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stepladder [879]
3 years ago
15

Use the table to determine the degree of the power function.

Mathematics
1 answer:
valkas [14]3 years ago
5 0

9514 1404 393

Answer:

  3

Step-by-step explanation:

The x-values in the table are evenly-spaced, so we can determine the degree of the function by looking at successive differences of the f(x) terms.

f(x): -23, -4, 3, 4, 5, 12, 31

first differences: 19, 7, 1, 1, 7, 19

second differences: -12, -6, 0, 6, 12

third differences: 6, 6, 6, 6

The third differences are constant, so the function values can be matched by a <em>third degree</em> polynomial.

_____

<em>Additional comment</em>

The first differences are found by subtracting the function value from the next one. Likewise, the second differences are found by subtracting each first-difference value from the next one. An so on for the third differences.

The level at which the differences are constant is the degree of the polynomial that will match the function values. (Compare this to what you know about an arithmetic sequence, where first differences are constant and the sequence is described by a linear (degree 1) equation.)

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Answer:

10.25 gallons

Step-by-step explanation:

432 miles / 6 gallons=72 miles to gallon

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6 0
3 years ago
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The United States is about the only country that still uses the units feet, miles, and gallons. However, you might see some car
Black_prince [1.1K]

Answer: 4.5 \text{ miles per gallon}

Step-by-step explanation:

Given :  The fuel efficiency of car = 7.6 km per kilogram

We also given that

1 mile = 1.609 km

Then, \text{1 km}=\dfrac{1}{0.609}\text{ mile}

1 gallon = 3.785 liters

\text{1 liter}=\dfrac{1}{3.785}\text{ gallon}

1 liter of gasoline = 0.729 kg

Then, \text{1 kg}=\dfrac{1}{0.729}\text{ liter}

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Now, the fuel efficiency of car will be :

7.6\times\dfrac{1}{0.729}\times\dfrac{1}{3.785}\times\dfrac{1}{0.609}\\\\=4.52275317827\approx4.5 \text{ miles per gallon}

Hence,  the car’s fuel efficiency in miles per gallon= 4.5

3 0
3 years ago
The number of coffee bar on different streets of a NY city are 9, 18, 24, 9, 5,
Serjik [45]

Answer:

9

Step-by-step explanation:

The mode is the number that occurs most often. The number nine occurs 4 times.

7 0
1 year ago
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Can someone help me with this and show their work and how they found the answer?
Semenov [28]

Answer:

2kg

Step-by-step explanation:

Let the sum of the other 2 bricks be R. Given that the heaviest brick weighs 2/3 times as much as the other 2 bricks in total, then the weight of the heaviest brick H in terms of the weight of the other 2 will be

H = 2/3 * R

= 2R/3

Given that the 3 bricks weigh 5kg in total then,

2R/3 + R = 5

Multiply through the equation by 3

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5R = 15

Divide both sides by 5

R = 15/5

= 3

The weight of the heaviest brick is 2R/3. Since R = 3, the heaviest block weighs

= 2 * 3/3

= 2kg

4 0
3 years ago
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