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Lera25 [3.4K]
3 years ago
12

Amanda only has $30 to buy pens and notebooks. Each pen costs $2. Each notebook coats $3. Which of the following graph represent

s the possible combinations of pens and notebooks that she may purchase?
Mathematics
1 answer:
sineoko [7]3 years ago
4 0

Answer:

3p + 8n,    12p + 2n,    9p+4n,    6p+6n

8 columns bar graph.

Step-by-step explanation:

$2 = pen

$3 = notebook

This could be written as a bar graph in multiples of $6.00 along y axes.

3 pens + 8 notebooks. Then 12 pens + 2 notebooks.

Then 9 pens + 4 notebooks . Then 6 pens + 6 notebooks

3p + 8n,    12p + 2n,    9p+4n,    6p + 6n

3p = $6

8n = $24

12p = $24

2n = $6

9p = $18

4n = $12

6p = $12

6n = $18

and so on...

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sdas [7]

Answer:

y=-\dfrac{13}{49}x^2

Step-by-step explanation:

The shape of an arch corresponds to a parabola.

the general equation for a parabola is:

y=ax^2+bx+c

we're given three coordinates: (-7,-13),(7,-13) and (0,0)

so we can plug these values in the general equation to make 3 separate equations:

(x,y) = (-7,-13)

-13=a(-7)^2+b(-7)+c

49a-7b+c=-13

(x,y) = (7,-13)

-13=a(7)^2+b(7)+c

49a+7b+c=-13

(x,y) = (0,0)

0=a(0)^2+b(7)+c

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so we have three equations. and we can solve them simultaneously to find the values of a,b, and c.

we've already found c = 0, let's use substitute it to other equations.

49a-7b+c=-13\quad\Rightarrow\quad49a-7b=-13

49a+7b+c=-13\quad\Rightarrow\quad49a+7b=-13

we can solve these two equation using the elimination method, by simply adding the two equations

\quad\quad49a-7b=-13\\+\quad49a+7b=-13

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

\quad\quad 98a=-26

\quad\quad a=-\dfrac{13}{49}

Now we can plug this value of a in any of the two equations.

49a-7b=-13

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We have the values of a,b, and c. We can plug them in the general equation to find the equation of the arch.

y=\left(-\dfrac{13}{49}\right)x^2+0x+0

y=-\dfrac{13}{49}x^2

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This our equation of the arch!

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