MATHEMATICS COLLEGE

In the coordinate plane, triangle ABC has vertices A(1,-2), B(1,0.5), and C(2,1) and triangle DEF has vertices D(4,-3), E(4,2), and F(6,3). The triangles are similar because DEF is the image of ABC under a dilation with center (_,_) and scale factor ___.PLEASE HELPP​

Answers

Answer 1
Answer:

The triangle DEF is a dilation of triangle ABC with center of dilation at (0,0) and scale factor of 0.5.

What is Triangle?

A triangle is a three-sided polygon that consists of three edges and three vertices.

The ratio of the lengths of corresponding sides of triangles ABC and DEF.

AB and DE are corresponding sides, so:

AB/DE = (distance between A and B) / (distance between D and E)

= 2.5 / 5

= 0.5

BC and EF are corresponding sides, so:

BC/EF = (distance between B and C) / (distance between E and F)

=1.118 / 2.236

= 0.5

AC and DF are corresponding sides, so:

AC/DF = (distance between A and C) / (distance between D and F)

AC/DF = 2.236 / 4.472

= 0.5

We see that all three ratios are equal to 0.5.

Hence, the triangle DEF is a dilation of triangle ABC with center of dilation at (0,0) and scale factor of 0.5.

To learn more on Triangles click:

brainly.com/question/2773823

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Answer 2
Answer:

Answer:

(A) the center of dilation is at (-2,-1)

(E) the scale factor is 2

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What is the circumference of a circle with a diameter of 10 feet? Use 3.14 forTTd = 10A. 31.4 ftB. 62.8 ftC. 13.14 ftD. 15.7 ftPREVIOUS

Is 4 a solution to the equation 5+x=10? Explain.

Answers

9514 1404 393

Answer:

  no, it makes the equation false

Step-by-step explanation:

A "solution" is a value of x that makes the equation true. When we use 4 in place of x here, we get ...

  5 + 4 = 10

  9 = 10 . . . . . . . a false statement

The value x=4 does not make the equation true, so it is not a solution.

Answer:no

Step-by-step explanation:

Seventy percent of light aircraft that disappear while in flight in a certain country are subsequently discovered. Of the aircraft that are discovered, 60% have an emergency locator, whereas 90% of the aircraft not discovered do not have an emergency locator. Suppose that a light aircraft has disappeared.a) If it has an emergency locator, what is the probability that it will not be discovered?b) If it does not have an emergency locator, what is the probability that it will be discovered?c) If we consider 10 light aircraft that disappeared in flight with an emergency recorder, what is the probability that 7 of them are discovered?

Answers

Answer:

Figure out the various probabilities first, that will make the rest of the questions easier:

P(discovered) = .7

P(not discovered) = 1 - .7 = .3

P(locator|discovered) = .6

P(no locator|discovered) = 1 - .6 = .4

P(locator|not discovered) = 1 - .9 = .1

P(no locator|not discovered) = .9

P(discovered and locator) = .7 * .6 = .42

P(discovered and no locator) = .7 * .4 = .28

P(not discovered and locator) = .3 * .1 = .03

P(not discovered and no locator) = .3 * .9 = .27

a) The total probability that an aircraft has a locator is .42 + .03 = .45. So the probability it will not be discovered, given it has a locator, is .03/.45 = .067

b) The total probability that an aircraft does not have a locator is .28 + .27 = .55. So the probability it will be discovered, given it does not have a locator, is .28/.55 = .509

c) Probability that 7 are discovered = C(10,7) * P(discovered|locator)^7 * P(not discovered|locator)^3

We already figured out P(not discovered|locator) = .067, so P(discovered|locator) = 1-.067 = .933. C(10,7) = 10*9*8, so we can compute total probability: 10*9*8 * .933^7 * .067^3 = .133

Step-by-step explanation:

What number is 10 times as much as 90?

Answers

Answer:

900

Step-by-step explanation:

10 times as much means *10

so we have

90*10=900

Answer:

900

Step-by-step explanation:

10 x 90 = 900

OR

90 + 90 + 90 + 90 + 90 + 90 + 90 + 90 + 90 + 90 = 900

What is the value of x?

Answers

Answer:

x=-14

Step-by-step explanation:

The 2 angles are opposite of each other. This means that they are vertical angles, are they are congruent.

Since they are congruent, we can set them equal to each and solve for x.

9x+184=7x+156

To solve the equation, we want to find out what x is. In order to do this, we have to get x by itself. Perform the opposite of what is being done to the equation. Keep in mind, everything done to one side, has to be done to the other.

First, subtract 7x from both sides.

9x-7x+184=7x-7x+156

9x-7x+184=156

2x+184=156

Next, subtract 184 from both sides.

2x+184-184=156-184

2x=156-184

2x=-28

Finally, divide both sides by 2.

2x/2= -28/2

x=-28/2

x= -14

The value of X is -14.

please see the attached picture for full solution

Hope it helps

Good luck on your assignment

Solve the matrix equation for a, b, c, and d. [1 2] [a b] [6 5][3 4] [c d]= [19 8]

Answers

Answer:

The answer is "\bold{\left[\begin{array}{cc}a&b\nc&d\end{array}\right] = \left[\begin{array}{cc}7&-2\n -(1)/(2)&(7)/(2)\end{array}\right]}".

Step-by-step explanation:

\bold{\left[\begin{array}{cc}1&2\n3&4\end{array}\right] \left[\begin{array}{cc}a&b\nc&d\end{array}\right] = \left[\begin{array}{cc}6&5\n 19&8\end{array}\right]}

Solve the L.H.S part:

\left[\begin{array}{cc}1&2\n3&4\end{array}\right] \left[\begin{array}{cc}a&b\nc&d\end{array}\right]\n\n\n\left[\begin{array}{cc}a+2c&b+2d\n3a+4c&3b+4d\end{array}\right]

After calculating the L.H.S part compare the value with R.H.S:

\left[\begin{array}{cc}a+2c&b+2d\n3a+4c&3b+4d\end{array}\right]= \left[\begin{array}{cc}6&5\n 19&8\end{array}\right]} \n\n

\to a+2c =6....(i)\n\n\to b+2d =5....(ii)\n\n\to 3a+4c =19....(iii)\n\n\to 3b+4d = 8 ....(iv)\n\n

In equation (i) multiply by 3 and subtract by equation (iii):

\to 3a+6c=18\n\to 3a+4c=19\n\n\text{subtract}... \n\n\to 2c = -1\n\n\to c= - (1)/(2)

put the value of c in equation (i):

\to a+ 2 (- (1)/(2))=6\n\n\to a- 2 * (1)/(2)=6\n\n\to a- 1=6\n\n\to a =6 +1\n\n\to a = 7\n

In equation (ii) multiply by 3 then subtract by equation (iv):

\to 3b+6d=15\n\to 3b+4d=8\n\n\text{subtract...}\n\n\to 2d = 7\n\n\to d= (7)/(2)\n

put the value of d in equation (iv):

\to 3b+4 ((7)/(2))=8\n\n\to 3b+4 * (7)/(2)=8\n\n\to 3b+14=8\n\n\to 3b =8-14\n\n\to 3b = -6\n\n\to b= (-6)/(3)\n\n\to b= -2

The final answer is "\bold{\left[\begin{array}{cc}a&b\nc&d\end{array}\right] = \left[\begin{array}{cc}7&-2\n -(1)/(2)&(7)/(2)\end{array}\right]}".

Plz help me simply this

Answers

Answer:

Step-by-step explanation:

\sqrt[5]{u^(10)*p^(15)}*\sqrt[4]{u^(16)*p^(18)}= \sqrt[5]{u^(2*5)*p^(3*5)}*\sqrt[4]{u^(4*4)*p^(16*2)}\n\n\n=\sqrt[5]{(u^(2))^(5)*(p^(3))^(5)}*\sqrt[4]{(u^(4))^(4)*p^(4*4)*p^(2)}\n\n=\sqrt[5]{(u^(2))^(5)*(p^(3))^(5)}*\sqrt[4]{(u^(4))^(4)*(p^{4)^(4)}*p^(2)}\n\n=u^(2)*p^(3) * u^(4)*p^(4)*\sqrt[4]{p^(2)}\n\n=u^(2+4)*p^(3+4)*\sqrt[4]{p^(2)}\n\n= u^(6)p^(7)\sqrt[4]{p^(2)}
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