Ben is eating some pretzels and an entire small package of mustard as a snack. Based on

Mathematics

1 answer:

PIT_PIT [12.4K]1 month ago

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Please take a look at the graph provided.

It’s stated that Ben is snacking on some pretzels along with a complete small pack of mustard. Our task is to determine the equation that illustrates the correlation between the quantity of pretzels Ben consumes, denoted as x, and the overall sodium content in his snack, y.

To start, we’ll calculate the slope of the line using the points (1,80) and (5,140).

$m=\frac{140-80}{5-1}$

$m=\frac{60}{4}$

$m=15$

Next, we will apply the point-slope formula $y-y_1=m(x-x_1)$ , where the slope m is what we calculated, and the coordinates of point $(x_1,y_1)$ lie on the line.

We will input $m=15$ along with the coordinates of point (1,80) into the previously mentioned formula.

$y-80=15(x-1)$

$y-80=15x-15$

$y-80+80=15x-15+80$

$y=15x+65$

Consequently, the equation $y=15x+65$ signifies the relationship between the number of pretzels that Ben eats and the total sodium present in his snack.

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At the warm-up event for Oscar’s All Star Hot Dog Eating Contest, Al ate one hot dog. Bob then showed him up by eating three hot

Inessa [12570]

Answer: Zeno consumed 51 hot dogs.

The total number of hot dogs consumed was 676.

Step-by-step explanation:

Al started by eating one hot dog. Bob then outperformed him by devouring three hot dogs. Carl, not wanting to fall behind, ate five hot dogs. This pattern continued, with each participant consuming two hot dogs more than the previous one. This indicates that the quantity of hot dogs eaten by each contestant followed an arithmetic sequence.

The formula for finding the nth term in an arithmetic series is given by

Tn = a + (n - 1)d

Where

a denotes the first term in the sequence.

d signifies the common difference.

n stands for the total terms in the sequence.

<pBased on the details provided,

a = 1 hot dog

d = 3 - 1 = 2 hot dogs

We aim to find how many hot dogs the 26th contestant, T26, consumed. Thus,

T26 = 1 + (26 - 1)2 = 1 + 50

T26 = 51 hot dogs