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defon
3 years ago
6

What does it mean if the distance between a point p and a line l is zero? What does it mean if the distance between two lines is

zero?
Mathematics
1 answer:
-Dominant- [34]3 years ago
4 0

Answer:

a) the point is on the line

b) the lines are the same line

Step-by-step explanation:

a) The distance from a point to a line is zero when the point satisfies the equation of the line. That is, the point is on the line.

b) Two lines are zero distance apart when they are on top of each other, indistinguishable. That is, they are the same line.

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Explain why leg leg(LL) theorem is the same as the side angle side postulate
Sveta_85 [38]
Recall that the LL theorem, as well as the LA theorem, both apply only to right-triangles.

now, in the LL, if a right-triangle has congruent Legs with another, both right-triangles are congruent.

in the LA, if a right-triangle has one Leg and one Angle congruent with another right-triangle, then they're congruent.

well, in the LA, once you have a Leg and then an Angle touching that Leg, the angle is also touching another Leg, since it is an angle and is cornered by two Legs.  The second Leg touched or stemming from that Angle, can only be of one possible length, because the first Leg and the Angle will constrain it to be of certain length.

and that is true for both triangles, and since both triangles will have a second Leg constrained to be a certain length, because of LA, then a second Leg will also be congruent on both right-triangles, so the theorem kinda becomes LAL theorem, Leg Angle Leg, but we can just do away with the Angle part and call it LL.
3 0
3 years ago
An individual is presented with three different glasses of cola, labeled C, D, and P. He is asked to taste all three and then li
Lelu [443]

Question:

An individual is presented with three different glasses of cola, labeled C, D, and P. He is asked to taste all three and then list them in order of preference. Suppose the same cola has actually been put into all three glasses.

(a) What are the simple events in this ranking experiment? (Enter your answers as a comma-separated list.

What probability would you assign to each one?

(b) What is the probability that C is ranked first? (Round your answer to three decimal places.)

(c) What is the probability that C is ranked first and D is ranked last? (Round your answer to three decimal places.)

Answer:

(a)

Sample Space= {CDP, CPD,DCP,DPC,PCD,PDC}

Probability of each = 1/6

(b)

Probability of C ranking first = 0.333

(c)

Probability of C ranking first and D ranking last = 0.167

Step-by-step explanation:

Let C = Cup 1

Let D = Cup 2

Let P = Cup 3

(a) The possible events

Let SS = Sample Space = The possible outcomes

The possible outcomes are

CDP

CPD

DCP

DPC

PCD

PDC

So, SS = {CDP, CPD,DCP,DPC,PCD,PDC}

Possibly outcome = 6

Probability of each event = number of possible outcomes/Number of Total outcomes

Probability of each event = 1/6

(b)

Probability that C is ranked first

Looking at the sample space (SS), you'll notice that only two events starts with C

The events are CDP and CPD

So the probability = 2/6

Probability = 0.333

(c)

Probability that C ranks first and D ranked last.

Looking at the sample space, you'll notice that only one event satisfies the condition

The event is CPD

So, the probability is 1/6

Probability = 0.167

6 0
4 years ago
Substitute the values for a, b, and c into b2 – 4ac to determine the discriminant. Which quadratic equations will have two real
hoa [83]

Answer: 0=2x^2-7x-9\\0=4x^2-3x-1\\0=x^2-2x-8


Step-by-step explanation:

We know that the standard quadratic equation is  ax^2+bx+c=0

Let's compare all the given equation to it and , find discriminant.

1. a=2, b= -7, c=-9

b^2-4ac=(-7)^2-4(2)(-9)=49+72>0

So it has 2 real number solutions.

2. a=1, b=-4, c=4

b^2-4ac=(-4)^2-4(1)(4)=16-16=0

So it has only 1 real number solution.

3. a=4, b=-3, c=-1

b^2-4ac=(-3)^2-4(4)(-1)=9+16=25>0

So it has 2 real number solutions.

4. a=1, b=-2, c=-8

b^2-4ac=(-2)^2-4(1)(-8)=4+32=36>0

So it has 2 real number solutions.

5. a=3, b=5, c=3

b^2-4ac=(5)^2-4(3)(3)=25-36=-9

Thus it does not has real solutions.



5 0
3 years ago
Read 2 more answers
For which polygon is the sum of the interior angles equal to 720 degrees?
Goshia [24]
The answer to this is Hexagon.
4 0
3 years ago
Graph the line that passes through the given point and has the given slope m.
Firdavs [7]

Answer:

The line equation is:

  • y=-\frac{1}{4}x+9

Step-by-step explanation:

Given

  • The point = (4, 8)
  • m = -1/4

We know that point-slope form of the line equation is

y-y_1=m\left(x-x_1\right)

where

  • m = slope
  • (x₁, y₁) = point

substituting the values m = -1/4 and the point (4, 8)

y-y_1=m\left(x-x_1\right)

y-8=\frac{-1}{4}\left(x-4\right)

Add 8 to both sides

y-8+8=\frac{-1}{4}\left(x-4\right)+8

y=-\frac{1}{4}x+9

Thus, the line equation is:

  • y=-\frac{1}{4}x+9
5 0
3 years ago
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