Answer:
See method below.
Step-by-step explanation:
m/n + n/3 = 2
2/m + n = 4
First eliminate the fractions by multiplying the first equation by 3n:-
3m + n^2 = 6n...........(1)
and the second equation by m:-
2 + mn = 4m..............(2)
Now we solve using substitution:-
From equation (2):-
4m - mn = 2
m = 2 / (4 - n)
Now substitute for m in equation (1):-
6/ (4 - n) + n^2 = 6n
6 + n^2(4 - n) = 6n(4 - n)
6 + 4n^2 - n^3 = 24n - 6n^2
n^3 - 10n^2 + 24n - 6 = 0
This will not factor so we could solve this using graphical software.
To find the values of the variable m we substitute the found values of n into one of the original equations and solve for m.
Answer:
150.72
Step-by-step explanation:
2πr = circumference
2π(24) = 48π = approx. 150.72
π = 3.14
14: increase
15: decrease
Hope this helps!
Answer:
x = -1
y = 5
Step-by-step explanation:
x+y=4
3x+7y=32
<em><u>To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.</u></em>
x+y=4,3x+7y=32
<em><u>Choose one of the equations and solve it for x by isolating x on the left hand side of the equal sign.</u></em>
x+y=4
<em><u>Subtract y from both sides of the equation</u></em>.
x=−y+4
<em><u>Substitute −y+4 for x in the other equation, 3x+7y=32.</u></em>
3(−y+4)+7y=32
<em><u>Multiply 3 times −y+4.</u></em>
−3y+12+7y=32
<em><u>Add −3y to 7y.</u></em>
4y+12=32
<em><u>Subtract 12 from both sides of the equation</u></em>.
4y=20
<em><u>Divide both sides by 4</u></em>.
y=5
<em><u>Substitute 5 for y in x=−y+4. Because the resulting equation contains only one variable, you can solve for x directly.</u></em>
x=−5+4
<em><u>Add 4 to −5.</u></em>
x=−1
Answer:
(-3, 0) and (1, 0)
(0, 4)
Step-by-step explanation:
x-intercept is the point where y = 0.
y-intercept is the point where x = 0.
or points ...
f(x) = y = -4×|x + 1| + 8
let's start with the y-intercept (x = 0)
y = -4×1 + 8 = -4 + 8 = 4
the y-intercept point (only 1 point) is (0, 4).
for x = 0 the absolute value function contains 0+1. and that is always +1.
the x-intercept(s) :
0 = -4×|x + 1| + 8 (dividing by -4)
0 = |x + 1| - 2
|x + 1| = 2
because of the absolute value we have 2 possibilities :
+(x + 1) = 2
x + 1 = 2
x = 1
and
-(x + 1) = 2
-x - 1 = 2
-x = 3
x = -3
so the points of x-intercept are (-3, 0) and (1, 0)
