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
finlep [7]
2 years ago
8

Two cyclists , A and B , are going on a bike ride and are meeting at an orchard . They left home at the same time . Functions A

and B give their distance from the orchard , in miles , after riding for x hours . The functions are defined by these equations
Mathematics
1 answer:
vova2212 [387]2 years ago
5 0

Answer:

Cyclist A lives farther from the Orchard

Step-by-step explanation:

Given

A(x) =48.5 -21x

B(x) =42 -16.8x

Required:

Who lives farther from the Orchard.

To do this, we simply calculate the y intercept.

This represents the total distance traveled to get to the Orchard

To calculate y intercept, we set x = 0

So:

A(x) =48.5 -21x

A(0) = 48.5-21*0 =48.5-0 =48.5

B(x) =42 -16.8x

B(0) = 42 - 16.8*0 =42-0 =42

From the above computation:

A(0) > B(0) \to 48.5 > 42

Hence;

Cyclist A lives farther from the Orchard

You might be interested in
20 points!!!
Svetlanka [38]
The answer is:  {4, 1} .
________________________________________________________
Explanation:
________________________________________
Given the equations:
________________________________________
      "12x = 54 −<span> 6y ;
     "-17x = -62 </span>− 6y ;
_________________________________________
Multiply the second equation (both sides) by "-1" ;
___________________________________________
  -1*{-17x = -62 − 6y} ;

to get: 

17x = 62 + 6y ;
___________________________________________
{Note: The reason we do this is that we notice the TWO "-6y" values; and by multiplying one of the entire equations by "-1" ; we can change said equation to an equation with a "(+6y)" value; and the "(+6y)" and the "(-6y)" values cancel out to "zero" ; providing an opportunity to isolate "x"; and to solve for "x".}.
___________________________________________
Now, rewrite the two equations:
___________________________________________

       12x = 54 − 6y ;
       17x = 62 +  6y ;
___________________________________________
↔  Rewrite; and then add the two together:

       6y + 62 = 17x 
      -6y + 54 = 12x 
____________________
       0  +  116 = 29x ;

↔ 29x = 116 ;

Divide EACH SIDE of the equation by "29" ; to isolate "x" on one side of the <span>equation ; and</span> to solve for "x" ;
________________________________________________
   29x / 29 = 116 / 29  ;
________________________________________________
to get:
________________________________________________
           x  = 4 .
______________________________________________
Now that we have the value for "x" , which is "4" ; let us plug in "4" for "x" for either of the original two equations, to solve for "y".  In fact, let us try substituing "4" for "x" ;  for BOTH of the two original equations; to see if the value is correct.
_____________________________________________
Our original two given equations are:
_____________________________________________
      "12x = 54 − 6y ;

     "-17x = -62 − 6y ;
_____________________________________________
 Let us start with the first equation:
 ________________________
      " 12x = 54 − 6y " ;
__________________________________
When "x = 4" ; what does "y" equal ?

Plug in "4" for "x" ; to solve for "y" ;

  12(4) = 54 − 6y ;

→ 48 = 54 − 6y ;

Subtract "54" from EACH SIDE of the equation;

→ 48 − 54 = 54 − 6y − 54 ;

to get:

→  -6 = -6y ; 

→ Divide EACH side of the equation by "-6" ; to isolate "y" on one side of the <span>equation ; and</span> to solve for "y" ; 

→ -6/-6 = -6y / -6 ;

to get:

1 = y ;  ↔ y = 1 ;  So, we have:  x = 4, y = 1 ;  or,  {4, 1}.
______________________________________________
Let us check to see, if the second (orginal equation) holds true when "x = 4" and "y = 1 " ;
______________________________________________
The second "original equation" given is:
______________________________________________
       " -17x = -62 − 6y " ;
______________________________________________
   →    -17(4) = ?  -62  − 6(1) ?

    →  -68 = ? -62 − 6 ?

    →  -68 = ? -68 ?  Yes!
________________________________________________________
The answer is:  {4, 1} .
________________________________________________________
4 0
2 years ago
Four less than the square of a number is 0​
marusya05 [52]

Answer:

± 2

Step-by-step explanation:

let the number be n , then

n² - 4 = 0 ( add 4 to both sides )

n² = 4 ( take square root of both sides )

n = ± \sqrt{4} = ± 2

The number is - 2 or 2

5 0
3 years ago
Read 2 more answers
Create a memory device to help you remember the quadratic formula. The device could be a song, drawing, rhyme, mnemonic device,
vredina [299]

Look up Quadratic Formula Pop Goes the Weasel

its like 30 seconds and is pretty easy to remember

7 0
2 years ago
From the top of an 95 meter cliff, Tim spots a hiker down below at an angle
kirza4 [7]

Step-by-step explanation:

jsvsbsbbssnbshsshvsvsv

7 0
3 years ago
The area of a circle is 81 ft 2 . What is the π circumference? Leave in terms of Pi.
KonstantinChe [14]

Answer:

10.2π

Step-by-step explanation:

Given data

Area of circle=  81 ft^2

Also, the expression for the area of a circle is

A=πr^2

substitute

81=3.142*r^2

r^2= 81/3.142

r^2= 25.77

square both sides

r= √25.77

r= 5.1

Also, the expression for the circumference is

C= 2πr

substitute

C= 2*π*5.1

C= 10.2π

Hence the circumference is 10.2π

7 0
2 years ago
Other questions:
  • Greg bought 2 boxes of balloons he used half of them to decorate his yard he used 40 to decorate his porch he used the rest insi
    15·1 answer
  • Alice works at a health care facility. She has measured the hemoglobin levels of 200 people. The data follows a normal distribut
    15·1 answer
  • A line segment that has both endpoints on the circumference
    7·1 answer
  • Two trains leave stations 238 miles apart at the same time and travel toward each other. One train travels at 95 miles per hour
    6·1 answer
  • If your cell phone bill was $67.82 and there is a 7.5% late fee How much will your bill be with the late fee included
    15·1 answer
  • A square mat has an area of 324 square inches. What is the length of the mat?
    6·1 answer
  • A right triangle has an angle measure of 52.4 degrees. What is the value of 'x', the missing angle?
    13·1 answer
  • Can someone help me please ASAP? Correct answer gets brainliest!! :)
    15·1 answer
  • 7. The rectangle below is dilated by a scale factor of
    14·1 answer
  • Given: g(n)= 3n²+2 and h(n) =-1-5<br> Find:<br> (g/h)(5)
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!