Can someone help me please

f(x) = 2<img src="https://tex.z-dn.net/?f=x%5E%7B2%7D" id="TexFormula1" title="x^{2}" alt="x^{2}" align="absmiddle" class="latex

loris [4]

Answer:

No answer is possible

Step-by-step explanation:

First, we can identify what the parabola looks like.

A parabola of form ax²+bx+c opens upward if a > 0 and downward if a < 0. The a is what the x² is multiplied by, and in this case, it is positive 2. Therefore, this parabola opens upward.

Next, the vertex of a parabola is equal to -b/(2a). Here, b (what x is multiplied by) is 1 and a =2, so -b/(2a) = -1/4 = -0.25.

This means that the parabola opens upward, and is going down until it reaches the vertex of x=-0.25 and up after that point. Graphing the function confirms this.

Given these, we can then solve for when the endpoints of the interval are reached and go from there.

The first endpoint in -2 ≤ f(x) ≤ 16 is f(x) = 2. Therefore, we can solve for f(x)=-2 by saying

2x²+x-4 = -2

add 2 to both sides to put everything on one side into a quadratic formula

2x²+x-2 = 0

To factor this, we first can identify, in ax²+bx+c, that a=2, b=1, and c=-2. We must find two values that add up to b=1 and multiply to c*a = -2 * 2 = -4. As (2,-2), (4,-1), and (-1,4) are the only integer values that multiply to -4, this will not work. We must apply the quadratic formula, so

x= (-b ± √(b²-4ac))/(2a)

x = (-1 ± √(1-(-4*2*2)))/(2*2)

= (-1 ± √(1+16))/4

= (-1 ± √17) / 4

when f(x) = -2

Next, we can solve for when f(x) = 16

2x²+x-4 = 16

subtract 16 from both sides to make this a quadratic equation

2x²+x-20 = 0

To factor, we must find two values that multiply to -40 and add up to 1. Nothing seems to work here in terms of whole numbers, so we can apply the quadratic formula, so

x = (-1 ± √(1-(-20*2*4)))/(2*2)

= (-1 ± √(1+160))/4

= (-1 ± √161)/4

Our two values of f(x) = -2 are (-1 ± √17) / 4 and our two values of f(x) = 16 are (-1 ± √161)/4 . Our vertex is at x=-0.25, so all values less than that are going down and all values greater than that are going up. We can notice that

(-1 - √17)/4 ≈ -1.3 and (-1-√161)/4 ≈ -3.4 are less than that value, while (-1+√17)/4 ≈ 0.8 and (-1+√161)/4 ≈ 2.9 are greater than that value. This means that when −2 ≤ f(x) ≤ 16 , we have two ranges -- from -3.4 to -1.3 and from 0.8 to 2.9 . Between -1.3 and 0.8, the function goes down then up, with all values less than f(x)=-2. Below -3.4 and above 2.9, all values are greater than f(x) = 16. One thing we can notice is that both ranges have a difference of approximately 2.1 between its high and low x values. The question asks for a value of a where a ≤ x ≤ a+3. As the difference between the high and low values are only 2.1, it would be impossible to have a range of greater than that.

7 0

3 years ago

1. Jennifer can mow the lawn in 20 min. Kristen can mow the lawn in 30 min. If they work together, how long will it take them to

vladimir1956 [14]

Answer:

Sam can do the job in 20 min. So he can do the whole job at the rate of 1 job in 20 minutes.

So he does 1/20 of the job per minute.

.

Rob can do the job in 30 min. His rate is 1/30 of the job per minute.

.

Working together how does it take?

.

1/20*x + 1/30*x = 1 job done

, where x = minutes.

.

Step-by-step explanation:

7 0

2 years ago

Write a real-world situation that can be modeled by y=3t y equals 3 to the power of t.

chubhunter [2.5K]

I start with 1 friend on Facebook. Every month I find that the number of friends I have triples.

Month 0 --> y = 3^0 = 1 friend 
Month 1 --> y = 3^1 = 3 friends 
Month 2 --> y = 3^2 = 9 friends 
Month 3 --> y = 3^3 = 27 friends 
... 
Month t --> y = 3^t

6 0

3 years ago

Because of a manufacturing error, 3 cans of regular soda were accidentally filled with diet soda and placed into a 24-pack. Supp

kipiarov [429]

Answer:

161/184 or 0.875

Step-by-step explanation:

Total number of cans = 24 cans

Total number of diet soda = 3 cans

Total number of regular soda = 21 cans

We are asked to find the probability that:that at least one contain regular soda if two cans are selected randomly

We have two ways for this happening

a) two of the cans are regular soda

b) one of the cans is regular , while one is diet

Hence,

Probability (that at least one contain regular soda) = Probability(that two of the cans are regular soda) + Probability ( one of the cans is regular , while one is diet)

Probability(that two of the cans are regular soda) = 21/24 × 20/23

= 35/46

Probability ( one of the cans is regular , while one is diet) = 21/24 × 3/23

= 21/184

Probability (that at least one contain regular soda) = 35/46 + 21/184

We find the Lowest common multiple of the denominators = 184

= 35/46 + 21/184

= (35 × 4) + (21 × 1)/184

= 140 + 21/184

= 161/184

= 0.875

Therefore, the probability that at least one can contains regular soda = 161/184 or 0.875

8 0

4 years ago

Between what two multiples of 100 is 788?

Ne4ueva [31]

Answer:

788, 1576, 2364, 3152, 3940, 4728, 5516, 6304, 7092, 7880, 8668, 9456, 10244, 11032, 11820, 12608, 13396, 14184, 14972, 15760, 16548, 17336, 18124, 18912, 19700, 20488, 21276, 22064, 22852, 23640, 24428, 25216, 26004, 26792, 27580, 28368, 29156, 29944, 30732, 31520, 32308, 33096, 33884, 34672, 35460, 36248, 37036, 37824, 38612, 39400, 40188, 40976, 41764, 42552, 43340, 44128, 44916, 45704, 46492, 47280, 48068, 48856, 49644, 50432, 51220, 52008, 52796, 53584, 54372, 55160, 55948, 56736, 57524, 58312, 59100, 59888, 60676, 61464, 62252, 63040, 63828, 64616, 65404, 66192, 66980, 67768, 68556, 69344, 70132, 70920, 71708, 72496, 73284, 74072, 74860, 75648, 76436, 77224, 78012, 78800

Step-by-step explanation:

788, because 788 × 1 = 788

1576, because 788 × 2 = 1576

2364, because 788 × 3 = 2364

3152, because 788 × 4 = 3152

3940, because 788 × 5 = 3940

4728, because 788 × 6 = 4728

5516, because 788 × 7 = 5516

6304, because 788 × 8 = 6304

7092, because 788 × 9 = 7092

7880, because 788 × 10 = 7880

8668, because 788 × 11 = 8668

9456, because 788 × 12 = 9456

10244, because 788 × 13 = 10244

11032, because 788 × 14 = 11032

11820, because 788 × 15 = 11820

12608, because 788 × 16 = 12608

13396, because 788 × 17 = 13396

14184, because 788 × 18 = 14184

14972, because 788 × 19 = 14972

15760, because 788 × 20 = 15760

16548, because 788 × 21 = 16548

17336, because 788 × 22 = 17336

18124, because 788 × 23 = 18124

18912, because 788 × 24 = 18912

19700, because 788 × 25 = 19700

20488, because 788 × 26 = 20488

21276, because 788 × 27 = 21276

22064, because 788 × 28 = 22064

22852, because 788 × 29 = 22852

23640, because 788 × 30 = 23640

24428, because 788 × 31 = 24428

25216, because 788 × 32 = 25216

26004, because 788 × 33 = 26004

26792, because 788 × 34 = 26792

27580, because 788 × 35 = 27580

28368, because 788 × 36 = 28368

29156, because 788 × 37 = 29156

29944, because 788 × 38 = 29944

30732, because 788 × 39 = 30732

31520, because 788 × 40 = 31520

32308, because 788 × 41 = 32308

33096, because 788 × 42 = 33096

33884, because 788 × 43 = 33884

34672, because 788 × 44 = 34672

35460, because 788 × 45 = 35460

36248, because 788 × 46 = 36248

37036, because 788 × 47 = 37036

37824, because 788 × 48 = 37824

38612, because 788 × 49 = 38612

39400, because 788 × 50 = 39400

40188, because 788 × 51 = 40188

40976, because 788 × 52 = 40976

41764, because 788 × 53 = 41764

42552, because 788 × 54 = 42552

43340, because 788 × 55 = 43340

44128, because 788 × 56 = 44128

44916, because 788 × 57 = 44916

45704, because 788 × 58 = 45704

46492, because 788 × 59 = 46492

47280, because 788 × 60 = 47280

48068, because 788 × 61 = 48068

48856, because 788 × 62 = 48856

49644, because 788 × 63 = 49644

50432, because 788 × 64 = 50432

51220, because 788 × 65 = 51220

52008, because 788 × 66 = 52008

52796, because 788 × 67 = 52796

53584, because 788 × 68 = 53584

54372, because 788 × 69 = 54372

55160, because 788 × 70 = 55160

55948, because 788 × 71 = 55948

56736, because 788 × 72 = 56736

57524, because 788 × 73 = 57524

58312, because 788 × 74 = 58312

59100, because 788 × 75 = 59100

59888, because 788 × 76 = 59888

60676, because 788 × 77 = 60676

61464, because 788 × 78 = 61464

62252, because 788 × 79 = 62252

63040, because 788 × 80 = 63040

63828, because 788 × 81 = 63828

64616, because 788 × 82 = 64616

65404, because 788 × 83 = 65404

66192, because 788 × 84 = 66192

66980, because 788 × 85 = 66980

67768, because 788 × 86 = 67768

68556, because 788 × 87 = 68556

69344, because 788 × 88 = 69344

70132, because 788 × 89 = 70132

70920, because 788 × 90 = 70920

71708, because 788 × 91 = 71708

72496, because 788 × 92 = 72496

73284, because 788 × 93 = 73284

74072, because 788 × 94 = 74072

74860, because 788 × 95 = 74860

75648, because 788 × 96 = 75648

76436, because 788 × 97 = 76436

77224, because 788 × 98 = 77224

78012, because 788 × 99 = 78012

78800, because 788 × 100 = 78800

7 0

3 years ago