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saul85 [17]
3 years ago
13

Which of the following rules could represent the function shown in the table?

Mathematics
2 answers:
kvasek [131]3 years ago
5 0
ANSWER

The rule is given by the relation,

y = 2x + 1


EXPLANATION

We need to check and see if there is a constant difference between the y-values.


1 -  - 1 = 2 = 3 - 1


We can see that, there is a constant difference of 2.

This means that the table represents a linear relationship.


Let the rule be of the form,
y = mx + c


Then the points in the table should satisfy the above rule.


So let us plug in


(0,1)


This implies that,


1 =m (0) + c


1 = 0 + c


c = 1



Our rule now becomes,


y = mx + 1 -  - (1)


We again plug in another point say, (-1,-1) in to equation (1) to get,



- 1 = m( - 1)   + 1

we solve for m now to obtain,

- m=-1-1


- m =  - 2


m = 2
We now substitute back in to equation (1) to get

y = 2x  + 1
nevsk [136]3 years ago
4 0

Answer:

Option (C) is correct

f(x) = 2x + 1

Step-by-step explanation:

Slope-intercept form:

The equation of line is given by:

y=mx+b               .....[1]

where, m is the slope and b is the y-intercept.

As per the statement:

Let y = f(x)

Given the table as shown

Let any two points:

(-1, -1) and (0, 1)

Formula for slope(m):

m = \frac{y_2-y_1}{x_2-x_1}

Substitute the given values we have;

m = \frac{1-(-1)}{0-(-1)}

⇒m = \frac{2}{1} = 2

Substitute in [1] we have;

y = 2x+b                ....[2]

Substitute the point (-1, -1) in [2] we have;

-1 = 2(-1)+b

⇒-1 = -2+b

Add 2 to both sides we have;

1 = b

or

b = 1

then, we get the equation:

y =2x+1

or

f(x) = 2x+1

Therefore,  the following rules could represent the function is, f(x) = 2x+1

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Step-by-step explanation:

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It's required to find the recursive term for the sequence.

A recursive formula calculates each term as a function of one or more previous terms.

To find the recursive formula, we must find a pattern and transform it into a math expression.

Let's write the sequence, and below it, the difference of consecutive terms:

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Note the difference between consecutive terms is always a power of 2, starting from 2^1, 2^2, 2^3.

The exponent is one less than the number of the term, thus:

a_n-a_{n-1}=2^{n-1}

Thus:

\mathbf{a_n=a_{n-1}+2^{n-1}\ \ n>1}

Testing:

n=1

a_1=-1 (given).

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Sterre charges $ 3 5 $35dollar sign, 35 to file tax returns, but files for free if she only needs the easiest form. Then she don
blagie [28]

Given:

  • $35 is charged per form, but $0 if only the easiest form is filed.
  • $2 donated for every single tax return filed (since it is not explicitly mentioned otherwise, I will assume she donates $2 whether she charges $35 or does it for free)
  • Total amount charged for the full year = $7245
  • Total amount donated for the full year = $1242

To Find: The number of forms for which Sterre charged $35 and the number of forms Sterre did it for free.

Concept:

We can make use of the Unitary Method here. <u>Given the number of units in a group, the Unitary Method can be used to find the value of a single unit or and individual unit when we are given the value for a group.</u>

So,

<u>Value of Single Unit = Value of Entire Group of Units ÷ Number of Units in the Group</u>


Explanation & Calculation:

We are given that Sterre charged $7245 for the full year. Taking each Unit as the $35 type of form, and value of each Unit would be the amount that Sterre charges per form which is obviously $35, we can find the number of $35 forms using the expression written above.

So, putting in the values into the expression,

$35 = $7245 ÷ number of $35 forms

Therefore, number of $35 forms = $7245 ÷ $35

Using simple division, number of $35 forms = 207

Next, we are given Sterre donated $1242 in the full year and she donates $2 for every form (whether it is the $35 form or the free form).

If this time, we define each Unit as being each form (both $35 form and free form), value of each unit we define as the $2 donation money, we see that the value of the full group of units is $1242.

So, putting the values into the expression,

$2 = $1242 ÷ total number of forms

Therefore, total number of forms = $1242 ÷ $2

Using simple division, total number of forms = 621


Conclusion:

Sterre has filed <u>a total of 621 tax returns</u> (both charged and for free).

Of these 621 returns filed, <u>for 207 forms, Sterre charged $35</u>.

The number of returns Sterre filed for free (that is, the easiest forms) is

Total number of forms - Chargeable forms = 621 - 207 = 414

Thus, Sterre filed <u>414 tax returns for free</u>.


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