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4 years ago

Equation for the line containing (4,5) and (-2,-4)

Mathematics

2 answers:

pashok25 [27]4 years ago

8 0

Answer:2y - 3x = -2

Step-by-step explanation:

The equation of line in two point form is given as :

$\frac{y-y_{1}}{x -x_{1}}$ = $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

from the question,

$x_{1}$ = 4

$x_{2}$ = -2

$y_{1}$ = 5

$y_{2}$ = - 4

substituting into the formula , we have

$\frac{-4-5}{-2-4}$ = $\frac{y-5}{x-4}$

$\frac{9}{6}$ = $\frac{y-5}{x-4}$

$\frac{3}{2}$ = $\frac{y-5}{x-4}$

cross multiplying , we have

2(y-5) = 3(x-4)

2y - 10 = 3x - 12

2y - 3x = -12 +10

2y - 3x = -2

mars1129 [50]4 years ago

4 0

Answer:

Step-by-step explanation:

first need to find the slope

-4-5=-9

-2-4=-6

=3/2

y-5=3/2(x-4) this is your point slope equation

y-5=3/2x-6

y=3/2x-1 this is your slope intercept equation

-3/2x+y=-1

muliply by -2

3x-2y=2 this is your equation in standard form

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f(x) = 6x^3 + 3x^2 - 3x - 7

is a polynomial function

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4 years ago

Please help me out with this

Naddik [55]

Answer:

(x - 5)² + (y + 3)² = 16

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

here (h, k) = (5, - 3) and r = 4, so

(x - 5)² + (y - (- 3))² = 4², that is

(x - 5)² + (y + 3)² = 16

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3 years ago

Find the distance between points p(8, 2) and q(3, 8) to the nearest tenth.

grandymaker [24]

Distance between two points, d, is given by
$d= \sqrt{ ( x_{2} - x_{1}) ^{2} + (y_{2} - y_{1}) ^{2} }
$
where: (x1, y1) = (8, 2) and (x2, y2) = (3, 8)
$d= \sqrt{ ( 3 - 8) ^{2} + (8 - 2) ^{2} } \\ d= \sqrt{ (-5)^{2} + 6^{2} } \\ d= \sqrt{25+36} \\ d= \sqrt{61} \\ d=7.8 \ units$

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3 years ago

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Two thirds of a number decreased by six is two. what is the number?

Kisachek [45]

Answer: The number is: " 12 ".

____________________________________
Let "x" represent "the unknown number" (for which we wish to solve.

The expression:

$\frac{2}{3}$ x − 6 = 2 ; Solve for "x" ;
_______________________________________________
Method 1)

Add "6" to EACH SIDE of the equation;
_______________________________________________
→ $\frac{2}{3}$ x − 6 + 6 = 2 + 6 ;

to get:

→ $\frac{2}{3}$ x = 8 ;
______________________________________________
Multiply each side of the equation by " $\frac{3}{2}$ " ; to isolate "x" on one side of the equation ; and to solve for "x" ;
______________________________________________
→ $\frac{3}{2}$ * $\frac{2}{3}$ x = 8 * $\frac{3}{2}$ ;

→ x = 8 * $\frac{3}{2}$ ;

= $\frac{8}{1}$ * $\frac{3}{2}$ ;

= $\frac{8*3}{1*2}$ ;

= $\frac{24}{2}$ ;

= 12 .
______________________________________________
x = 12 .
______________________________________________
Method 2)
______________________________________________
$\frac{2}{3}$ x − 6 = 2 ; Solve for "x" ;

Add "6" to EACH SIDE of the equation;
_______________________________________________
→ $\frac{2}{3}$ x − 6 + 6 = 2 + 6 ;

to get:
→ $\frac{2}{3}$ x = 8 ;
______________________________________________
Multiply each side of the equation by "3" ; to get rid of the "fraction" ;
 → 3 * $\frac{2}{3}$ x = 8 * 3 ;
→ $\frac{3}{1}$ * $\frac{2}{3}$ x = 8 * 3 ;
→ $\frac{3*2}{1*3}$ x = 8 * 3
→ $\frac{6}{3}$ x = 24 ;

→ 2x = 24 ;

→ Divide each side of the equation by "2" ; to isolate "x" on one side of the equation; & to solve for "x" :

2x / 2 = 24 / 2 ;

x = 12 .
__________________________________________________
Method 3).
__________________________________________________
$\frac{2}{3}$ x − 6 = 2 ; Solve for "x" ;
_______________________________________________
Add "6" to EACH SIDE of the equation;
_______________________________________________
→ $\frac{2}{3}$ x − 6 + 6 = 2 + 6 ;

to get:

→ $\frac{2}{3}$ x = 8 ;
______________________________________________
Now, divide each side of the equation by " $\frac{2}{3}$ " ;
to isolate "x" on one side of the equation; & to solve for "x" ;
___________________________________________________
{ $\frac{2}{3}$ x } / { $\frac{2}{3}$ } = 8 / { $\frac{2}{3}$ } ;

to get: x = 8 / { $\frac{2}{3}$ } ;

= 8 * ( $\frac{3}{2}$ ;

= $\frac{8}{1}$ * $\frac{3}{2}$ ;

= $\frac{8*3}{1*2}$ ;

= $\frac{24}{2}$ ;

= 12 ;
___________________________________________
x = 12 .
___________________________________________
NOTE: Variant: (in "Methods 2 & 3") :
___________________________________________
At the point where:
___________________________________________
= 8 * ( $\frac{3}{2}$ ) ;

= $\frac{8}{1}$ * $\frac{3}{2}$ ;
__________________________________________
We can cancel out the "2" to a "1" ; and we can cancel out the "8" to a "4" ;
__________________________________________
{since: "8÷2 = 4" ; and since: "2÷2 =1" } ;
__________________________________________
and we can rewrite the expression:
__________________________________________
$\frac{8}{1}$ * $\frac{3}{2}$ ;
__________________________________________
as: $\frac{4}{1}$ * $\frac{3}{1}$ ;
__________________________________________
which equals:
__________________________________________
→ $\frac{4*3}{1*1}$ ;

= $\frac{12}{1}$ ;

= 12 .
__________________________________________
x = 12 .
__________________________________________
Answer: The number is: " 12 ".
__________________________________________

8 0

4 years ago

Simplify to lowest form. a. 1/2 + 3/2 = ? b. 2/5 + 3/5 = ?

forsale [732]

For letter the answer is 2

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6 0

3 years ago

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