<1 and <2 are complementary. Solve for the measure of <1. <1 = 12x + 4
<2 = 9x + 2

A. 52
B. 4
C. 38
D. 8.3

A) 52

Step-by-step explanation:

If < 1 and < 2 are complementary angles, then it means that the sum of their measures add up to 90°.

< 1 + < 2 = 90°

12x + 4 + 9x + 2 = 90°

21x + 6 = 90°

21x + 6 - 6 = 90° - 6

21x = 84°

21x/21 = 84°/21

x = 4

Substitute the value of x = 4 into < 1 and < 2:

m < 1: 12x + 4 = 12(4) + 4 = 52°

m < 2: 9x + 2 = 9(4) + 2 = 38°

Therefore, the correct answer is A) m < 1 = 52°.

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

equation image indicator

x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

equation image indicator

x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

equation image indicator

x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!

hi,

i'm 75% sure the answer is 1,1 to both lines.

have a great day