Answer:
c = 13
m∡A = 60°
m∡B = 30°
Step-by-step explanation:
This is a 5-12-13 triangle. However, to make sure, I will put the steps.
Allow for each sides to be denoted as a-b-c, in which c is the hypotenuse (longest side). Set the equation:
a² + b² = c²
Plug in the corresponding numbers to the corresponding variables:
5² + 12² = c²
Simplify. First, solve the exponents, and then add:
(5²) = 5 * 5 = 25
(12²) = 12 * 12 = 144
25 + 144 = c²
c² = 169
Note the equal sign, what you do to one side, you do to the other. Isolate the variable, c, by rooting both sides:
√c² = √169
c = √169 = √(13 * 13) = 13
c = 13
13 is your answer for c.
Note the measurements of the angles. We know that this is a 30-60-90 triangle, and so it will be easy to figure it out. Note that the corresponding angles will depend on that of the opposite side's measurement lengths. The hypotenuse will always be on the opposite side of the largest angle (as given), as c, the longest side, is opposite of ∡C, which is the largest angle (90°). Based on this information, it means that ∡A would be 60° (as it is opposite of the middle number, 12), and ∡B would be 30° (opposite of the smallest number, 5).
If at least one has to be heads then it would be 1/5
Answer:
<em>The coefficient of the squared expression in the parabolas equation will be 5.</em>
Step-by-step explanation:
<u>The vertex form of parabola</u> is: 
, where 
is the vertex point and 
is the coefficient of 
term.
The vertex is given as 
. That means, 
and 
So, the vertex form will be: 
Given that, when the x-value is 4, the y-value is 3. So, plugging these values into the above equation, we will get.....
Thus, the coefficient of the squared expression in the parabolas equation will be 5.
Answer:
24 red marbles
Step-by-step explanation:
Ok, why not let R = number of red marbles.
The first sentence says:
3 * R = (33 and 1/3) % * R + 64
or
3R = 100/3 %*R + 64
3R = (1/3)*R + 64
9R = R + 192
8R = 192
R = 24 red marbles
