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3 years ago

Which expressions are equivalent to 3(x + 3y + 2x − y )?

Mathematics

2 answers:

aleksandrvk [35]3 years ago

8 0

Hello,

The correct answer is A) 3(3x + 2y) and 9x + 6y

Hope this helps!!!! (:

valina [46]3 years ago

5 0

3(3x+2y) and 9x+6y.....

You might be interested in

Find the standard equation of a sphere that has diameter with the end points given below. (3,-2,4) (7,12,4)

DiKsa [7]

Answer:

The standard equation of the sphere is $(x-5)^{2} + (y-5)^{2} + (z-4)^{2} = 53$

Step-by-step explanation:

From the question, the end point are (3,-2,4) and (7,12,4)

Since we know the end points of the diameter, we can determine the center (midpoint of the two end points) of the sphere.

The midpoint can be calculated thus

Midpoint = $(\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2}, \frac{z_{1} + z_{2} }{2})$

Let the first endpoint be represented as $(x_{1}, y_{1}, z_{1})$ and the second endpoint be $(x_{2}, y_{2}, z_{2})$ .

Hence,

Midpoint = $(\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2}, \frac{z_{1} + z_{2} }{2})$

Midpoint = $(\frac{3 + 7 }{2}, \frac{-2+12 }{2}, \frac{4 + 4 }{2})$

Midpoint = $(\frac{10 }{2}, \frac{10}{2}, \frac{8 }{2})\\$

Midpoint = $(5, 5, 4)$

This is the center of the sphere.

Now, we will determine the distance (diameter) of the sphere

The distance is given by

$d = \sqrt{(x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2} + (z_{2}- z_{1})^{2} }$

$d = \sqrt{(7 - 3)^{2} +(12 - -2)^{2} + (4- 4)^{2}$

$d = \sqrt{(4)^{2} +(14)^{2} + (0)^{2}$

$d = \sqrt{16 +196 + 0$

$d =\sqrt{212}$

$d = 2\sqrt{53}$

This is the diameter

To find the radius, r

From $Radius = \frac{Diameter}{2}$

$Radius = \frac{2\sqrt{53} }{2}$

∴ $Radius = \sqrt{53}$

r = $\sqrt{53}$

Now, we can write the standard equation of the sphere since we know the center and the radius

Center of the sphere is $(5, 5, 4)$

Radius of the sphere is $\sqrt{53}$

The equation of a sphere of radius r and center $(h,k,l)$ is given by

$(x-h)^{2} + (y-k)^{2} + (z-l)^{2} = r^{2}$

Hence, the equation of the sphere of radius $\sqrt{53}$ and center $(5, 5, 4)$ is

$(x-5)^{2} + (y-5)^{2} + (z-4)^{2} = \sqrt{(53} )^{2}$

$(x-5)^{2} + (y-5)^{2} + (z-4)^{2} = 53$

This is the standard equation of the sphere

6 0

3 years ago

PLEASE HELP.. How do you do this?

juin [17]

Answer:

Step-by-step explanation:

(7x-5)(6x+10)=0

42x + 70x - 30x - 50 = 0

82x = 50

x = 50/82

3 0

3 years ago

A line segment has endpoints A(4, 8) and B(2, 10). The point M is the midpoint of AB. What is an equation of a line perpendicula

Vera_Pavlovna [14]

I)

The Midpoint M of the line segment AB is found using the Midpoint formula:

$M=( \frac{4+2}{2} , \frac{8+10}{2})=(3, 9)$

ii)

the slope of the line through A and B is found by the slope formula:

$m= \frac{y_1-y_2}{x_2-x_1}= \frac{10-8}{2-4}= \frac{2}{-2}=-1$

iii)

the product of the slopes of 2 perpendicular lines is -1, so the slope of the line perpendicular to the line through A and B is -1/(-1)=1

iv)

the equation of the line with slope 1, which contains point M(3, 9) is found by the slope point form equation of a line:

y-9=1(x-3)

y-9=x-3

y=x+6

Answer: y=x+6

7 0

3 years ago

This isn’t math but can someone please give me an example on how you would answer this?

Jobisdone [24]

Answer:

So I would say something like: My living situation doesn't effect my school work I have plenty of time to do my academics. I don't travel between homes I stay in one house. And I have access to a computer and cell phone. -Your friend, Bill Cipher

Step-by-step explanation:

3 0

3 years ago

What is the answer 5+5(9b - 7)

Otrada [13]

5+5= 10
10 time 9b is 90b
10 times -7 is -70
Then 90b-70

3 0

3 years ago