X - unit of length
w,l - the sides of a rectangle
7 : 2 ⇒ 7x : 2x
Perimeter: P = 207cm
Perimeter: P = 2w + 2l
therefore: 2w + 2l = 207 |divide both sides by 2
w + l = 103.5 (cm)
w : l = 7 : 2 ⇒ w : l = 7x : 2x ⇒ w = 7x; l = 2x
subtitute
7x + 2x = 103.5
9x = 103.5 |divide both sides by 9
x = 11.5 (cm)
7x = 7 · 11.5cm = 80.5cm
2x = 2 · 11.5cm = 23cm
w = 80.5cm; l = 23cm
Area = wl
Area: A = 80.5cm · 23cm = 1851.5cm²
Answer:
When six guests choose cheesecake and eight choose apple pie, the ratio is 6:8. If we use the same prompt but change 6 to 3 and change 8 to 4, the ratio becomes 3:4 with the pie graph looking exactly the same.
6:8 comes out to a total of 14 people
and 3:4 comes out to a total of 7 people
The two ratios are equivalent due to the graphs looking exactly the same as well as that 14 is double of 7.
Step-by-step explanation:
Answer:
The vertex is the point 
Step-by-step explanation:
we know that
The general form of an absolute value equation is

The variable a tells us how far the graph stretches vertically, and whether the graph opens up or down. The variables h, and k, tell us how far the graph shifts horizontally and vertically
The vertex is the point (h,k)
we have

Rewrite the expression (3x+1)

substitute



therefore
The vertex is the point 
see the attached figure to better understand the problem
Answer:
Step-by-step explanation:
We need to first find the perimeter of this oddly-shaped rink. We have a rectangle for which we are enclosing 3 of its sides, and the fourth "side" is a half-circle. Let's find the perimeter (or circumference) of the circle, divide it in half because we have half a circle, then add in the remaining 3 sides from the rectangle, shall we?
C = πd. The diameter of the circle is the same as the shorter length in the rectangle, 26. Therefore,
C = (3.14)(26) so
C = 81.64 m for a whole circle, and for half of that circle, the circumference is
C = 40.82 m
Now we can find the perimeter of the rink:
40.82 + 61 + 26 + 61 = p so
p = 188.82 m
If the fencing costs $6.20 per meter and we have 188.82 m, then the total cost is
. The label "meter" cancels out, leaving us with
cost = $1170.82