Two cars are driving towards an intersection from perpendicular directions. The first car's velocity is 10 meters per second and the second car's velocity is 6 meters per second. At a certain instant, the first car is 4 meters from the intersection and the second car is 3 meters from the intersection. What is the rate of change of the distance between the cars at that instant (in meters per second)?

STEP

1

:

           5

Simplify   —

           4

Equation at the end of step

1

:

  1          5

 (— +  a) -  —  = 0

  3          4

STEP

2

:

           1

Simplify   —

           3

Equation at the end of step

2

:

  1          5

 (— +  a) -  —  = 0

  3          4

STEP

3

:

Rewriting the whole as an Equivalent Fraction

3.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  3  as the denominator :

        a     a • 3

   a =  —  =  —————

        1       3  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

3.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

1 + a • 3     3a + 1

—————————  =  ——————

    3           3  

Equation at the end of step

3

:

 (3a + 1)    5

 ———————— -  —  = 0

    3        4

STEP

4

:

Calculating the Least Common Multiple :

4.1    Find the Least Common Multiple

     The left denominator is :       3

     The right denominator is :       4

       Number of times each prime factor

       appears in the factorization of:

Prime

Factor   Left

Denominator   Right

Denominator   L.C.M = Max

{Left,Right}

3 1 0 1

2 0 2 2

Product of all

Prime Factors  3 4 12

     Least Common Multiple:

     12

Calculating Multipliers :

4.2    Calculate multipliers for the two fractions

   Denote the Least Common Multiple by  L.C.M

   Denote the Left Multiplier by  Left_M

   Denote the Right Multiplier by  Right_M

   Denote the Left Deniminator by  L_Deno

   Denote the Right Multiplier by  R_Deno

  Left_M = L.C.M / L_Deno = 4

  Right_M = L.C.M / R_Deno = 3

Making Equivalent Fractions :

4.3      Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example :  1/2   and  2/4  are equivalent,  y/(y+1)2   and  (y2+y)/(y+1)3  are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

  L. Mult. • L. Num.      (3a+1) • 4

  ——————————————————  =   ——————————

        L.C.M                 12    

  R. Mult. • R. Num.      5 • 3

  ——————————————————  =   —————

        L.C.M              12  

Adding fractions that have a common denominator :

4.4       Adding up the two equivalent fractions

(3a+1) • 4 - (5 • 3)     12a - 11

————————————————————  =  ————————

         12                 12  

Equation at the end of step

4

:

 12a - 11

 ————————  = 0

    12  

STEP

5

:

When a fraction equals zero :

5.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 12a-11

 —————— • 12 = 0 • 12

   12  

Now, on the left hand side, the  12  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  12a-11  = 0

Solving a Single Variable Equation:

5.2      Solve  :    12a-11 = 0

Add  11  to both sides of the equation :

                     12a = 11

Divide both sides of the equation by 12:

                    a = 11/12 = 0.917

a = 11/12 = 0.917

Answer:

11/12

Step-by-step explanation:

You want to subtract 5/4 minus 1/3 but you cant so you have to find the greatest denominator first which would be 12 because 3x4=12.

Since you multiplied 4x 3 to get 12 then you will multiply the 5 by 3 and the 1 by 4 to get this -> 5/4= 15/12     1/3= 4/12

Then subtract 15/12- 4/12= 11/12

a=11/12

Answer:

8/25.

Step-by-step explanation:

As a fraction it is 32/100 but simplified is 8/25 :)

Answer:

4.4 hours

Step-by-step explanation:

It would take Shawn 4.4 hours, as this would give a time of .4 hours to Michelle, totaling 4.8 hours

Answer:

x is the input, or independent variable and f(x) is the output, or dependent variable or quantity. f(2) represents the output (y-value) when x = 2. The value of f(2) is 2.

Step-by-step explanation:

If the values of a variable depends on the other variable, then it called dependent variable.

If the value of a variable does not depend on the other, then it is called independent variable.

If a function is f(x)=x, then x is an independent variable and f(x) is a dependent variable.

The given function is

Here, x is the input, or independent variable and f(x) is the output, or dependent variable or quantity.

The notation f(a) represents the output (y-value) when x = a. So, f(2) represents the output (y-value) when x = 2.

Substitute x=2 in the given function.

The value of f(2) is 2.

Answer:

f(x)

Step-by-step explanation:

Answer:

He should change 3.6 to 36

and

he should change 8.42 to 84.2

He should also move the decimal up when dividing like in the picture I posted.

Step-by-step explanation:

I other words, he should shift the decimal points to the right one

I hope that I could help!

He should also move the decimal up when dividing in the picture that is posted.

When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get.

Division, thus, can be interpreted as equally dividing the number that is being divided in total x parts, where x is the number of parts the given number is divided.

We need to find 8.42 divided by 3.6 longhand.

8.42 / 3.6

= 2.33

He should change 3.6 to 36 and he should change 8.42 to 84.2

He should also move the decimal up when dividing in the picture that is posted.

Learn more about division here:

https://brainly.com/question/26411682

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Answer:

A. 28x + 94y

Step-by-step explanation:

First, line up the like terms as if you were adding vertically, and combine them.

(42x + 59y)

+ (-14x + 35y)

(28x + 94y)

Hope this helps :)

Answer:

Option 3

Evens

. . . . . .. . ..

Answer:

SSS

Step-by-step explanation:

are 2 isosceles right triangles congruent, have both sides and angles equal, so the answers are all valid, the simplest is SSS, 2 sides are the same and marked on the drawing, the third is the same accordingly

Answer:

  137/150

Step-by-step explanation:

We can solve for w by adding -1/6 to both sides of the equation.

  w -(-1/6) = 1.08

  w = 1.08 +(-1/6) = 108/100 -1/6

  w = 54/50 =1/6 = 162/150 -25/150

  w = 137/150

Answer:

n = 1

Step-by-step explanation:

"The sum of" is addition

"2 times a number" is 2n

"and 5" is + 5

equals 7 is =7

2n + 5 = 7

     - 5   - 5

2n = 2

2n/2 = 2/2

n = 1

Answer:

The answer is 125.6

Step-by-step explanation:

C= 2x3.14x20

C=6.28x 20

C= 125.6

Answer:

C) 2/5×1/4

Step-by-step explanation:

Dividing by a number is the same by multiplying by the reciprocal of the number.

For Example:

1/2 divided by 3 would be the same as 1/2 x 1/3

So for this problem we are given that 2/5 is divided by 4 which would be the same as 2/5 multiplied by the reciprocal of 4 which is 1/4 and thus the answer is option C which is 2/5×1/4

Answer:

This is indeed a function

Answer: x=80

Let that be x

Answer: slope is 2 and the y-intercept is 1  intercept form is y=2x+1

Step-by-step explanation:

Answer:

40 students earned a B on this paper.

40%×80=32 people who chose action as their fav.

Answer:

33/44 = 0.75

0.75*44 = 33

Answer:

44% of 75 = 33

Step-by-step explanation:

The graphs of f(x) and g(x) are related by transforming one of the two graphs.

The equation of the blue graph is [tex]\mathbf{g(x) =(x - 4)^2}[/tex]

From the graphs, we have:

[tex]\mathbf{f(x) =x^2}[/tex]

f(x) is transformed to the right by 4 units.

The rule of this transformation is:

[tex]\mathbf{g(x) \to f(x - 4)}[/tex]

So, we start by calculating f(x - 4)

Given that:

[tex]\mathbf{f(x) =x^2}[/tex]

Substitute x - 4 for x in f(x)

[tex]\mathbf{f(x - 4) =(x - 4)^2}[/tex]

Also, recall that:

[tex]\mathbf{g(x) \to f(x - 4)}[/tex]

So, we have:

[tex]\mathbf{g(x) =(x - 4)^2}[/tex]

Hence, the equation of g(x) is [tex]\mathbf{g(x) =(x - 4)^2}[/tex]

Read more about transformation at:

https://brainly.com/question/11707700

Answer:

493/40

i tried my best on it

Answer:

493 /40

Step-by-step explanation:

(12.325 × 100) /  (1 × 1000)  =  

=12325/ 1000

Answer:

240oz.

Step-by-step explanation:

15oz=1batch

She needs 16 batches.

15oz. x 16batches = 240oz.

Hope this helps :)

Answer:

4

Step-by-step explanation:

2+2=4

Answer:

Step-by-step explanation:

Assuming the string is straight (it will not be so due to gravity and wind load)

θ arcsin(354 / (200(3)) = 36°

Answer:

4(2x raise to power 2-4-7x)

Answer:

(2)

Step-by-step explanation:

Answer:

319973/400

Step-by-step explanation:

800 - 27/4%

800 - ( 27/4 × 1/100)

800 - 27/400

= 319973/400

Answer: 52.3 seconds

Step-by-step explanation:

209.2 divided by 4

which is 52.3 seconds

Answer:

Just in case you want me to answer all the questions, I will

Step-by-step explanation:

Question 1): answer is 25

Question 2): answer is 24

Question 3): answer is 100%

24/25 = 96/100

Box Question 1): 21/25 = 84/100

Box Question 2): 15/20 = 75/100

Box Question 3): 47/50 = 94/100

Box Question 4): 28/30 = 93.3/100

Box Question 5): 19/45 = 42.2/100

Box Question 6): 3/4 = 75/100

If a digit is underlined, put a line ONLY over the underlined digit, it is repeating

I'm not completely sure if this is correct, but I really think it is..

I hope this helps!

Step-by-step explanation:

brand a is better option why because we have paint and paint roller

If you buy 1 gallon can of paint both brands will cost $30 and brand B paint is a better option because it costs less.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

Suppose y is the total cost and x is the gallons cases,

The equations according to the given condition are,

y = 27 x + 3

y = 2x +5

The values obtained after solving the above equation will be (1,30). As a result, 1 gallon of paint cost you $ 30.

For condition 2 Juanita needs 15 gallons of paint, x =15

For A, y = 408

For B, y = 380

The brands A and B cost $408 and $380.So the brand costs Juanita more.

Thus, if you buy 1 gallon can of paint both brands will cost $30 and brand B paint is a better option because it costs less.

Learn more about the equation here,

https://brainly.com/question/10413253

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Answer:

Step-by-step explanation:

if 50 AED= 12 Euro

for 1 AED ? Euro

50AED/1AED= 12Euro/x

cross multiplication:

50*x=12*1

50*x=12

x=12/50

x=0.24 Euro

so for 1AED you will get 0.26 Euro