How many solutions are there to the equation below 6×+30+4×=10(×+3)
1 answer:
Answer:
Infinite many solutions. Any x-value can satisfy the equation.
Step-by-step explanation:
Let's work on simplifying the equation a little to investigate which x-values satisfy it. Start by combining like terms on the left side (6x +4x=10x),
then distribute the factor "10" into the binomial (x+10), obtaining 10x +30.
Now we have the same expression on the left and the right of the equal sign:
10x +30=10x+30. We may subtract 30 from both sides, and obtain 10x=10x, and at this point divide by 10 both sides, and we obtain: x=x
The process is shown below.
x=x is an equation that is verified by absolutely ANY x value on the number line, and there are infinite x-values in the number line.
Therefore there are infinite many solutions to this equation (any x-value will satisfy it).
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0=70-4t-16t²
based on your previous questions, you should have learned how to complete the square
solve by copmleting the square
minus 70 both sides
-70=-4t-16t²
times both sides by -1
70=4t+16t²
16t²+4t=70
divide both sides by 16
t²+1/4t=35/8
take 1/2 of the linear coefint and square it
half of 1/4=1/8, (1/8)²=1/64
add that to both sides
t²+1/4t+1/64=35/8+1/64
factor perfect square trionomial
square root both sides, remember to take positive and negative roots
minus 1/8
the 2nd solution is not valid because that gives us a negative time, before the ball was dropped
so
t≈1.97
1.97 seconds