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Inessa [10]
3 years ago
8

Indicate the equation of the given line in standard form.The line containing the median of the trapezoid whose vertices are R(-1

, 5) , S(1, 8), T(7, -2), and U(2, 0).
Mathematics
1 answer:
maxonik [38]3 years ago
7 0
RS => y - 5 = (8 - 5)/(1 - (-1)) (x - (-1))
y - 5 = 3/2 (x + 1) => slope = 3/2
ST => y - 8 = (-2 - 8)/(7 - 1) (x - 1)
y - 8 = -10/6 (x - 1) = -5/3 (x - 1) => slope = -5/3
TU => y - (-2) = (0 - (-2))/(2 - 7) (x - 7)
y + 2 = 2/5(x - 7) => slope = 2/5
UR => y = 5/(-1 - 2) (x - 2)
y = -5/3 (x - 2) => slope = -5/3

The median is the line joining the midpoints of the non-parallel sides.
Midpoint of RS = ((-1 + 1)/2, (5 + 8)/2) = (0, 13/2)
Midpoint of TU = ((7 + 2)/2, -2/2) = (9/2, -1)

Equation of the line joining (0, 13/2) and (9/2, -1) is given by y - 13/2 = (-1 - 13/2)/(9/2) x
y - 13/2 = (-15/2)/(9/2) x
y - 13/2 = -15/9x
18y - 117 = -30x
30x + 18y = 117
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X/x+1-1/x-1+2x/x^2-1
Dvinal [7]

Answer:

Input:

x/x + 1 - 1/x - 1 + 2×x/x^2 - 1

Result:

1/x

7 0
3 years ago
Use the counting techniques from the last chapter. A bag contains three red marbles, four green ones, one fluorescent pink one,
sergiy2304 [10]

Answer:

The probability that she gets all the red ones, given that she gets the fluorescent pink one, is P=0.0035 or 0.35%.

Step-by-step explanation:

Susan grabs four marbles at random.

We have to calculate the probabilities that he picks the 3 red ones, given that she already picked the fluorescent pink.

If it is given that the fluorescent pink is already picked, we are left with three red marbles, four green ones, two yellow ones, and four orange ones. A total of 13 marbles.

The probability that the second marble is red is 3 in 13.

The probability that the third marble is also red is 2 (the red marbles that are left) in 12 (the total amount of marbles left), as there is a picking without replacement.

The probability that the fourth marble is 1 in 11.

Then, the probability that the 3 red marbles are picked, is:

P=P_1\cdot P_2\cdot P_3=\dfrac{3}{13}\cdot \dfrac{2}{12}\cdot \dfrac{1}{11}=\dfrac{6}{1716}=0.0035

4 0
3 years ago
I NEED HELP ON THIS PLZZZ HELPP
adell [148]

Answer:

76 \:  {in}^{2}

Step-by-step explanation:

Area of the figure = Are of square with side 8 in + 2 times the area of one triangle with base (8 - 5 = 3) 3 in and height 4 in

=  {(8)}^{2}  + 2 \times  \frac{1}{2}  \times 3 \times 4 \\  \\  = 64 + 12 \\  \\  = 76 \:  {in}^{2}

3 0
3 years ago
Find the area of the figure.EXPlAIN THE STEPS!!!!
hichkok12 [17]

Answer:

30.56 yd²

Step-by-step explanation:

To determine the area of the composite shape, we need to:

  1. Divide the shape into two smaller "known" shapes (Refer to image).
  2. Determine the area of those "known" shapes.
  3. Add the area of the known shapes to obtain the area of the figure.

<u>Determining the area of shape 1 (Rectangle 1):</u>

⇒ Area of rectangle = Lenght × Breadth

⇒                               = 2.1 × 4.8

⇒                               = 10.08 yd²

<u>Determining the area of shape 2 (Rectangle 2):</u>

⇒ Area of rectangle = Lenght × Breadth

⇒                               = 6.4 × 3.2

⇒                               = 20.48 yd²

<u>Determining the area of the figure:</u>

⇒ Area of figure = Area of rectangle 1 + Area of rectangle 2

⇒                         = 10.08 + 20.48

⇒                         = 30.56 yd²

6 0
2 years ago
Show work and Factor 4x^2+xy-18y^2
grigory [225]

Answer:

4x^2+xy-18y^2=(4x+9y)\,(x-2y)

Step-by-step explanation:

Let's examine the following general product of two binomials with variables x and y in different terms:

(ax+by)\,(cx+dy)= ac\,x^2+adxy+bcxy+bdy^2

so we want the following to happen:

a\,c = 4\\ad+bc=1\\bd--18

Notice as well that ad+bc =1 means that those two products must differ in just one unit so, one of them has to be negative, or three of them negative. Given that the product bd=-18, then we can consider the case in which one of this  (b or d) is the negative factor. So let's then assume that a\,\,and \,\,c are positive.

We can then try combinations for  a\,\,and \,\,c  such as:

a = 4;\,\,c=1\\a=2;\,\,c=2\\a=1;\,\,c=4

Just by selecting the first one (a=4;\,\,c=1)

we get that 4d_b=1\\b=-4d-1

and since

bd=-18\\(-4d-1)\,d=-18\\-4d^2-d=-18\\4d^2+d-18=0

This quadratic equation give as one of its solutions the integer: d = -2, and consequently,

d=-18/(-2)\\d=9

Now we have a good combination of parameters to render the factoring form of the original trinomial:

a=4; \,\,b=9;\,\,c=1;\,\,d=-2

which makes our factorization:

(4x+9y)\,(x-2y)=4x^2+xy-18y^2

6 0
3 years ago
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