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Lana71 [14]
3 years ago
9

In the diagram, the circle will be dilated by a scale factor of 3 about the origin. The points C, A, and B map to C', A', and B'

after the dilation. What is the length of ? Use the distance formula to help you decide

Mathematics
1 answer:
stellarik [79]3 years ago
4 0
Original coordinates of the points:
A (8,15) ; B (12,13) ; C (8,10)

Dilated scale factor of 3.

A ⇒ 3x = 3(8) = 24 ; 3y = 3(15) = 45 ⇒ A' (24,45)
B ⇒ 3x = 3(12) = 36 ; 3y = 3(13) = 39 ⇒ B' (36, 39)
C ⇒ 3x = 3(8) = 24 ; 3y = 3(10) = 30 ⇒ C' (24, 30)

The given image forms a right triangle. So, I'll get the short leg and long leg of the right triangle to solve for the hypotenuse, length of CB.

Short leg: y value of B and C
39 - 30 = 9

Long leg: x value of B and C
36 - 24 = 12

a² + b² = c²
9² + 12² = c²
81 + 144 = c²
225 = c²
√225 = √c²
15 = c

The length of CB is 15 units.
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Please help me I’m super confused on this problem!
Lorico [155]

Answer:

m < amc = 54°

Step-by-step explanation:

< amb and < bmc are complementary angles whose sum equals 90°.

Therefore, to find the value of 2x°, we must first solve for x.

We can establish the following equality statement:

< amb + < bmc = < amc

< 2x° + (x + 9)° = 90°

Combine like terms:

2x° + x° + 9° = 90°

3x° + 9° = 90°

Subtract 9 from both sides:

3x° + 9° - 9° = 90° - 9°

3x = 81°

Divide both sides by 3 to solve for x:

3x/3 = 81°/3

x = 27°.

Since x = 27°, substitute its value into 2x° to find m < amc:

2x° = 2(27°) = 54°

Therefore, m < amc = 54°

Please mark my answers as the Brainliest, if you find this helpful :)

5 0
2 years ago
Pls find the data value no links please!
Varvara68 [4.7K]

Answer:

15

Step-by-step explanation:

5 0
3 years ago
For f(x) = 2x + 3 and g(x) = x2 – 8, find (f + g)(x).
Nataly_w [17]

Answer:

x² + 2x - 5

Step-by-step explanation:

(f + g)(x) = f(x) + g(x)

f(x) + g(x)

= 2x + 3 + x² - 8 ← collect like terms

= x² + 2x - 5

8 0
3 years ago
A membership committee of three is formed from four eligible members. Let the eligible members be represented by A, B, C, and D.
yKpoI14uk [10]

The correct statement is:

  • There are four ways to choose the committee.
  • There are three ways to form the committee if person D must be on it.
  • If persons B and C must be on the committee, there are two ways to form the committee.

It is given that:

A membership committee of three is formed from four eligible members.

1) There are four ways to choose the committee.

This statement is true.

Since we have to choose 3 members out of the 4 members so we can use the method of combination.

2) There are three ways to form the committee if person D must be on it.

This statement is also true.

Since D has to be in the committee, this means we have to choose 2 more people out of the three people to form the committee.

3) If seven members are eligible next year, then there will be fewer combinations.

This statement is wrong.

Since we have to choose 3 members out of 7 members so the number of possible combinations will be:

There are 35 combinations possible.

4) If persons B and C must be on the committee, there are two ways to form the committee.

If B and C have to be in the committee then we have to choose just one person out of the two people left.

Hence, the statement is true.

5) If persons A and C must be on the committee, then there is only one way to form the committee.

If A and C have to be on the committee then as in the last option we have to choose any one of the two-person left.

So possible number of ways is 2.

Hence, the statement is false.

Learn more about committee here: brainly.com/question/425830

#SPJ4

<em>Your question is incomplete. Please read below to find the missing content.</em>

<em />

A membership committee of three is formed from four eligible members. Let the eligible members be represented by A, B, C, and D. The possible outcomes include S = {ABC, ABD, ACD, BCD}.

Which statements about the situation are true? Check all that apply.

There are four ways to choose the committee.

There are three ways to form the committee if person D must be on it.

If seven members are eligible next year, then there will be fewer combinations.

If persons B and C must be on the committee, there are two ways to form the committee.

If persons A and C must be on the committee, then there is only one way to form the committee.

8 0
2 years ago
F(x)=4(x-1)^2-1 axis of symmetry
Levart [38]
The vertex of this parabola has coordinates (1,-1).
The axis symmetry goes trough the vertex. The equation of the axis of symmetry is x=1.
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