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4 years ago

State whether the lines are parallel, perpendicular, coinciding, or neither: 6x+3y=–15 and y–3=–2x

Mathematics

1 answer:

lianna [129]4 years ago

4 0

Answer:

Parallel

Step-By-Step Explanation:

Put the Function in Slope Intercept Form and Find the Slope of 6x+3y = 15

6x+3y = 15

3y = -6x + 15

3y/3 = -6x/3 + 15/3

y = -2x + 5

We can see that the slope of 6x+3y = 15 is -2

Put the Function in Slope Intercept Form and Find the Slope of y–3=–2x

y–3=–2x

y = -2x + 3

Here are our two Functions In Slope Intercept Form

y = -2x + 5

y = -2x + 3

Remember the m = slope and the b = y-intercept

y = mx + b

y = -2x + 5

y = -2x + 3

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We can see both equations have the same slope of -2 so this means they could be parallel because parallel functions have the same slope but coinciding functions have the same slope too. To tell if the two functions are coinciding, the functions need to have the same slope and the same y-intercept. Looking at the two functions, we can see they have the same slope of -2 but their y-intercept are different so this makes the two functions parallel.

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Find an equation for the perpendicular bisector of the line segment whose endpoints

TEA [102]

Answer:

y= -2x -8

Step-by-step explanation:

I will be writing the equation of the perpendicular bisector in the slope-intercept form which is y=mx +c, where m is the gradient and c is the y-intercept.

A perpendicular bisector is a line that cuts through the other line perpendicularly (at 90°) and into 2 equal parts (and thus passes through the midpoint of the line).

Let's find the gradient of the given line.

$\boxed{gradient = \frac{y1 -y 2}{x1 - x2} }$

Gradient of given line

$= \frac{1 - ( - 5)}{3 - ( - 9)}$

$= \frac{1 + 5}{3 + 9}$

$= \frac{6}{12}$

$= \frac{1}{2}$

The product of the gradients of 2 perpendicular lines is -1.

(½)(gradient of perpendicular bisector)= -1

Gradient of perpendicular bisector

= -1 ÷(½)

= -1(2)

= -2

Substitute m= -2 into the equation:

y= -2x +c

To find the value of c, we need to substitute a pair of coordinates that the line passes through into the equation. Since the perpendicular bisector passes through the midpoint of the given line, let's find the coordinates of the midpoint.

$\boxed{midpoint = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2}) }$

Midpoint of given line

$= ( \frac{3 - 9}{2} , \frac{1 - 5}{2} )$

$= ( \frac{ - 6}{2} , \frac{ - 4}{2} )$

$= ( - 3 , - 2)$

Substituting (-3, -2) into the equation:

-2= -2(-3) +c

-2= 6 +c

c= -2 -6 (-6 on both sides)

c= -8

Thus, the equation of the perpendicular bisector is y= -2x -8.

5 0

3 years ago

Oranges sell 8 for $1.84. Find the unit rate.

sweet-ann [11.9K]

Step-by-step explanation:

oranges sell 8 for 1.84$

so,

1 unit orange = $\tt{\dfrac{1.84}{8}=0.23\$ }$ ⠀

3 0

3 years ago

The ratio of students who prefer comedic plays to students who prefer romantic plays in the drama club is 2 to 3. If all student

masha68 [24]

Answer:

Step-by-step explanation:

2 to 3 means that the ratio of romantic students has a numerator of 3. If there is a numerator of 3 the denominator has to be 5 because 2+3 is five if the fraction is 3/5, then the answer is A.

4 0

3 years ago

Which expression is equivalent to 6+4.5(32f-14f)

vichka [17]

Answer:

$6 + 4.5(32f - 14f) = 6 + 81f$

Step-by-step explanation:

Let us apply the distributive property to find an equivalent expression for:

$6 + 4.5(32f - 14f)$

For all real numbers a, b, and c, the distributive property says that:

$a(b + c) = ab + ac$

We apply this property to get:

$6 + 4.5(32f - 14f) = 6 + 4.5 \times 32f + 4.5 \times - 14f$

$6 + 4.5(32f - 14f) = 6 + 144f - 63f$

We simplify the RHS to get:

$6 + 4.5(32f - 14f) = 6 + 81f$

8 0

4 years ago

Last question!!!!! explain if posible

emmasim [6.3K]

Answer:

Step-by-step explanation:

Given, 

Line BT is the bisector of <ABC

So,

3x + 13 = 5x - 7

=> 13 + 7 = 5x - 3x

=> 20 = 2x

$= > x = \frac{20}{2}$

=> x = 10

As, 

We got the value of x = 10

Therefore, 

<ABT = 3x + 13 °

= 3×10 + 13 °

= 30 + 13°

= 43°

<TBC = 5x - 7°

= 5 × 10 - 7°

= 50 - 7°

= 43°

Hence,

Value of <ABT = 43° and value of <TBC = 43° (Ans)

6 0

3 years ago