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tatiyna
2 years ago
13

Screen-printing a batch of shirts requires 3 minutes per shirt in addition to 19.87 minutes of initial set-up time. How long doe

s it take to screen-print a batch of 143 shirts? Write and solve an equation to find the answer.
Mathematics
1 answer:
Svetlanka [38]2 years ago
4 0

Answer:

So the equation and solution will be:

Total time taken = 3 × number of shirts + 19.87 min (setup time)

                            = 3 × 143 + 19.87

                           =429+19.87

                             =448.87

Step-by-step explanation:

From the question statement, it is clear that

  • screen-printing a batch of shirts requires 3 minutes per shirt in addition to 19.87 minutes of initial set-up time.

we have to determine how long does it take to screen-print a batch of 143 shirts.

so the equation and solution will be:

Total time taken = 3 × number of shirts + 19.87 min (setup time)

                           = 3 × 143 + 19.87

                           =429+19.87

                             =448.87  min

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3 years ago
If y=5x - 2 were changed to y=3/4 x- 2, how would the graph of the new function compare with the first one?
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3 years ago
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zavuch27 [327]

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 x^2, 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 f(x)=ax^2+bx+c is given by the expression: x_v=\frac{-b}{2a}

Since in our case a=1 and b=5, we get that the x-position of the vertex is: x_v=\frac{-b}{2a} \\x_v=\frac{-5}{2(1)}\\x_v=-\frac{5}{2}

Now we can find the y-value of the vertex by evaluating this quadratic expression for x = -5/2:

y_v=f(-\frac{5}{2})\\y_v=(-\frac{5}{2} )^2+5(-\frac{5}{2} )+4\\y_v=\frac{25}{4} -\frac{25}{2} +4\\\\y_v=\frac{25}{4} -\frac{50}{4}+\frac{16}{4} \\y_v=-\frac{9}{4}

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We can now continue plotting different parabola's points, by selecting x-values to the right and to the left of the x_v=-\frac{5}{2}. 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):

f(-1) = (-1)^2+5(-1)+4= 1-5+4 = 0\\f(-4)=(-4)^2+5(-4)_4=16-20+4=0

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.

5 0
3 years ago
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