I'm sorry I had to repost, but this is urgent and i need it done by today!!
Can someone please show me how to do these problems? I've been trying but I'm having a hard time...
1.Simplify the expressions on each side of the equation to obtain an equivalent equation:
5x + 12 + 4x -16= 100/2
2.Angles UVW and angles XYZ are complementary angles. m of angle UVW is 18 degress less than m of angle XYZ. What is m of angle UVW?
3.After a 24% increase, the price of a tennis racquet was $37.82. What was it's original price?
Thanks so much!!
-MC
1.
5x + 12 + 4x -16= 100/2
9x - 4 = 50
9x = 54
x = 6
3.
1.24x = 37.82
x = ?
2.
let angle XYZ = x
then angle UVW = x-18
don't complemenatry angles add up to 90 ?
so x + x-18 = 90
solve for x, sub into x-18
No problem! I'll walk you through how to solve each of these problems step by step.
1. Simplifying the expressions on each side of the equation:
You have the equation: 5x + 12 + 4x - 16 = 100/2.
To simplify, start by combining like terms on each side of the equation. On the left side, you have 5x and 4x. Combine those terms to get 9x. You also have 12 and -16, which combine to give -4.
Now your equation becomes 9x - 4 = 100/2.
To simplify further, divide 100 by 2 to get 50. Your equation can now be written as 9x - 4 = 50.
Next, to isolate the variable x, you can add 4 to both sides of the equation to get rid of the -4 on the left side. This leaves you with 9x = 50 + 4, which simplifies to 9x = 54.
Finally, divide both sides of the equation by 9 to solve for x. This gives you x = 6.
So the solution to the equation is x = 6.
2. Finding the measure of angle UVW:
We are given that angles UVW and XYZ are complementary angles, which means they add up to 90 degrees.
Let's assume the measure of angle XYZ is x degrees.
It is stated that the measure of angle UVW is 18 degrees less than angle XYZ. So, angle UVW can be represented as (x - 18) degrees.
Since the sum of the measures of complementary angles is 90 degrees, we can set up the equation: x + (x - 18) = 90.
Now, simplify the equation by combining like terms: 2x - 18 = 90.
To solve for x, add 18 to both sides of the equation: 2x = 90 + 18, which gives 2x = 108.
Finally, divide both sides of the equation by 2 to solve for x: x = 54.
Therefore, the measure of angle UVW (x - 18) is 54 degrees - 18 degrees, which equals 36 degrees.
So, the measure of angle UVW is 36 degrees.
3. Finding the original price of a tennis racquet:
Let's assume the original price of the tennis racquet is x dollars.
After a 24% increase, the price became $37.82.
To find the original price, we need to "undo" the 24% increase.
First, convert the 24% increase to a decimal by dividing it by 100. 24% is equal to 0.24.
Now, set up the equation: x + 0.24x = $37.82.
Combine like terms by adding the two terms on the left side of the equation: 1.24x = $37.82.
To solve for x, divide both sides of the equation by 1.24: x = $37.82 / 1.24.
Using a calculator to perform the division, you'll find x to be approximately $30.50.
Therefore, the original price of the tennis racquet was $30.50.
I hope this helps you solve the problems! Let me know if you have any further questions.