Answer: (b)-175 ft
Step-by-step explanation:
In ![\triangle ABC\ \text{and}\ \triangle CDE](https://tex.z-dn.net/?f=%5Ctriangle%20ABC%5C%20%5Ctext%7Band%7D%5C%20%5Ctriangle%20CDE)
![\angle ACB=\angle ECD\quad [\text{vertically opposite angles}]\\\angle ABC=\angle CDE\quad [\text{Each angle is }90^{\circ}]\\\therefore \triangle ABC \sim\ \triangle CDE\quad [\text{by AA similarity criteria}]](https://tex.z-dn.net/?f=%5Cangle%20ACB%3D%5Cangle%20ECD%5Cquad%20%5B%5Ctext%7Bvertically%20opposite%20angles%7D%5D%5C%5C%5Cangle%20ABC%3D%5Cangle%20CDE%5Cquad%20%5B%5Ctext%7BEach%20angle%20is%20%7D90%5E%7B%5Ccirc%7D%5D%5C%5C%5Ctherefore%20%5Ctriangle%20ABC%20%5Csim%5C%20%5Ctriangle%20CDE%5Cquad%20%5B%5Ctext%7Bby%20AA%20similarity%20criteria%7D%5D)
(ii)for similar triangles, we can write
![\Rightarrow \dfrac{100}{d}=\dfrac{4x}{7x}\\\\\Rightarrow d=100\times \dfrac{7}{4}=175\ ft](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cdfrac%7B100%7D%7Bd%7D%3D%5Cdfrac%7B4x%7D%7B7x%7D%5C%5C%5C%5C%5CRightarrow%20d%3D100%5Ctimes%20%5Cdfrac%7B7%7D%7B4%7D%3D175%5C%20ft)
Answer:
1. (x+2y)^2-ab x^2+4xy+4y^2-ab
2. 3n-13<9 n<22/3
3. 6+n/7=4 n/7=-2
Answer:
6x - 12
Step-by-step explanation:
In this question, we area asked to write an expression for a mother’s age given some information about the children’s age. We proceed as follows:
Charlie is x years old and his sister is 4 years younger. His sister’s age would be x -4. The total of both ages would be their addition and that is x + x - 4 = 2x - 4
Now, the mother’s age is 3 times this quantity.
Mathematically, that is 3(2x -4) = 6x -12
The expression of the mother’s age is (6x-12) years
By using the calculator on your phone