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luda_lava [24]
3 years ago
9

1 question pleasee i need this asap!! thank you :D

Mathematics
1 answer:
nydimaria [60]3 years ago
6 0
The correct answer is:  [A]:  " x = 6 " or  " x = - 9 " .
________________________________________________________
Explanation:
________________________________________________________
Given the following equation:
________________________________________________________
   
   " x² + 3x – 54 = 0 " ;  Solve for "x" ; 
_____________________________________________________
Check if the part of the equation on the "left-hand side" can be "factored":

   " x² + 3x – 54 " ; 

→  We see the " + 3x " and the " – 54 "

Factors of " -54 " that add up to " +3" ;

Let us try:  " -9, 6" ;   →  " -9 + 6 = -3 " ;  →  " -3 ≠ +3 ;

Let us try:  " 9, -6" ;   →  " 9 + (-6) = 9 – 6 = 3 " ;   YES!
       →   {that is:  " +9 , -6 "} ; 


So, we can rewrite the entire equation:

→  " (x + 9)(x – 6) = 0 " ;

→  " x = -9 " ;  or,  " x = 6 " ; which is:  

→  Answer choice:  [A]:  " x = 6 "  or  " x = - 9 " .
______________________________________________________
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barxatty [35]

Answer:

<u>graphically</u> :

The graph is symmetrical about the origin.

Then it represents an odd function.

<u>symmetry </u>:

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Find the distance from point A(−9,−3) to the line y = x−6. Round your answer to the nearest tenth.
Vladimir79 [104]

The distance from point A(−9,−3) to the line y = x−6 is 8.5 units

<u>What is slope ?</u>

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

step 1

Find the slope of the perpendicular line to the given line

y=x-6 ---> given line

The slope is m=1

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

m1*m2 = -1

we have

m1=1

substitute

(1)*m2 = -1

so

m2 = -1

step 2

Find the equation of the perpendicular line to the given line

The equation in point slope form is

y-y1=m(x-x1)

we have

m=-1

(x1,y1)=(−9,−3)

substitute

y+3=-1(x+9)--> equation in point slope form

y+3= -x-9

y= -x-12---> equation in slope intercept form

step 3

Find the intersection point between the given line and the perpendicular line to the given line

we have the system of equations

y = x−6.

y= -x-12

Solve the system by graphing

The intersection point is (-3,-9)

see the attached figure

step 4

we know that

The distance between the point A and the point (-3,-9) is the same that the distance between point A and the line y=x-6

the formula to calculate the distance between two points is equal to

d=√[(y2-y1)² + (x2-x1)²]

substitute the values

d=√[(-9+3)² + (-3+9)²]

d= √72 units

simplify

d= 6√2 = 8.5 units

To learn more about the slope from the given link

brainly.com/question/16949303

#SPJ1

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Please help me !!!!
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Answer:

2(x+3)

Hope u get it correct!!!

Step-by-step explanation:

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