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tensa zangetsu [6.8K]
3 years ago
14

Simplify number 17 please

Mathematics
2 answers:
SpyIntel [72]3 years ago
5 0
( \frac{4x^{5}y}{16xy^{4}} )^{3}\\
(\frac{1x^{4}}{4y^{3}})^{3}\\
\frac{x^{4*3}}{4^{3}y^{3*3}}\\\\
\frac{x^{12}}{64y^{9}}
Brrunno [24]3 years ago
4 0
64x^15y^3/4096x^3y^12
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What would be a line perpendicular to (2,3) (5,5)?
ladessa [460]

9514 1404 393

Answer:

  3x + 2y = 0   or   y = -3/2x

Step-by-step explanation:

The relationship between a line and its perpendicular is that their slopes are opposite reciprocals of each other. So, the thing you need to know about the line through the two given points is its slope. That is found using the slope formula:

  m = (y2 -y1)/(x2 -x1) . . . . . . where the two give points are (x1, y1) and (x2, y2)

Putting your point coordinates in this formula gives ...

  m = (5 -3)/(5 -2) = 2/3

Then the perpendicular line will have a slope that is the opposite reciprocal:

  slope of perpendicular = -1/m = -1/(2/3) = -3/2

You have not said whether the perpendicular line must meet any other requirement, so the simplest one we can write is ...

  y = mx + b . . . . . m is the slope and b is the y-intercept

  y = -3/2x . . . . . . has a y-intercept of 0 (goes through the origin)

Multiplying by 2 and adding 3x gives ...

  3x + 2y = 0 . . . . . standard form equation

_____

<em>Comment on the attachment</em>

The geometry program I used to create the attachment wrote the equation of the line through the given points as ...

 2x -3y = -5 . . . . . standard form equation

The equation of a perpendicular line can be created from this form by swapping the x- and y-coefficients and negating one of them. Simply swapping the coefficients would give ...

  -3x +2y = <something>

In standard form, we want the leading coefficient to be positive, so we can choose to negate the x-coefficient. The <something> can be zero to make the line go through the origin.

  3x +2y = 0 . . . . . a perpendicular in standard form

__

If you need to have the line go through a particular point, you can determine the constant value (on the right of the = sign) by putting the point coordinates in for x and y.

_____

Method summary:

  • find the slope of the given line
  • determine its opposite reciprocal to find the slope of the perpendicular line
  • use that new slope in an appropriate form to have the line go where you want it to go. (Point-Slope Form is often useful)

3 0
2 years ago
6. Find the sum or difference<br> 1/3(9 - 6m) + 1/4 (12m-8)
romanna [79]

Answer:

m+1

Step-by-step explanation:

1/3(9 - 6m) + 1/4 (12m-8)

Distribute

1/3 *9  - 1/3 *6m  + 1/4 * 12m - 1/4 *8

3 -2m + 3m -2

Combine like terms

-2m+3m +3-2

m+1

6 0
3 years ago
What is the volume of the pyramid
alexgriva [62]

Answer:

Option A - 32 cm³

Step-by-step explanation:

Volume of a pyramid is given by the formula :

V = \frac{lwh}{3}

Substituting values given gives us :

V = (4)(4)(6)/3

V = (16)(6)/3

V = 96/3

V = 32

Units will be cm³ as this is volume

Hope this helped and have a good day

5 0
1 year ago
Read 2 more answers
Geometry help help help
Kruka [31]
BD = AC/2
4x+2 = (5x+13)/2

2(4x+2) = 5x+13
8x + 4 = 5x+13
8x - 5x = 13 -4
3x = 9
x = 3

8 0
3 years ago
Solve similar triangles advanced part 1​
balu736 [363]

9514 1404 393

Answer:

  x = 4

Step-by-step explanation:

Corresponding segments of similar triangles are proportional. Here, the similar triangles are ...

  ΔABC ~ ΔADE

so the relationship between the sides is ...

  BC/BA = DE/DA . . . . . . we put the unknown value in the numerator

  x/4 = 12/(4+8)

  x = 4(1) = 4

The length of side x is 4.

4 0
3 years ago
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