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trapecia [35]
2 years ago
15

Consider the line y=−4/3x+3. Find the equation of the line that is parallel to this line and passes through the point , −4 6. Fi

nd the equation of the line that is perpendicular to this line and passes through the point , −4 6.
Mathematics
1 answer:
andriy [413]2 years ago
7 0

Answer:

The equation of the line parallel to y=4/3x−4 that passes through (-4,6) is y=4/3x−10/3 .

The equation of the line perpendicular to y=43x−4 that passes through (-4,6) is y=−3/4x+10 .

Step-by-step explanation:

Parallel means equal slopes. Hence, the slope of the line parallel to y=4/3x+3 is 4/3 . We know our slope and we know a point. We can therefore use point-slope form to determine the equation of the new line.  

y−y1=m(x−x1)  

y−6=4/3(x−4)  

y−6=4/3x−16/3  

y=4/3x−7/3  

The equation of the line parallel to y=4/3x−4 that passes through (-4,6) is y=4/3x−10/3 .

Question #2:

Perpendicular means negative reciprocal slopes. Hence, the slope perpendicular to y=4/3x+3 is y=−3/4 . We know our slope and we know a point. We can therefore use point-slope form to determine the equation of the new line.  

y−y1=m(x−x1)  

y−6=−3/4(x-4)  

y−6=−3/4x+6  

y=−3/4x+10

The equation of the line perpendicular to y=43x−4 that passes through (-4,6) is y=−3/4x+10 .

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The royal fruit company produces two types of fruit drinks the first type is 70% pure fruit juice and the second type is 95% pur
Ipatiy [6.2K]
This is a typical mixture problem where using a table is the best thing.
                 pints juice        % juice     =      total % juice
juice A            x                  .70          =        .70x
juice B        60-x                 .95          =    .95(60-x)
total              60                  .75          =    60(.75)

The last row gives you a total that you need to use, so do that multiplication to get 45. You now to need to add the last columns together for rows 1 and 2 and set them equal to 45: .7x +.95(60-x) = 45. When you do that math, you'll get that x = 48. This means that you need 48 pints of juice A and 60-48 pints of juice B, which is 12 pints.
6 0
2 years ago
In the first quadrant you start at (7,3) and move 5 unit left
AveGali [126]

Answer:

That would be (2,3)

Step-by-step explanation:

When we're moving left in the coordinate plane, we are subtracting the x-coordinate by how much distance we move.

In this case, 7-5=2, so the new x-coordinate is 2, but the y-coordinate doesn't change since we're going horizontally and not vertically.

7 0
3 years ago
The quotient of x and 6.
vovikov84 [41]

The answer is 1/6. To solve, simply set up an equation. It will be x/6. As you know, x can stand for anything. 1 will be the reasonable number for variable, x. Why? Well since x=1x. You don't actually write "1" Hope this makes your understanding clear.

4 0
3 years ago
You buy items costing $1900 and finance the cost with a fixed installment loan for 24 months at 8% simple interest per year.
ddd [48]

9514 1404 393

Answer:

  1. $304
  2. $91.83

Step-by-step explanation:

1. The finance charge is found from the simple interest formula;

  I = Prt

where P is the principal amount, r is the annual rate, and t is the number of years.

24 months is 2 years, so the interest charged is ...

  I = $1900×0.08×2 = $304

The finance charge is $304.

__

2. The monthly payment will be the total amount due, divided by the number of months.

  payment = ($1900 +304)/24 = $2204/24 ≈ $91.83

The monthly payment is $91.83.

6 0
3 years ago
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