Answer:
x = 56.25
Step-by-step explanation:
The sides of the rectangle are in the ratio 3:4, so those together with the diagonal of the rectangle make a 3-4-5 right triangle. The sum of these adjacent-side ratio units is 3+4 = 7, so the perimeter in ratio units is 2×7 = 14. The actual perimeter is 42 inches, so each ratio unit must stand for ...
(42 in)/(14 units) = 3 in/unit
The diagonal of the rectangle is the diameter of the circle. Its length is 5 units, or ...
(5 units)×(3 in/unit) = 15 inches.
Then the radius is half the diameter, or 7.5 inches.
The area of a circle is given by ...
A = πr² = π(7.5 in)² = 56.25π in²
The value of x is 56.25.
Using linear combination method, the solution to given system of equations are (-7, -15)
<h3><u>Solution:</u></h3>
Linear combination is the process of adding two algebraic equations so that one of the variables is eliminated
Addition is used when the two equations have terms that are exact opposites, and subtraction is used when the two equations have terms that are the same.
<u><em>Given system of equations are:</em></u>
2x - y = 1 ---- eqn 1
3x - y = -6 ------ eqn 2
Subtract eqn 2 from eqn 1
2x - y = 1
3x - y = -6
(-) -------------
-x = 7
<h3>x = -7</h3>
Substitute x = -7 in eqn 1
2(-7) - y = 1
-14 - y = 1
y = -14 - 1 = -15
<h3>y = -15</h3>
Thus the solution to given system of equations are (-7, -15)
If you would like to simplify <span>7 - 3[(n^3 + 8n) / (-n) + 9n^2], you can do this using the following steps:
</span>7 - 3[(n^3 + 8n) / (-n) + 9n^2] = 7 - 3[(-n^2 - 8) + 9n^2] = 7 - 3[-n^2 - 8 + 9n^2] = 7 - 3[ - 8 + 8n^2] = 7 - 3[8<span>n^2 - 8] = 7 - 24n^2 + 24 = - 24n^2 + 31
</span>
The correct result would be <span>- 24n^2 + 31.</span>
This is a case for multiplication of #Students by#Cans and then subtract.
Ms Lee.........
24 students × 18 cans = 432
Mr Galvez...21 students × 25 cans = 525
..525
- 432
= 093
Mr Galvez' s class collected 93 more cans than
