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2 years ago

Mike has a total of 50 quarters and dimes. The coins total value is $10.55. How many quarters

Mathematics

1 answer:

Mariana [72]2 years ago

3 0

Answer:

Mike will only need 42 quarters to make 10.50

Step-by-step explanation:

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-12 + 18. = 70<br><br> complete the square

FromTheMoon [43]

-12 + 18 = 70 - 64 or(-12+18)+(6*12)-2

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3 years ago

Choose the answer based on the most efficient method as presented in the lesson.

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The next step is to add 9

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Use the figure to answer the questions below.

alina1380 [7]

Answer:

parallelogram
x = 5
60 units

Step-by-step explanation:

A. Opposite sides are the same length, so the figure is a parallelogram.

B. Diagonals of a parallelogram cross at their midpoints, so ...

9x +3 = 10x -2

5 = x . . . . . . . . add 2-9x to both sides

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3 years ago

You are a lifeguard and spot a drowning child 60 meters along the shore and 40 meters from the shore to the child. You run along

sukhopar [10]

Answer:

The lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

Step-by-step explanation:

This is a problem of optimization.

We have to minimize the time it takes for the lifeguard to reach the child.

The time can be calculated by dividing the distance by the speed for each section.

The distance in the shore and in the water depends on when the lifeguard gets in the water. We use the variable x to model this, as seen in the picture attached.

Then, the distance in the shore is d_b=x and the distance swimming can be calculated using the Pithagorean theorem:

$d_s^2=(60-x)^2+40^2=60^2-120x+x^2+40^2=x^2-120x+5200\\\\d_s=\sqrt{x^2-120x+5200}$

Then, the time (speed divided by distance) is:

$t=d_b/v_b+d_s/v_s\\\\t=x/4+\sqrt{x^2-120x+5200}/1.1$

To optimize this function we have to derive and equal to zero:

$\dfrac{dt}{dx}=\dfrac{1}{4}+\dfrac{1}{1.1}(\dfrac{1}{2})\dfrac{2x-120}{\sqrt{x^2-120x+5200}} \\\\\\\dfrac{dt}{dx}=\dfrac{1}{4} +\dfrac{1}{1.1} \dfrac{x-60}{\sqrt{x^2-120x+5200}} =0\\\\\\ \dfrac{x-60}{\sqrt{x^2-120x+5200}} =\dfrac{1.1}{4}=\dfrac{2}{7}\\\\\\ x-60=\dfrac{2}{7}\sqrt{x^2-120x+5200}\\\\\\(x-60)^2=\dfrac{2^2}{7^2}(x^2-120x+5200)\\\\\\(x-60)^2=\dfrac{4}{49}[(x-60)^2+40^2]\\\\\\(1-4/49)(x-60)^2=4*40^2/49=6400/49\\\\(45/49)(x-60)^2=6400/49\\\\45(x-60)^2=6400\\\\$

$x$

As $d_b=x$ , the lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

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3 years ago

Drilon got 63 out of 72 correct in his test. What fraction of the marks did he get correct?

tatyana61 [14]

Answer:

87.5%

Step-by-step explanation:

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