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3 years ago

What is an equation of the line that passes through the points (4, -6)and (8, -4)

Mathematics

2 answers:

kow [346]3 years ago

7 0

Answer:

y = 1/2x - 8.

Step-by-step explanation:

The slope of the line = rise / run

= (-4 - (-6)) / (8 - 4)

= 2/4

= 1/2.

Using the point/slope form of the equation of a line:

y - y1 = m(x - x1)

Here we have m = 1/2 and (x1, y1) = (4, -6):

y - (-6) = 1/2 (x - 4)

y + 6 = 1/2x - 2

y = 1/2x - 8.

QveST [7]3 years ago

3 0

$\bf (\stackrel{x_1}{4}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-4}-\stackrel{y1}{(-6)}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{4}}}\implies \cfrac{-4+6}{4}\implies \cfrac{2}{4}\implies \cfrac{1}{2}$

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-6)}=\stackrel{m}{\cfrac{1}{2}}(x-\stackrel{x_1}{4}) \\\\\\ y+6=\cfrac{1}{2}x-2\implies y=\cfrac{1}{2}x-8$

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It takes two hours for two machines to manufacture 10000 parts. If machine #1 can do the job in one hour less than machine #2, h

elena-14-01-66 [18.8K]

Answer:

Time machine one = 3.56

Time machine two = 4.56

Step-by-step explanation:

Let machine 2 do the job in x hours

Let machine 1 do the job in x - 1 hours.

The general formula for this problem is

Time = A*B/(A + B)

Givens

Time = 2 hours

B = x hours alone

A = x - 1 hours alone.

#################

x *( x - 1)

======= = 2

(x + x - 1)

(x^2 - x)/(2x - 1) = 2

x^2 - x = 2(2x - 1)

x^2 - x = 4x - 2

x^2 - 5x + 2 = 0

a = 1

b = - 5

c = 2

This gives 2 roots

x = 4.56

x = 0.43

The second root will not work because when 1 is subtracted from 0.43 the time give will be minus, which won't work.

Time for machine 2 is 4.56

The time for machine 1 is 3.56

Check

(A * B)/(A + B) = 2

A = 4.56

B = 3.56

Time = 4.56*3.56/(4.56 + 3.56)

Time = 16.2336/(8.12)

Time = 1.9992

The rounding error in the check comes from the rounding error in the times.

4 0

3 years ago

Triangle PQR is reflected across a line, P = (4,–5), and P’ = (–4, –5). What is the line of reflection? the x-axis the y-axis th

Evgesh-ka [11]

For this case we have that the original vertex is given by:

P = (4, -5)

We apply the following transformation:

(x, y) (-x, y)

We have then:

(4, -5) (- (4), -5) (- 4, -5)

Therefore, we have a reflection on the y axis.

The point obtained is the vertice:

P '= (-4, -5)

Answer:

the line of reflection is:

the y-axis

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GenaCL600 [577]

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2 years ago

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Anyone wanna help?please

timama [110]

$\large\underline{\underline{\red{\rm\blue{\longmapsto} Step-by-step\: Explanation:-}}}$

Given to points to us are :-

( 3 , -6 )
( -1 , -8 )

( As these are plotted on graph with yellow dots .)

Now , we can use Distance Formula , which is :-

$\boxed{\pink{\tt Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}}$

Here ,

x1 = 3 .
x2 = -1.
y1 = (-6)
y2 = (-8).

<u>→ Substituting the respective values , </u>

⇒ Distance = √ [ { 3 - (-1)}² + { -6 -(-8)²} ] .

⇒ Distance = √ (3+1)² + (8-6)²

⇒ Distance = √ 4² + 2²

⇒ Distance = √ 16 + 4

⇒ Distance = √20 = √4 × √5

⇒ Distance = 4√5units .

<u>Hence the distance between two points is 4√5u.</u>

3 0

3 years ago

What is the measure of angle A?

I am Lyosha [343]

First you have to find the angle B (check attachment)

$B = 180^{\circ} - 137^{\circ} = 43^{\circ}\\$

Then you can find the last angle inside the triangle, which I'll call C

$C = 180^{\circ} - 102^{\circ} - 43^{\circ} = 35^{\circ}$

Now you can find angle A

$A = 180^{\circ} - C = 180^{\circ} - 35^{\circ} = 145^{\circ}$

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3 years ago