Question
The hypotenuse of an isosceles right triangle is 11 centimeters longer than either of its legs. find the exact length of each side.
Answer:


Step-by-step explanation:
Let the hypotenuse be y and the other legs be x.
So:

Required
Determine the exact dimension of the triangle
Using Pythagoras theorem;


This gives:

Open bracket

Collect like terms


Using quadratic formula:




Split


x can not be negative.
So:


Recall that:



Hence, the dimensions are:


Answer:
The distance from Greentown to Glenavon is D1 = g*(15+x) miles downstream.
The distance from Glenavon to Cambria is D2 = g*(15-x) miles upstream.
The difference D1 - D2 is 2 miles, according to the condition.
It gives you an equation g*(15+x) - g*(15-x) = 2, which you can easily solve and find "x", the rate of the current. x = 1/g miles per hour.
Start with an equation summing all the angles in this triangle:
180 = <M + <N + <P
we are given <M and <N but not <P. But, since MN=NP, the angle <P is the same as the angle <M (isosceles, make a drawing to see). So
180 = 2<M + <N
180 = 2(3x+1) + x-11
180 = 7x - 9
x = 27
<P = 3*27+1 = 82 degrees
Answer:
<h3>
The percentage is <u>
60%</u>
of the total amount paid with the gift card. </h3>
Step-by-step explanation:
Given:
Total worth of clothing is $178.25 and the amount paid with cash is $71.30.
Let us find the part of amount paid with the gift card:
Amount of gift card(G) = Total worth(T) - Amount paid in cash(C).

.
So, the amount paid with the gift card is $106.95.
Now, according to question:


%.
Therefore, the percentage is <u>60%</u> of the total amount paid with the gift card.