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1 year ago

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On a coordinate plane, a triangle has points A prime (negative 2, 10), B prime (negative 6, 4), and (negative 10, 8). What is th

e pre-image of vertex A' if the image shown on the graph was created by a reflection across the line y = x?

1 answer:

schepotkina [342]1 year ago

8 0

Answer:

A(10,-2).

Step-by-step explanation:

It is given that, on a coordinate plane, a triangle has points A'(-2, 10), B'(-6, 4), and C'(-10, 8).

We need to find the pre-image of vertex A' if the image shown on the graph was created by a reflection across the line y = x.

If a figure reflected across the line y=x, then

$A(x,y)\rightarrow A'(y,x)$

It is given that A'(-2,10).

$A(y,x)=A'(-2,10)$

On comparing both sides, we get

$x=10,y=-2$

Therefore, the coordinates of preimage of A' are (10,-2).

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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

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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:

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

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1 year ago

Find a right triangle that has legs with your irrational Lengths and a hypotenuse with a rational Length

cluponka [151]

gg easy

the legs of a triangle are related as $a^2+b^2=c^2$ wehre a, b, and c are the legs and the hypotonuse of a triangle respectively

let's find some stuff

one easy way is to find a rational value for c find values of a and b

lets pick c=5

$a^2+b^2=5^2$

$a^2+b^2=25$

now split up 25 into 2 things that don't have rational square roots

if we say $a^2=19$ and $b^2=6$ then we get

$a=\sqrt{19}$ and $b=\sqrt{6}$ (which are both irrational)

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1 year ago

Tad and Janice are installing new wood floors in a house. Tad can install 144 square feet of flooring in three hours. Janice can

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Answer:

1.) How many square feet of flooring can Tad install in eight hours? 384 square feet

2.) How many square feet of flooring can Janice install in five hours? 480 square feet

3.) If they each work for 12 hours, how many square feet of flooring can they install? 1,728 square feet.

I hope i helped alot :)

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1 year ago

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Juanita receives her paycheck and knows that her gross pay and federal tax are correct. Using the fact that Social Security tax

bagirrra123 [75]

Answer:

The net pay is correct.

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2 years ago

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Suppose 1000 people enter a chess tournament. Use a rooted tree model of the tournament to determine how many games must be play

Vlada [557]

Answer: 999 games

Step-by-step explanation:

There are many ways to illustrate the rooted tree model to calculate the number of games that must be played until only one player is left who has not lost.

We could go about this manually. Though this would be somewhat tedious, I have done it and attached it to this answer. Note that when the number of players is odd, an extra game has to be played to ensure that all entrants at that round of the tournament have played at least one game at that round. Note that there is no limit on the number of games a player can play; the only condition is that a player is eliminated once the player loses.

The sum of the figures in the third column is 999.

We could also use the formula for rooted trees to calculate the number of games that would be played.

$i=\frac{l - 1}{m - 1}$

where i is the number of "internal nodes," which represents the number of games played for an "<em>m</em>-ary" tree, which is the number of players involved in each game and l is known as "the number of leaves," in this case, the number of players.

The number of players is 1000 and each game involves 2 players. Therefore, the number of games played, i, is given by

$i=\frac{l - 1}{m - 1} = i=\frac{1000 - 1}{2 - 1} = \frac{999}{1} =999$

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1 year ago