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yawa3891 [41]
2 years ago
10

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

Mathematics
1 answer:
Alexxandr [17]2 years ago
5 0

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.

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If the polynomials p(x)=2x³ +bx² +3x-5 and q(x)= x³+x² -4x-b leave the same remainder, when divided by x-2, prove that b = -13/5
Tju [1.3M]

Step-by-step explanation:

Lets first find the remainder when p(x) is divided by x-2

p(2)=2(2)³+b(2)²+3(2)-5

p(2)=16+4b+6-5

p(2)=4b+17

Now let's find the remainder when q(x) is divided by x-2

q(2)=(2)³+(2)²-4(2)-b

q(2)=8+4-8-b

q(2)=4-b

Now let's equate both of them

4b+17=4-b

4b+b=4-17

5b=-13

b=-13/5 as required

5 0
2 years ago
The length of a rectangle is 8 inches more than the width. The perimeter is 36 inches. Find the length and the width (in inches)
Fofino [41]

Answer: w = 4 and l = 12

Step-by-step explanation:

7 0
3 years ago
Cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 5 inches. The height of the cone is 15 inche
ss7ja [257]

Answer:

V_{cylinder}=251.2\ in^3,

V_{cone}=251.2\ in^3,

V_{cylinder}=V_{cone}.

Step-by-step explanation:

The volume of the cylinder is

V_{cylinder}=\pi r^2 h,

where r is the radius of a base circle and h is the cylinder's height.

If cylinder has diameter of 8 inches, then its radius is 4 inches. The height of the cylinder is 5 inches. Thus, the volume of the cylinder is

V_{cylinder}=3.14\cdot 4^2\cdot 5=251.2\ in^3.

The volume of the cone is

V_{cone}=\dfrac{1}{3}\pi r^2 h,

where r is the radius of a base circle and h is the cone's height.

If cone has diameter of 8 inches, then its radius is 4 inches. The height of the cone is 15 inches. Thus, the volume of the cone is

V_{cylinder}=\dfrac{1}{3}\cdot 3.14\cdot 4^2\cdot 15=251.2\ in^3.

As you can see the cylinder and the cone have the same volume.

4 0
3 years ago
Who can give me this answer
-BARSIC- [3]
The believe the answer is 3/5
3 0
3 years ago
The probability of picking two black marbles from a box at random without replacement is 10/91 .
sasho [114]
The probability of the 2 events are multiplied to get the result 10/91

so we have the relation 5/14 *  x  = 10/91

where x is the probability of drawing the second black

so x =  10/91 * 14/5 =  4/13   answer
8 0
3 years ago
Read 2 more answers
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