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olga2289 [7]
3 years ago
7

Simone claims that the slope of the line through (-2, 7) and (3, 0) is the same as the slope of the line through (2, 1) and (12,

-13) is simone's claim true or false
Mathematics
1 answer:
JulijaS [17]3 years ago
3 0

Answer:

Simone is correct

Step-by-step explanation:

Given

Line 1:

(x_1,y_1) = (-2, 7)

(x_2,y_2) = (3, 0)

Line 2:

(x_1,y_1) = (2, 1)

(x_2,y_2) =(12, -13)

Required

Is Simone correct?

Slope (m) is calculated using:

m = \frac{y_2 - y_1}{x_2 - x_1}

For Line 1

m = \frac{0 - 7}{3 - (-2)}

m = \frac{0 - 7}{3 +2}

m = \frac{-7}{5}

m = -\frac{7}{5}

For Line 2:

m = \frac{-13 - 1}{12 -2}

m = \frac{-14}{10}

Divide by 2/2

m = \frac{-14/2}{10/2}

m = \frac{-7}{5}

m = -\frac{7}{5}

By comparison, both lines have the same slope.

Hence, Simone is correct

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PLZ SHOW ALL WORK
lara31 [8.8K]

Part I
We have the size of the sheet of cardboard and we'll use the variable "x" to represent the length of the cuts. For any given cut, the available distance is reduced by twice the length of the cut. So we can create the following equations for length, width, and height.
width:  w = 12 - 2x
length: l = 18 - 2x
height: h = x

Part II
v = l * w * h
v = (18 - 2x)(12 - 2x)x
v = (216 - 36x - 24x + 4x^2)x
v = (216 - 60x + 4x^2)x
v = 216x - 60x^2 + 4x^3
v = 4x^3 - 60x^2 + 216x

Part III
The length of the cut has to be greater than 0 and less than half the length of the smallest dimension of the cardboard (after all, there has to be something left over after cutting out the corners). So 0 < x < 6

Let's try to figure out an x that gives a volume of 224 in^3. Since this is high school math, it's unlikely that you've been taught how to handle cubic equations, so let's instead look at integer values of x. If we use a value of 1, we get a volume of:
v = 4x^3 - 60x^2 + 216x
v = 4*1^3 - 60*1^2 + 216*1
v = 4*1 - 60*1 + 216
v = 4 - 60 + 216
v = 160

Too small, so let's try 2.
v = 4x^3 - 60x^2 + 216x
v = 4*2^3 - 60*2^2 + 216*2
v = 4*8 - 60*4 + 216*2
v = 32 - 240 + 432
v = 224

And that's the desired volume.
So let's choose a value of x=2.
Reason?
It meets the inequality of 0 < x < 6 and it also gives the desired volume of 224 cubic inches.
3 0
3 years ago
ACDF,BE is a mid segment what is x?
Ksenya-84 [330]

Answer:

X= 15

Step-by-step explanation:

the above equation will be used to determine the value of x.

the above equation will be used to determine the value of x.

6x-12= 2x+20+18

6x-2x = 20+12+18

4x= 60.

X= 60/4

X= 15

x = 15

7 0
3 years ago
Choose two angles that are each separately alternate exterior angles with 412.
Alborosie

Answer:

∠2 and ∠5

Step-by-step explanation:

we know that

<u>Alternate Exterior Angles</u> are a pair of angles on the outer side of each of those two lines but on opposite sides of the transversal

In this problem

∠12 and ∠2 are alternate exterior angles

∠12 and ∠5 are alternate exterior angles

therefore

∠2 and ∠5 are each separately alternate exterior angles with ∠12

6 0
3 years ago
Consider the statement "There are no simple solutions to life’s problems." Write an informal negation for the statement, and the
Blizzard [7]

solution is in the attachment

3 0
3 years ago
Read 2 more answers
Please help on this one ?
omeli [17]

1 ║ 1               2                  -3               2

                       1                   3               0

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

       1              3                   0              \boxed{2}

⇒ The Remainder is 2

4 0
3 years ago
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