Answer:
(x, y) = (1/2, -1)
Step-by-step explanation:
Subtracting twice the first equation from the second gives ...
(2/x +1/y) -2(1/x -5/y) = (3) -2(7)
11/y = -11 . . . . simplify
y = -1 . . . . . . . multiply by y/-11
Using the second equation, we can find x:
2/x +1/-1 = 3
2/x = 4 . . . . . . . add 1
x = 1/2 . . . . . . . multiply by x/4
The solution is (x, y) = (1/2, -1).
_____
<em>Additional comment</em>
If you clear fractions by multiplying each equation by xy, the problem becomes one of solving simultaneous 2nd-degree equations. It is much easier to consider this a system of linear equations, where the variable is 1/x or 1/y. Solving for the values of those gives you the values of x and y.
A graph of the original equations gives you an extraneous solution of (x, y) = (0, 0) along with the real solution (x, y) = (0.5, -1).
At it's peak the rock is going 0mph the acceleration is .0000038 m/s^2 if on earth
Answer:
The measure of the three angles are;
The first angle is 62°
The second angle is 28°
The third angle is 90°
Step-by-step explanation:
The given information are;
The shape of the parking lot = Triangular
Let the angles of the triangle be given as follows
First angle = A
Second angle = B
Third angle = C
The given triangle interior angle dimensions are;
A = 6 + 2× B
C = A + B
However, we have;
A + B + C = 180° (Angle sum property for a triangle)
Therefore;
A + B + C = 180° gives;
C + C = 180° (Transitive property)
2·C = 180°
C = 180°/2 = 90°
C = 90°
However, C = A + B therefore;
90° = A + B and, A = 6 + 2 × B, we get;
A + B = 90° (Symmetric property)
6 + 2× B + B = 90° (Substitution property)
6 + 3·B = 90°
3·B = 90° - 6° = 84°
B = 84°/3 = 28°
B = 28°
From, A = 6 + 2 × B, we have;
A = 6 + 2 × 28° = 62°
A = 62°
First angle = A = 62°
Second angle = B = 28°
Third angle = C = 90°
The measure of the three angles are;
First angle is 62°
Second angle is 28°
Third angle is 90°.
Answer:
42
Step-by-step explanation:
Let the number be "x"
We translate the word equation to algebraic equation.
First,
subtract 6 from me, so we have:
x - 6
Now,
Multiply by 2, so we have:
2(x-6)
Now,
Subtract 40, then divide by 4:
Now, you get "8", so equate this to 8, we get:
We now solve using algebra:
The number is 42
Answer:
The answer is 85
Step-by-step explanation:
The equation used to find the sum of an arithmetic series is: (n/2) * (a1 + an).
n in this case is 10 (the number of numbers in the series)
an is 22 (plug in 10 to the expression 3n-8)
and a1 is -5 (plug in 1 to the expression 3n-8)
so when you plug everything in to the final equation, you get
(10/2) * (-5 + 22)
5 * 17
85
