All categories

3 years ago

A line with a slope of 3 passes through the points (-8,f) and (-9,7). What is the value of f

Mathematics

2 answers:

shepuryov [24]3 years ago

8 0

Answer: f = 10

Step-by-step explanation: Start with the slope formula.

m = y₂ - y₁ / x₂ - x₁

Plugging the given information into the

slope formula, we get 3 = 7 - f / -9 - (-8).

This simplifies to 3 = 7 - f / -1.

Multiply both sides of the equation by -1 to get -3 = 7 - f.

Solving from here, you be should be able to easily find that 10 = f.

Remember, it's very easy to check your

answer to these kinds of problems.

Since 10 = f, you can plug a 10 back in for f in the original problem.

Then check to see if the line that passes through the points

(-8, 10) and (-9, 7) really does have a slope of 3.

larisa [96]3 years ago

3 0

Answer:

Step-by-step explanation:

Slope can be calculated by:

$m = \frac{y_2-y_1}{x_2-x_1}$

We know M, y1, x2, and x1. We want to calculate for y2

$\frac{f-7}{-8-(-9)} = 3\\\frac{f-7}{1} = 3\\f-7 = 3\\f = 10\\$

You might be interested in

Adam bought a apples for $1.50 each and b oranges for $2 each. He spent 1.50a+2b dollars. What does 2b represent? Solve for a wh

mario62 [17]

2b represents the price of the oranges times the number of oranges bought
1.50a+2(7)=20 : 2(7)=14 : 20-14=6: 1.50a =6 A=4

6 0

4 years ago

What is the length of the side opposite D?

Kamila [148]

Answer:

5 units

sin(D)= 5/13

Step-by-step explanation:

i just did the question

6 0

3 years ago

Find the slope and the y-intercept of the graph of the linear equation. Then, graph the equation

Stels [109]

Answer:

the y intercept is 0,2

the slope is -6

Step-by-step explanation:

5 0

3 years ago

Simplify 5 x 5² leaving your answer in index form.

kotegsom [21]

Answer:125

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

A ship sails 250km due North qnd then 150km on a bearing of 075°.1)How far North is the ship now? 2)How far East is the ship now

olga_2 [115]

Answer:

1) 288.8 km due North

2) 144.9 km due East

3) 323.1 km

4) 207°

Step-by-step explanation:

Bearing: The angle (in degrees) measured clockwise from north.

Trigonometric ratios

$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$

where:

$\theta$ is the angle
O is the side opposite the angle
A is the side adjacent the angle
H is the hypotenuse (the side opposite the right angle)

Cosine rule

$c^2=a^2+b^2-2ab \cos C$

where a, b and c are the sides and C is the angle opposite side c

-----------------------------------------------------------------------------------------------

Draw a diagram using the given information (see attached).

Create a right triangle (blue on attached diagram).

This right triangle can be used to calculate the additional vertical and horizontal distance the ship sailed after sailing north for 250 km.

Question 1

To find how far North the ship is now, find the measure of the short leg of the right triangle (labelled y on the attached diagram):

$\implies \sf \cos(75^{\circ})=\dfrac{y}{150}$

$\implies \sf y=150\cos(75^{\circ})$

$\implies \sf y=38.92285677$

Then add it to the first portion of the journey:

⇒ 250 + 38.92285677... = 288.8 km

Therefore, the ship is now 288.8 km due North.

Question 2

To find how far East the ship is now, find the measure of the long leg of the right triangle (labelled x on the attached diagram):

$\implies \sf \sin(75^{\circ})=\dfrac{x}{150}$

$\implies \sf x=150\sin(75^{\circ})$

$\implies \sf x=144.8888739$

Therefore, the ship is now 144.9 km due East.

Question 3

To find how far the ship is from its starting point (labelled in red as d on the attached diagram), use the cosine rule:

$\sf \implies d^2=250^2+150^2-2(250)(150) \cos (180-75)$

$\implies \sf d=\sqrt{250^2+150^2-2(250)(150) \cos (180-75)}$

$\implies \sf d=323.1275729$

Therefore, the ship is 323.1 km from its starting point.

Question 4

To find the bearing that the ship is now from its original position, find the angle labelled green on the attached diagram.

Use the answers from part 1 and 2 to find the angle that needs to be added to 180°:

$\implies \sf Bearing=180^{\circ}+\tan^{-1}\left(\dfrac{Total\:Eastern\:distance}{Total\:Northern\:distance}\right)$

$\implies \sf Bearing=180^{\circ}+\tan^{-1}\left(\dfrac{150\sin(75^{\circ})}{250+150\cos(75^{\circ})}\right)$

$\implies \sf Bearing=180^{\circ}+26.64077...^{\circ}$

$\implies \sf Bearing=207^{\circ}$

Therefore, as bearings are usually given as a three-figure bearings, the bearing of the ship from its original position is 207°

8 0

2 years ago

Read 2 more answers