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zhannawk [14.2K]
3 years ago
5

The table of values shows the output values of three different equations for the same

Mathematics
1 answer:
zubka84 [21]3 years ago
6 0

Answer:

  1. x+3
  2. 3x^2
  3. 3^x

Step-by-step explanation:

<u>Relationship 1</u>

The y-values have a common difference of 1, so the relationship is linear with as slope of 1. The only matching choice is (x+3), which matches the values of y1.

__

<u>Relationship 2</u>

The y-values have differences that increase with a common difference. They are (3-0) = 3, (12-3) = 9, (27-12) = 15, (48 -27) = 21. The second differences are (9-3) = 6, (15-9) = 6, and so on with all second differences being 6. This tells you that a second-degree polynomial can model this sequence. The only matching choice is (3x^2), which matches the values of y2.

__

<u>Relationship 3</u>

The y-values have increasing differences that also have increasing differences. The values have a common ratio of 3, indicating an exponential function will model this sequence. The only matching choice is (3^x), which matches the values of y3.

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Evaluate −x+| y | when x=1/3 and y=−7/4. Write your answer as a fraction in simplest form.
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Answer:

Step-by-step explanation:

- 1 / 3 + - 7/4

-4/12 - 21/12

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5 0
3 years ago
Reverse the two digits of my age, divide by three, add 20, and the result is my age. How many years old am I
lapo4ka [179]

Answer:

  • 48 years old.

Step-by-step explanation:

Let the age be xy or 10x + y.

Reverse the two digits of my age, divide by three, add 20, and the result is my age, convert this to equation:

  • (10y + x)/3 + 20 = 10x + y
  • (10y + x)/3 = 10x + y - 20
  • 10y + x = 3(10x + y - 20)
  • 10y + x = 30x + 3y - 60
  • 30x - x + 3y - 10y = 60
  • 29x - 7y = 60

We should consider both x and y are between 1 and 9 since both the age and its reverse are 2-digit numbers.

Possible options for x are:

  • 29x ≥ 7*1 + 60 = 67 ⇒ x > 2, at minimum value of y,

and

  • 29x ≤ 7*9 + 60 = 123 ⇒ x < 5, at maximum value of y.

So x can be 3 or 4.

<h3>If x = 3</h3>

  • 29*3 - 7y = 60
  • 87 - 7y = 60
  • 7y = 27
  • y = 27/7, discarded as fraction.

<h3>If x = 4</h3>

  • 29*4 - 7y = 60
  • 116 - 7y = 60
  • 7y = 56
  • y = 8

So the age is 48.

6 0
1 year ago
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Answer:

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Step-by-step explanation:

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5 0
3 years ago
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Sliva [168]

Answer:

Option C (1, 0)

Step-by-step explanation:

We have a system with the following equations:

y = x ^ 2-1\\\\y = 2x-2

The first equation is a parabola.

The second equation is a straight line

To solve the system, substitute the second equation in the first and solve for x.

2x-2 = x ^ 2 -1

Simplify

x ^ 2-2x + 1 = 0

You must search for two numbers that when you add them, obtain as a result -2 and multiplying both results in 1.

These numbers are -1 and -1

Therefore

x ^ 2-2x + 1= (x-1)(x-1)\\\\x ^ 2-2x + 1= (x-1)^2=0

Finally the solutions are

x = 1\\y =0

8 0
3 years ago
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A plumber had a pipe that was 2 yards long he cut 18 inches off the end of the pipe
balandron [24]
To convert yards to feet, you would multiply it by 3. So, since there the pipe is 2 yards long, you could multiply 2*3 to get 6 feet. Then you can convert feet to inches by multiplying it by 12. 6*12 is equal to 72, so 2 yards is equal to 72 inches. Lastly, you can subtract 18 from 72, to get 54, and 54 inches would be your final answer.
7 0
3 years ago
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