Find the 25th term in the arithmetic sequence: 23, 223, 423, 623,...

Answer: Alana's training experience in (weeks, minutes per mile) is (1, 12) and (5, 6).

Kelsa's training experience is (1, 10), (11, 5).

Find:

A linear equation in standard form that describes Alana's experience

A linear equation in standard form that describes Kelsa's experience

A solution to the pair of linear equations

The week in which the number of minutes per mile is the same

Minutes per mile for Alana and Kelsa at week 25

Comment on the use of a linear model in this context

Solution:

Please note that in parts 1 and 2 a "standard form" linear equation has a positive leading coefficient and the numbers have no common factor.

1. A linear equation can be written from two points (x1, y1) and (x2, y2) as ...

... (y2 -y1)(x -x1) -(x2 -x1)(y -y1) = 0

Using the given points in order, this becomes

... (6-12)(x -1) -(5 -1)(y -12) = 0 . . . . above equation with values filled in

... -6x +6 -4y +48 = 0 . . . . . . . . . . eliminate parentheses

... 3x +2y -27 = 0 . . . . . . . . . . . . . divide by -2 to make x-coefficient positive

... 3x +2y = 27 . . . . . . . . . . . . . . . . Alana's training experience

2. In similar fashion, we can write the equation for Kelsa's experience.

... (5 -10)(x -1) -(11 -1)(y -10) = 0

... -5x +5 -10y +100 = 0 . . . . . . eliminate parentheses

... x +2y -21 = 0 . . . . . . . . . . . . . divide by -5

... x +2y = 21 . . . . . . . . . . . . . . . . Kelsa's training experience

3. We note that both equations have the term 2y, so we can subtract the second equation from the first to eliminate that term:

... (3x +2y) -(x +2y) = (27) -(21)

... 2x = 6 . . . . . . . simplify

... x = 3 . . . . . . . . divide by 2

... 3·3 +2y = 27 . . . substitute x=3 into Alana's equation

... 2y = 18 . . . . . . . . subtract 9

... y = 9 . . . . . . . . . . divide by 2

The solution is (weeks, minutes) = (x, y) = (3, 9).

4. The solution of part 3 tells us both have an average time of 9 minutes per mile in week 3 of training.

5. Substituting x=25 into the equations of parts 1 and 2, we get ...

... 3·25 +2y = 27

... y = (27 -75)/2 = -24 . . . . Alana's time per mile at week 25

... 25 + 2y = 21

... y = (21 -25)/2 = -2 . . . . . Kelsa's time per mile at week 25

6. A linear model makes no sense in this context. At some point a linear equation for minutes per mile will always have a value of 0. We know that marathon runners will never have a time of zero minutes per mile. Under the best of conditions, we expect training to improve time toward some asymptotic limit determined by body mechanics. A linear model is completely inappropriate for describing such training effects. Not every real-world problem is appropriately represented by a linear equation.

Step-by-step explanation:

Answer:

Blue marbles: 18

Green marbles: 25

Step-by-step explanation:

First off, we have to define our variables.

g = # of green marbles

b = # of blue marbles

We know two equations:

g + b = 43 and g = b + 7

If you're wondering how I got the first equation, it was because the number of green and blue marbles is 43. For the second equation, we know that there are 7 more green marbles than blue marbles.

Now, we have an equation for the number of green marbles. We can plug that equation into the equation g + b = 43.

So, (b + 7) + b = 43.

When we simplify it, we get 2b + 7 = 43.

We subtract 7 from both sides, which gets us 2b = 36.

Now, b = 36/2.

b = 18.

So, we found out the number of blue marbles that we have. We know that g + b = 43. Now, all we have to do is plug in the number of blue marbles into that equation to find out the number of green marbles.

g + 18 = 43.

g = 43 - 18.

g = 25.

Thus, the number of green marbles we have is 25 and the number of blue marbles is 18.

Answer:

rrrrrrreeeeeeeeeee

Step-by-step explanation:

jjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjj

Answer:

If [tex]p[/tex] is people and [tex]h[/tex] is hot dogs, the equation is [tex]3h=4p[/tex].

The  relation among people who attend and hot dog sold is 4x = 3y.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

At the Football game they expect that for every 4 people that attend 3 hot dogs will be sold.

let the are total x people and y number of hot dogs will be sold.

So, the relation among people who attend and hot dog sold is

4x = 3y

Learn more about equation here:

https://brainly.com/question/29538993

#SPJ2

Answer:

9 hours

Step-by-step explanation:

208 / 13 = $16 per hour

144 / 16 = 9 hours

Answer:

9 hours

Step-by-step explanation:

208 divided by 13 is 16. So then u take 16 and divide it by 144, and if you do long division you would get 9. Hopefully this helps

The domain of the function f(x) = 2x² + 2x + 4  is (-∞, ∞).

The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics. It is expressed in the form of:

ax² + bx + c = 0

where x is the unknown variable and a, b and c are the constant terms.

You have the quadratic function

f(x) = 2x² + 2x + 4 ,

and remember that all quadratic functions are parabolas opening at point called the vertex.

Since you can plug any real number in our parabola here, its domain is all the real numbers, and this is true for all the quadratic functions of the form ax² + bx + c = 0.

Thus, in interval notation the domain of the function  is (-∞, ∞).

Learn more about Quadratic Equation from;

https://brainly.com/question/2263981

#SPJ1

y=2

There is no slope because the y value stays constant. When the table is graphed, it is a horizontal line at 2. I hope this helps!

Answer:

you would save 11.51 dollars

Step-by-step explanation:

12 cans times the vending machine price of 1.25$= $15

15-3.49=11.51

Answer:

sonn 12 laalkznjsnl nalslaonhfj. alallkzhdbb nLaojahdnldl

Answer:

This family spend for the meal plus the tip : $56.95 + $8.54 = $65.49

The tip = $56.95 x 15% =$8.54

Step-by-step explanation:

y=2x

Step-by-step explanation:

I dont know what else there is sry

Answer:

ANSWER

Step-by-step explanation:

Answer:

False b=9

Step-by-step explanation:

In the equation 5b+45, b is equal to 9

The way we get this answer is by dividing each term by 5 and then simplifying

45/5

45/5=9

Hope this helps :)

Answer:

I think it is C.

Step-by-step explanation:

Answer:

volume is length x width x height, the answer is 160 cubed feet.

Step-by-step explanation:

Length x width x height and bam, there is your answer

Answer:

y=18

Step-by-step explanation:

explanation is in the attachment above

Answer:

Yes

Step-by-step explanation:

For example

Doctors have two methods of calculating maximum heart rate. With the first method, maximum heart rate, y, in beats per minute is y=220−x, where x is the person’s age.

Step-by-step explanation:

____2__divisible by both 2 and 5

Answer:

k = -13

Step-by-step explanation:

-143/11 = -13

Answer:

11k = -143

k=-143/11=-13 is a required answer

Answer:

Step-by-step explanation:  sin β = [tex]\frac{oposite }{hypotenuse}[/tex] ; cos β = [tex]\frac{Adjacent}{Hypotenuse}[/tex]

10) sin [tex]32^{0}[/tex] = [tex]\frac{x}{18}[/tex]

18 sin [tex]32^{0}[/tex] = x

18 (0.53) = x

x= 9.5 units

cos [tex]32^{0}[/tex] = [tex]\frac{y}{18}[/tex]

18 cos [tex]32^{0}[/tex] = y

y = 18 (0.85)

y = 15.3 units

You use the same strategy for the rest of the questions. Feel free to reach out if you have more questions.

Answer:

I know some .

median : 24

Step-by-step explanation:

Mean : you add all of them up then divide by how many numbers there are .

range : the biggest number minus the smallest number .

median : the middle number . the middle number is 24 .

I know what is mode but the answer is not in there

Answer:

C=10. They did distributive property. Hope this helped!

Step-by-step explanation:

Answer:

=3x^2+4

Step-by-step explanation:

Subtract 8 from 12.

3x^2+4

Answer:

50.24 inches

Step-by-step explanation:

[tex]3.14 * 4^{2}[/tex]

3.14 * 16

= 50.24

Step-by-step explanation:

y=5x-5

y= -4x+22

1- use y=5x-5 solve for y (here you don't really have to do anything)

       This stays the same, Therefore y = 5x-5

2- you will substitute y=5x-5 for y in y= -4x+22. The problem should now look like this:

               5x-5= -4x+22

now, with the equation above you will solve for x-

5x-5= -4x+22         (add 4x to both sides)

9x-5= 22               (add 5 to both sides)

9x=27                   (divide by 9)

x=3

Now that you Know that x=3 you can substitute x=3 for x in y=5x-5. The problem should look like this:

                                                    y= 5(3)-5

Now with the equation above you can solve for y

y= 5(3)-5              (multiply 5 by 3)

y= 15-5                 (subtract)

y=10

Now you have your answers X=3  Y=10

i hope this helps!

Answer:

40 hours

Step-by-step explanation:

did 18.25*40 then subtracted 182.50 and it equaled 547.50