<em>Question:</em>
The measures of two complementary angles have a ratio of 3 : 2. What is the measure of the larger angle?
—————
<em>Solution:</em>
Call those two angles x and y, where x is the larger one.
If they are complementary, then their sum equals 90°:
x + y = 90° (i)
Also, the ratio between x and y is 3 : 2, so
x 3
—— = ——
y 2
Product of the extremes = product of the means:
2x = 3y
2x – 3y = 0 (ii)
Now, just solve this system of equations:
x + y = 90° (i)
2x – 3y = 0 (ii)
Solve it with elimination. Since you want to know the value of the larger angle, which is x, then eliminate the variable y by doing the following:
Multiply the equation (i) by 3,
3x + 3y = 270° (iii)
2x – 3y = 0 (ii)
then add both equations, so you cancel out the variable y:
3x + 2x + 3y – 3y = 270° + 0
3x + 2x = 270°
5x = 270°
270°
x = ———
5
x = 54° <——— this is the measure of the larger angle.
I hope this helps. =)
Tags: <span><em>system of linear equations elimination method solve complementary angles algebra geometry</em>
</span>
Y = -3x + 5
5x - 4(-3x + 5) = -3
5x + 4(3x) - 4(5) = -3
5x + 12x - 20 = -3
17x - 20 = -3
+ 20 + 20
17x = 17
17 17
x = 1
y = -3x + 5
y = -3(1) + 5
y = -3 + 5
y = 2
(x, y) = (1, 2)
Answer:
n = 34.4
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality<u>
</u>
Step-by-step explanation:
<u>Step 1: Set Up</u>
Let's let our number be set by variable <em>n</em>.
We add 7 to it: n + 7
We then double that entire expression: 2(n + 7)
That expression is equal to 82.8: 2(n + 7) = 82.8
<u>Step 2: Solve for </u><em><u>n</u></em>
- [Division Property of Equality] Divide 2 on both sides: n + 7 = 41.4
- [Subtraction Property of Equality] Subtract 7 on both sides: n = 34.4
∴ Caroline's original number is 34.4.
Answer:
y= 5.7x-10.7
Step-by-step explanation:
the formula is y=mx+b
Base salary = $400.00
Commission = 5% of $1650 = 0.05 x 1650 = $82.50
Total pay = $400 + $82.50 = $482.50
Answer: $482.50
