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devlian [24]
3 years ago
8

A student uses the method of successive approximations to estimate a positive solution of f(x) = g(x), where f(x) = x2 + 10 and

g(x) = 2x + 17. The table shows her results for different input values of x. x f(x) g(x) 0 10 17 1 11 19 2 14 21 3 19 23 4 26 25 3.5 22.25 24 Using this method, the next number selected should be between and .
Mathematics
1 answer:
serious [3.7K]3 years ago
7 0

Answer:

The next number selected should be between 2 and 3 .

Step-by-step explanation:

x. x    f(x)             g(x)

0        10               17

1           11              19

2          14              21

3          19              23

4         26             25

3.5      22.25        24

<u>2.5      16.25         22</u>

1.5       12.25        20

0.5       10.25       18

We see the pattern that it is increasing with only a unit. The last given data is mid of the last two values that is 3 and 4.

So the next value would be the mid of the next last two values that is 2 and 3 and will be 2.5

Now it is moving in the reverse direction in the same pattern  with a difference of a unit.

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A group of friends went out for dinner and decided to split the cost of the bill equally. If each person contributed $32, the fr
lianna [129]

Answer:

The number of friends that went out for dinner is 8

And their bill is $238

Step-by-step explanation:

Let's assume that the number of friends that went out for dinner to be x

And the bill for the dinner to be y

If each person contributed $32 and paid off the bill,they will have a balance of $18

32x - 18 = y_____equation 1

If each person contributed $35 and paid off the bill and also 15% tip,they will have a balance of $6.30

35x - 6.3 = y + (15% of y)

35x - 6.3 = y + (3y/20)

Open up the bracket

35x - 6.3 =(20y + 3y)/20

700x - 126 = 23y______equation 2

From equation 1,y = 32x - 18

Put the above in equation 2 and we have

700x - 126 = 23(32x -18)

700x - 126 = 736x - 414

collect like terms

36x = 288

x = 288/36

x = 8

Remember that equation 1 says that y = 32x - 18 and we now know that x = 8 .

Substitute and we have

(32 × 8) - 18

y = 238

The number of friends that went out for dinner is 8

And their bill is $238

3 0
3 years ago
Someone help me with this
DaniilM [7]

Answer: 7.5

Step-by-step explanation:

3 0
3 years ago
I need help with this algebra question
ioda

Answer:

4.58258

Step-by-step explanation:

Pythagorean Theorem:

a² + b² = c²

Input:

2² + x² = 5²

Remember, c² is always the side opposite of the right angle...

4 + x² = 25

21 = x²

x = 4.58258

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

7 0
3 years ago
Read 2 more answers
Mr. Lombardo took his two children to a water park. He used the coupon shown below to buy one adult ticket. The price of admissi
KatRina [158]

Answer:

A. The price would be 24 because 28-4 dollars is 24

B. How much a cost altogether and the fact that he has two kids

C. You can take the total of the price of all their tickets combined to subtract 24 and you would get 52 so so I slice and a half in and you have the answer

D 26 dollars each

E. 76-24=52 52/2=26

Step-by-step explanation:

7 0
2 years ago
9. In a rhombus whose side measures 34 and the smaller angle is 42°. Find the length of the larger diagonal, to the nearest tent
Veseljchak [2.6K]

Answer:

63.5

Step-by-step explanation:

The diagonals of a rhombus bisect opposite angles.

The longer diagonal bisects the 42° angle

The larger angle of the rhombus is 180 - 42 = 138

Let x = the length of the longer diagonal

You know two sides and the included angle of a triangle.

Using the law of cosines we get

x^{2} = 34^{2} + 34^{2} -2(34)(34) cos 138\\         = 1156 + 1156 - 2312 cos 138\\         = 4030.150837...\\x = \sqrt{4030.150837} = 63.48x^{2} = 34^{2} + 34^{2} -2(34)(34)cos 138\\         = 1156 + 1156 - 2312 cos 138\\         = 4030.1508...\\     x = \sqrt{4030.1508} \\          =  63.48x^2 = 34^2 + 34^2 - 2(34)(34) cos 138

      = 1156 + 1156 - 2312 c0s 138

      = 4030.1508...

x = sq rt 4030.1508...

  =  63.5

7 0
2 years ago
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