1) 3x-8 =x
subtract x from both sides
2x-8=0
add 8 to each side
2x=8
divide both sides by 2
x=4
<span>1) Number of fish in the pond: y
Number of years: x
</span>A pond had an initial population of 120 fish. Then when x=0, y=120. The graph must begin at point (x,y)=(0,120). Only the graph above at right and below at left begin in this point (0,120).
<span>The number of fish is exponentially decreasing by one-fourth each year. Then the first year the number of fish must decrease 120*(1/4)=120/4=30, and the number of fish after the first year must be:
</span>120-30=90=120(1-1/4)=120(4-1)/4=120(3/4). Then when x=1, y=90. The point is (x,y)=(1,90)
In the graph above at right when x=1, y is between 24 and 36. y=90 is not in this interval. then this graph is not the correct.
In the graph below at left when x=1, y is between 84 and 96. y=90 is in this inverval. Then this is the correct graph.
Answer: T<span>he graph of the solution set for this situation is the graph below at left.
2) The equation has the form:
y=y0(r)^x
Where y0 is the initial population and r is the rate of reduction. In this case:
y0=120 and
r=1-1/4=(4-1)/4→r=3/4
Then the equation modeled by the graph is:
y=120(3/4)^x
Answer: The equation modeled by the graph is that above at right:
y=120(3/4)^x</span>
Answer:
x = 9
Step-by-step explanation:
6x - 2(x - 5) = 46 ← distribute parenthesis and simplify left side
6x - 2x + 10 = 46
4x + 10 = 46 ( subtract 10 from both sides )
4x = 36 ( divide both sides by 4 )
x = 9
Answer:
y=0.5(x+6)(x+5)
Step-by-step explanation:
Since the parabola goes upwards as it expands from the vertex, the "a" value is definitely positive so the answer must be either the top-left or bottom-right. Next, use the roots to find the final answer. The roots are on the left side of the y-axis which indicates that they are negative. Now you know that the answer is the bottom-right answer because if both roots are negative, then the expressions must include addition to create 0 which is the y-value at the bases.
