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3 years ago

Find the distance between the point P(0, 0) and the line y = −x + 4 using the distance formula

Mathematics

1 answer:

Verdich [7]3 years ago

4 0

Answer:

The distance between the point P(0, 0) and the line y = −x + 4 is $2\sqrt{2}$ units.

Step-by-step explanation:

Distance between the point $(x_0,y_0)$ and the line $ax+by+c=0$ is

$d=\dfrac{|ax_0+by_0+c|}{\sqrt{a^2+b^2}}$

The given equation is

$y=-x+4$

Taking all terms on the left side.

$x+y-4=0$

The distance between the point $(0,0)$ and the line $x+y-4=0$ is

$d=\dfrac{|0+0-4|}{\sqrt{1^2+1^2}}$

$d=\dfrac{|-4|}{\sqrt{2}}$

$d=\dfrac{4}{\sqrt{2}}$

Rationalize denominator.

$d=\dfrac{4}{\sqrt{2}}\times \dfrac{\sqrt{2}}{\sqrt{2}}$

$d=\dfrac{4\sqrt{2}}{2}$

$d=2\sqrt{2}$

Therefore, the distance between the point P(0, 0) and the line y = −x + 4 is $2\sqrt{2}$ units.

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Plot the x- and y-intercepts to graph the equation y=-x-5

Rainbow [258]

The y intercept is the y value determined when x = 0
y = -0 - 5
y = - 5
The y intercept is (0,-5)

The x intercept is where y = 0
0 = -x - 5
5= -x
x = - 5
The x intercept is (- 5, 0)

6 0

3 years ago

Read 2 more answers

The two-way table shows the distribution of gender to favorite film genre for the senior class at Mt. Rose High School.

Studentka2010 [4]

Answer:

The second statement is correct

Step-by-step explanation:

Hello!

The table shows the information of the favorite film genre of the students of the class regarding their gender.

You have to prove which statement is correct:

1)The probability of randomly selecting a student who has a favorite genre of drama and is also female is about 17 percent.

If you chose a student at random, you need to calculate the probability of its favorite genre being "Drama" (D) and the student being female (F), symbolically: P(D∩F)

To do so you have to divide the number of observed students that are female and like drama by the total number of students:

P(D∩F)= $\frac{24}{240}= \frac{1}{10} =0.10$

This means that the probability of choosing a student at random and it being a female that likes drama is 10%.

This statement is incorrect.

2) Event F for female and event D for drama are independent events.

Two events are independent when the occurrence of one of them doesn't affect the probability of occurrence of the other one.

So if F and D are independent then:

P(F)= P(F|D)

-or-

P(D)=P(D|F)

The probability of the event "Female" is equal to $P(F)= \frac{Total females in the class}{n} = \frac{144}{240} = \frac{3}{5}= 0.6$

The probability of the event "Drama" is:

$P(D)= \frac{Total students that like "Drama"}{n}= \frac{40}{240}= \frac{1}{6}= 0.166$

$P(F|D)= \frac{P(FnD)}{P(D)}= \frac{\frac{1}{10} }{\frac{1}{6} }= \frac{3}{5} = 0.6$

As you can see P(F)= 0.6 and P(F|D)= 0.6 so both events are independent.

This statement is correct.

3) The probability of randomly selecting a male student, given that his favorite genre is horror, is 16/40

This is a conditional probability, you already know that the student likes horror movies (H), and out of that group you want to know the probability of the student being male (M):

$P(M|H)= \frac{number of male students that like horror movies}{total students that like horror movies}= \frac{16}{38}= \frac{8}{19} = 0.42$

This statement is incorrect.

4) Event M for male and event A for action are independent events.

Same as the second statement, if the events "Male" and "Action" are independent then:

P(M)= P(M|A)

-or-

P(A)= P(A|M)

$P(M)= \frac{96}{240}= \frac{2}{5}= 0.4$

$P(A)= \frac{72}{240} =\frac{3}{10}= 0.3$

$P(AnM)= \frac{28}{240}= \frac{7}{60}= 0.11666$

$P(M|A)= \frac{P(MnA)}{P(A)}= \frac{\frac{7}{60} }{\frac{3}{10} } = \frac{7}{18}= 0.3888$

$P(M)= \frac{2}{5}$ and $P(M|A)= \frac{7}{18}$

P(M)≠ P(M|A) the events are not independent.

This statement is incorrect.

I hope this helps!

6 0

3 years ago

A motor cyclist makes a trip of 500km. If he had increased his speed by 10kmh-1, he could have covered 600km in the same time. W

amm1812

Answer:

the original speed is 50 km/h

Step-by-step explanation:

Let us assume the original speed be x

and fastest speed be (x+ 10)

Now here apply the time formula

i.e. distance by the speed

Original time = Fastest time

500 ÷ x = 600 ÷ x + 10

Now do cross multiplication

600x = 500(x + 10)

600x = 500x + 5000

100x = 5000

x = 50 km/h

Hence, the original speed is 50 km/h

4 0

3 years ago

How do i do this: 5. graph f(x)=|x-1| and g(x)=|1/2x-1| Compare the graph of g to the graph of f 6. graph f(x)=|x+2|+2 and g(x)=

kari74 [83]

To graph f(x)=|x-1| and g(x)=|1/2x-1| pick some numbers for x and insert them into the equation for x. After inserting the numbers for x, solve and find f(x) and g(x)
For instance, am going to insert 1 for f(x) and g(x)

f(x)=|x-1| and g(x)=|1/2x-1|

f(1)=|1-1| and g(1)=|1/2(1)-1|
f(1)= 0 and g(1)=|1/2x-1|

(1,0) and (1, -1/2)

After working the equation above we got our first point, which you can plot. Do the same to get the rest of your points to plot

7 0

4 years ago

Hey can you please help me posted picture of question

Anika [276]

When a number is added to or subtracted from a function it moves it vertically up or down.

G(x) is obtained by subtracting 3 from F(x). This means G(x) is obtained by vertical translation of F(x). Since 3 is subtracted from F(x), the vertical translation is downwards.

So, we can say: G(x) is obtained by moving F(x) 3 units vertically down.

Therefore, the correct answer is option D

4 0

3 years ago