$\text{Given:}\\\\AB=3x-4\\AC=2x+12\\BC=7x-2\\AB:AC=1:2\Rightarrow(3x-4):(2x+12)=1:2\\\\\dfrac{3x-4}{2x+12}=\dfrac{1}{2}\qquad\text{cross multiply}\\\\(3x-4)(2)=(2x+12)(1)\qquad\text{use the distributive property}\\\\(3x)(2)+(-4)(2)=2x+12\\\\6x-8=2x+12\qquad\text{add 8 to both sides}\\\\6x-8+8=2x+12+8\\\\6x=2x+20\qquad\text{subtract}\ 2x\ \text{from both sides}\\\\6x-2x=2x-2x+20\\\\4x=20\qquad\text{divide both sides by 4}\\\\\dfrac{4x}{4}=\dfrac{20}{4}\\\\x=5$

$\text{Put the value of}\ x\ \text{to}\ AC\ \text{and}\ BC:\\\\AC=2(5)+12=10+12=22\\\\BC=7(5)-2=35-2=33\\\\AC:BC=22:33=\dfrac{22}{33}=\dfrac{22:11}{33:11}=\dfrac{2}{3}=2:3$

4 0

3 years ago

A. What is the area of the base? Use complete sentences to explain your reasoning.

Lynna [10]

Answer:

For the first answer (A)

The area of the base is the area of the 8 by 4 rectangle, minus the missing 2 by 2 square in the top-right. This is 8*4-2*2=32-4=28 square centimeters.

For the second answer (B)

The volume of the prism is the base area multiplied by the height, or 28*10=280 cubic centimeters.

8 0

2 years ago

Read 2 more answers

Add. (4x2 - 2x) + (5x-7)

Sloan [31]

Answer:

4x²+3x-7 is the answer

Step-by-step explanation:

=(4x²-2x)+(5x-7)

opening brackets

=4x²-2x+5x-7

=4x²+3x-7

i hope this will help you :)

7 0

3 years ago

(7*10^5)*(3*10^2) answer in standard form

(710^5)(3*10^2) answer in standard form