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tigry1 [53]
3 years ago
5

What is the range of the function f(x) = 4x + 9, given the domain D = {-4, -2, 0, 2}? please help

Mathematics
1 answer:
neonofarm [45]3 years ago
8 0
Since this is a linear function, filling in the minimum and maximum of the domain is sufficient.

f(-4) = -16 + 9 = -7
f(2)= 8 + 9 = 17

So the range of the function (given the domain) :
R = {-7, 17}
You might be interested in
A team of 15 workers picked 1,050 apples. Each person picked the same number of apples. How many did each worker pick?
GarryVolchara [31]

Answer:

70 apples

Step-by-step explanation:

Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)

4 0
2 years ago
3,6,11,18,27,38
MakcuM [25]

Answer:  The pattern is x^2+2

where x is the term number

Example: the 5th term is 27 because x = 5 leads to x^2+2 = 5^2+2 = 27

=================================================

Explanation:

  • The jump from 3 to 6 is +3
  • The jump from 6 to 11 is +5
  • The jump from 11 to 18 is +7
  • The jump from 18 to 27 is +9
  • The jump from 27 to 38 is +11

The pattern of jumps is: 3, 5, 7, 9, 11

Those increments are going up by 2 each time.

Since we have a consistent pattern of increments, this means that the sequence follows a quadratic model.

Quadratics are stuff like x^2+7x+10 or 3x^2-7. The leading term has an exponent of 2.

-----------

If x is the term number and y is the term itself, then we have these points

(1,3)

(2,6)

(3,11)

(4,18)

(5,27)

(6,38)

The x coordinates increase by 1 each time. The y coordinates are the terms given by your teacher.

Pick exactly 3 of those points. I'll pick the first 3.

Why 3? Because we'll have 3 unknowns to solve for, in which we'll need 3 equations.

  • Plug (x,y) = (1,3) into y = ax^2+bx+c, then simplify. You should get the equation a+b+c = 3
  • Repeat for (x,y) = (2,6) and you should get 4a+2b+c = 6
  • Repeat for (x,y) = (3,11) and you should get 9a+3b+c = 11

-----------

We have this system of equations

\begin{cases}a+b+c = 3\\ 4a+2b+c = 6\\9a+3b+c = 11\end{cases}

There are a number of methods to solve this system. Substitution is what I'll go for.

Solve the first equation for c

a+b+c = 3

c = 3-a-b

Then use substitution.

4a+2b+c = 6

4a+2b+(3-a-b) = 6

3a+b+3 = 6

3a+b = 6-3

3a+b = 3

and

9a+3b+c = 11

9a+3b+(3-a-b) = 11

8a+2b + 3 = 11

8a+2b = 11-3

8a+2b = 8

We now have this reduced system of equations.

\begin{cases}3a+b = 3\\8a+2b = 8\end{cases}

I'll skip the steps as this solution is getting very lengthy as it is. The basic idea is to use substitution again. You should find that a = 1 and b = 0 form the solution set here.

Use those values to find c

c = 3-a-b

c = 3-1-0

c = 2

-----------

To summarize the previous section, we have these solutions:

a = 1, b = 0, c = 2

Therefore the equation y = ax^2+bx+c becomes y = 1x^2+0x+2 aka y = x^2+2. This lets us find any term.

Let's test it out.

  • If x = 1, then y = x^2+2 = 1^2+2 = 3
  • If x = 2, then y = x^2+2 = 2^2+2 = 6
  • If x = 3, then y = x^2+2 = 3^2+2 = 11

And so on. I'll let you test the other x values (4 through 6).

Another way to confirm the answer is to subtract 2 from each item in the original set {3,6,11,18,27,38} and you'll end up with {1,4,9,16,25,36}. This is the list of perfect squares. It shows that term x is simply x^2 but add on 2 so things are adjusted accordingly.

Side note: you can use a tool like GeoGebra or WolframAlpha to quickly solve the system of equations. However, I recommend it only as a means to check your answer rather than do the work for you.

7 0
2 years ago
A jar contains 2 red and 4 blue marbles. A marble is drawn from the jar. What is the probability that a red marble will be drawn
allsm [11]
Salutations!

<span>A jar contains 2 red and 4 blue marbles. A marble is drawn from the jar. What is the probability that a red marble will be drawn?

So lets solve this! 

Probability is an event of chance; an occurrence of chance.

The probability that a red marble will be drawn is 2/6

Simply 2/6 which is 1/3

Thus, your answer is option C.

Hope I helped :D
</span>
5 0
3 years ago
Read 2 more answers
Pls help pls pls ): precalc
Lena [83]
<h3>Answer: Choice A</h3>

\log_p N = b is not the same as b^p = N

The base of the log is p, while the base of the exponential is b. The two don't match. If it said \log_p N = b \text{ is the same as } p^b = N then it would be a valid statement since the bases are both p.

-----------------

Extra info:

Choice B is a valid statement because Ln is a natural log with base 'e'

Choice C is valid as any square root is really something to the 1/2 power

Choice D is valid for similar reasons mentioned earlier

5 0
3 years ago
Read 2 more answers
4(3x+2)−7x simplified
baherus [9]

Answer:

19x+8

Step-by-step explanation:

1) distribute the term outside the parenthesis to each term inside:

4*3x=12x

4*2=8

12x+8-7x

2) 12x+7x=19x

19x+8

Hope this helps!

7 0
3 years ago
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