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stiv31 [10]
11 months ago
7

What is the equation of the line that passes through the origin and is perpendicular to the line 4x+3y=6

Mathematics
1 answer:
frez [133]11 months ago
5 0

The Equation of a Line

The slope-intercept form of a line can be written as:

y = mx + b

Where m is the slope of the graph of the line and b is the y-intercept.

In the specific case where the line passes through the origin (0,0), we can find the value of b by substituting x=0 and y=0:

0 = m(0) + b

Solving for b:

b = 0.

Thus, the equation of the line reduces to:

y = mx

We only need to find the value of the slope.

That is where we need the second data. Our line is perpendicular to the line of equation 4x + 3y = 6.

Solving for y:

y=-\frac{4}{3}x+2

The slope of the second line is -4/3.

We must recall that if two lines of slopes m1 and m2 are perpendicular, then:

m_1\cdot m_2=-1

Substituting the value of m1 and solving for m2:

\begin{gathered} -\frac{4}{3}\cdot m_2=-1 \\ m_2=\frac{3}{4} \end{gathered}

The slope of our line is 3/4 and the required equation is:

y=\frac{3}{4}x

From this last equation, we need to find the general form of the line.

Multiply both sides of the equation by 4:

4y = 3x

Subtract 3x on both sides:

4y - 3x = 0

Reorder:

-3x + 4y = 0

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(5⁷)(55)x=8⁵<br>Solve Asap​
Ostrovityanka [42]
  • Calculate

\sf\longmapsto4296875x=32768

  • Divide both sides by 4296875

\sf\longmapsto \dfrac{4296875x}{4296875}  =  \dfrac{32768}{4296875}

  • Answer

\sf\longmapsto \: x =  \dfrac{32768}{4296875}

5 0
2 years ago
Read 2 more answers
You are mowing a lawn. After 12 minutes, 52% of the lawn still needs mowed. How long does it take to mow the entire lawn? Write
aleksley [76]
12/x = 52/48
12 * 48 = 52x
x = 11.07 This is one way to do it.

Let the time = x
Let the part of the lawn = y

The general equation
y = k*x
52/100 = k * 12
k = 0.043333 
y = 0.043333*x
y = 0.043333* 11.08
y = 0.48 which is what it should be.

Yet another way is to let y = kx
52 = k*12
k = 52/12
k = 4.33333333

y = 4.333333 * x
y = 4.333333 * 48
48  = 4.333333 * x
x = 11.07 which is just what you should expect.
7 0
3 years ago
12/21 in its simplest form
UNO [17]
12/21 in its simplest form is 4/7.

To find this out we need to divide the numerator and denominator by the GCF of 12 and 21 which is 3.

12/21

12 ÷ 3 = 4
21 ÷ 3 = 7
4/7

12/21 in its simplest form is 4/7.

12/21 = 4/7
5 0
3 years ago
Read 2 more answers
Need help on the answer
lions [1.4K]

Answer:

The second choice is the answer.

Step-by-step explanation:

In math, there are two types of numbers: real numbers and imaginary numbers. Imaginary numbers build upon the premise that the equation

x^2 +1 = 0 has no real solution. It is said that one of the imaginary solutions to this equation is <em>i</em>, or √-1. Real numbers are numbers that can represent the "distance" of a line. Real numbers have subsets known as natural numbers, whole numbers, integers, natural numbers. It also has a region of irrational numbers.

Natural numbers are numbers you use to count w/ your fingers (1, 2, 3 ...)

Whole numbers are natural numbers and 0 (0, 1, 2, 3 ...)

Integers are whole numbers and their opposites ( -1, 0, 1, ...)

Rational numbers integers and numbers that can be put into a fraction of two integers. for example, 1/2 is a fraction of the integers 1 and 2 ( -1, -1/2, 0, 1/2, 1 ...)

Irrational numbers are numbers that cannot be written as a simple fraction or cannot be written as terminating or repeating decimals (√2, π, <em>e, ...</em>).

The answer is not the first choice because it has whole numbers.

The answer is not the third choice because it has integers.

The answer is not the fourth choice because it has irrational numbers.

The answer is not the fifth choice because it has imaginary numbers.

The second choice is the one that has rational numbers and is the answer.

4 0
3 years ago
Shelby will take a total of 6 tests. On the first 5 tests, her scores were: 80, 85, 73, 78, 90. If she wants a mean grade of 80,
Andrew [12]

Answer:

74

Step-by-step explanation:

4 0
3 years ago
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