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3 years ago

What is the simplest form for the expression (-12.7y-3.1x) Plus 5.9y-(4.2y Plus x)

Mathematics

2 answers:

Elodia [21]3 years ago

4 0

Answer:

$\boxed{-4.1x-11y}$

Step-by-step explanation:

$(-12.7y-3.1x) + 5.9y-(4.2y + x)$

Expand brackets.

$-12.7y-3.1x+ 5.9y-4.2y - x$

Combining like terms.

$- x-3.1x-12.7y+ 5.9y-4.2y$

$-4.1x-11y$

irina1246 [14]3 years ago

3 0

Answer:

$\boxed{\red{ - 11y - 4.1x}}$

Step-by-step explanation:

$(- 12.7y - 3.1x) + 5.9y - (4.2y + x) \\ - 12.7y - 3.1x + 5.9y - 4.2y - x \\ - 12.7y + 5.9y - 4.2y- 3.1x - x \\ = - 11y - 4.1x$

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What is the equation of the line that passes through the points (1,5) and (0,3)?

Pavlova-9 [17]

Answer:

y=2x+3

Step-by-step explanation:

first use the y2-y1/x2-x1 then use y=mx+b after

plug in 3 for y2 and 5 for y1

then plug in 0 for x2 and 1 for x1

$\frac{3-5}{0-1}$ = $\frac{-2}{-1} =2$ and 2 is ur slope

___________________

now use y=mx+b

i usually use the first point but u can u anyone u want

plug in 1 for x

plug in 5 for y

and plug in 2 for m

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3 years ago

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Andrei [34K]

Answer:

$\bold{(x+2))^2+(y-2)^2+(z-2)^2=17}$

Step-by-step explanation:

Given the center of sphere is: (-2, 2, 3)

Passes through the origin i.e. (0, 0, 0)

To find:

The equation of the sphere ?

Solution:

First of all, let us have a look at the equation of a sphere:

$(x-a)^2+(y-b)^2+(z-c)^2=r^2$

Where ( $x,y,z$ ) are the points on sphere.

$(a, b, c)$ is the center of the sphere and

$r$ is the radius of the sphere.

Radius of the sphere is nothing but the distance between any point on the sphere and the center.

We are given both the points, so we can use distance formula to find the radius of the given sphere:

$D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}$

Here,

$x_1 =0 \\y_1 =0 \\z_1 =0 \\x_2 =-2 \\y_2 =2 \\z_2 =3$

So, Radius is:

$r = \sqrt{(-2-0)^2+(2-0)^2+(3-0)^2}\\\Rightarrow r = \sqrt{4+4+9} = \sqrt{17}$

Therefore the equation of the sphere is:

$(x-(-2))^2+(y-2)^2+(z-2)^2=(\sqrt{17})^2\\\bold{(x+2))^2+(y-2)^2+(z-2)^2=17}$

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