Answer:
y = 5 and x = -3
Step-by-step explanation:
Given,
y = x + 8 ...............( equation 1 )
x + y = 2 ...............( equation 2 )
Now, by substituting the value of y in equation 2, we get;
⇒ x + x + 8 = 2
⇒ x = -3
and now, by substituting the value of x in equation 1, we get;
⇒ y = -3 + 8
⇒ y = 5
Ah...Trigonometry is fun!
The law of sines states:

The transitive property (switching the orders of the equations) applies here. Therfore, we can say that

We then plug in our given values to find C


Solving, we get 0.8557316387.
We're not done yet!We are trying to find an angle measure, so we'll do the inverse of the ratio we used (sin).
arcsin0.8557316387 (arcsin is the same as inverse sin)
=
58.8 (approximate)
So the measure of angle C is 58.8. You could check this by reinserting it into the equation

.
:)
a) We have that the discount is 65 %
Scott buys a jacket for $150
First, we will calculate the discount

then we need to subtract the quantity calculated above from the original price

After the markdown Scott paid $52.5
b.
In order to know the taxes first, we need to calculate the 5% of $52.5

then we will sum the 5% plus the price after the markdown

The total cost of the jacket is $55.125
Answer:

Step-by-step explanation:
For this exercise it is important to remember that a Right triangle is a triangle that has an angle that measures 90 degrees.
According to the Altitude Rule, given a Right triangle, if you draw an altitude from the vertex of the angle that measures 90 degrees (The right angle) to the hypotenuse, the measure of that altitude is the geometric mean between the measures of the two segments of the hypotenuse.
In this case, you can identify that the altitude that goes from the vertex of the right angle (
) to the hypotenuse of the triangle, is:

Then, based on the Altitude Rule, you can set up the following proportion:

According to the Leg Rule, each leg is the mean proportional between the hypotenuse and the portion of the hypotenuse that is located directly below that leg of the triangle.
Knowing this, you can set up the following proportions:
