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3 years ago

In 42 minutes, Mr. Goo can run 6 miles. How long does it take him to run 1 mile?

Mathematics

2 answers:

valkas [14]3 years ago

6 0

Answer:

7 min

Step-by-step explanation:

Sedbober [7]3 years ago

5 0

Answer:

7 Minutes

Step-by-step explanation:

If you divide 42 by 6, you get 7.

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In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD= 2 cm.

konstantin123 [22]

Consider right triangle ΔABC with legs AC and BC and hypotenuse AB. Draw the altitude CD.

1. Theorem: The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.

According to this theorem,

$BC^2=BD\cdot AB.$

Let BC=x cm, then AD=BC=x cm and BD=AB-AD=3-x cm. Then

$x^2=(3-x)\cdot 3,\\ \\x^2=9-3x,\\ \\x^2+3x-9=0,\\ \\D=3^2-4\cdot (-9)=9+36=45,\\ \\\sqrt{D}=\sqrt{45}=3\sqrt{5},\\ \\x_1=\dfrac{-3-3\sqrt{5} }{2}0.$

Take positive value x. You get

$AD=BC=\dfrac{-3+3\sqrt{5} }{2}\ cm.$

2. According to the previous theorem,

$AC^2=AD\cdot AB.$

Then

$AC^2=\dfrac{-3+3\sqrt{5} }{2}\cdot 3=\dfrac{-9+9\sqrt{5} }{2},\\ \\AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.$

Answer: $AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.$

This solution doesn't need CD=2 cm. Note that if AB=3cm and CD=2cm, then

$CD^2=AD\cdot DB,\\ \\2^2=AD\cdot (3-AD),\\ \\AD^2-3AD+4=0,\\ \\D$

This means that you cannot find solutions of this equation. Then CD≠2 cm.

8 0

4 years ago

Read 2 more answers

Find the inverse function for

kifflom [539]

$\bf \stackrel{f(x)}{y}=\sqrt{2x-6}\qquad \qquad \stackrel{f^{-1}(x)}{y}=\cfrac{x^2+6}{2}$

that is correct hmmmm, yes, I think the restriction is also correct, it has to be x > 0, because, the domain on the original, has a restriction of x⩾3, otherwise the radicand turns negative.

now, the graph of that original function is a parabola sideways opening to the right, if you include both sides of the vertex of the parabola, it will not pass the vertical-line-test and not be a function, but if you restrict it to only positive roots, so it'll only be on the 1st quadrant, then it functions ok.

that means, the range of the original function, has to stick to only 0 or positive root values, now, recall that the range of the original is the domain of the inverse. Therefore, the domain of the inverse, will have to stick to only 0 or positive values, since it's bound to the same restriction as the original's range.

notice the picture below of both, the dashed section is the positive range for each, if you include it, the original will fail the vertical-line-test, and the inverse will fail the horizontal-line-test.

recall that for a function to have an inverse, they both must pass the vertical and horizontal line test, or be a one-to-one functions.

6 0

4 years ago

The sum of x and ten is twenty( write the equation

iren [92.7K]

Answer:

2x10=20 X=2

Step-by-step explanation:

Please mark brainliest

5 0

3 years ago

Read 2 more answers

What is 11.25 as a fraction?

s2008m [1.1K]

11.25 is 11 1/4 because if you were to do 1 divided by 4, you would find that the answer is 0.25. But if you need an improper fraction, you would get 45/4 because if you were to put 11 times 4, you would get 44, and 44+1=45. Then you put that on the numerator spot, and you will get 45/4 for improper fraction.

7 0

4 years ago

A cubical container measures 9 ft on each edge. What does it cost to fill the container at $2.58 per cubic ft?

Oxana [17]

Answer:

1,880.82

Step-by-step explanation:

4 0

3 years ago