with the pythagorean theorem
using the formula of the quadratic equation
the length cannot be negative, therefore x=7
length of the shorter leg is: 7ft
length of the longer leg is: 3+3(7)= 24ft
length of the hypotenuse is: 4+3(7)= 25ft
Answer:
Please check explanations
Step-by-step explanation:
Here, we want to make an interpretation
From the question, we have that initially when the count was started, there were 5,428 people; this means that the initial value of the data is 5,428
For the rate of change, we have that there is an average increase of 142 people for each of 5 years;
That means per 5 years, there is an increase of 142 people and this is what represents the rate of change
Since the triangle is an equilateral triangle we know all of it's sides must be the same length, with that in mind the angles that make up the triangle must be equal as well. Knowing that a triangle's three interior angles make up 180 degrees we know that the size of each angle must be one third of this (as each angle must be equal).
180/3 = 60
then we may split the triangle along it's altitude into two special right triangles
more specifically two 30-60-90 triangles.
this means that the side with 30 degrees will be some value "x" where the side for 60 degrees will be related as it is "x*sqrt(3)" and the hypotenuse (which would be the side of the triangle) would be proportionally "2x"
this would mean that the altitude is the side associated with the 60 degree angle as such we can solve for "x" using this.
12= x*sqrt(3)
12/sqrt(3)=x
4sqrt(3)=x (simplifying the radical we get "x" equals 4 square root 3)
now we may solve for the side length of the triangle which is "2x"
2*4sqrt(3) -> 8sqrt (3)
eight square root of three is the answer.
Step-by-step explanation:
2/3p+3
where p=3/5
substitute p into 2/3p + 3
2/3(3/5) + 3
2/(9/5) + 3
10/9 + 3
10+3)/9
13/9
1 4/9
The answer is 5x + 30 = 12x
x - the number of pies
It costs her $5 to make each pie<span>, plus a one-time cost of $30 for baking supplies:
</span>COST: f(c) = 5x + 30
<span>She plans to sell the pies for $12 each:
PROFIT: f(p) = 12x
</span><span>To find the number of pies she needs to sell to break even:
f(c) = f(p)
5x + 30 = 12x</span>
