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noname [10]
2 years ago
11

Find the distance between the parallel lines m and n whose equations are

Mathematics
1 answer:
MA_775_DIABLO [31]2 years ago
8 0

Answer:Find the distance between the parallel lines m and n whose equations are y = x + 4 and y = x - 6, respectively.

There are several ways to do this...here's one

Let (0, 4) be a point on the first line

Then.......a line with a negative reciprocal slope going through this point will have the equation :

y = -x + 4........so......we can find the intersection of this line with y = x - 6....set both equations equal

-x + 4  = x - 6   add x, 6 to both sides

10 = 2x     divide both sides by 2

5  = x

So...using -x + 4, the y value  at intersection  = -1.......

So...we just need to find the distance from  (0,4)  to ( 5, -1)  =

√[ (5)^2 + (4 + 1)^2 ] =  5√2  ≈  7.07 units

Here's a pic....AB is the distance  with A = (0,4)  and B = (5, -1)

Step-by-step explanation:

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Which statement BEST describes the equation where A represents the initial value and x represents time in years?
serg [7]

The function of exponential growth or decay is given as  y= a(1 ± r)ˣ.  y represents a function of exponential decay with 45%. The correct option is D.

<h3>What is exponential growth or decay function?</h3>

Consider the function:

y= a(1 ± r)ˣ

where m is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.

  • If there is plus sign, then there is exponential growth happening by r fraction or 100r %.
  • If there is negative sign, then there is exponential decay happening by r fraction or 100r %.

If we compare the given function with the exponential function, then it can be observed that the value of (1±r) is less than 1, therefore, the function will be of exponential decay.

Now, if the (1-r) is compared with 0.55 given in the function than the value of r will be,

1 - r = 0.55

-r = 0.55 - 1

-r = -0.45

r = 0.45

r = 45%

Hence, y represents a function of exponential decay with 45%.

Learn more about exponential growth and decay here:

brainly.com/question/2193820

#SPJ1

6 0
2 years ago
A lot is 21 ft by 30 ft. To support a fence, an architect wants an upright post at each corner and an upright post every 3 ft in
Bogdan [553]
What we know:
Lot= 21 x 30ft
Perimeter=2l+2w
Want to put 4 corner post and one post every 3 ft

What we need to find:
How many post we need.

Perimeter=2 (21)+2 (30)=42+60=102ft

102/3=34

34 posts are needed.
6 0
3 years ago
Julio and David were in Target and decided to check out the clearance section. They found pencils and erasers that were on sale
Sati [7]

Answer:

Cost of one pencil: \$0.07

Cost of one eraser: \$0.03

Step-by-step explanation:

Let be "p" the cost in dollars of one pencil and "e" the cost in dollars of one eraser.

Based on the information given in the exercise, you can set up the following system of equations:

\left \{ {{4p+3e=0.37} \atop {3p+4e=0.33 }} \right.

You can use the Elimination Method to solve the system of equations.

Multiply the first equation by -3 ad the second one by 4. Then add the equations and solve for "e":

{\left \{ {{-12p-9e=-1.11} \atop {12p+16e=1.32}} \right.\\..........................\\7e=0.21\\\\e=0.03

Substitute the value of "e" into any original equation  and solve for "p":

4p+3(0.03)=0.37\\\\p=\frac{0.28}{4}\\\\p=0.07

5 0
2 years ago
Hey! Can someone do this real quick? 20 points!!!
likoan [24]

Answer:

i think about 80 cm or 100cm

5 0
3 years ago
Read 2 more answers
How to solve step by step [(7,5-1,5) x 10^-11]^2 ??
Oliga [24]
1.7,5-1,5=6
2.10-11=-1
3.6×-1=-6
4.-6+2=-4
5 0
3 years ago
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