Hilda adds 5 to a number, then multiplies the sum by -2. The result is 6. Write an equation to find the number, x. What is the number?

Let the original fraction be

[tex]\dfrac{n-1}{n}[/tex]

Now let's increase both numerator and denominator by 2:

[tex]\dfrac{n+1}{n+2}[/tex]

This produces a 1/12 increase:

[tex]\dfrac{n+1}{n+2}-\dfrac{n-1}{n}=\dfrac{1}{12}[/tex]

The left hand side can be rearranged as

[tex]\dfrac{2}{n^2+2n}=\dfrac{1}{12}[/tex]

Invert both sides:

[tex]\dfrac{n^2+2n}{2}=12 \iff n^2+2n=24[/tex]

Solve the quadratic equation:

[tex]n^2+2n-24=0 \iff n=-6 \lor n=4[/tex]

So, in the first case, the original fraction is

[tex]\dfrac{n-1}{n}=\dfrac{-6-1}{-6}=\dfrac{7}{6}[/tex]

In the second case, we have

[tex]\dfrac{n-1}{n}=\dfrac{4-1}{4}=\dfrac{3}{4}[/tex]

Answer: 4x² + 3x + 8

Work: I combined Like Terms, put them in the right form, from the x² to the number.

I hope this helps and Happy Holidays! :)

Answer:

25

Step-by-step explanation:

3+2=5×2 ×2 +5=25

add the 10 to the other 10 and then add 5

Answer:

-7/-9 pretty sure

Step-by-step explanation:

x2-x1

y2-y1

3-10= -7

1-10= -9

Answer:

it will take her  [tex]13\frac{5}{24}[/tex] minutes more to walk down to Raj's House

Step-by-step explanation:

It took Sheldon [tex]17 \frac{5}{6}[/tex]  minutes to walk to Raj's house

It also took Sheldon [tex]4\frac{5}{8}[/tex] minutes to use the bus.

To get the time difference between the two transport mechanisms, we subtract their different time durations.

This will be

[tex]17\frac{5}{6} - 4\frac{5}{8}=317/24[/tex]

We can convert this to Mixed fractions as shown [tex]13\frac{5}{24}[/tex] minutes.

Therefore, it will take her  [tex]13\frac{5}{24}[/tex] minutes more to walk down to Raj's House

Answer:

All systems have 2 real solutions.

Step-by-step explanation:

there are X and Y unknowns.

Answer:

B

Step-by-step explanation:

3+5+7=3+7+5

Answer:

3.2

Step-by-step explanation:

Answer:

width of the sidewalk = 1 feet

Step-by-step explanation:

Area of the pool = length × width

Length = 10 feet

Width = 6 feet

Area of the pool = length × width

= 10 feet × 6 feet

= 60 feet²

Area of the pool = 60 feet²

Total area = Area of the pool + Area of sidewalk

96 feet² = 60 feet ² + Area of sidewalk

Area of sidewalk = 96 feet² - 60 feet ²

Area of sidewalk = 36 feet²

Length of pool + sidewalk = 10 + 2x

width of pool + sidewalk = 6 + 2x

( 10 + 2 x ) ( 6 + 2 x ) -60 = 36

60 + 20x + 12x + 4x² - 60 = 36

4x² + 32x - 36 = 0

4x² + 36x - 4x - 36 = 0

4x (x + 9) -4(x + 9) = 0

(4x - 4) (x + 9) = 0

4(x - 1) (x + 9) = 0

(x - 1) = 0 (x + 9) = 0

x = 1 or x = -9

The width of the side walk can't be a negative value

Therefore, width of the sidewalk = 1 feet

A rectangular pool has a sidewalk around it. Width of the sidewalk is 1 feet.

Given

A rectangular pool has a sidewalk around it. The pool measures 6 feet by 10 feet and the total area of the pool and sidewalk is 96 square feet.

Let 'w' be the width of sidewalk

The pool measures 6 feet by 10 feet . The width of the rectangular pool with side walk is 6+x+x=6+2x

The length  of the rectangular pool with side walk is 10+2x

The total area of the pool and side walk is length times width

Total area= [tex](6+2x)(10+2x)\\[/tex]

[tex]96=(6+2x)(10+2x)\\96=60+32x+4x^2\\60+32x+4x^2-96=96-96\\4x^2+32x-36=0[/tex]

apply quadratic formula to solve for x

[tex]x=\frac{-32\pm \sqrt{32^2-4\cdot \:4\left(-36\right)}}{2\cdot \:4}\\x=\frac{-32\pm \:40}{2\cdot \:4}\\x= \frac{-32+40}{2\cdot \:4}=1\\x=\frac{-32-40}{2\cdot \:4}=-9[/tex]

Width of the sidewalk cannot be negative

so the width of the sidewalk is 1 feet

Learn more :  brainly.com/question/21860114

Answer:

Ordinal

Step-by-step explanation:

The ordinal measurement level means the arrangement of the number so that it could tell the position of something in the list

Since in the question it is mentioned that the day care center ask the children for listing their five favorite toys and the arrangement could be done from most favorite to least favorite

So this represent the ordinal measurement level

Answer:

(-4,-2); y=4x+2

Step-by-step explanation:

Answer:

F. 10

Step-by-step explanation:

6d - 2c

6 * 3 - 2 * 4

18 - 8

10

Answer:

your photo is not visible for me

Answer:

54

Step-by-step explanation:

11x=26=180

x=14

8x+p+14=180

p=54

Answer:

2 13/20 cm

Step-by-step explanation:

The screen on Brianna's new phone is 2.65 cm. Long. What mixed number represents the length of the phone screen ?

From the above question, we are converting, from decimal to mixed number , hence:

2.65 has 2 decimal places

Hence:

2.65 cm = (265/100)cm

= ( 2 + 65/100) cm

= ( 2 13/20 )cm

The mixed number that represents the length of the phone screen is 2 13/20 cm

Answer:

$48

Step-by-step explanation:

Because he has 3/4 you would divide 36 by 3 whick is 12 then multiply by 4 to get the total of $48

Answer:

$48 :)

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

0.13 and 0.1 hope it will help you..

Answer:

D. 16

Step-by-step explanation:

32/2 = 16

Answer:

8. Number of student tickets = 460

Number of teacher tickets = 100

9. Speed of plane = 727.5 km/hr

Speed of wind = 48.5 km/hr

Step-by-step explanation:

8.

Let number of students' tickets = [tex]x[/tex]

Let number of teachers' tickets = [tex]y[/tex]

Total number of tickets = 480

[tex]x+y=480[/tex] ...... (1)

Price for one student's ticket = $1

Price for one teacher's ticket = $5

Total money collected by the tickets = $560

[tex]x +5y = 560[/tex] ...... (2)

Subtracting (1) from (2):

[tex]4y = 80\\\Rightarrow y = 20[/tex]

By equation (1):

[tex]x = 460[/tex]

Number of student tickets = 460

Number of teacher tickets = 100

9.

Let the speed of airplane in still air = [tex]u[/tex] km/hr

Let the speed of air = [tex]v[/tex] km/hr

Total distance = 5432 km

Time taken with the wind = 7 hours.

Speed with the wind = [tex]u+v[/tex] km/h

Time taken against the wind = 8 hours.

Speed with the wind = [tex]u-v[/tex] km/h

Using the formula:

Distance = Speed [tex]\times[/tex] Time

[tex]5432 = (u+v)\times 7\\\Rightarrow u +v = 776 .... (1)[/tex]

[tex]5432 = (u-v)\times 8\\\Rightarrow u - v = 679 .... (2)[/tex]

Adding (1) and (2):

[tex]2u = 1455\\\Rightarrow u = 727.5\ km/hr[/tex]

By equation (1):

[tex]v = 48.5\ km/hr[/tex]

Speed of plane = 727.5 km/hr

Speed of wind = 48.5 km/hr

Answer:

Since it's a parallelogram, the length of AD and BC are the same.

Hence, [tex]x + 21 = 12x - 1[/tex].

[tex]x + 21 = 12x - 1[/tex]

[tex]12x - x = 21 + 1[/tex]

[tex]11x = 22[/tex]

[tex]x = 2[/tex]

Therefore, x = 2.

Step-by-step explanation:

Hope this helped!

Answer:

[tex]y = \frac{3}{2}x +2[/tex]

Step-by-step explanation:

Required:

Write an equation to represent this  situation

Let x represents the number of weeks and y represents the growth.

When he planted it:

[tex](x_1,y_1) = (0,2)[/tex]

Two weeks later:

[tex](x_2,y_2) = (2,5)[/tex]

At 6 weeks:

[tex](x_3,y_3) = (6,11)[/tex]

Start by calculating the slope (m)

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]m = \frac{5-2}{2-0}[/tex]

[tex]m = \frac{3}{2}[/tex]

Then calculate the equation using:

[tex]y - y_3 = m(x - x_3)[/tex]

[tex]y - 11 = \frac{3}{2}(x - 6)[/tex]

[tex]y - 11 = \frac{3}{2}x - 9[/tex]

Solve for y

[tex]y = \frac{3}{2}x - 9+11[/tex]

[tex]y = \frac{3}{2}x +2[/tex]

Answer: There is not enough info and I can't see  because the picture is not clear enough. Sorry. :(

Merry (early) Christmas tho! :)

Answer:

b

Step-by-step explanation:

Answer:

the answer is D

Given:

Steve gets 4 points for every correct answer and loses 1 point for every wrong answer.

Total question answered by Steve =  30

Total score = 20 points

To find:

The system of equations for the given problem.

Solution:

Let x be the number of correct answers and y be the number of wrong answers.

Total question answered by Steve =  30

[tex]x+y=30[/tex]       ...(i)

Steve gets 4 points for every correct answer and loses 1 point for every wrong answer.

Score for 1 correct answer = 4

Score for x correct answer = 4x

Score for 1 wrong answer = -1

Score for y correct answer = -y

Total score = 20 points

[tex]4x-y=20[/tex]        ...(ii)

The system of equations contains (i) and (ii).

Therefore, the system of equations have two equations [tex]x+y=30[/tex] and [tex]4x-y=20[/tex].

Answer:

3.07×10^8

Step-by-step explanation:

:)

hope this helps

Answer: 307,000,000 in scientific notation is 3.07 × 10^8.

Answer:

I think it is C.

Step-by-step explanation:

Answer:

12 songs

Step-by-step explanation:

Brenda's band plays songs in sets of 4

Melissa's band plays songs in sets of 6.

After performing together, both bands realize that they have played the same number of songs.

What is the smallest number of songs each band could have performed?

The smallest number of songs each band could have performed can be calculated by finding the lowest common multiple of 4 and 6

4 = 8, 12, 16, 20, 24, 28, 32, 36, 40

6 = 12, 18, 24, 30, 36, 42

The lowest common multiple of 4 and 6 is 12

The smallest number of songs each band could have performed is 12 dongs

Answer:

10

Step-by-step explanation:

So I belive the answer consists of- 18 divided by 4 equals 4.5 and 45 divided by 4.5 is 10 so ten should be your answer.