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djverab [1.8K]
3 years ago
6

Find the equation of a line that passes through (0,0) that is perpendicular to 2x+3y=-6

Mathematics
1 answer:
Dovator [93]3 years ago
8 0

The slope-intercept form of a line:

y=mx+b

m - slope

b - y-intercept

Convert 2x + 3y = -6 to the slope-intercet form:

2x+3y=-6         <em>subtract 2x from both sides</em>

3y=-2x-6         <em>divide both sides by 3</em>

y=-\dfrac{2}{3}x-2

Let k:y=m_1x+b_1 and l:y=m_2x+b_2

l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}

We have m_1=-\dfrac{2}{3}

Therefore

m_2=-\dfrac{1}{-\frac{2}{3}}=\dfrac{3}{2}

We have the equation of a line:

y=\dfrac{3}{2}x+b

Put the coordinates of the point (0, 0) to the equation:

0=\dfrac{3}{2}(0)+b

0=b\to b=0

Answer: \boxed{y=\dfrac{3}{2}x}


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Is x = 7 a solution to the equation 3x - 4 = 15? No Yes
Elis [28]

Answer:

No, because 3 x 7 = 21 - 4 = 17

Step-by-step explanation:

8 0
2 years ago
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An unconditional acceptance into a graduate program at a university will be given to students whose GMAT score plus 100 times th
Talja [164]

Answer:

​Robbin's grade point average must be at least 2.75 in order to be unconditionally accepted into the program. ​

Step-by-step explanation:

An unconditional acceptance into a graduate program at a university will be given to students whose GMAT score plus 100 times the undergraduate grade point average is at least 1075

Considering the GMAT score x, and the GPA y, this situation is modeled by the following inequality:

x + 100y \geq 1075

Robbin's GMAT score was 800.

This means that x = 800, and thus:

x + 100y \geq 1075

800 + 100y \geq 1075

100y \geq 275

What must her grade point average be in order to be unconditionally accepted into the​ program?

Solving the above inequality for y:

100y \geq 275

y \geq \frac{275}{100}

y \geq 2.75

Thus:

​Robbin's grade point average must be at least 2.75 in order to be unconditionally accepted into the program. ​

7 0
2 years ago
What I would like to know is how to solve this problem
ratelena [41]
30 - 29 = 1 for the first one.
3 0
2 years ago
Is the spinner below , what is the probability of lading on 2 ? Help me !!!!
-BARSIC- [3]

Answer:

c

Step-by-step explanation:

1/6. theres only one 2, and theres 6 numbers total.

3 0
3 years ago
PLEASE HELP ASAP!!!!
lina2011 [118]
<h3>Answer:</h3>

System

  • p + m = 10
  • 0.8m = 0.4·10

Solution

  • p = m = 5 — 5 lb peanuts and 5 lb mixture
<h3>Step-by-step explanation:</h3>

(a) Generally, the equations of interest are one that models the total amount of mixture, and one that models the amount of one of the constituents (or the ratio of constituents). Here, there are two constituents and we are given the desired ratio, so three different equations are possible describing the constituents of the mix.

For the total amount of mix:

... p + m = 10

For the quantity of peanuts in the mix:

... p + 0.2m = 0.6·10

For the quantity of almonds in the mix:

... 0.8m = 0.4·10

For the ratio of peanuts to almonds:

... (p +0.2m)/(0.8m) = 0.60/0.40

Any two (2) of these four (4) equations will serve as a system of equations that can be used to solve for the desired quantities. I like the third one because it is a "one-step" equation.

So, your system of equations could be ...

  • p + m = 10
  • 0.8m = 0.4·10

___

(b) Dividing the second equation by 0.8 gives

... m = 5

Using the first equation to find p, we have ...

... p + 5 = 10

... p = 5

5 lb of peanuts and 5 lb of mixture are required.

8 0
3 years ago
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