1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Gala2k [10]
3 years ago
6

A walking path across a park is represented by the equation A walking path across a park is represented by the equation y= -3x-3

. A New path will be built perpendicular to this path. The Paths will intersect at a point paths will intersect at a point (-3, 6). Identify The equation that represents the new path.
Mathematics
1 answer:
kkurt [141]3 years ago
5 0

Answer:

The equation representing the new path is;

y = \dfrac{1}{3} \cdot x + 7

Step-by-step explanation:

The equation of the first walking park across the park is y = -3·x - 3

By comparison to the equation of a straight line, y = m·x + c, where m = the slope of the line, the slope of the line y = -3·x - 3  is -3

The park's new walking path direction = Perpendicular to first walking path

A line perpendicular to a line of  (as example) y = m₁·x + c has a slope of -1/m

∴ The park's new walking path slope = -1/(Slope of first path) = -1/(-3) = 1/3

The point the paths will intersect = (-3, 6)

The equation of the line is found by recalling that Slope, \, m_1 =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}

Where:

y₂ and x₂ are coordinates of a point on the new walking path

y₁ and x₁ are coordinates of a point on the new walking path intersecting the first walking path

Given that (-3, 6) is the intersection of the two walking paths, therefore, it is a point on the new walking path and we can say x₁ = -3, y₁ = 6

Therefore, we have;

Slope, \, m_1 =\dfrac{y_{2}-6}{x_{2}-(-3)} = \dfrac{y_{2}-6}{x_{2}+3} =\dfrac{1}{3}

Which gives;

(y₂ - 6) × 3 = x₂ + 3

y₂ - 6 = (x₂ + 3)/3

y₂ = (x₂ + 3)/3 + 6  = 1/3·x₂ + 1 + 6 = 1/3·x₂ + 7

Which gives the equation representing the new path as y = \dfrac{1}{3} \cdot x + 7.

You might be interested in
What is the volume of the triangular prism prism? <br> 8cm<br> 13cm<br> 3cm
Vika [28.1K]

Answer:

156 cm3

If the length is 8cm and the base is 13cm and the prism height is 3cm

8 0
3 years ago
Which are solutions of the equation 4x2 - 7x = 3x + 24? Check all that apply.
riadik2000 [5.3K]

Answer:

all work is shown and pictured

4 0
3 years ago
Explain how to find the product 3^5 x 3^2 using rules for exponents.
AlekseyPX

Step-by-step explanation:

\because \:  {a}^{m}  \times  {a}^{n}  =  {a}^{m + n}  \\  \\  \therefore \:  {3}^{5}  \times  {3}^{2}  =  {3}^{5 + 3}  =  {3}^{8}  = 6,561 \\

7 0
3 years ago
A number increased by 3 and then multiplied by 5 is at least -10. What are the three lowest natural number values this can be?
Vilka [71]

Step-by-step explanation:

It is impossible for the number values of this number to be a natural number since natural numbers are defined as being positive integers while the number "x" has to be less than -5 to satisfy the equation.

4 0
3 years ago
What is it called when you have two burgers but one of them is half?
antiseptic1488 [7]

1 1/2? I pretty sure this is the answer.

4 0
3 years ago
Read 2 more answers
Other questions:
  • Which is the general form of the equation of the circle shown? x2 + y2 + 4x – 2y – 4 = 0 x2 + y2 + 4x – 2y + 2 = 0 x2 + y² – 4x
    6·2 answers
  • It snowed 4. Times during October. The snowfall amounts were 0.75 inches, 1.93 inches,4.73 inches, and 2.33 inches. What was the
    14·2 answers
  • f. A fair coin is thrown in the air four times. If the coin lands with the head up on the first three tosses, what is the probab
    11·2 answers
  • Kelly answered 3 items in a test incorrectly. This was 6% of the items. How many items were on the test?
    11·2 answers
  • What is the likelihood that a fair coin will land heads or tails?
    10·2 answers
  • What can you break down 29 into
    12·2 answers
  • According to the National Oceanic and Atmospheric Administration, the blue whale is the largest animal on Earth. Blue whales wei
    12·1 answer
  • Oh please help me i don't know how to do it
    11·2 answers
  • Claudia will randomly pick one M&amp;M from a bag
    5·1 answer
  • A spinner with 8 equally sized slices has 8 yellow slices. The dial is spun and stops on a slice at random. What is the probabil
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!