To train for an upcoming marathon, Susie plans to run 2 miles per day the first week and then increase the daily distance by a half a mile each of the following weeks.

There are many ways to approach this problem.




Week Miles

1 2

2 2.5

3 3

4 3.5

5 4

6 4.5


Write an equation to represent the nth term of the sequence.

Answer:The cordinates of A and B are (-3.8, 5.2) and (7, -2).

Step-by-step explanation:From (1), we get x = (8 - 3y) / 2 ––(3)

Substitute (3) into (2),

2 [(8 - 3y) / 2]² + 3y² = 110

(8 - 3y)² + 3y² = 220

15y² - 48y - 156 = 0

Therefore y = 5.2, then x = (8 - 3×5.2) / 2 = -3.8

OR y = -2, then x = [8 - 3×(-2)] / 2 = 7

Answer:

The coordinates are A. (-3.8, 5.2) and B. (7, -2).

Step-by-step explanation:

At A and B the coordinates satisfy both equations so we solve simultaneously using substitution:

2x^2 + 3y^2 = 110

2x + 3y = 8

From the above equation

x = (8 - 3y)/2

So substituting for x in the first equation:

2 [(8-3y)/2]^2 + 3y^2 = 110

(8-3y)^2 / 2 + 3y^2 = 110

Multiply through by 2:

(8 - 3y)^2 + 6y^2 = 220

64 + 9y^2 - 48y + 6y^2 - 220 = 0

15y^2 - 48y - 156 = 0

3(5y^2 - 16y - 52) = 0

(5y - 26)(y + 2) = 0

y = 26/5, 2

y = 5.2,  -2.

So substituting in 2x + 3y = 8

When y = -2:

2x - 6 = 8

2x = 14

x = 7.

When y = 5.2

2x + 3(5.2) = 8

2x = 8 - 15.6 = -7.6

x = -3.8.

Answer:

156

1.56×10²

after you get your answer move the decimal however many spaces to where you only have one number before the decimal then you multiply it by 10 in your square root is however many times do you move the decimal

Answer:

  y = 18

Step-by-step explanation:

Direct variation means y will change by the same factor x does. When x changes by a factor of 15/10 = 1.5, the value of y will change by that same factor

  x = 10, y = 12

  x= 15, y = 1.5×12 = 18

The new value of y is y = 18.

_____

Written as a proportion, you have ...

  y/15 = 12/10

  y = 15×12/10 = 18

__

Written as a direct variation equation, you have ...

  y = kx

  12 = k·10   ⇒   k = 1.2

  y = 1.2·15 = 18 . . . . for x=15

Step-by-step explanation:

3×|x + 4| + 2 >= 5

you handle this basically like an equation :

3×|x + 4| >= 3

|x + 4| >= 1

because of the absolute value we have 2 solutions for that :

x + 4 = 1

and

x + 4 = -1

as in both cases the absolute value turns the result into 1.

so,

x + 4 = 1

x = -3

x + 4 = -1

x = -5

so, to satisfy the inequality

x >= -3 or x <= -5

please consider : if the inequality would have been > instead of >=, we would have had to use > and < for the solution.

Answer:

the third one

Step-by-step explanation:

iiiieeeeew edgeuinty

Answer:

15 inch. By 27 inch.

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

the translation rule (x, y ) → (2x, [tex]\frac{1}{3}[/tex] y )

means multiply the x- coordinate by 2 and multiply the y- coordinate by [tex]\frac{1}{3}[/tex] ), so

A (- 1, - 3 ) → A' (- 2, - 1 )

B (4, - 3 ) → B' (8, - 1 )

C (4, 3 ) → C' (8, 1 )

D (- 1, 3 ) → D' (- 2, 1 )

Answer:

16

Step-by-step explanation:

Given is a degree in decimals as 55.27 degrees

But normally in degrees, we use for part of degrees minutes and seconds

60 seconds make one minute and 60 minutes make one degree.

Here 55 degrees would be the same

But part degree 0.27 = 27/100

If we want to convert this into minutes multiply by 60

No of minutes =

1/5 minutes = 12 seconds

Hence 55.27 = 55 deg 16 min and 12 seconds

The Missing number in the middle is 16

Answer:

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Exact Form:

x=3/2

Decimal Form:

x=1.5

Mixed Number Form:

x =1 1/2

Answer:

3. 314 student and 226 adult

4. x = 6.5, y = -0.5

Step-by-step explanation:

3. First we will take our information and make a system of equations:

[tex]2.4a+1.25s=934.9[/tex]

[tex]a+s=540[/tex]

[tex]a[/tex] is the number of adult tickets sold and [tex]s[/tex] is the number of student tickets sold.

From the second equation we can rearange it to be:

[tex]a=540-s[/tex]

Then we can plug in our new value of [tex]a[/tex] to our first equation

[tex]2.4(540-s)+1.25s=934.9[/tex]

[tex]1296-2.4s+1.25s=934.9[/tex]

[tex]1.15s=361.1[/tex]

[tex]s=314[/tex]

We can then find [tex]a[/tex] by plugging in s to our second equation

[tex]a+314=540[/tex]

[tex]a=226[/tex]

4. It is mostly solved already. We can take the value of y from the first equation and plug it into the second to get:

[tex]3x -5(-5x+32)=22[/tex]

[tex]3x+25x-160=22[/tex]

[tex]28x=182[/tex]

[tex]x=6.5[/tex]

Then plug our value of x into the first equation to get:

[tex]3(6.5)-5y=22[/tex]

[tex]19.5-5y=22[/tex]

[tex]5y=-2.5[/tex]

[tex]y=-0.5[/tex]

Answer:

256= 4 power 4 and 125 = 5 power 3

Answer:

x > 29

Hope you level up in khan :)

[tex]-x <-29 <=>\frac{-x}{-1} >\frac{-29}{-1} <=>x >29[/tex]

Ok done. Thank to me :>

Answer:

1. (2^3)^3 = 2^x  x=9

2. 4^x  x = 6   5^y  y= 9

3. 3^6/3^3 = 3^x   x = 3

Answer:

30 liters

Step-by-step explanation:

To me it's kind of like multiplying and dividing.

So, what I did was 30,000 divided by 30 and got 1,000.

1,000 x 30 = 30,000.

That's what I did. You probably have your own way of doing it, but the answer is 30. I'm sorry if my explanation isn't good enough but I tried. Thanks for the question and enjoy your answer :)

Answer: Image A

Step-by-step explanation:

math

Answer:

A

Step-by-step explanation:

Answer:

y-inctercept=4, x-intecept=7

Step-by-step explanation:

I did it with the standard to slope again!

[tex]7y=28-4x[/tex]

[tex]y=4-\frac{4}{7}x[/tex]

Now don't get confused here, 4 is the y incetecept, not -4.

When y=0, x=7

UPDATE:

To determine x and y intercept using graph, see where the line intersects at the x or y axis.

Answer:

34

Step-by-step explanation:

Answer:

b=4 a=3

The first digit is 3 and the second 4 so the original number is 34

To be honest! It would be much quicker to solve by trial and error.

Explanation:

Building the equations

Let the first digit be  

a

Let the second digit be  

b

The first condition

a

+

b

=

7

...............................(1)

Step-by-step explanation:

Answer: A. 20%

Step-by-step explanation:

First, to find the total number of teachers, we can add 25+32+18+5+20=100

Next, we divide the number of teachers in 2014 (20) by the total number of teachers (100) as follows:

20 ÷ 100 = 0.2

Finally, to make 0.2 a percentage, we can multiply 0.2 X 100 = 20

Therefore, the correct answer is A.

Answer

if there´s any answer choice, the answer is 1

Step-by-step explanation:

32 / 4 = 8

When it states that her mom visited x 4 the amount of states as her, divide the amount her mom has visited by 4 and find out how many states Kelly visited.

32 / 4 = 8

So, Kelly has visited 8 states.

Answer: The answer to this inequality is C.

Answer: 9

Step-by-step explanation:

Answer:

9!

Step-by-step explanation:

Answer:

D. 2900.

Step-by-step explanation:

Because it ends in 00.

Answer:

D. 2900

Step-by-step explanation:

It ends in 900, which is already at the nearest 100.

101 would change to 100

990 would change to 1000

1150 would change to 1200

Answer:

The greatest number of arrangements possible would be 5

Step-by-step explanation:

If we look at the x values (in this case # of tulips remaining) we can find the number 20. And we see that there is a line going through it. We then stop at the point and go down to see what number it would fall on on the y axis.

Answer:

1 a is your answer

Step-by-step explanation:

mark brainlest pls and i hope this helps

Answer:

[tex] < rsq + < qrs + sqr = 180 \\ 50 + 37 + < sqr = 180 \\ < sqr = 180 - (50 + 37) \\ < sqr = 180 - 87 \\ = 93[/tex]

I hope it helps you

Answer:

Go have fun at your Christmas party!

Multiple Choice= 2 points each

Short Response= 4 points each

Step-by-step explanation:

You can set up a system of equations to find out how many points each type of question is worth.

x= multiple choice

y= short response

Equation 1 (You)

23x+10y=86

Equation 2 (Your Friend)

28x+5y=76

Solve with elimination. Multiply the second equation by negative 2 to cancel out the y-variable.

-2(28x+5y=76)

-56x-10y=-152

Subtract both equations together.

23x+10y=86

-56x-10y=-152

-33x= -66

x=2

Now that we found x, plug it into the first equation to solve for y.

23x+10y=86

23(2)+10y=86

46+10y=86

10y=40

y=4

Each multiple choice is worth 2 points, and each short answer response is worth 4 points.

Step-by-step explanation:

female workers:2250

% female workers:?

First, find the percentage of workers who aren't men since we are told the number of workers who aren't men

100-55=45

Therefore 45% of workers aren't men

Let the total number of workers =x

Now form an equation for the problem

[tex]x \times \frac{45}{100} = 2250[/tex]

[tex]x = 2250 \div \frac{45}{100} [/tex]

[tex]x = 5000[/tex]

Therefore, there are 5000 workers in total

The following statements are true:

The given diagram is a triangular prism. From the diagram, some of the sides are parallel to each other (that is facing each other directly)

Some of the lines are also parallel to each other. From the given diagram, the sides that are parallel to each other are;

For the lines, the lines that are parallel to each other are:

For skew lines, they are straight lines that do not intersect and are not in the same plane. Hence the line that is skewed to DE is BC

Learn more about parallel and skew lines here: https://brainly.com/question/18013592