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Vikentia [17]
3 years ago
14

Five swimmers are entered into a competition. Four of the swimmers have had their

Mathematics
1 answer:
Mamont248 [21]3 years ago
7 0

Answer:

9

Step-by-step explanation:

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Find an equation of the line passing through the pair of points. Write the equation in the form Ax +By = C.
Alexxandr [17]

9514 1404 393

Answer:

  5x -y = -37

Step-by-step explanation:

One way to find the coefficients A and B is to use the differences of the x- and y-coordinates:

  A = Δy = y2 -y1 = 2 -(-3) = 5

  B = -Δx = -(x2 -x1) = -(-7 -(-8)) = -1

Then the constant C can be found using either point.

  5x -y = 5(-7) -2 = -37

The equation of the line is ...

  5x -y = -37

_____

<em>Additional comment</em>

This approach comes from the fact that the slope of a line is the same everywhere.

  \dfrac{y-y_1}{x-x_1}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{\Delta y}{\Delta x}\\\\\Delta x(y-y_1)=\Delta y(x-x_1)\qquad\text{cross multiply}\\\\\Delta y(x-x_1)-\Delta x(y-y_1)=0\qquad\text{subtract y term}\\\\\Delta y(x) -\Delta x(y) = \Delta y(x_1)-\Delta x(y_1)\qquad\text{Ax+By=C form}

The "standard form" requires that A be positive, so we chose point 1 and point 2 to make sure that was the case.

5 0
2 years ago
Giving brainliest and alot of points! A projectile is launched at an angle (θ) of 36° and travels a distance of 375 feet; gravit
abruzzese [7]

Answer:

(c) 112 ft/sec

Step-by-step explanation:

4 = 112.33 ft/sec = 112 ft/sec

6 0
2 years ago
Use the figure below. What is m
tankabanditka [31]

Answer:

150

Step-by-step explanation:

90-60 is 30

180-30 is150

3 0
3 years ago
If a club charges dues of $200 a year, it will have 50 members. For each $5 it raises its dues, it loses a member. USE AN EQUATI
Vikentia [17]

Answer:

The value is      y  =  \$ 225

Step-by-step explanation:

From the question we are told that

   The amount charge per year is  k  =  \$ 200

   The  number of members it will have at this amount is  n  =  50

   The amount amount increase that will lead to the loss of a single member is   z =  \$ 5

        Generally the total amount the club would obtain from  its members is mathematically represented as

      I  =  Amount \  due\ paid *  Number \  of members

Now let x denote the number of member lost

Hence

      I  =  (k + zx) (n-x )

=>    I  =  (200 + 5x) (50-x )

=>  I  = 10000+50x-5x^2

Thus the number of members that be removed to  give the maximum  income from dues is obtained by differentiating the above equation and equating it to zero

           \frac{dI}{dx}  =  50-10x

=>         x   =  5

So from  I  =  (200 + 5x) (50-x ) we have

          I  =  (200 + 5 (5)) (50-5 )

           I  = \$ 10125

So the amount the club should charge is    

         y  =  \frac{10125}{50 - 5}

         y  =  \$ 225

         

7 0
3 years ago
10 ways to divide 96 into equal groups
Andrew [12]

These are the ten ways to divide 96 into equal groups:

96 divided by 2 = 2 groups of 48


96 divided by 48 = 48 groups of 2


96 divided by 12 = 12 groups of 8


96 divided by 8 = 8 groups of 12


96 divided by 32 = 32 groups of 3


96 divided by 3 = 3 groups of 32


96 divided by 24 = 24 groups of 4


96 divided by 4 = 4 groups of 24


96 divided by 6 = 6 groups of 16


<span>96 divided by 16 = 16 groups of 6</span>

4 0
3 years ago
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