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2 years ago

Given the image below, what is the image of C after a dilation with a scale factor of 3

Mathematics

1 answer:

Ne4ueva [31]2 years ago

6 0

Answer: The coordinates of point C after the dilation are (-2, 5)

Step-by-step explanation:

I guess that you want to find where the point C ends after the dilation.

Ok, if we have a point (x, y) and we do a dilation with a scale A around the point (a,b), then the dilated point will be:

(a + A*(x - a), b + A*(y - b))

In this case we have:

(a,b) = (2,1) and A = 3.

And the coordinates of point C, before being dilated, are: (1, 2)

Then the new location of the point C will be:

C' = (1 + 3*(1 - 2), 2 + 3*(2 - 1)) = (1 -3, 2 + 3) = (-2, 5)

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A player of a video game is confronted with a series of four opponents and an 80% probability of defeating each opponent. Assume

mixer [17]

Answer:

(a) 0.4096

(b) 0.64

Step-by-step explanation:

The probability that the player wins is,

$P(W)=0.80$

Then the probability that the player losses is,

$P(L)=1-P(W)=1-0.80=0.20$

The player is playing the video game with 4 different opponents.

It is provided that when the player is defeated by an opponent the game ends.

All the possible ways the player can win is: {L, WL, WWL, WWWL and WWWW)

(a)

The results from all the 4 opponents are independent, i.e. the result of a game played with one opponent is unaffected by the result of the game played with another opponent.

The probability that the player defeats all four opponents in a game is,

P (Player defeats all 4 opponents) = $P(W)\times P(W)\times P(W)\times P(W)=[P(W)]^{4} =(0.80)^{4}=0.4096$

Thus, the probability that the player defeats all four opponents in a game is 0.4096.

(b)

The probability that the player defeats at least two opponents in a game is,

P (Player defeats at least 2) = 1 - P (Player losses the 1st game) - P (Player losses the 2nd game) = $1-P(L)-P(WL)$

$=1-(0.20)-(0.80\times0.20)\\=1-0.20-0.16\\=0.64$

Thus, the probability that the player defeats at least two opponents in a game is 0.64.

(c)

Let X = number of times the player defeats all 4 opponents.

The probability that the player defeats all four opponents in a game is,

P(WWWW) = 0.4096.

Then the random variable $X\sim Bin(n=3, p=0.4096)$

The probability distribution of binomial is:

$P(X=x)={n\choose x}p^{x} (1-p)^{n-x}$

The probability that the player defeats all the 4 opponents at least once is,

P (X ≥ 1) = 1 - P (X < 1)

= 1 - P (X = 0)

$=1-[{3\choose 0}(0.4096)^{0} (1-0.4096)^{3-0}]\\=1-[1\times1\times (0.5904)^{3}\\=1-0.2058\\=0.7942$

Thus, the probability that the player defeats all the 4 opponents at least once is 0.7942.

3 0

2 years ago

In isosceles △ABC (AC = BC) with base angle 30° CD is a median. How long is the leg of △ABC, if sum of the perimeters of △ACD an

SIZIF [17.4K]

Note necessary facts about isosceles triangle ABC:

The median CD drawn to the base AB is also an altitude to tha base in isosceles triangle (CD⊥AB). This gives you that triangles ACD and BCD are congruent right triangles with hypotenuses AC and BC, respectively.
The legs AB and BC of isosceles triangle ABC are congruent, AC=BC.
Angles at the base AB are congruent, m∠A=m∠B=30°.

1. Consider right triangle ACD. The adjacent angle to the leg AD is 30°, so the hypotenuse AC is twice the opposite leg CD to the angle A.

AC=2CD.

2. Consider right triangle BCD. The adjacent angle to the leg BD is 30°, so the hypotenuse BC is twice the opposite leg CD to the angle B.

BC=2CD.

3. Find the perimeters of triangles ACD, BCD and ABC:

$P_{ACD}=AC+CD+AD=2CD+CD+AD=3CD+AD;$

$P_{BCD}=BC+CD+BD=2CD+CD+AD=3CD+AD;$

$P_{ABC}=AC+BC+AB=2CD+2CD+AD+BD=4CD+2AD.$

4. If sum of the perimeters of △ACD and △BCD is 20 cm more than the perimeter of △ABC, then

$P_{ACD}+P_{BCD}=P_{ABC}+20,\\ \\3CD+AD+3CD+AD=4CD+2AD+20,\\ \\6CD+2AD=4CD+2AD+20,\\ \\2CD=20.$

5. Since AC=BC=2CD, then the legs AC and BC of isosceles triangles have length 20 cm.

Answer: 20 cm.

8 0

2 years ago

Read 2 more answers

Korey starts a small carwash business to save up some cash. He decides to offer two different price packages to his clients. Pac

rosijanka [135]

Answer:

Package A

Step-by-step explanation:

Hello there!

The reason that package A is a better deal is beacause it goes down by a fixed rate, not by a percentage. If you get 15 carwashes, you will pay nothing for the 15th, but even if you washed your car 100 times with Package B, you would still pay something!

Have a great day!

5 0

2 years ago

In the expression 4 (2m-n), determine which of the following best describes the role of (2m-n).

Dmitrij [34]

Answer:

Step-by-step explanation:

(2m-n) is a factor of 4(2m-n)

4 0

2 years ago

Two wires with lengths of 448 cm and 616 cm are to be cut into pieces of all the same length without a remainder. Find the great

Y_Kistochka [10]

Answer:

56 cm

Step-by-step explanation:

We need ro find the GCD of these numbers. In finding the GCD, we list the multiples of the number, beginning with the smallest number. Here, the

The factors of 616=2*2*2*7*11

The factors of 448 =2*2*2*2*2*2*7

Common factors in both are 2*2*2*7=56

Therefore, the greatest possible length is 56 cm

6 0

2 years ago