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Softa [21]
4 years ago
7

Ms. Hussain told her class that some dilations make figures bigger, some make figures smaller, and some make figures stay the sa

me size.
Select two of the scale factors that support Ms. Hussain's claim that some dilations make figures smaller.

Mathematics
1 answer:
bearhunter [10]4 years ago
4 0

Answer:

To make the figures smaller, scale factor must be divided.  

Step-by-step explanation:

1) Firstly, consider a pentagon ABCDE, if we take the scale factor 1\3, the dilations will be smaller.

As distance between A and B = 6

after dilation, distance between A' and B' = 2

Similarly continuing for each side, we get the figure smaller A'B'C'D'E' which is smaller than the original figure.

2) Secondly, consider a hexagon ABCDEF, if we take scale factor 1\2, the dilated figure will be smaller.

A s distance between A and B = 4

After dilations, distance between A' and B' = 2

Similarly continuing for each side, we get the figure A'B'C'D'E'F' which is smaller than the original figure.

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zepelin [54]
<h2>2.</h2><h3>Given</h3>
  • y=2x(2 -3x)
<h3>Find</h3>
  • y·y'' +x·y' -16 in simplest form
<h3>Solution</h3>

It is convenient to expand the expression for y to ease determination of derivatives.

... y = 4x -6x²

... y' = 4 -12x

... y'' = -12

Then the differential expression can be written as

... (4x -6x²)(-12) +x(4 -12x) -16

... = -48x +72x² +4x -12x² -16

... = 60x² -44x -16

<h2>3.</h2><h3>Given</h3>
  • y = 16/x +x³/3
<h3>Find</h3>
  • the turning points
  • the extreme(s)
<h3>Solution</h3>

The derivative is

... y' = -16x^-2 + x^2

This is zero at the turning points, so

... -16/x^2 +x^2 = 0

... x^4 = 16 . . . . . . . . . multiply by x^2, add 16

... x^2 = ±√16 = ±4

We're only interested in the real values of x, so

... x = ±√4 = ±2 . . . . . . . x-values at the turning points

Then the turning points are

... y = 16/-2 +(-2)³/3 = -8 +-8/3 = -32/3 . . . . for x = -2

... y = 16/2 + 2³/3 = 8 +8/3 = 32/3 . . . . . . . for x = 2

The maximum is (-2, -10 2/3); the minimum is (2, 10 2/3).

3 0
4 years ago
Which statements are true? Select all that apply.
AveGali [126]

cosθ = cotθ/cscθ is a true statement. The answer is option B

<h3>How to determine which of the trigonometric statements are true?</h3>

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles

A. tan²θ = 1 - sec²θ

tan²θ = 1 - sec²θ  

tan²θ = 1 - 1/cos²θ               (Note: sec²θ  = 1/cos²θ)

tan²θ = (cos²θ- 1)/cos²θ

tan²θ =  -sin²θ/cos²θ            (Note: cos²θ- 1  =  -sin²θ)

tan²θ = -tan²θ

This statement is not true

B. cosθ = cotθ/cscθ

cosθ = cotθ/cscθ

cosθ = (1/tanθ) / (1/sinθ)

cosθ = (cosθ/sinθ).sinθ

cosθ = cosθ

This statement is true

C. 1/sec²θ   = sin²θ + 1  

1/sec²θ   = 1/(1/cos²θ)

1/sec²θ  = cos²θ

1/sec²θ  = 1 - sin²θ

This statement is not true

D. sec²θ - 1 = 1/cot²θ  

sec²θ - 1 = 1/cos²θ - 1

sec²θ - 1 = (1-cos²θ)/cos²θ

sec²θ - 1 = sin²θ/cos²θ

sec²θ - 1 = tan²θ

This statement is not true

E. sinθ cscθ  = tan θ  

sinθ cscθ  = tan θ

sinθ cscθ = sinθ (1/sinθ)

sinθ cscθ = 1  

This statement is not true

Therefore, the true statement is cosθ = cotθ/cscθ

Learn more about Trigonometry on:

brainly.com/question/29529966

#SPJ1

7 0
2 years ago
What is the math question 2/5+?=7/10
KIM [24]
4/7 is the answer to your question
7 0
3 years ago
Anyone know? been stuck on it for 5 minutes now lol
WARRIOR [948]
The answer is the 4th or 119
3 0
3 years ago
Solve the system of equations below<br>5x+2y=9<br>2×-3y=15<br>​
nirvana33 [79]

Answer:

The solution is (3, -3)

Step-by-step explanation:

5x + 2y = 9

2x - 3y = 15

Use elimination by addition/subtraction.  Multiply the first equation by 3 and the second by 2, obtaining:

15x + 6y = 27

4x   - 6y  =  30

----------------------

19x        = 57

This yields x = 3.

Substituting 3 for x into 5x + 2y = 9, we get  5(3) + 2y = 9, or

15 + 2y = 9, or

2y = -6

This yields y = -3.

The solution is (3, -3)

4 0
3 years ago
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