Troy is chasing his little brother Kyle, but Kyle got a 30 second head start. If Kyle is traveling at 2 feet per second on his tri cycle and Troy is traveling at 5 feet per second on his skateboard, how many seconds will it be before Troy catches Kyle?

Answer:

Step-by-step explanation:

Parabola's equation is

y

=

1

16

(

x

−

7

)

2

+

1

and vertex is

(

7

,

1

)

.

Explanation:

Parabola is locus of a point which moves so that its distance from a given point calld focus and a given line ccalled directrix is always constant.

Let the point be

(

x

,

y

)

. Here focus is

(

7

,

5

)

and distance from focus is

√

(

x

−

7

)

2

+

(

y

−

5

)

2

. Its distance from directrix

y

=

−

3

i.e.

y

+

3

=

0

is

|

y

+

3

|

.

Hence equaion of parabola is

(

x

−

7

)

2

+

(

y

−

5

)

2

)

=

|

y

+

3

|

2

or

x

2

−

14

x

+

49

+

y

2

−

10

y

+

25

=

y

2

+

6

y

+

9

or

x

2

−

14

x

+

65

=

16

y

i.e.

y

=

1

16

(

x

2

−

14

x

+

49

−

49

)

+

65

16

or

y

=

1

16

(

x

−

7

)

2

+

65

−

49

16

or

y

=

1

16

(

x

−

7

)

2

+

1

Hence parabola's equation is

y

=

1

16

(

x

−

7

)

2

+

1

and vertex is

(

7

,

1

)

.

graph{(1/16(x-7)^2+1-y)((x-7)^2+(y-1)^2-0.15)((x-7)^2+(y-5)^2-0.15)(y+3)=0 [-12.08, 27.92, -7.36, 12.64]}

Step-by-step explanation:

= x + x -2+ 1 -2x

=2x-3- 2x

=3 ans

hope it help you.

Answer:

2+1=3-2x= -5+x+x =5x square

Answer:

yes, 8.5 and 3.5

Step-by-step explanation:

8.5 + 3.5 = 12

8.5 - 3.5 = 5

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The two numbers are 8.5 and 3.5.

Yes, it is possible to have two numbers that have a difference of 5 and a sum of 12.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 4 is an equation.

3x = 4 + 3 is an equation.

We have,

Let the two numbers be M and N.

Now,

Two numbers have a difference of 5.

This can be written as,

M - N = 5 _____(1)

Two numbers sum is 12.

This can be written as,

M + N = 12 _____(2)

From (1) and (2) we get,

M - N = 5

M = 5 + N _____(3)

Putting (3) in (2)

M + N = 12

5 + N + N = 12

5 + 2N = 12

2N = 12 - 5

2N = 7

N = 7/2

N = 3.5

Putting in (3) we get,

M = 5 + 3.5

M = 8.5

We can cross-check.

M - N = 5

8.5 - 3.5 = 5 (PROVED)

M + N = 12

8.5 + 3.5 = 12 (PROVED)

Thus,

The two numbers are 8.5 and 3.5.

Yes, it is possible to have two numbers that have a difference of 5 and a sum of 12.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ2

Answer:

6 days

Step-by-step explanation:

hope this helps

A librarian sorts 450 books at a constant rate. After 4 days, the librarian still has 150 books to sort. Then 6 days  time does it take to sort the books from start to finish

Two or more expressions with an Equal sign is called as Equation.

The librarian sorted at a constant rate, then they sorted the same amount of books all 4 days.

450-150=300

If they still have 150 books left to sort, then they sorted 300 books over 4 days.

300/4=75

This means that they sorted 75 books per day.

150 divided by 75 is 2

So it will take 2 more days to finish sorting all the books.

So altogether, it will take 6 days to sort all of the books.

Hence 6 days time does it take to sort the books from start to finish

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ5

Answer:

-Freddy tiene 25 billetes de diez dólares.

-A Freddy le quedan 19 billetes de diez dólares.

Step-by-step explanation:

Para encontrar la cantidad de billetes de diez dólares que tiene Freddy, tienes que dividir la cantidad total que tiene entre diez:

250/10=25

Esto significa que Freddy tiene 25 billetes de diez dólares.

Para saber cuantos billetes le quedan a Freddy, tienes que restar los 6 billetes que le dio a su hermano del total de billetes que tenía:

25-6=19

De acuerdo a esto, a Freddy le quedan 19 billetes de diez dólares.

Answer:

2

Step-by-step explanation:

Divide 45 and 3, then divide 26 and 2. subtract those answers and u get 2. (the dude that said your mom has no life and got his mom raped)

Grason's Bike is 2 miles/hour faster than Maya's if Grayson biked 45 miles in 3 hours. Maya bikes 26 miles in 2 hours.

Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.

It is given that:

Grayson biked 45 miles in 3 hours. Maya bikes 26 miles in 2 hours.

As we know,

The speed = distance/time

Plug the respective values in the above formula:

For Grayson:

speed = 45/3 = 15 miles/hour

For Maya:

speed = 26/2 = 13 miles/hour

Difference in speed = 15 - 13 = 2 miles/hour

Thus, Grason's Bike is 2 miles/hour faster than Maya's if Grayson biked 45 miles in 3 hours. Maya bikes 26 miles in 2 hours.

Learn more about the distance here:

brainly.com/question/26711747

#SPJ2

Answer:

false

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

[tex]\frac{1}{2}=\frac{-3}{7}q[/tex]

1/2*7/-3= -7/6

q = -7/6 NOT -11/6 so the statement is false

Answer:

don't cheat

Step-by-step explanation:

no answer for you

Answer:

y = 15

Step-by-step explanation:

-1/3 y -6 = -11

Add 6 to each side

-1/3 y -6+6 = -11+6

-1/3 y = -5

Multiply each side by -3

-1/3 y * -3 = -5*-3

y = 15

Check

-1/3 *15 -6 = -11

-5 -6 = -11

-11=-11

Answer:

x=20

Step-by-step explanation:

5x+4x=180

9x=180

/9 on both sides

x=20

The value of 4x and 5x is 80° and 100° respectively .

The same-side interior angle theorem states that when two lines that are parallel are intersected by a transversal line, the same-side interior angles that are formed are supplementary, or add up to 180 degrees.

According to the question

4x , 5x are angles given

As,

They are angles between  parallel line and same side of transversal line  

according to same-side interior angle theorem that are formed are supplementary .

i.e  there sum = 180°

4x + 5x= 180°

9x = 180°

x = 180°/9

x = 20°

So,

4x = 20 * 4 = 80°

5x = 20 * 5 = 100°

Hence, The value of 4x and 5x is 80° and 100° respectively .

To know more about same-side interior angle theorem here:

https://brainly.com/question/15066024

#SPJ2

Answer:

1. Slope = -4/5

2. Slope = 2/3

3. Slope = 0

4. Slope = 3/-4

5. Slope = 7/-12

6. Slope = 1/2

7. Slope = -2/0 --> Undefined

8. Slope = 3/-2

9. Slope = 5/-4

10. Slope = 4/3

Step-by-step explanation:

Ok so I'm assuming that you want the slope for all the two points. Basically, the formula for slope is rise/run, or y2-y1/x2-x1. Solve using that. For example, for number 1, it would be:

10-2/1-11 = 8/-10 = -4/5

Answer:

the answer is B

Answer:

s/(1-r)=R

Step-by-step explanation:

S=R-rR

S=R(1-r)

s/(1-r)=R

Answer:

lol

Step-by-step explanation:

what the hell where I the question lol

Carmen has the largest red to green apple ratio.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

here, we have,

from the given chart , we get,

the  ratio as,

Carmen= 20:12

            =1.6

Dylan = 12:10

          =1.2

Eli = 16:20

    =0.8

now, we have,

Carmen has the largest red to green apple ratio.

This is because his red to green apple ratio is equal to 1.6.

In order to determine that you take 20 and divide it by 12.

To learn more on ratio click:

brainly.com/question/13419413

#SPJ2

Answer:

350

Step-by-step explanation:

Let [tex]s=[/tex] total number of sixth-grade students.

It is given that 60% of sixth-grade students prefer pizza which is equivalent to 210 sixth-grade students. With this, the following can be written:

[tex]60\%s = 210[/tex]

[tex]0.6s=210[/tex] ([tex]60\%[/tex] can be converted into the decimal form [tex]0.6[/tex])

[tex]s = 210\div 0.6[/tex]

[tex]=350[/tex]

∴ There is a total of 350 sixth-grade students in the school.

Hope this helps :)

Answer:

$42

Step-by-step explanation:

138/23 = $6 per kg

6*7 = 42

Answer with no step-by-step explanation:

13

Answer:

$0.65 per pound

Step-by-step explanation:

Divide the total cost by the number of pounds to find price per pound.

$2.60 ÷ 4 = $0.65 per pound

Answer:

c = 40 and d = 76

Step-by-step explanation:

this is going to take me a long time to explain but here we go

so you need to do 180 - 116 and get 64.

then create a equation that is like this 7y + 6 + 4y + 64 = 180

when you solve it you get y = 10

then plug in 10 in for y in 4y. and you get 40 for c

do the same for d and you will get 76

pls mark me brainleist because i didnt waster your time.

Answer:

i did not understant your question

i think u want the definition of relation

A relation between two sets is a collection of ordered pairs containing one object from each set. If the object x is from the first set and the object y is from the second set, then the objects are said to be related if the ordered pair (x,y) is in the relation. A function is a type of relation.

Step-by-step explanation:

plssssssssssss markkkk meee brainlist

A relation is a collection of Ordered pairs where each x-value is paired with only one y-value.

For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of x for which [y] exists.

Given is the graph of a equation

A relation between two sets is a collection of ordered pairs containing one object from each set. If the object x is from the first set and the object y is from the second set, then the objects are said to be related if the ordered pair (x, y) is in the relation.

Therefore, a relation is a collection of Ordered pairs where each x-value is paired with only one y-value.

To solve more questions on functions and relations, visit the link below -

brainly.com/question/1632425

#SPJ2

Answer:

Step-by-step explanation:

f(n) = 128[tex](\frac{1}{4}) ^{n}[/tex]

Step-by-step explanation:

Let aron's variable be = a

Let davids variable be( 6 less tan 3 times aron) = 3×a-6

Thier sum is =214

So,

3×a-6 + a = 214

3a -6 +a = 214

(transpose)

3a + a = 214 + 6

4a = 220

a = 220/4

a= 55

Thus,aron's score is = 55

And davids score is (3×a-6) = 3×55-6 = 159

Checking,

Aron score + david score = 214

55 + 159 = 214

SO, ITS CORRECT

HOPE IT HELPS :)

If a certain stock has grown continuously from 1980 to 2015, for this period of time  its average annual growth rate   is 18%.

It is given that A certain stock has grown continuously from 1980 to 2015.

Stock's initial value in 1980 (I) = $10,000

Stock's final value in  2015 (F) = $3,500,000

time period t = 2015-1980 = 35 years.

Since, the stock has grown continuously,  it should have grown compounded annually.

Stock's average annual growth rate (r) is calculated as:

[tex]\text{r} = {(\dfrac{F}{I})^{\frac{1}{t}}-1[/tex]

Substitute all the given values in the above formula:

[tex]\text{r} ={ (\dfrac{3500000}{10000})^{\frac{1}{35}}-1[/tex]

[tex]\text{r} = {(350})^{\frac{1}{35}}-1[/tex]

[tex]r = (350)^{0.02857142857}-1[/tex]

[tex]r=1.18219102629-1[/tex]

[tex]r=0.18219102629[/tex]

[tex]r=0.18[/tex]

[tex]r\approx 18\%[/tex]

Hence, stock's average annual growth rate during the period of 35 years is 18%.

Learn more about growth rate here:

https://brainly.com/question/12609944

#SPJ12

Answer:

A translation moves a shape up, down or from side to side but it does not change its appearance in any other way. Translation is an example of a transformation. A transformation is a way of changing the size or position of a shape. Every point in the shape is translated the same distance in the same direction

Step-by-step explanation:

Answer:

I disagree.............................................................................

Step-by-step explanation: