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EastWind [94]
3 years ago
10

Express the equation in the slope y-intercept form: y = mx + b. 2x−3y+1 = 0

Mathematics
1 answer:
horrorfan [7]3 years ago
5 0

Answer:

y = 2/3x+1/3

Step-by-step explanation:

2x−3y+1 = 0

Solve for y

Add 3y to each side

2x−3y+1 +3y= 0+3y

2x +1 = 3y

Divide by 3

2/3 x + 1/3 =3y/3

2/3x +1/3 = y

The slope is 2/3 and the y intercept is 1/3

y = 2/3x+1/3

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This is a 3 part 1 question each part on how to locate the plane and a small explanation report working out the recovery details
sesenic [268]

Third leg.

The crew flies at a speed of 560 mi/h in direction N-20°-E.

The wind has a speed of 35 mi/h and a direction S-10°-E.

We then can draw this as:

We have to add the two vectors to find the actual speed and direction.

We will start by adding the x-coordinate (W-E axis):

\begin{gathered} x=560\cdot\sin (20\degree)+35\cdot\sin (10\degree) \\ x\approx560\cdot0.342+35\cdot0.174 \\ x\approx191.53+6.08 \\ x\approx197.61 \end{gathered}

and the y-coordinate (S-N axis) is:

\begin{gathered} y=560\cdot\cos (20\degree)-35\cdot\cos (10\degree) \\ y\approx560\cdot0.940-35\cdot0.985 \\ y\approx526.23-34.47 \\ y\approx491.76 \end{gathered}

Then, the actual speed vector is v3=(197.61, 491.76).

The starting location for the third leg is R2=(216.66, 167.67) [taken from the previous answer].

Then, we have to calculate the displacement in 20 minutes using the actual speed vector.

We can calculate the movement in each of the axis. For the x-axis:

\begin{gathered} R_{3x}=R_{2x}+v_{3x}\cdot t \\ R_{3x}=216.66+197.61\cdot\frac{1}{3} \\ R_{3x}=216.66+65.87 \\ R_{3x}=282.53 \end{gathered}

NOTE: 20 minutes represents 1/3 of an hour.

We can do the same with the y-coordinate:

\begin{gathered} R_{3y}=R_{2y}+v_{3y}\cdot t \\ R_{3y}=167.67+491.76\cdot\frac{1}{3} \\ R_{3y}=167.67+163.92 \\ R_{3y}=331.59 \end{gathered}

The final position is R3 = (282.53, 331.59).

To find the distance from the origin and direction, we transform the cartesian coordinates of R3 into polar coordinates:

The distance can be calculated as if it was a right triangle:

\begin{gathered} d^2=x^2+y^2_{} \\ d^2=282.53^2+331.59^2 \\ d^2=79823.20+109951.93 \\ d^2=189775.13 \\ d=\sqrt[]{189775.13} \\ d\approx435.63 \end{gathered}

The angle, from E to N, can be calculated as:

\begin{gathered} \tan (\alpha)=\frac{y}{x} \\ \tan (\alpha)=\frac{331.59}{282.53} \\ \tan (\alpha)\approx1.1736 \\ \alpha=\arctan (1.1736) \\ \alpha=49.56\degree \end{gathered}

If we want to express it from N to E, we substract the angle from 90°:

\beta=90\degree-\alpha=90-49.56=40.44\degree

Answer: the final location can be represented with the vector (282.53, 331.59).

1) The distance from the origin is 435.63 miles and

2) the direction is N-40°-E.

7 0
1 year ago
5 rational and irrational numbers in decimal form
alexira [117]

Answer:

A rational number is a number that can be expressed as a fraction (ratio). This includes whole numbers, square roots that can be solved evenly, negatives, decimals, and repeating decimals that can be solved with a fraction.

  1. \frac{1}{2}   ↔  .5
  2. 5  ↔ 5.0
  3. \sqrt{4} ↔ 2.0
  4. -13  ↔  -13.0
  5. 0.38462... (\frac{5}{13})

An irrational number is a number that is NOT rational. It's the complete opposite!

  1. π  ↔  3.14159
  2. .13133133...
  3. \frac{\sqrt{3} }{2}   ↔  0.86603...
  4. -\sqrt{5}  ↔  -2.23607...
  5. \sqrt{5}   ↔   2.23607...

Hope this helps!!!

3 0
3 years ago
??????????????????????????
Zinaida [17]

Answer:

D

Step-by-step explanation:

A)

3(2) + 4(-2) = -2                    2(2)-4(-2) = -8

6 - 8 = -2                              4 + 8 = -8

Correct                                 Incorrect  

B)

3(6) + 4(-5) = -2                    2(6) - 4(-5) = -8  

18 - 20 = -2                            12 + 20 = -8

Correct                                 incorrect

C)

3(4) + 4(4) = -2

12 + 8 = -2

incorrect

D)

3(-2) + 4(1) =-2                        2(-2) - 4(1) = -8

-6 + 4 = -2                                 -4 - 4 = -8

Correct                                      Correct

Best way is process of elimination

5 0
2 years ago
Which table represents a linear function?<br> Please hurry I have to finish this soon!
denis23 [38]

Answer:

C

Step-by-step explanation:

A linear function is the repeating of the same word. Therefore, C would be the correct option. Due to the order 3 9 3 9, this is a linear function. This is just the most logical answer. Please let me know if I am wrong. Sorry if I am :(

6 0
2 years ago
Read 2 more answers
The coaches at Xavier Elementary School bought cases of sports drinks for a field day. They bought 76 cases of drinks. Each case
solong [7]

Answer:

608

Step-by-step explanation:

There are a total of 1,824 drinks since there were 76 cases at 24 drinks a piece. This creates a total number of 24*76 = 1824.

If each student receives 3 then 1824/3 = 608. There were 608 students.

7 0
3 years ago
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