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3 years ago

What are three collinear points in the figure below?

Mathematics

1 answer:

algol [13]3 years ago

7 0

Answer:

B. W,V,Z

Step-by-step explanation:

Collinear points are two more points in the same plane that lie in a straight line.

From the diagram, Z is the intersection of the two diagonals of quadrilateral VXWY.

The points V, Z and W lie along the same diagonal, hence they are collinear.

The point y, Z, and X also lie along the same diagonal, these are also collinear.

The correct choice is B

You might be interested in

Find the point on the line y = 3x + 2 that is closest to the origin.

anzhelika [568]

1.
the slope of the line y=3x+2 is the coefficient of x, that is 3.

2.
the slope of any line perpendicular to the line y=3x+2, is m, such that:

$3*m=-1$

so $m= \frac{-1}{3}$

3.
so any line with equation y=-1/3x+k is perpendicular to y=3x+2.

moreover, the line y=-1/3x (so k=0) is the line passing through the origin
(0, 0) and perpendicular to y=3x+2

4. This means that the closest point of y=3x+2 to the origin is the intersection point of lines y=3x+2 and y=-1/3x

5.
to find this point:

3x+2=(-1/3)x
x(3+1/3)=-2
x(9/3+1/3)=-2

x*10/3=-2

$x= \frac{-2*3}{10} = \frac{-6}{10}=-0.6$

thus y is : (-1/3)(-6/10)=0.2

Answer: (-0.6, 0.2)

3 0

3 years ago

Factor the cubic polynomial 6x3 – 11x2 – 12x 5. use the rational root theorem and synthetic division

pochemuha

The factorization of given cubic polynomial 6x³ - 11x² - 12x + 5 is:

6x³ - 11x² - 12x + 5 = (x + 1)(x - $\frac{5}{2}$ )(x - $\frac{1}{3}$ )

For given question,

We have been given the cubic polynomial 6x³ - 11x² - 12x + 5

We need to factorize given cubic polynomial.

By the rational roots theorem, any rational zero of f(x) is expressible in the form ± $\frac{p}{q}$ for integers p, q with p a divisor of the constant term 5 and q a divisor of the coefficient 6 of the leading term.

Factors of p = 5: 1, 5

Factors of q = 6: 1, 2, 3, 6

That means that the only possible rational zeros are:

±{ $\frac{1}{1} ,\frac{1}{2} ,\frac{1}{3} ,\frac{1}{6} ,\frac{5}{1} ,\frac{5}{2} ,\frac{5}{3} ,\frac{5}{6}$ }

= ±{ $1 ,\frac{1}{2} ,\frac{1}{3} ,\frac{1}{6} ,5 ,\frac{5}{2} ,\frac{5}{3} ,\frac{5}{6}$ }

We need to find the exact zeros of given cubic polynomial.

For x = 1,

6(1)³ - 11(1)² - 12(1) + 5 = -12

This means, x = 1 is not a zero of given cubic polynomial.

For x = -1,

6(-1)³ - 11(-1)² - 12(-1) + 5 = 0

This means, x = -1 is a zero of given cubic polynomial and (x + 1) is a factor.

To factorize given cubic polynomial we use synthetic division.

The synthetic division (6x³ - 11x² - 12x + 5) ÷ (x + 1) is as shown in following image.

⇒ 6x³ - 11x² - 12x + 5 = (x + 1)(6x² - 17x + 5)

The factors of above quadratic polynomial 6x² - 17x + 5 are:

⇒ 6x² - 17x + 5 = (x - $\frac{5}{2}$ )(x - $\frac{1}{3}$ )

So, the factors of given cubic polynomial are:

⇒ 6x³ - 11x² - 12x + 5 = (x + 1)(x - $\frac{5}{2}$ )(x - $\frac{1}{3}$ )

Therefore, the factorization of given cubic polynomial 6x³ - 11x² - 12x + 5 is: 6x³ - 11x² - 12x + 5 = (x + 1)(x - $\frac{5}{2}$ )(x - $\frac{1}{3}$ )

Learn more about the polynomial here:

brainly.com/question/16594008

#SPJ4

4 0

1 year ago

A rock is thrown from the top of a tall building.The distance in feet between the rock and the ground t seconds after thrown is

marusya05 [52]

Answer:

0.448 seconds

Step-by-step explanation:

d = -16t² -4t + 412

find t when d = 407

substituting d = 407 into the equation:

407 = -16t² -4t + 412 (subtract 407 from both sides)

-16t² -4t + 412 - 407 = 0

-16t² -4t + 5 = 0 (multiply both sides by -1)

16t² + 4t - 5 = 0

solving using your method of choice (i.e completing the square or using the quadratic equation), you will end up with

t = (-1/8) (1 + √21)= -0.70 seconds (not possible because time cannot be negative)

t = (-1/8) (1 -√21) = 0.448 seconds (answer)

4 0

3 years ago

Assume the sample is a random sample from a distribution that is reasonably normally distributed and we are doing inference for

e-lub [12.9K]

Answer:

a) Hence the endpoints of a t-distribution with 5% beyond them in each tail if the sample has size n=12 is ± 1.796.

b) Hence the endpoints of a t-distribution with 1% beyond them in each tail if the sample has size n=20 is ± 2.539.

Step-by-step explanation:

Here the answer is given as follows,

5 0

2 years ago

The standard deviation of the midterm scores at ucb for stats 2 is 50 points. the teacher takes a sample of 100 students' scores

Alborosie

<span>The measure standard deviation quantifies the amount of variation or dispersion of a set of data values.</span>The standard deviation is the square root of the variance.
The standard deviation in this case is 50/ sqrt(100)= 50/10=5.

6 0

3 years ago