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
ELEN [110]
4 years ago
9

Find the distance between the pair of parallel lines, y = x-11 & y = x-7

Mathematics
2 answers:
kenny6666 [7]4 years ago
6 0
k:\ y = x-11\ \ \ \Leftrightarrow\ \ \ x-y-11=0\\ and\\ l:\ y = x-7\ \ \ \Leftrightarrow\ \ \ x-y-7=0\\\\the\ distance:\\\\ d(k;l)= \frac{\big{|-11-(-7)|}}{\big{ \sqrt{1^2+1^2} }} =\frac{\big{|-11+7|}}{\big{ \sqrt{2} }} =\frac{\big{|-4|}}{\big{ \sqrt{2} }} =\frac{\big{4\cdot \sqrt{2} }}{\big{ \sqrt{2}\cdot \sqrt{2}  }} =\frac{\big{4 \sqrt{2} }}{\big{2 }} =2 \sqrt{2}
Anarel [89]4 years ago
6 0
Given \ the \ equations \ of \ two \ non-vertical \ parallel \ lines:\\\\y = mx+b_1\\y = mx+b_2\\\\the \ distance \ between \ them \ can \ be \ expressed \ as : \\\\d= \frac{|b_{1}-b_{2}|}{ \sqrt{ m^2+1} }

y = x-11 \\ y = x-7 \\\\\\d= \frac{| -11- (-7)|}{ \sqrt{ 1^2+1} } =\frac{| -11+7|}{ \sqrt{ 1+1} } = \frac{|-4|}{ \sqrt{2} } = \frac{4}{ \sqrt{2} }\cdot \frac{\sqrt{2}}{\sqrt{2}}=\frac{4\sqrt{2}}{2}=2\sqrt{2}
 

You might be interested in
Amy drove to her Mother’s house, which is 204 miles away. If it took her 3 hours, what was her average speed mph?
lora16 [44]

Answer:

68

Step-by-step explanation:

204/3 = Avg MPH

5 0
3 years ago
Read 2 more answers
Solve these [7x+5](8x+3)<br> (3-8x)(4-5x)<br> 2(4x+7)(6x-5)
masha68 [24]

Answer:

107520x6+89344x5−241808x4−55444x3+121478x2+6030x−12600

Step-by-step explanation:

brailiest

7 0
3 years ago
The temperature fell 4 degrees in the last hour. Now it is 21 degrees. Write an equation to find the temperature it was 1 hour a
Sloan [31]

Answer:

21 + 4  = 25

Step-by-step explanation:

this is the answer because the temperature fell 4 degrees in the last hour.

so we have to add back that 4 to get the answer.

our equation will be 21 + 4 equals 25.

hope this helps!

sakuracherry

6 0
3 years ago
Jeanne babysits for $6 per hour. She also works as a reading tutor for $10 per hour. She is only allowed to work 20 hours per we
Allushta [10]

Part a) Use a system of inequalities to model the scenario

Let

x-------> represent babysitting hours

y-------> represent tutoring hours  

we know that

--------> inequality    

--------> inequality  

Part b) Use the model created in part A to create a graph representing Jeanne’s probable income earned and possible number of hours worked this week

we know that

--------> inequality  

This inequality represent Jeanne’s possible number of hours worked this week

Using a graph tool

the solution of this inequality is the shaded area

see the attached figure N  

--------> inequality    

This inequality represent Jeanne’s probable income earned this week

Using a graph tool

the solution of this inequality is the shaded area

see the attached figure N  

Part c) Analyze the set of coordinate values that represent solutions for the model created in part A. Choose one of the coordinates within the solution and algebraically prove that the coordinate represents a true solution for the model

we have the system of inequalities

--------> inequality  

--------> inequality  

the solution of the system of inequalities is the shaded area

using a graph tool

see the attached figure N  

Let

------> see the attached figure N  

The point belongs to the shaded area, so it is a system solution.

If the point is a solution, it must satisfy both inequalities.

Prove algebraically

substitute the value of x and y in the inequalities

inequality  

------> is ok

inequality  

-------> is ok

the point A satisfy both inequalities

therefore

the point A is a solution of the system

5 0
3 years ago
Read 2 more answers
What is x if x+85=x+105
vaieri [72.5K]

Answer:x+85=x+105

x+x=105+85

2x=190

x=190/2

x=95

Step-by-step explanation:

4 0
3 years ago
Other questions:
  • How do you work out y?
    15·2 answers
  • You have an aquarium in the shape of a rectangular prism. The base is 4 feet by 3 feet. The height is 2 feet. How many square fe
    12·1 answer
  • What multiplies to 36 and adds to 10
    8·1 answer
  • 05.02)A doghouse is to be built in the shape of a right trapezoid, as shown below. What is the area of the doghouse?
    13·1 answer
  • What is the value of n?<br> •3<br> •5<br> •17<br> •25
    8·2 answers
  • 4. y=-x(squared) -8x - 16<br> Axis of Symmetry:<br> Vertex:<br> Domain:<br> Range:
    9·2 answers
  • What is the surface area of the solid that this net can form?
    9·1 answer
  • Can someone please help me and write out the answer​
    8·1 answer
  • Y = 4x + 8 when x = 3y
    5·1 answer
  • Which shows the domain and range of these functions? Domain: (Negative infinity, infinity) Range: (Negative infinity, infinity)
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!