Answer:
120 sq cm
Step-by-step explanation:
Solve the following system using elimination:
{y = 4050 x + 2949 | (equation 1)
{y = 5165 x + 93 | (equation 2)
Express the system in standard form:
{-(4050 x) + y = 2949 | (equation 1)
{-(5165 x) + y = 93 | (equation 2)
Swap equation 1 with equation 2:
{-(5165 x) + y = 93 | (equation 1)
{-(4050 x) + y = 2949 | (equation 2)
Subtract 810/1033 × (equation 1) from equation 2:
{-(5165 x) + y = 93 | (equation 1)
{0 x+(223 y)/1033 = 2970987/1033 | (equation 2)
Multiply equation 2 by 1033:
{-(5165 x) + y = 93 | (equation 1)
{0 x+223 y = 2970987 | (equation 2)
Divide equation 2 by 223:
{-(5165 x) + y = 93 | (equation 1)
{0 x+y = 2970987/223 | (equation 2)
Subtract equation 2 from equation 1:
{-(5165 x)+0 y = (-2950248)/223 | (equation 1)
{0 x+y = 2970987/223 | (equation 2)
Divide equation 1 by -5165:
{x+0 y = 2856/1115 | (equation 1)
{0 x+y = 2970987/223 | (equation 2)
Collect results:
Answer: {x = 2856/1115 , y = 2970987/223
______________________________________________
Solve the following system using substitution:
{y = 4050 x + 2949
{y = 5165 x + 93
Substitute y = 4050 x + 2949 into the second equation:
{y = 4050 x + 2949
{4050 x + 2949 = 5165 x + 93
In the second equation, look to solve for x:
{y = 4050 x + 2949
{4050 x + 2949 = 5165 x + 93
Subtract 5165 x + 2949 from both sides:
{y = 4050 x + 2949
{-1115 x = -2856
Divide both sides by -1115:
{y = 4050 x + 2949
{x = 2856/1115
Substitute x = 2856/1115 into the first equation:
{y = 2970987/223
{x = 2856/1115
Collect results in alphabetical order:
Answer: {x = 2856/1115, y = 2970987/223
The length (L) of the rectangle can be written as a function of the width (W)
:
Now since we know Area = Width*Length, we can write the area as a function of the width:
Distributing the W inside the parentheses we have:
We know the area is 54 ft^2, so we can rewrite it as:
Now solve for W by factoring (or by applying the quadratic formula):
Factor out a common 2W from the first two terms and a 9 from the last two terms:
Regroup the terms to get our fully factored equation:
This gives us the roots W = 6 and W = -9/2, but width can't be negative so we have width = 6 ft. Then remember that the length L = 2W - 3, so our length is:
So now we know that our rectangle is 9 feet long and 6 feet wide.
Answer:
1.375
Step-by-step explanation:
3/4 is 0.75,
5/8 is 0.625
so 0.75 + 0.625=1.375
Basically, we have to find out what 72% of 92 minutes is. A way to do this is turn 92 minutes into a decimal: 92 / 100 = 0.92 and then multiply the decimal by 72: 0.92 x 72 = 66.24 minutes. Rounding to the nearest tenth, however, changes the number to 66.2 minutes. Hope this helps!