Answer: the cost of a milkshake is $2.59
Step-by-step explanation:
Let x represent the cost of a banana split.
Let y represent the cost of a milkshake.
At the ice cream shop, one banana split and five milkshakes cost $16.24. This is expressed as
x + 5y = 16.24- - - - - - - - - - - - -1
If three banana splits and two milkshakes cost $15.05. This is expressed as
3x + 2y = 15.05- - - - - - - - - - - - -2
Multiplying equation 1 by 3 and equation 2 by 1, it becomes
3x + 15y = 48.72
3x + 2y = 15.05
Subtracting, it becomes
13y = 33.67
y = 33.67/13
y = 2.59
Substituting y = 2.59 into equation 1, it becomes
x + 5 × 2.59 = 16.24
x + 12.95 = 16.24
x = 16.24 - 12.95
x = 3.29
The prime factorization of 6000<span> = 2^4</span>•3•5^3.
<span>The prime factors of </span>6000<span> are 2, 3 and 5.</span>
All you need to know is that
So, the first function grows exponentially and the second decays exponentially. The rate of growth/decay are the bases of the exponentials, which means 1.08 and 0.205
The ladder must be 9.4 ft to reach the top of the building
Here, we want to get the length of the ladder that will reach the top of the building
Firstly, we need a diagrammatic representation
We have this as;
As we can see, we have a right triangle with the hypotenuse being the length of the ladder
We simply will make use of Pythagoras' theorem which states that the square of the hypotenuse is equal to the sum of the squares of the two other sides
Thus, we have;
![\begin{gathered} x^2=5^2+8^2 \\ x^2=\text{ 25 + 64} \\ x^2\text{ = 89} \\ x=\text{ }\sqrt[]{89} \\ x\text{ = 9.4 ft} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%5E2%3D5%5E2%2B8%5E2%20%5C%5C%20x%5E2%3D%5Ctext%7B%2025%20%2B%2064%7D%20%5C%5C%20x%5E2%5Ctext%7B%20%3D%2089%7D%20%5C%5C%20x%3D%5Ctext%7B%20%7D%5Csqrt%5B%5D%7B89%7D%20%5C%5C%20x%5Ctext%7B%20%3D%209.4%20ft%7D%20%5Cend%7Bgathered%7D)
The slope of the line is 2 if that is what you're looking for
