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eduard
3 years ago
13

If f(x)=2x²-x find f(-3)

Mathematics
2 answers:
zzz [600]3 years ago
4 0

Answer: 21

Step-by-step explanation: To find f(-3) or the value of the function when x = -3, we plug in a -3 for the x in our function and we have 2(-3)² - (-3).

Start by simplifying the exponent to get 9.

So we have 2(9) - (-3) or 18 + 3 which is 21.

ivolga24 [154]3 years ago
3 0

Answer:

21

Step-by-step explanation:

f(x) = 2x^2 - x

f(-3) = 2*(-3)^2 - (-3)

=2*9 +3

=18 +3

=21

You might be interested in
In base $10$, the number $2013$ ends in the digit $3$. in base $9$, on the other hand, the same number is written as $(2676)_{9}
skelet666 [1.2K]
Note that

2013_{10}=2(10)^3+1(10)^1+3(10)^0

so that

\dfrac{2013}{10}=200+1+\dfrac3{10}

i.e. the remainder upon dividing 2013 (in base 10) by 3 is 3. The point is that any base-b representation of 2013_{10} will end in the digit 3 whenever division of 2013 by b leaves a remainder of 3.

First, we require that b\ge4, because any smaller base simply won't have 3 as a possible digit.

Second, we clearly can't have b\ge2014, because any value of b beyond that point will have 2013 as its first digit. That is, in base 2014, for instance, if we separate the digits of numbers by colons, we would simply have 2013_{10}=0:0:0:2013_{2014} (the 0s aren't necessary here, but only used for emphasizing that 2013 would be its own digit, regardless of how we represent digits outside of 0-9).

Third, we can't have b=2013 because 2013 divides itself and has no remainder. That is, 2013_{10}=10_{2013}.

So we've reduced the possible domain of solutions from all positive integers to just those lying within 4\le b\le2012.

Now, in terms of modular arithmetic, we're essentially solving the following equivalence for b:

2013\equiv3\pmod b

which, if you're not familiar with the notation or notion of modular arithmetic, means exactly "2013 gives a remainder of 3 when divided by b". It's equivalent to saying "there exists an integer n such that 2013=bn+3.

From this equation, we have 2010=bn. Now, we know both b,n must be integers, so we need only find the factors of 2010. These are

1, 2, 3, 5, 6, 10, 15, 30, 67, 134, 201, 335, 402, 670, 1005, 2010

So we have 16 total possible choices for b,n. But we're omitting 1, 2, and 3 from the solution set, which means there are 13 base-b representations of the base-10 number 2013_{10} such that the last digit 2013_b is 3. They are

2013_{10}=31,023_5
2013_{10}=13,153_6
2013_{10}=2013_{10}
2013_{10}=8:14:3_{15}
2013_{10}=2:7:3_{30}
2013_{10}=30:3_{67}
2013_{10}=15:3_{134}
2013_{10}=10:3_{201}
2013_{10}=6:3_{335}
2013_{10}=5:3_{402}
2013_{10}=3:3_{670}
2013_{10}=2:3_{1005}
2013_{10}=1:3_{2010}

- - -

Added a link to some code that verifies this solution. In case you're not familiar with Mathematica or the Wolfram Language, in pseudocode we are doing:

1. Start with a placeholder list called "numbers", consisting of all 0s, of length 2010. We know 4\le b\le2013, which contains 2010 possible integers.
2. Iterate over b:
2a. Start with b=4.
2b. Ensure b doesn't exceed 2013.
2c. After each iteration, increment b by 1; in other words, after each step, increase b by 1 and use this as a new value of b.
2d. Check if the last digit of the base-b representation of 2013 ends is a 3. In the WL, IntegerDigits[x, n] gives a list of the digits of x in base-n. We only want the last digit, so we take Last of that. Then we check the criterion that this value is exactly 3 (===).
2d1. If the last digit is 3, set the (b-3)-th element of "numbers" to be a list consisting of the base b and the list of digits of 2013 in that base.
2d2. Otherwise, do nothing, so that the (b-3)-th element of "numbers" remains a 0.
3. When we're done with that, remove all cases of 0 from "numbers" (DeleteCases). Call this cleaned list, "results".
4. Display "results" in Grid form.
5. Check the length of "results".
7 0
3 years ago
Herr is a balance hanger diagram a circle has a mass of three grams and a square has a mass of two grams which is the mass of th
Naily [24]

The hanger diagram ideally should be in balance with all the shapes hung on it.

On the left side, it shows that the circles are 9 grams and the squares are 12 grams. The triangles are 2t grams. Therefore, on the left side we have,

9 + 12 + 2t

On the right side, it shows the circles are 6 grams and the squares are 6 grams, while the triangles are 5t grams. Therefore on the right side we have

6 + 6 + 5t.

For the hanger to be in balance, we should have

undefined

3 0
1 year ago
Answer all questions, your combing like terms. Show ALL of you work! Thank you!!
Elanso [62]

Answer:

1. -12x - 9y - 6

2. -12x + 36

3. -240

4. -2

5. x = -57

6. x = -6

7. x = 48

8. x = 20

9. x = -288

10. n = 8

Step-by-step explanation:

1.

-5x - 13 + 3y - 7x - 12y + 7

-12x - 13 + 3y - 12y +  7

-12x - 6 + 3y - 12y

-12x - 6 - 9y

-12x - 9y - 6

2.

-3(4x - 12)

-3(4x) + (-3)(-12)

-12x + 36

3.

6x - 282

6(7) - 282

42 - 282

-240

4.

6x + 2(y + x)

6(-2) + 2(7 + (-2))

-12 + 2(7 - 2)

-12 + 2(5)

-12 + 10

-2

5.

x - 23 = -80

 + 23    +23

x = -57  

6.

12x = -72

/12     /12

x = -6

7.

x/4 = 12

* 4    * 4

x = 48

8.

3x + 12 = 72

    -  12  - 12

3x = 60

/3     /3

x = 20

9.

x/4 - 8 = -80

     + 8    + 8

x/4 = -72

* 4    * 4

x = -288

10.

-4(1 - 5n) - 8n = 92

-4 + (-4)(-5n) - 8n = 92

-4 + 20n - 8n = 92

-4 + 12n = 92

12n - 4 = 92

     + 4    + 4

12n = 96

/12     /12

n = 8

6 0
3 years ago
Time Warner Cable charges $30 per hour and a trip fee of $55 for each service call.
r-ruslan [8.4K]

Answer:

y=30x+55

Step-by-step explanation:

$55 is constant because for each trip he will take $55 dollars so that gives you your y-intercept and m=$30 and x is the amount of hours worked. every time x increases he will be making more money

3 0
2 years ago
Can somebody help me??
Dominik [7]

Answer:

1. -72

2. -64

Step-by-step explanation:

it is increasing by 4 so,

-76, -72, -68, -64, -60, -56.

4 0
3 years ago
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