Last year, Gilbert contributed $75 toward his 401(k) account each month. If his employer matched 16% of his contributions, what
2 answers:
Answer:
$1044 was contributed.
Step-by-step explanation:
Last year, Gilbert contributed toward his 401(k) account each month = $75.00
Contribution in a year = $75.00 × 12 = $900.00
His employer matched 16% of his contribution
Employer's contribution = 16% of $900.00
× 900
= 0.16 × 900 = $144.00
Total contribution = $900 + $144 = $1044
The total amount $1044 was contributed to the 401(k) at the end of the year.
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Attached the solution with work shown.
Answer:
The equation contains exact roots at x = -4 and x = -1.
See attached image for the graph.
Step-by-step explanation:
We start by noticing that the expression on the left of the equal sign is a quadratic with leading term , which means that its graph shows branches going up. Therefore:
1) if its vertex is ON the x axis, there would be one solution (root) to the equation.
2) if its vertex is below the x-axis, it is forced to cross it at two locations, giving then two real solutions (roots) to the equation.
3) if its vertex is above the x-axis, it will not have real solutions (roots) but only non-real ones.
So we proceed to examine the vertex's location, which is also a great way to decide on which set of points to use in order to plot its graph efficiently:
We recall that the x-position of the vertex for a quadratic function of the form is given by the expression:
Since in our case and
, we get that the x-position of the vertex is:
Now we can find the y-value of the vertex by evaluating this quadratic expression for x = -5/2:
This is a negative value, which points us to the case in which there must be two real solutions to the equation (two x-axis crossings of the parabola's branches).
We can now continue plotting different parabola's points, by selecting x-values to the right and to the left of the . Like for example x = -2 and x = -1 (moving towards the right) , and x = -3 and x = -4 (moving towards the left.
When evaluating the function at these points, we notice that two of them render zero (which indicates they are the actual roots of the equation):
The actual graph we can complete with this info is shown in the image attached, where the actual roots (x-axis crossings) are pictured in red.
Then, the two roots are: x = -1 and x = -4.
Answer:
135 cm³
Step-by-step explanation:
- To find volume: you multiply length*width*height
2.
3. 6*5*4 1/2
4. 6*5=30
5. 30*4 1/2=135
6. 135 cm³
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