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3 years ago

Jim is running on a trail that is 5/4 of a mile long. So far he has run 2/3 of the trail. How many miles has he run so far?

1 answer:

7 0

You have to subtract 5/4 by 2/3 but in order to do that you must find a common denominator or least common multiple so the least common denominator of 4 and 3 is 12 so you have to multiply 4 by 3 and three by 4 to make both denominators 12 but you have to do the same thing on the top as you did the bottom so: 5/4*3= 15/12 and 2/3*4=8/12 Then 15/12-8/12 is 7/12 so Jim has to run 7/12 more

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Select the graph for the solution of the open sentence. Click until the correct graph appears.

marin [14]

The solution of the inequality will be x > 2 and x < -2. And the graph is drawn below.

<h3>What is inequality?</h3>

Inequality is defined as an equation that does not contain an equal sign.

The inequality is given below.

3|x| > 6

By solving the equation, we have

|x| > 2

x > 2

x < -2

Then the graph will be drawn.

More about the inequality link is given below.

brainly.com/question/19491153

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2 years ago

Solve for x: 2/3=8/x+6

Tresset [83]

Answer:

x = 6

Step-by-step explanation:

2/3=8/x+6

Using cross products

2 * (x+6) = 3*8

2(x+6) = 24

Divide by 2

x+6 =12

Subtract 6

x = 6

8 0

2 years ago

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Vitek1552 [10]

Answer:

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Step-by-step explanation:

8 0

1 year ago

Where should the point P be chosen on line segment AB so as to maximize the angle θ? (Assume a = 4 units, b = 5 units, and c = 9

taurus [48]

From the figure, let the distance of point P from point A on line segment AB be x and let the angle opposite side a be M and the angle opposite side c be N.

Using pythagoras theorem,
$\tan M= \frac{a}{b-x} \\ \\ M=\tan^{-1}\left(\frac{a}{b-x}\right)$
and
$\tan N= \frac{c}{x} \\ \\ N=\tan^{-1}\left(\frac{c}{x}\right)$

Angle θ is given by
$\theta=180-M-N \\ \\ =180-\tan^{-1}\left(\frac{a}{b-x}\right)-\tan^{-1}\left(\frac{c}{x}\right)$

Given that a = 4 units, b = 5 units, and c = 9 units, thus
$\theta=180-\tan^{-1}\left(\frac{4}{5-x}\right)-\tan^{-1}\left(\frac{9}{x}\right)$

To maximixe angle θ, the differentiation of <span>θ with respect to x must be equal to zero.
i.e.
$\frac{d\theta}{dx} = -\frac{4}{x^2-10x+41} + \frac{9}{x^2+81} =0 \\ \\ -4(x^2+81)+9(x^2-10x+41)=0 \\ \\ -4x^2-324+9x^2-90x+369=0 \\ \\ 5x^2-90x+45=0 \\ \\ x^2-18x+9=0 \\ \\ x=9\pm6 \sqrt{2}$

Given that x is a point on line segment AB, this means that x is a positive number less than 5.

Thus
$x=9-6 \sqrt{2}=0.5147$

Therefore, The distance from A of point P, so that </span>angle θ is maximum is 0.51 to two decimal places.

6 0

3 years ago

A stack of 5 books weighs 9.5 pounds. If each book weighs the same amount, how much does each book weigh?

hjlf

Answer: The same amount of book weighed is 14.5.

Step-by-step explanation:

So there is 5 books

9.5 pounds

9.5 + 5 = 14.5

So, Each book weighs about 14.5.

8 0

2 years ago