Please help me!!!!!!!!!!!!!!!!!!!!!!

Find the obtuse angle the line y-2x=7 makes with the x- axis

Kazeer [188]

In analytical geometry, there are already derived equations to find the distance of lines and points as well as the angle made between two lines. As special case is when the other line is one of the coordinate axis. Then, the formula can be simplified to

tan θ =m, where m is the slope of the equation

In the next step, we also incorporate operations of calculus. Since the slope is equal to Δy/Δx, this is equivalent to dy/dx in calculus. Therefore, you can find the slope by differentiating the equation in terms of x.

y-2x=7
y = 2x+7
dy/dx = 2 =m

So,

tan θ = 2
θ = tan⁻¹(2)
θ = 63.43°

5 0

3 years ago

An airport limousine can accommodate up to four passengers on any one trip. The company will accept a maximum of six reservation

miss Akunina [59]

Answer:

a) 0.109375 = 0.109 to 3 d.p

b) 1.00 to 3 d.p

Step-by-step explanation:

Probability of someone that made a reservation not showing up = 50% = 0.5

Probability of someone that made a reservation showing up = 1 - 0.5 = 0.5

a) If six reservations are made, what is the probability that at least one individual with a reservation cannot be accommodated on the trip?

For this to happen, 5 or 6 people have to show up since the limousine can accommodate a maximum of 4 people

Let P(X=x) represent x people showing up

probability that at least one individual with a reservation cannot be accommodated on the trip = P(X = 5) + P(X = 6)

P(X = x) can be evaluated using binomial distribution formula

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = 6

x = Number of successes required = 5 or 6

p = probability of success = 0.5

q = probability of failure = 0.5

P(X = 5) = ⁶C₅ (0.5)⁵ (0.5)⁶⁻⁵ = 6(0.5)⁶ = 0.09375

P(X = 6) = ⁶C₆ (0.5)⁶ (0.5)⁶⁻⁶ = 1(0.5)⁶ = 0.015625

P(X=5) + P(X=6) = 0.09375 + 0.015625 = 0.109375

b) If six reservations are made, what is the expected number of available places when the limousine departs?

Probability of one person not showing up after reservation of a seat = 0.5

Expected number of people that do not show up = E(X) = Σ xᵢpᵢ

where xᵢ = each independent person,

pᵢ = probability of each independent person not showing up.

E(X) = 6(1×0.5) = 3

If 3 people do not show up, it means 3 people show up and the number of unoccupied seats in a 4-seater limousine = 4 - 3 = 1

So, expected number of unoccupied seats = 1

5 0

3 years ago

Solve the inequality for x. Show each step of the solution. 4x-6(x+1)>12

VLD [36.1K]

Answer:

x < - 9

steps:

4x - 6(x + 1) > 12

2x - 3(x + 1) > 6

2x - 3x - 3 > 6

2x - 3x > 6 + 3

-x > 6 + 3

-x > 9

x < -9

hope this helps, have a great day
mark brainliest :)!!

8 0

3 years ago

A whole number is 6 more than 2 times another number. The sum of the two numbers is less than 50. This can be written in an ineq

alukav5142 [94]

Answer:

13, 14

Step-by-step explanation:

The parameters of the numbers are;

A whole number value = 2 × Another number + 6

The sum of the two numbers is less than 50

Given that the first number is equal to more than twice the second number, we have that the first number is the larger number, while the second number is the smaller number

Where 'x' represents the second number, we get;

x + 2·x + 6 < 50

Simplifying gives;

3·x + 6 < 50

x < (50 - 6)/3 = 14. $\overline 6$

x < 14. $\overline 6$

Therefore, the numbers for which the inequality holds true are numbers less than 14. $\overline 6$ . From the given option, the numbers are 13, and 14.

3 0

3 years ago

Write a recursive rule for the sequence. Assume it starts with the 1st term. 10, 14, 18, 21...

Papessa [141]

Option D is correct. The correct option for the recursive formula is $f(0) =6;f(n)=f(n - 1)+4$