How would you solve the area

Mathematics

1 answer:

zvonat [6]3 years ago

8 0

Check the picture below.

so the composite is just 2 triangles, one rectangle and one parallelogram.

we know the height and base of the triangles and length and width of the rectangle.

now, the parallelogram, we can simply split in in two triangles and a rectangle, like you see the split in the middle, and that gives us two more triangles and one rectangle.

so, we can simply get the area of each of those figures and sum them up, and that's the area of the composite.

$\bf \stackrel{\textit{left triangle}}{\cfrac{1}{2}(11)(8)}~~+~~\stackrel{\textit{left rectangle}}{11\cdot 9}~~+~~\stackrel{\textit{upper middle triangle}}{\cfrac{1}{2}(11)(2)}
\\\\\\
+~~\stackrel{\textit{middle rectangle}}{7\cdot 11}~~+~~\stackrel{\textit{lower middle triangle}}{\cfrac{1}{2}(11)(2)}~~+~~\stackrel{\textit{right triangle}}{\cfrac{1}{2}(8)(9)}\\\\
-------------------------------\\\\
44+99+11+77+11+36\implies 278$

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At one gym, there is a $12 start-up fee, and after that each month at the gym costs $20. At another gym, it costs $4 to startup,

mart [117]

Answer:

In 4 months the cost of both gyms will be the same.

Step-by-step explanation:

At first we need to model the function to calculate the cost of the 2 gyms.

Slope-intercept equation of linear function

$f(x)=mx+b$

where

$m\rightarrow$ slope of line

$b\rightarrow$ y-intercept

Let linear function to calculate total cost of gym be:

$c(n)=mn+b$

where

$c\rightarrow$ total cost of gym

$m\rightarrow$ cost per month (slope)

$n\rightarrow$ number of months

$b\rightarrow$ start-up fee (y-intercept)

For Gym 1

$m=20$ , $b=12$

$c(n)=20n+12$

For Gym 2

$m=22$ , $b=4$

$c(n)=22n+4$

In order to find the number of months the cost of both gyms will be the same, we need to equate both functions and solve for number of months $(n)$

$20n+12=22n+4$

$\\\textrm{Subtracting 22n from both sides}\\20n-22n+12=22n-22n+4\\-2n+12=4\\\textrm{Subtracting 12 from both sides}\\-2n+12-12=4-12\\-2n=-8\\\textrm{Dividing both sides by -2}\\\frac{-2}{-2}n=\frac{-8}{-2}\\n=4\textrm{ months}$