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stira [4]
2 years ago
8

Jacob finished his test 10 minutes before Mark. Which equation represents the time, j, Jacob spent on the test compared to the t

ime, m, Mark spent on the test?
Mathematics
1 answer:
Marina CMI [18]2 years ago
6 0

Answer:

The time Jacob spent on the test represented by J = (m + 10) minutes

where m is the number of minutes spent by Mark on the test

Step-by-step explanation:

Here, we want to give an equation which represents the time taken for Jacob to finish his test compared to the time m which Mark spent on the test.

Since Jacob finished 10 minutes before Mark, it means Mark actually took longer on the test.

Now, we are told that Mark spent m minutes on the test, the time spent by Jacob on the test is thus (m + 10) minutes

Let the amount of time spent by Jacob be J minutes. This in relation to the amount of time spent by Mark will be ;

J = (m + 10) minutes

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Graph a system of equations to solve log (−5.6x + 1.3) = −1 − x. Round to the nearest tenth. From the least to the greatest, the
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Answer:

  • See the graph attached
  • x₁ ≈ - 2.1
  • x₂ ≈ 0.2

Explanation:

To solve log (−5.6x + 1.3) = −1 − x graphycally, you must graph this system of equations on the same coordinate plane:

  • Equation 1: y = log (5.6x + 1.3)
  • Equatin2:    y = - 1 - x

1) To graph the equation 1 you can use these features of logarithmfunctions:

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  • Range: all real numbers (- ∞ , ∞)

  • x-intercept:

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  • y-intercept:

       x = 0 ⇒ log (0 + 1.3) = log (1.3) ≈ 0.11

  • Pick some other values and build a table:

        x            log (-5.6x + 1.3)

        -1           0.8

        -2           1.1

        -3           1.3

  • You can see such graph on the picture attached: it is the red curve.

2) Graphing the equation 2 is easier because it is a line: y = - 1 - x

  • slope, m = - 1 (the coeficient of x)
  • y - intercept, b = - 1 (the constant term)
  • x - intercept: y = 0 = - 1 - x ⇒ x = - 1
  • The graph is the blue line on the picture.

3) The solution or solutions of the equations are the intersection points of the two graphs. So, now the graph method just requires that you read the x coordinates of the intersection points. From the least to the greatest, rounded to the nearest tenth, they are:

  • <u><em>x₁ ≈ - 2.1</em></u>
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Length of larger square = 6cm
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