Garrett already has 5 bracelts made to sell at the craft fair. after working for 3 hours he has a total of 11 bracelets.

Graph the data in the table below. Which kind of function best models the data? write an equation to model the data.

harina [27]

Answer:

A quadratic function.

$y=2.5x^{2}$

Step-by-step explanation:

If you plot the points given in the table, you obtain the graph shown in the figure attached.

As you can see, it is a parabola, therefore, the function that best models the data is a quadratic function.

By definition, the parent function of a quadratic function is:

$y=x^{2}$

You can compress or stretch it in the y-direction by multiplying the function by a constant $C$ :

$y=Cx^{2}$

If $0$ , then the function is compressed.

If $C>1$ , then the function is stretched.

You can find the constant of the function asked as following:

- Substitute x=1 into the parent function to obtain the y-coordinate:

$y=(1)^{2}=1$

Then the point is (1,1)

- As you can see, with x=1 you obtain y=1 in the parent function, and in the function given in the table when x=1, y=2.5, therefore, the function is multiplied by 2.5. Therefore the constant is:

$C=2.5$

Then the function is:

$y=2.5x^{2}$

7 0

3 years ago

The grade received on a certain teacher's 100-point test varies in direct proportion to the amount of time a student spends prep

dolphi86 [110]

Answer:

She would receive 96 points

Step-by-step explanation:

The grade (Y) received on a certain teacher's 100-point test varies in direct proportion to the amount of time(t) a student spends preparing for the test.

Mathematically

Y= kt

Where k is constant of proportionality

If y= 72 and t= 3

72=k3

72/3= k

24= k

So

Y= 24t

If t= 4

Y= kt

Y= 24(4)

Y= 96

Y = 96 points

She would receive 96 points

8 0

3 years ago

Find the slope of the line that passes through the points (2, 5) and (-7, -4).

Umnica [9.8K]

Answer:

1

Step-by-step explanation:

because yes nsnsnsnsnsnsnnsns. nsnsnd

8 0

3 years ago

Sixty is 12% of what number? 500 720 7.2 5

Fantom [35]

60 is 12% of what number

60 = 0.12x
60 / 0.12 = x
500 = x......so 60 is 12% of 500

5 0

4 years ago

The locations in a city are mapped out on a grid, where the origin represents the city center. A traffic helicopter travels due

Elenna [48]

Answer:

Helicopter have traveled 5.55 units of distance approximately if it went directly from one location to the other.

Step-by-step explanation:

We are given the following in the question:

A traffic helicopter travels due north and then due east to get to the location at (-3,4) to the location at (7,13).

The attached image shows the path of helicopter.

Distance Formula:

$(x_1,y_1), (x_2,y_2)\\\\d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

Distance traveled by helicopter =

$d((-3,4),(-3,13)) + d((-3,13),(7,13))\\\\=\sqrt{(-3+3)^2 + (13-4)^2} + \sqrt{(7+3)^2 + (13-13)^2}\\= 9+10\\= 19 \text{ units}$

If the helicopter goes directly:

$d((-3,4),(7,13))\\\\=\sqrt{(7+3)^2+(13-4)^2}\\\approx 13.45 \text{ units}$

Difference in distances =

$19 - 13.45 = 5.55\text{ units}$

Thus, helicopter have traveled 5.55 units of distance approximately if it went directly from one location to the other.

7 0

4 years ago