First, we are going to use the Pythagorean identity:
to rewrite our expression. Solving for
in our Pythagorean identity we get that
, so we can rewrite our expression as follows:
Next, we are going to use the trig identity:
to completely simplify our expression:
We can conclude that
Answer:
Person A paints the house in 12 days.
person B paints the house in 60 days.
Step-by-step explanation:
The together rate is the sum of each separate rate.
Person A can paint the neighbor's house 5 times as fast as Person B.
This means that the rate of person A is 1/x, and the rate of person B is 1/5x.
The year A and B worked together, it took them 10 days.
This means that:
Multiplying everything by 10x
This means that:
Person A paints the house in 12 days.
person B paints the house in 60 days.
Let's solve your equation step-by-step.<span><span>−<span>5<span>(<span>x−4</span>)</span></span></span>=<span>−<span>30
</span></span></span>Step 1: Simplify both sides of the equation.<span><span>−<span>5<span>(<span>x−4</span>)</span></span></span>=<span>−30</span></span>
<span>Simplify: (Show steps)</span><span><span><span>−<span>5x</span></span>+20</span>=<span>−<span>30
</span></span></span>Step 2: Subtract 20 from both sides.<span><span><span><span>−<span>5x</span></span>+20</span>−20</span>=<span><span>−30</span>−20</span></span><span><span>−<span>5x</span></span>=<span>−<span>50
</span></span></span>Step 3: Divide both sides by -5.<span><span><span>−<span>5x</span></span><span>−5</span></span>=<span><span>−50</span><span>−5</span></span></span><span>x=<span>10
</span></span>Answer:<span>x=<span>10</span></span>
To find the percent discount you will write the following equation:
x% of 60 is 18
<u>60x</u> = <u>18</u>
60 60
x = 0.3
The discount is 30%.
