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Arturiano [62]
3 years ago
11

HELP NEEDED, GIVING BRAINLIEST!

Mathematics
1 answer:
Nataly_w [17]3 years ago
4 0

The correct answer is:

B. This is a dilation about (0, 0) with a scale factor of 4; A'(8, 4), B' (16, 4), C' (16, -12).

Step-by-step explanation:

Given

Dilation: D : (x,y) => (4x,4y)

And Vertices

A ( 2, 1 ), B ( 4, 1 ), C ( 4, -3 )

Applying dilation on all vertices

A ( 2, 1 ) => A'(4*2, 4*1) => A'(8,4)\\B ( 4, 1 ) = > B' (4*4 ,4*1) = > B'(16,4)\\C(4,-3) => C' (4*4 , 4*-3) => C'(16, -12)

To find the scale factor,

As we are multiplying each vertex coordinate by 4, the dilation factor is 4.

Moreover,

\frac{A'}{A} = \frac{(8,4)}{(2,1)} = (4,4)

Hence the scale factor is 4.

So,

The correct answer is:

B. This is a dilation about (0, 0) with a scale factor of 4; A'(8, 4), B' (16, 4), C' (16, -12).

Keywords: Dilation, Scale factor

Learn more about dilation at:

  • brainly.com/question/10435836
  • brainly.com/question/10541435

#LearnwithBrainly

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7. A movie theatre just opened 2 new theatres. One theatre has
Nataly_w [17]
The smallest number of seats that both theatres can have us 60
8 0
3 years ago
Can someone help me
erik [133]

Answer:

   6 < x < 23.206

Step-by-step explanation:

To properly answer this question, we need to make the assumption that angle DAC is non-negative and that angle BCA is acute.

The maximum value of the angle DAC can be shown to occur when points B, C, and D are on a circle centered at A*. When that is the case, the sine of half of angle DAC is equal to 16/22 times the sine of half of angle BAC. That is, ...

  (2x -12)/2 = arcsin(16/22×sin(24°))

  x ≈ 23.206°

Of course, the minimum value of angle DAC is 0°, so the minimum value of x is ...

  2x -12 = 0

  x -6 = 0 . . . . . divide by 2

  x = 6 . . . . . . . add 6

Then the range of values of x will be ...

  6 < x < 23.206

_____

* One way to do this is to make use of the law of cosines:

  22² = AB² + AC² -2·AB·AC·cos(48°)

  16² = AD² + AC² -2·AD·AC·cos(2x-12)

The trick is to maximize x while satisfying the constraints that all of the lengths are positive. This will happen when AB=AC=AD, in which case the equations be come ...

  22² = 2·AB²·(1-cos(48°))

  16² = 2·AB²·(1 -cos(2x-12))

The value of AB drops out of the ratio of these equations, and the result for x is as above.

4 0
2 years ago
Read 2 more answers
Raul bought a soft drink and a sandwich for $9.90 . Which is he price of each if the sandwich cost 3.5 times as much as the soft
Radda [10]
B. Sandwich costs $7.70 and the soda costs $2.20
8 0
3 years ago
In the figure, angle ZYX is measured in degrees. The area of the shaded sector can be determined using the formula StartFraction
tensa zangetsu [6.8K]

<u>The given options are:</u>

(A)the central angle measure of the sector divided by the total angle measure of a circle multiplied by the area of the circle will yield the area of the sector.

(B)the central angle measure of the sector divided by the total angle measure of a circle multiplied by the circumference of the circle will yield the area of the sector.

(C)the central angle measure of the sector multiplied by the area of the circle will yield the area of the sector.

(D)the central angle measure of the sector multiplied by the circumference of the circle will yield the area of the sector.

Answer:

(A)the central angle measure of the sector divided by the total angle measure of a circle multiplied by the area of the circle will yield the area of the sector.

Step-by-step explanation:

The area of the shaded sector can be determined using the formula:

\frac{m\angle ZYX}{360^\circ} \cdot \pi r^2

m\angle XYZ=$Central angle of XYZ\\\pi r^2$=Area of a Circle

360^\circ =$Total Angle

Therefore, the formula is:

\dfrac{m\angle ZYX}{360^\circ} \cdot \pi r^2\\\text{Area of XYZ}=\dfrac{\text{Cental Angle of XYZ}}{\text{Total Angle}} X \text{Area of the Circle}

Therefore, the formula is best explained by Option A.

7 0
3 years ago
The angles 3x+6 and 5x + 6 are supplements. What are the two angles
yarga [219]

Answer:

x = 21

Step-by-step explanation:

<u>Step 1:  Make an expression</u>

Since they are supplements, that means that they add up to 180 degrees.

3x + 6 + 5x + 6 = 180

<u>Step 2:  Combine like terms</u>

3x + 6 + 5x + 6 = 180

(3x + 5x) + (6 + 6) = 180

8x + 12 = 180

<u>Step 3:  Subtract 12 from both sides</u>

8x + 12 - 12 = 180 - 12

8x = 168

<u>Step 4:  Divide both sides by 8</u>

8x / 8 = 168 / 8

x = 21

Answer:  x = 21

6 0
3 years ago
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