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
oee [108]
1 year ago
7

5. Find the value(s) of x so that the line containing the points (2x + 3, x + 2) and (0, 2) is

Mathematics
1 answer:
Dvinal [7]1 year ago
4 0

Answer:

  x = -2 or -9

Step-by-step explanation:

You want the values of x such that the line defined by the two points (2x+3, x+2) and (0, 2) is perpendicular to the line defined by the two points (x+2, -3-3x) and (8, -1).

<h3>Slope</h3>

The slope of a line is given by the slope formula:

  m = (y2 -y1)/(x2 -x1)

Using the formula, the slopes of the two lines are ...

  m1 = (2 -(x+2))/(0 -(2x+3)) = (-x)/(-2x-3) = x/(2x +3)

and

  m2 = (-1 -(-3-3x))/(8 -(x+2)) = (2+3x)/(6 -x)

<h3>Perpendicular lines</h3>

The slopes of perpendicular lines have product of -1:

  \dfrac{x}{2x+3}\cdot\dfrac{2+3x}{6-x}=-1\\\\x(3x+2)=(2x+3)(x-6)\qquad\text{multiply by $(2x+3)(6-x)$}\\\\3x^2+2x=2x^2-9x-18\qquad\text{eliminate parentheses}\\\\x^2+11x+18=0\qquad\text{put in standard form}\\\\(x+2)(x+9)=0\qquad\text{factor}

<h3>Solutions</h3>

The values of x that satisfy this equation are x = -2 and x = -9. The attached graphs show the lines for each of these cases.

You might be interested in
What is the value of the expression below
natulia [17]

Answer:

a=2,b=4. (3a+b)=3*2+4=10.

5 0
2 years ago
The bedroom of a house is 1,200 cubic meters. We know that there are 3.4 x 109 particles of dust per cubic meter. How many parti
Brrunno [24]
Norteo lo se
awdwqmedowmesdsaa sddasdasdasd asdasd asdqasd asd 
3 0
3 years ago
Mark is 7 years older than his brother, who is y years old. Which expression correctly represents Mark's age?
Alex787 [66]

7 + Y = X (x= His unknown age)



3 0
2 years ago
What are the sum of the two pink angles?
jenyasd209 [6]

Answer:

45 degrees

Step-by-step explanation:

5 0
3 years ago
100x+2y =1 and also 100x -2y=1 what is the value of y ?
solmaris [256]
Yeah bro just take the 2 and subtract on both side so the y is left alone flip the 100 so now its 001 divide it by 1 and the answer is 007 like the spy.
4 0
3 years ago
Other questions:
  • <img src="https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%7D%7B4%20%7D%20%20%2B%205%20%3D%207" id="TexFormula1" title=" \frac{x}{4 } + 5
    15·2 answers
  • What is the answer to the long question?
    9·1 answer
  • Jada is evaluating 8 × 3 × 4. She doesn't know the product of 24 and 4 off the top of her head, so she decides to multiply 3 by
    10·2 answers
  • Which of the following is the linear parent function?
    12·2 answers
  • The sum of two numbers is 57. The larger number is 11 more than the smaller number. What are the numbers?
    15·1 answer
  • A box rectangular prism has an end that is 3 by 5 ft in dimension it’s length is 10 feet what is the volume of the prism
    13·1 answer
  • Write a division problem that has a two-digit quotient that is greater than 40 but less than 50.
    13·1 answer
  • 1 2.2.5 Quiz: Volume
    14·1 answer
  • Please help this is due soon
    12·2 answers
  • Find the area of the polygon with vertices of A(2, 2), B(2, 7), C(8, 7),<br> and D(4, 2)
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!