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3 years ago

What is the equation of the line that is parallel to y-3x=2 and that passes through (6,1)?

Mathematics

2 answers:

Rudik [331]3 years ago

8 0

Slope-intercept form: y = mx + b

(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)

For lines to be parallel, they need to have the same slope.

y - 3x = 2 Add 3x on both sides to change the equation to slope-intercept form

y - 3x + 3x = 2 + 3x

y = 3x + 2 The slope is 3, so the parallel line's slope is also 3.

Now that you know the slope, substitute/plug it into the equation

y = mx + b

y = 3x + b To find "b", plug in the point (6, 1) into the equation, then isolate/get the variable "b" by itself

1 = 3(6) + b

1 = 18 + b Subtract 18 on both sides to get "b" by itself

1 - 18 = 18 - 18 + b

-17 = b

y = 3x - 17 Your answer is the 1st option

Sauron [17]3 years ago

6 0

Answer:

y=3x-17

Step-by-step explanation:

You first get y by its and you do this by adding 3x to both sides of the equal sign. You should then get y=3x+2 and then to find the parallel line, the x should stay the same as the first equation so that takes out the -3x. Then you continue to draw the line down until you get a y-intercept which turns out to be 17. You also know that the y-intercept is going to be negative so that takes out the two 19's.

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An economist for a sporting goods company estimates the revenue and cost functions for the production of a new snowboard. These

Vladimir79 [104]

Answer:

Between 1000 and 5000 snowboards will make the function AP(x) >0.

Step-by-step explanation:

Since x can only take possitive values, we have that AP(x) = P(x)/x > 0 if and only if P(x) > 0.

In order to find when P(x) > 0, we find the values from where it is 0 and then we use the Bolzano Theorem.

P(x) = R(x) - C(x) = -x²+10x - (4x+5) = -x²+6x - 5. the roots of P can be found using the quadratic formula:

$r_1,r_2 = \frac{-6 ^+_- \sqrt{6^2-4*(-1)*(-5)} }{2*(-1)} = \frac{-6^+_-\sqrt{16}}{-2} = \{1, 5\}$

Therefore, P(1) = P(5) = 0. Lets find intermediate values to apply Bolzano Theorem:

P(0) = -5 < 0 ( P is negative in (-∞ , 1) )
P(2) = -4+6*2-5 = 3 > 0 (P is positive in (1,5) )
P(6) = -36+36-5 = -5 < 0 (P is negative in (5, +∞) )

The production levels that make AP(x) >0 are between 1000 and 5000 snowboards (because we take x by thousands)

5 0

3 years ago

Simplify the rational Expression <br>

qaws [65]

Answer:

$\frac{x^2+2x}{x-3}$

Step-by-step explanation:

We need to factor out numerator and denominator in order to simplify the rational expression by cancelling common factors.

Numerator : x^3 - 4 x = x (x^2 - 4) = x (x - 2) (x + 2)

Denominator (factoring by grouping):

x^2 - 5 x + 6 = x^2 - 3 x - 2 x + 6 = x (x - 3) - 2 (x - 3) = (x - 3) (x - 2)

Then we can cancel out the common factor (x - 2) in both numerator and denominator, leading to:

x (x + 2) / (x - 3) = (x^2 + 2)/ (x-3)

$\frac{x^2+2x}{x-3}$

4 0

2 years ago

A college has a 30% completion rate, meaning that 30% of all students who start at the college complete the goal they set. The p

RSB [31]

Answer:

45%

Step-by-step explanation:

For simplicity, let use assume there are 100 students in the school.

No. of students to complete college = (30/100) x 100 = 30 Students

President wants to increase by 50% = (50/100) x 30 = 15 Students

New set goal = 30 + 15 = 45 students.

Total number of students = 100 students

Therefore;

Rate goal % = (45/100) x 100% = 45%

4 0

3 years ago

Flying against the wind, a jet travels 2190 miles in 3 hours. Flying with the wind, the same jet travels 9520 miles in 8 hours.

dezoksy [38]

Answer:

Velocity of jet in still air is 970 miles per hour and velocity of wind is 210 miles per hour.

Step-by-step explanation:

Jet's velocity against wind is

3040/4 = 760 miles per hour and flying with wind it is

8260/7 = 1180 miles per hour.

Let the velocity of jet in still air be x miles per hour and velocity of wind be y miles per hour.

As such its velocity against wind is x − y and with wind is x + y and therefore

x − y = 760 and x + y = 1180

Adding the two 2 x = 1940 and x = 970 and y = 1180 − 970 = 210

Hence velocity of jet in still air is 970 miles per hour and velocity of wind is

210 miles per hour.

Actual Answer:

https://socratic.org/questions/flying-against-the-wind-a-jet-travels-3040-miles-in-4-hours-flying-with-the-wind

7 0

3 years ago

3 On a coordinate grid, the location of a lighthouse is at L, and the location of a buoy is at B. At noon, a ship is at the midp

Zarrin [17]

Answer:

$(\frac{1}{2}, 2)$

Step-by-step explanation:

Using the midpoint formula, $M(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})$ , we can find the coordinates that represents the position of the ship at noon.