Answer:
x=-1/4
Step-by-step explanation:
2/5+3/5x=x+5/10
subtract 2/5 form both sides
3/5x=x+1/10
subtract x form both sides
-2/5x=1/10
Multiply both sides by 5
-2x=1/2
x= - 1/4
The first thing we must do for this case is to define variables.
We have then:
x: number of cats
y: number of dogs
We write the system of equations:
x / y = 2/3
(1/4) x + (1/2) y = 48
Solving the system we have:
x = 48
y = 72
The total number of animals is:
x + y = 48 + 72 = 120
Answer:
The total number of animals in the pet store is:
120
(12 2/3)*(3 1/4) = 41 1/6 . . . . . according to my calculator
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You are usually taught to multiply the improper fractions and simplify the result.
.. (38/3)*(13/4) = (38/4)*(13/3)
.. = (19/2)*(13/3)
.. = (19*13)/6
.. = 247/6
.. = 41 1/6
You can also multiply the parts.
.. (12 2/3)*(3 1/4) = 12*3 + 12*(1/4) +(2/3)*3 +(2/3)*(1/4)
.. = 36 +3 +2 +1/6
.. = 41 1/6
Answer:
l
Step-by-step explanation:
x = 5 is not an extraneous solution of the equation.
✓(2x + 6) - ✓(x - 1) = 2
✓(2x + 6) = 2 + ✓(x - 1)
Squaring both the sides of equation, we get
(✓(2x + 6))² = (2 + ✓(x - 1))²
2x + 6 = (2)² + (✓(x - 1))² + 2(2)(✓(x - 1))
2x + 6 = 4 + x - 1 + 4(✓(x - 1))
x + 3 = 4✓(x - 1)
Squaring again on both the side of the equation, we get
(x + 3)² = (4✓(x - 1))²
x² + 3² + 2×3×x = 16(x - 1)
x² + 9 + 6x = 16x - 16
x² - 10x + 25 = 0
By applying middle term splitting on equation (1), we get
x² - 5x - 5x + 25 = 0
x(x - 5) -5(x - 5) = 0
(x - 5) (x - 5) = 0
x = 5 and 5.
Check for extraneous solutions by putting value of x in original equation -
✓(2×5 + 6) - ✓(5 - 1) = 2
✓16 - ✓4 = 2
4 - 2 = 2
2 = 2
LHS = RHS
x = 5 is not an extraneous solution of the equation.
Know more about roots of equation -
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