Are the expressions 8a2 - 4b + 7a2 and 5(3a2 - 2b) + 6b equivalent? Explain your reasoning.

Yes, The expressions 8a² - 4b + 7a² and 5(3a² - 2b) + 6b are equivalent

Step-by-step explanation:

To answer the question you must simplify each expression, then compare them to find if they are equivalent or not  

∵ The 1st expression = 8a² - 4b + 7a²  

→ Add the like terms

∴ The 1st expression = (8a² + 7a²) - 4b

∴ The 1st expression = 15a² - 4b

∵ The 2nd expression = 5(3a² - 2b) + 6b

→ Multiply the bracket by 5

∴ The 2nd expression = 5(3a²) - 5(2b) + 6b

∴ The 2nd expression = 15a² - 10b + 6b

→ Add the like terms

∵ The 2nd expression = 15a² + (-10b + 6b)

∴ The 2nd expression = 15a² + -4b

→ Remember (+)(-) = (-)

∴ The 2nd expression = 15a² - 4b

∵ The 1st expression = The 2nd expression

∴ The two expressions are equivalent

∴ The expressions 8a² - 4b + 7a² and 5(3a² - 2b) + 6b are equivalent

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3