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3 years ago

3x - 2y + 3z = -20 4x - 3y - 2z = 7 -5x + 5y + z = 9

Mathematics

1 answer:

skelet666 [1.2K]3 years ago

8 0

Answer:

x= 4 y= 7 z= -6

Step-by-step explanation:

solve for one and you get them all

First, I got rid of the z by multiplying common factors (multiplied z by 2) and added equations 2 and 3 together after multiplying by 2

4x - 3y - 2z = 7

-10x+10y+2z= 18

-6x+7y= 25

Then multiplied z by -3 (to get rid of the z) with the original equation 3

3x - 2y + 3z = -20

15x-15y-3z= -27

18x-17y= -47

Next find common thing between the 2 equations we got and multiply it by that and combine (we can multiply first equation by 3 to get rid of the x and solve for y)

-18x+21y= 75

18x-17y= -47

y=7

Work backwards, substitute 7 into the above equation, you get x= 4 and then same for z to get z= -6

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Need help with homework

motikmotik

We have two points describing the diameter of a circumference, these are:

$\begin{gathered} A=(-12,-4) \\ B=(-4,-10) \end{gathered}$

Recall that the equation for the standard form of a circle is:

$(x-h)^2+(y-k)^2=r^2$

Where (h,k) is the coordinate of the center of the circle, to find this coordinate, we find the midpoint of the diameter, that is, the midpoint between points A and B.

For this we use the following equation:

$M=(\frac{x_1+x_2_{}_{}}{2},\frac{y_1+y_2}{2})$

Now, we replace and solve:

$\begin{gathered} M=(\frac{-12+(-4)}{2},\frac{-4+(-10)}{2} \\ M=(\frac{-12-4}{2},\frac{-4-10}{2}) \\ M=(\frac{-16}{2},\frac{-14}{2}) \\ M=(-8,-7) \end{gathered}$

The center of the circle is (-8,-7), so:

$\begin{gathered} h=-8 \\ k=-7 \end{gathered}$

On the other hand, we must find the radius of the circle, remember that the radius of a circle goes from the center of the circumference to a point on its arc, for this we use the following equation:

$r^2=\Delta x^2+\Delta y^2$

In this case, we will solve the delta with the center coordinate and the B coordinate.

$\begin{gathered} r^2=((-4)-(-8))^2+((-10)-(-7)) \\ r^2=(-4+8)^2+(-10+7)^2 \\ r^2=4^2+(-3)^2 \\ r^2=16+9 \\ r^2=25 \\ r=5 \end{gathered}$

Therefore, the equation for the standard form of a circle is:

$\begin{gathered} (x-(-8))^2+(y-(-7))^2=25 \\ (x+8)^2+(y+7)^2=25 \end{gathered}$

In conclusion, the equation is the following:

$(x+8)^2+(y+7)^2=25$

4 0

11 months ago

Four consecutive odd integers add up to -48. What is the least of these integers?

Semmy [17]

Answer:

-9

Step-by-step explanation:

Four consecutive odd integers be (2x - 3),(2x -1),(2x + 1),(2x + 3)

2x-3 + 2x - 1 +2x+1 + 2x+3 = -48

2x + 2x + 2x +2x - 3 - 1 + 3 + 1 = -48

8x = -48

x = -48/8

x = -6

Least of these integer = 2x + 3 = 2*(-6) + 3 = -12 + 3 = -9

3 0

3 years ago

Ayuda es para hoy

vichka [17]

Answer:

1,166 frascos

Step-by-step explanation:

4500 -2456=2044

2044 - 1678=366

366 + 800= 1166

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2 years ago

which property is BEST to use when combining 3/5 + 1/4 + 2/5? A) distributive property B) identity property of addition C) addit

Lana71 [14]

Answer:

D Community property of addition

Step-by-step explanation:

8 0

3 years ago

A dozen bran muffins cost $9.48. Which equation represents the cost, y, of x muffins

swat32

Answer:

12y+9.48x=0

Step-by-step explanation:

Note dozen means 12 in mathematics

So 12 muffins cost $9.48

X muffins cost $y

So let's cross multiply

12×y=9.48×x

12y=9.48x

Substrate 9.48x from both sides

12y-9.48x=0

So the final equation is 12y-9.48x=0

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3 years ago