%5C%5C%5CDilated%20%5C%20Area%20%3D%2054%20%5C%20ft%5E2)
More about the dilation link is given below.
brainly.com/question/2856466
#SPJ1
Step-by-step explanation:
Let the number be x. Then x + 10 = 20.
This is all you need to write out. But, for practice, find the solution as well.