12 a. The answer is 80%
Explain: 68/85 = 0.8 (I move two decimal places to the right)
In Percent: 80%
12 b. Marisol has the highest score in English.
The sides of the triangle are 20 in, 48 in and 52 in
<u>Explanation:</u>
Given:
Let x be the length of smaller leg
Hypotenuse, H = x + 32
Height, h = x + 28
Length of the sides of a triangle = ?
If the triangle is a right angle triangle then we use pythagoras theorm to solve the question.
So,
(Hypotenuse)² = (height)² + (Base)²
(x + 32)² = (x + 28)² + (x)²
x² + 1024 + 64x = x² + 784 + 56x + x²
240 + 8x - x² = 0
x² - 8x - 240 = 0
Solving the quadratic equation:
x² + 12x - 20x - 240 = 0
x(x+12) - 20(x+12) = 0
(x-20) (x+12) = 0
(x-20) = 0
x = 20 in
Hypotenuse, H = x + 32
H = 20 + 32 in
H = 52 in
Height, h = x + 28
h = 20 + 28 in
h = 48 in
Therefore, the sides of the triangle are 20 in, 48 in and 52 in
70 years old.
There was a 44-year age difference between the youngest and oldest signers. The oldest signer was Benjamin Franklin, 70 years old when he scrawled his name on the parchment.
Answer:
79 degrees
Step-by-step explanation:
A. Sum of interior angles is where you take two of the interior angles (ones inside the triangle) and add them to get the opposite angle outside the triangle, D in this case. So 41 + 38 = 79 degrees
B. a straight line has 180 degrees, you are given the angle next to D to be 101, so you find the difference between 180 and 101 to find D, so 180-101 = 79 degrees