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) Simply combine like terms on the left carry out the division on the right.
2) Let U = measure of UVW and let X = measure of XYZ. U = X - 16
Since the angles are also complementary, then their sum is 90. U + X = 90. You now have two equations to work with: substitution will allow you to find the value of U.
3) Let x = original price. x + 0.24x = 37.82. So 1.24x = 37.82 ... you can now divide both sides by the number needed to isolate x.
which angle is complementary to<uvw
Sure! I'd be happy to help you solve these problems.
1. Simplifying the equation:
To simplify the equation, we need to combine like terms on both sides of the equation. Let's start by combining the x-terms and the constant terms separately.
On the left side of the equation, we have 5x + 12 + 4x - 16. We can combine the x-terms by adding the coefficients:
5x + 12 + 4x - 16 = 9x - 4.
Now, let's simplify the right side of the equation. We have 100/2, which can be simplified to 50.
Our equation now becomes: 9x - 4 = 50.
2. Finding m of angle UVW:
Complementary angles are two angles whose measures add up to 90 degrees. We are given that angles UVW and XYZ are complementary angles.
Let's represent the measure of angle XYZ as x. It is mentioned that the measure of angle UVW is 18 degrees less than XYZ. So, the measure of angle UVW can be represented as (x - 18).
Since the sum of the measures of complementary angles is 90 degrees, we can write the equation:
x + (x - 18) = 90.
Simplifying the equation gives us:
2x - 18 = 90.
To solve for x, we add 18 to both sides of the equation:
2x - 18 + 18 = 90 + 18,
2x = 108.
Finally, we divide both sides by 2 to get the value of x:
2x/2 = 108/2,
x = 54.
Therefore, the measure of angle UVW is (x - 18): 54 - 18 = 36 degrees.
3. Finding the original price:
To find the original price, we can set up a proportion using the given information. We know that after a 24% increase, the price of a tennis racquet is $37.82.
Let's represent the original price of the tennis racquet as x. Since the price increased by 24%, the new price is 100% + 24% = 124% of the original price.
Setting up the proportion:
x/100% = $37.82/124%.
To solve for x, we can use cross-multiplication. Multiply $37.82 by 100% and x by 124%:
(37.82 * 100) / 124 = x.
So, the original price of the tennis racquet was $30.48.
I hope these explanations help you understand how to solve these problems. Let me know if you have any further questions!