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2 years ago

If e = 9 cm and f = 40 cm, what is the length of g?

Mathematics

1 answer:

rewona [7]2 years ago

8 0

(9,40,41) is a Pythagorean Triple, farther down the list than teachers usually venture.

Answer: D. 41 cm

There's a subset of Pythagorean Triples where the long leg is one less than the hypotenuse,

a^2+b^2 = (b+1)^2

a^2 + b^2 = b^2 + 2b +1

a^2=2b+1

So we get one for every odd number, since the square of an odd number is odd and the square of an even number is even.

b = (a^2 - 1)/2

a=3, b=(3^2-1)/2=4, c=b+1=5

a=5, b=(5^2-1)/2 =12, c = 13

a=7, b=24, c=25

a=9, b=40, c=41

a=11, b=60, c=61

a=13, b=84, c=85

It's good to be able to recognize Pythagorean Triples when we see them.

Otherwise we'd have to work the calculator:

√(9² + 40²) = √1681 = 41

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A stone is dropped into a barrel of water and sinks to the bottom. The ball is completely covered by water. By how much does the

Rom4ik [11]

Answer:

Answer: 5/12 or approx. 0.42

Step-by-step explanation:

The ball will displace as much water as its volume.

Meaning, the volume of the ball and the volume of the increase in water in the barrel will be equal.

Volume of a sphere:

$V_s=\frac{4}{3} \pi r^3$

The radius is half the diameter. The diameter of the sphere is 10, thus:

$r = d/2 = 10/2 = 5$

5^3 = 5*5*5 = 25*5 = 125

$V_s=\frac{4}{3} \pi * 5^3=\frac{4}{3} \pi * 125$

The volume of a cylinder, which will be the shape of the increase in water, is the following:

$V_c=\pi r^2 h$

We know the radius r, as we know the diameter.

$r=d/2=40/2=20$

$V_c=\pi r^2 h=\pi h * 20^2 = \pi h * 400$

We are looking for the height of the cylinder, h, as that will be the height of the water rise.

Since we know these 2 volumes are the same, we'll set them equal to each other and solve the equation:

$V_s = V_c$

$\frac{4}{3} * 125 * \pi = 400 * h * \pi$

We can get rid of pi by dividing both sides by pi:

$\frac{4}{3} * 125 = 400 * h$

And now divide both sides by 400:

$\frac{4}{3} * \frac{125}{400}= h$

Just reversing it and putting h to the left:

$h = \frac{4}{3} * \frac{125}{400} = \frac{4 * 125}{3 * 400}$

I see that I can divide both the numerator and the denominator by 4:

$h =\frac{125}{3 * 100}= \frac{125}{300}$

I'll now divide both the numerator and the denominator by 25 to simplify the expression:

$h=\frac{125}{300} =\frac{125 / 25}{300 / 25} = \frac{5}{12}$

Answer: The water rises by 5/12 (five twelfths).

If I want an approximate decimal answer, I can simply run this expression in a calculator:

$\frac{5}{12}$ ≈ $0.416666667$ ≈ $0.42$

7 0

1 year ago

A salesman’s commission on a $150,000 sale is $3,000. What percent is his commission?

Elenna [48]

Answer:

The commission percentage is 2%

Step-by-step explanation:

To find the percentage of a commission, start by dividing the commission amount by the total amount sold.

3,000/150,000 = .02 = 2%

5 0

1 year ago

Kay buys 12 pounds of apples. Each pound costs $3.if she gives the cashier two $20 bills, how much change should she receive.

zlopas [31]

12 pounds x $3 = $36

$40 - $36 = $4

7 0

1 year ago

What number must we multiply by $-\frac23$ to get a product of $\frac34$?

stich3 [128]

Let x be unknown number. If number x is multiplied by $-\dfrac{2}{3}$ and the product is equal to $\dfrac{3}{4},$ then

$x\cdot \left(-\dfrac{2}{3}\right)=\dfrac{3}{4}.$

To find x you should divide $\dfrac{3}{4}$ by $-\dfrac{2}{3}:$

$x=\dfrac{\dfrac{3}{4}}{-\dfrac{2}{3}}=\dfrac{3}{4}\cdot \left(-\dfrac{3}{2}\right)=-\dfrac{3\cdot 3}{4\cdot 2}=-\dfrac{9}{8}.$

Answer: $x=-\dfrac{9}{8}$

7 0

2 years ago

Ralph is paid twice per month. His work offers a flexible-spending account to be used for medical expenses. This plan allows Ral

slava [35]

In this question, we're assuming Ralph had 0 in his saving funds to start with.

The glasses cost 1200 dollars.

There are 12 months in a year.

Each month, Ralph is given his check two times, that means that Ralph receives his check 2(12), or 24, times per year.

Divide 1200 (the cost of the glasses) by 24 (the amount of times Ralph is given his check)

1200 / 24
Divide both numerator and denominator by 12
100 / 2
Simplify
50

Ralph should have put 50 dollars per pay check to pay for the glasses.

A is your answer.

Have an awesome day! :)

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2 years ago