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4 years ago

8. Line AB passes through A(-2,4) and B(-8,-6).

Mathematics

1 answer:

netineya [11]4 years ago

8 0

Answer:

AB : $\frac{5}{3}$

PT : $-\frac{1}{5}$

Step-by-step explanation:

The line AB passes through A(-2,4) and B(-8,-6) points.

Therefore, the slope of the line AB will be $\frac{4-(-6)}{-2-(-8)} =\frac{5}{3}$ (Answer)

Again line PT passes through P(3,-1) and T(8,-2) points.

Therefore, the slope of the line PT will be $\frac{-1-(-2)}{3-8} =-\frac{1}{5}$ . (Answer)

Here we have applied the formula of slope of a straight line passing through the points $(x_{1},y_{1})$ and $(x_{2},y_{2} )$ as given by $\frac{y_{1}-y_{2} }{x_{1}-x_{2} }$ .

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Step-by-step explanation:

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3 years ago

Let f(x)=t^2. What is f(t-4)?

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3 years ago

A’s DJ service charges a $200 setup fee and $75 an hour after that.

Bogdan [553]

The total cost includes the setup cost + per hour cost.

Let, x represents the time and y represents the total cost.

$y=200+75x$ .... (1)

Let Y represent the cost for B's DJ service.

$y=125x$ .... (2)

a. Graphing both the equations give the intersection point (solution) as (4,500)

It means for 4 hours, the total cost of both the DJ's is same at $500.

b. Substitution Method.

Plug y = 125x in equation (1)

$125x= 200+75x$

$125x-75x=200$

$50x=200$

$x=4$

$y=125\times 4 =500$

Hence, the total cost for 4 hours in both the service is $500.

c. Addition method.

Multiply equation (2) by -1

$-y = -125x$ .... Equation (3).

Add euation (1) and equation (3)

$y+(-y) = 200+75x-125x$

$0=200-50x$

$50x=200, x=4$

$y=500$

Solution: For x = 4, y = 500 ( same as the previous two methods)

For x = 2, equation (1)

$y=200+(75\times 2) = 350$

For x = 2, equation (2)

$y= 125\times 2 =250$

Hence, for 2 hours, DJ B would be a better choice since it would charge $250.

For x = 6 hours, equation (1)

$y=200+(75\times 6) =650$

For x= 6, equation (2)

$y=125\times 6=750$

For 6 hours, DJ A would be better option since it charges $650 for 6 hours.

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3 years ago