Rip van Winkle fell asleep for a very long time. When he fell asleep, his beard was 888 millimeters long, and each passing week

Answer:

The y-intercept for line MN is 2

The standard form of the equation is revealed as ⇒ x + y = 2

Step-by-step elucidation:

Coordinates marking the ends of line MN → M(-3, 5) and N(2, 0)

The slope of the line was computed as

                        =

                        = -1

For line MN which passes through (-3, 5) with a slope of -1, the equation formulated is given by

y - 5 = (-1)(x + 3)

This simplifies to

y - 5 = -x - 3

Thus resulting in

y = -x + 2

Here the equation appears in the y-intercept form of

y = mx + b

where m represents the slope of the line and b denotes the y-intercept

So, consequently, the y-intercept for line MN is 2

The equation generates in the standard form as

x + y = 2

Answer:

Michael purchases 60 kg of dark chocolate alongside 40 kg of milk chocolate.

Step-by-step explanation:

Let d signify the kilograms of dark chocolate bought by Michael and m signify the kilograms of milk chocolate he acquires.

He must acquire a total of 100 kg of chocolate, thus

With dark chocolate priced at $12 per kg, the cost for d kg would be $12d. The price of milk chocolate is $10 per kg, indicating the cost for m kg is $10m. Michael intends to spend $1,120 on the chocolate, therefore

Taking the first equation

By inserting this into the second equation:

Michael ends up buying 60 kg of dark chocolate and 40 kg of milk chocolate.

Let x represent the hot dogs

and y represent the snacks

The equation x + y = 175

Rewrite x as 175 - y

And the second equation: 2.50x + 0.75y = 262.50

Substitute to get 2.50(175 - y) + 0.75y = 262.50

Which simplifies to 437.50 - 2.50y + 0.75y = 262.50

Rearranging gives -1.75y = -175

Hence, solving for y results in y = -175 / -1.75 = 100

Thus, 100 snacks and 75 hot dogs were sold