Paul lives on the 13th avenue, which has houses numbered from 13 to 1300. Dennis wants to

Is AB parallel to Bo? Explain.

Svetradugi [14.3K]

Answer:

AB parallel to CD because both lines have a slope of

of 4/3

Step-by-step explanation:

The question is not complete, there is no graph.

A graph for the question is attached below.

From the image attached below, line 1 passes through points A = (-3, -3) and point B = (0, 1) while line 2 passes through point C = (0, -5) and point D = (3, -1).

Two parallel are said to be parallel if the have the same slope. The slope of a line passing through points:

$(x_1,y_1)\ asnd\ (x_2,y_2).\ The\ slope \ is\ given\ as:\\\\Slope(m)=\frac{y_2-y_1}{x_2-x_1}$

Line 1 passes through points A = (-3, -3) and point B = (0, 1), the slope of line 1 is:

$Slope(m)=\frac{y_2-y_1}{x_2-x_1}=\frac{1-(-3)}{0-(-3)}=\frac{1+3}{0+3}=\frac{4}{3}$

Line 2 passes through point C = (0, -5) and point D = (3, -1). the slope of line 2 is:

$Slope(m)=\frac{y_2-y_1}{x_2-x_1}=\frac{-1-(-5)}{3-0}=\frac{-1+5}{3}=\frac{4}{3}$

Therefore AB parallel to CD because both lines have a slope of

of 4/3

7 0

2 years ago

If angle AOB = 4x - 2 and BOC = 5x + 10 and COD = 2x + 14. What is x?

Softa [21]

Angle AOD = 180
4x-2 + 5x+10 + 2x+14 = 180
11x + 22 = 180
11x = 180 - 22 = 158
x = 158/11

5 0

1 year ago

Read 2 more answers

A function f(x) has x intercepts of -3 and -5. What is the constant term in the function?

Anon25 [30]

Answer:

The constant term in the function is 5

Step-by-step explanation:

we have

$f(x)=x^{2}+8x+b$

where

b is the y-intercept or the constant term of the function

Remember that

The x-intercept is the value of x when the value of the function is equal to zero

so

For x=-3 ----> f(x)=0

For x=-5 ----> f(x)=0

substitute any of the intercepts in the function

For x=-3

$0=(-3)^{2}+8(-3)+b$

$0=9-24+b$

$0=-15+b$

$b=15$

$f(x)=x^{2}+8x+15$

Verify with the other intercept

For x=-5

$0=(-5)^{2}+8(-5)+15$

$0=25-40+15$

$0=0$ ---> is true

therefore

The constant term in the function is 5

3 0

2 years ago

Find x in the given figure if m∠AOC = 124°.

Nastasia [14]

Answer:

A) 8

Step-by-step explanation:

Add angles AOB and BOC to get angle AOC.

Since we know the value of AOC is 124 and AOB+BOC=AO

Then (8x+25)+(6x-13)=124.

Combine like terms to get 14x+12= 124.

Solve for x by subtracting 12 from 124, then divide the answer by 14.

3 0

2 years ago

Let Y denote a geometric random variable with probability of success p. a Show that for a positive integer a, P(Y > a) = qa .

lakkis [162]

Answer:

a) For this case we can find the cumulative distribution function first:

$F(k) = P(Y \leq k) = \sum_{k'=1}^k P(Y =k')= \sum_{k'=1}^k p(1-p)^{k'-1}= 1-(1-p)^k$

So then by the complement rule we have this:

$P(Y>a) = 1-F(a)= 1- [1-(1-p)^a]= 1-1 +(1-p)^a = (1-p)^a = q^a$

b) $P(Y>a)= q^a$

$P(Y>b) = q^b$

So then we have this using independence:

$P(Y> a+b) = q^{a+b}$

We want to find the following probability:

$P(Y> a+b |Y>a)$

Using the definition of conditional probability we got:

$P(Y> a+b |Y>a)= \frac{P(Y> a+b \cap Y>a)}{P(Y>a)} = \frac{P(Y>a+b)}{P(Y>a)} = \frac{q^{a+b}}{q^a} = q^b = P(Y>b)$

And we see that if a = 2 and b=5 we have:

$P(Y> 2+5 | Y>2) = P(Y>5)$

c) For this case we use independent identical and with the same distribution experiments.

And the result for part b makes sense since we are interest in find the probability that the random variable of interest would be higher than an specified value given another condition with a value lower or equal.

Step-by-step explanation:

Previous concepts

The geometric distribution represents "the number of failures before you get a success in a series of Bernoulli trials. This discrete probability distribution is represented by the probability density function:"

$P(X=x)=(1-p)^{x-1} p$

If we define the random of variable Y we know that:

$Y\sim Geo (1-p)$

Part a

For this case we can find the cumulative distribution function first:

$F(k) = P(Y \leq k) = \sum_{k'=1}^k P(Y =k')= \sum_{k'=1}^k p(1-p)^{k'-1}= 1-(1-p)^k$

So then by the complement rule we have this:

$P(Y>a) = 1-F(a)= 1- [1-(1-p)^a]= 1-1 +(1-p)^a = (1-p)^a = q^a$

Part b

For this case we can use the result from part a to conclude that:

$P(Y>a)= q^a$

$P(Y>b) = q^b$

So then we have this assuming independence:

$P(Y> a+b) = q^{a+b}$

We want to find the following probability:

$P(Y> a+b |Y>a)$

Using the definition of conditional probability we got:

$P(Y> a+b |Y>a)= \frac{P(Y> a+b \cap Y>a)}{P(Y>a)} = \frac{P(Y>a+b)}{P(Y>a)} = \frac{q^{a+b}}{q^a} = q^b = P(Y>b)$

And we see that if a = 2 and b=5 we have:

$P(Y> 2+5 | Y>2) = P(Y>5)$

Part c

For this case we use independent identical and with the same distribution experiments.

And the result for part b makes sense since we are interest in find the probability that the random variable of interest would be higher than an specified value given another condition with a value lower or equal.

8 0

2 years ago