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Savatey [412]
3 years ago
10

The midpoint M and one endpoint of JK are given. Find the coordinates of the other endpoint. J(7,2) and M(1,-2)

Mathematics
1 answer:
djverab [1.8K]3 years ago
3 0

Step-by-step explanation:

Xj + Xk/2 = Xm

7 + Xk/2 = 1

to get rid of the bracket, multiply all two sides by the denominator.

2(7 + Xk/2) = 1(2)

7 + Xk = 2

Xk = 2 - 7

Xk = -5

Yj + Yk/2 = Ym

2 + Yk/2 = -2

to get rid of the bracket, multiply all two sides by the denominator.

2(2 + Yk/2) = -2(2)

2 + Yk = -4

Yk = -4 - 2

Yk = -6

Therefore the coordinates of point K is (-5,-6)

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Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in t
Tresset [83]

Answer: The volume of largest rectangular box is 4.5 units.

Step-by-step explanation:

Since we have given that

Volume = xyz

with subject to x+2y+3z=9

So, let z=\dfrac{9-x-2y}{3}

So, Volume becomes,

V=xyz\\\\V=xy(\dfrac{9-x-2y}{3})\\\\V=\dfrac{9xy-x^2y-2xy^2}{3}

Partially derivative wrt x and y we get that

9-2x-2y=0\implies 2x+2y=9\\\\and\\\\9-x-4y=0\implies x+4y=9

By solving these two equations, we get that

x=3,y=\dfrac{3}{2}

So, z=\dfrac{9-x-2y}{3}=\dfrac{9-3-3}{3}=\dfrac{3}{3}=1

So, Volume of largest rectangular box would be

xyz=3\times \dfrac{3}{2}\times 1=\dfrac{9}{2}=4.5

Hence, the volume of largest rectangular box is 4.5 units.

4 0
3 years ago
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Semmy [17]

The correct answer would be B because .47 is bigger than 42/100 or .42

8 0
3 years ago
HELPPPPPPP. Marie has two boxes of colored markers. Each box contains 3 markers. In
REY [17]

Answer: 16.6% percent chance she will pull out a blue or orange marker.

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4 0
2 years ago
Examine the system of equations. y = 4x + 8, y = 4x – 1 Which statements best describe the two expressions? Check all that apply
Lerok [7]

Answer:

The correct statements are as follows;

1. They have different y-intercepts

2. The substitution method results in false statement 8 = -1

3. There is no solution

Step-by-step explanation:

Here, we want to select the statement that best describes the equations

The equation for a straight line is generally;

y = mx + b

m is slope and b is the y-intercept

slope of both is same ; 4

So first assertion is wrong

they have different y-intercepts

First y-intercept is 8, second is -1

This is correct

The third statement is correct too

if we equated both y;

4x + 8 = 4x -1

We shall have 4x canceled out and left with 8 = -1

(8,-1) is not a solution

There is no solution is correct because after substituting, we have 8 = -1 which is not correct and also impossible

7 0
3 years ago
A town has a population of 1000 people at time t equals 0.The population increases by 30 people a year. Write a formula for the
anygoal [31]

The given point (t, P) is (0, 1000), and the slope is given as ∆P/∆t = 30. Using the point-slope form of the equation for a line, the equation can be written as

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3 years ago
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