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2 years ago

What is the slope of the line that passes through (-4, 6) and (-6, 20)?

Mathematics

1 answer:

Hatshy [7]2 years ago

3 0

Answer:

-7

Step-by-step explanation:

Since we have two points, we can use the slope formula

m = ( y2-y1)/(x2-x1)

= ( 20-6)/(-6- -4)

= ( 20-6)/ ( -6+4)

= 14/-2

= -7

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2 years ago

Two square sheets of cardboard used for making book covers differ in area by 64 square inches. An edge of the larger square is 2

photoshop1234 [79]

Answer:

15 inches

Step-by-step explanation:

We assume that the edge of the small square is x (inches).

As the edge of the larger square is 2 inches greater than that of the smaller one, so that the edge of the larger square = edge of the small square + 2 = x + 2 (inches)

The equation to calculate the are of a square is: Area = Edge^2

So that:

+) The area of the larger square is: Area large square = $(x+2)^{2}$ (square inches)

+) The area of the smaller square is: Area small square = $x^{2}$ (square inches)

As difference in area of both squares are 64 square inches, so that we have:

Area large square - Area small square = 64 (square inches)

=> $(x+2)^{2} -x^{2} =64$

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=> 4x + 4 = 64

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3 years ago

Can someone tell me if im right? PLEASE DONT JUST SAY YES if you don’t know

tia_tia [17]

Answer: You are incorrect, the slope is correct, but the actual y-intercept is 205 ft.

Then the equation is:

y = (-15 ft/min)*x + 205 ft

Step-by-step explanation:

Ok, let's solve this.

We know that water is drained from a reservoir, let's assume that we can model this situation with a linear relation:

y = a*x + b

Where x is time, y is the height of the water in the reservoir, a is the slope (in this case represents how much changes the height of the water in the reservoir in one unit of time) and b is the initial height of the water in the reservoir.

We know that for a line that passes through the points (x₁, y₁) and (x₂, y₂) the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

For this particular case we know that after 2 minutes the height of the water is 175 ft, then we have the point (2 min, 175 ft)

and after 5 minutes (so 7 minutes in total), the height of the water is 100ft, then: (7 ft, 100ft)

Then the slope of this:

a = (100 ft - 175 ft)/(7 min - 2 min) = (-75ft/5min) = - 15 ft/min

Then our line is something like:

y = (-15ft/min)*x + b

To find the value of b, we can use the fact that when x = 2 min, y = 175 ft

So if we replace these two values in the equation we get:

175ft = (-15 ft/min)*2 min + b

175 ft = -30 ft + b

175 ft + 30 ft = b

(here is your problem, it seems like you subtracted instead of adding in this part)

205 ft = b

Then the equation is:

y = (-15 ft/min)*x + 205 ft

So you are incorrect (but only for a little bit), you computed wrong the y-intercept.

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