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Final answer:

To partition a number line into fourths, divide it into four equal segments, with each representing 1/4. To decompose 3/4 into 6 equal lengths, divide 3/4 into six parts where each part is 1/8 of the whole.

Explanation:

Partitioning a Number Line into Fourths and Decomposing Fractions

To partition a number line from 0 to 1 into fourths, you would divide the line into four equal segments. Each segment represents a value of 1/4. Now, to decompose 3/4 into 6 equal lengths, realize that each 1/4 is being divided into two parts (since 6 divided by 3 equals 2), which means each part is 1/8 in length. Therefore, 3/4 divided into 6 equal lengths gives us 6 segments, each of length 1/8.

Step-by-Step Solution

Draw a number line from 0 to 1.

Mark off four equal lengths between 0 and 1, each representing 1/4.

Find 3/4 on the number line. It is three of these fourths.

Divide each fourth into two equal lengths to decompose 3/4 into 6 equal parts.

Mark these new lengths on the number line, showing that each length is 1/8.

Answer:

1. x² + 2x + 2

2. x² + 4

3. x² - 4x + 8

Step-by-step explanation:

(1) ( x+1+i ) ( x+1-i )

= ( x+1 )²- i²  [ Since ( a+b ) ( a-b ) = a² - b² ]

= x² + 1 + 2x - ( √-1 )²

= x² + 1 + 2x + 1

= x² + 2x + 2

(2) ( x+2i ) ( x - 2i )

= x² - (2i)² [ ( a+b ) ( a-b ) = a² b²

= x² - 4i²

= x² - 4 (-1) [Since i² = -1 ]

= x² + 4

(3) ( x - 2i - 2 ) (x + 2i - 2 )

= ( x-2 )² - ( 2i )² [ ( a+b ) ( a-b ) = a² - b² ]

= x² + 4 - 4x - 4 ( i )²

= x² + 4 - 4x - 4 ( -1 )²

= x² - 4x + 4 + 4

= x² - 4x + 8

7. 0.78 8. 0.55 9. 0.185 10. 0.574 11. 0.33 12. 0.09 13. 0.4763 14. 0.9125

15. 1.66 16. 2.17 17. 0.0006 18. 0.00034 19. 74% 20. 52% 21. 89% 22. 76.8%

23. 99% 24. 49% 25. 48.7% 26. 12.8% 27. 368% 28. 512% 29. 3.71%

30. 0.46% Converting Decimal to Percentage, Multiply Decimal by 100. Percentage to Decimal, divide by 100.

Answer:

for the changing decimal to percent just change each decimal to a whole number for example .99=99 percent and 3.68 = 368 percent

Step-by-step explanation:

Part A: The monthly amount payable by Victoria is $503.75. Option B shows the monthly payment made by Victoria.

Part B: The monthly amount payable by Victor is $276.17.

Interest is defined as the amount of money paid for the use of someone else's money.

Part A:

Given that the amount P is $6500, interest rate R is 13% and time period T is 15 months. The yearly time period is given as,

[tex]T = \dfrac {15}{12}[/tex]

[tex]T = 1.25 \;\rm Years[/tex]

The interest is calculated as given below.

[tex]I = P\times\dfrac {R}{100}\times T[/tex]

[tex]I = 6500 \times \dfrac {13}{100} \times 1.25[/tex]

[tex]I =\$ 1056.25[/tex]

The total amount after 15 months is given as,

A = P + I

A = $6500 + $1056.25

A = $7556.25

This is the amount of 15 months. The amount of one month is calculated as given below.

Monthly Amount = [tex]\dfrac {\$7556.25}{15}[/tex]

Monthly Amount = $503.75

Hence we can conclude that the monthly amount payable by Victoria is $503.75. Option B shows the monthly payment made by Victoria.

Part B:

Given that the amount P is $6800, interest rate R is 13.5% and time period T is 3 years.

The total amount after 3 years is given as,

[tex]A = P (1 + \dfrac {R}{100})^T[/tex]

[tex]A = 6800 (1 + \dfrac {13.5}{100})^3[/tex]

[tex]A = 6800 \times 1.4621[/tex]

[tex]A = \$ 9942.28[/tex]

This is the amount of 3 years or for 36 months. The amount of one month is calculated as given below.

Monthly Amount = [tex]\dfrac {\$9942.28}{36}[/tex]

Monthly Amount = $276.17

Hence we can conclude that the monthly amount payable by Victor is $276.17.

To know more about the interest, follow the link given below.

https://brainly.com/question/4605117.

Answer:

Rate column: 30, 20.

Distance column: x miles for both.

Step-by-step explanation:

Jorden drives to the store at 30 miles per hour. On her way home she averages only 20 miles per hour. If the total driving time takes half an hour, how far does she live from the store?

Fill out the Rate column in the table below.

a = 30

b = 20

Fill out the Distance column.

c = x miles

d = x miles

basically: 30, 20 for first question. x miles for both second

Answer:

855mm

Step-by-step explanation:

The area of the trapezoid can be calculated through the equation,

A = (b₁ + b₂)h / 2

where b₁ and b₂ are the bases and h is the height. Substituting the known values from the given,

A = (25mm + 32mm)(15 mm) / 2

A = 427.5 mm²

Since there are two trapezoids in the necklace, the area calculated is to be multiplied by two to get the total area.

total area = (427.5 mm²)(2)

total area = 855 mm²

Answer:

The amount before the tip  is $50.

Step-by-step explanation:

Given : Matt paid $55 at a restaurant. That amount included a 10% tip.

To find : What was the check amount before the tip?

Solution : We have given

Matt paid  = $55 .

amount included a 10% tip.

Let the amount before the tip = x.

Tip amount = 10% of x is

[tex]\frac{10 x}{100}[/tex] = 0.1 x .

Tip amount = 0. 1 x

Total amount = x + 0.1x = 55 .

1.1 x = 55.

On dividing both sides by 1.1

x = 50.

So, the amount before the tip  is $50.

Therefore, The amount before the tip  is $50.

the correct graph is the dotted diagonal one ( 3rd picture)

 Solve for y

y >x-2

Answer:

Third picture

Step-by-step explanation:

If you simplify the inequality, it is y > x - 2. Because of this, we can graph it as such.

Answer:

(r-7)(r+7)

hope this helps! :)

Answer:

C) 20.94 inches

Step-by-step explanation:

It right on edge

Answer:

A. [tex]I\approx \$103.16[/tex]

B. [tex]\text{Total payment}=\$1161.16[/tex]

C. [tex]\text{The monthly payment}\approx \$129.02[/tex]

Step-by-step explanation:

We have been given that Devin borrowed $1,058 at 13 percent for nine months.

A. To find the amount of interest paid by Devin we will use formula: [tex]I=Prt[/tex], where,

[tex]I=\text{Amount of interest}[/tex],

[tex]P=\text{Principal amount}[/tex],

[tex]r=\text{Interest rate in decimal form}[/tex],

[tex]t=\text{Time in years}[/tex].

Let us convert our given interest rate in decimal form and time in years.

[tex]13\%=\frac{13}{100}=0.13\\\text{9 months}=\frac{9}{12}\text{ year}=\frac{3}{4}=0.75\text{ year}[/tex]

Upon substituting our given values in interest formula we will get,

[tex]I=\$1058*0.13*0.75[/tex]

[tex]I=\$103.155\approx \$103.16[/tex]

Therefore, the amount of interest paid by $103.16.

B. Since total payment will be equal to interest rate plus amount of interest.

[tex]\text{Total payment}=\$1058+\$103.16[/tex]

[tex]\text{Total payment}=\$1161.16[/tex]

Therefore, Devin's total payment will be $1161.16.

C. To find the monthly payment we will divide total amount by 9.

[tex]\text{The monthly payment}=\frac{\$1161.16}{9}[/tex]

[tex]\text{The monthly payment}=\$129.01722\approx \$129.02[/tex]

Therefore, the amount of Devin's monthly payment is $129.02.

A zoo has 14 monkeys and 18 chimpanzees.

To write the ratio of numbers x and y we use three ways given below

1. x to y

2. x : y

3. [tex] \frac{x}{y} [/tex]

Now write the ratio in three ways comparing 14 monkeys and 18 chimpanzees.

Let x be the number of monkeys

y be the number of chimpanzees

So ratio becomes

14 to 18

14 : 18

[tex] \frac{14}{18} [/tex]

The algebraic expression that is equivalent to the given rational expression is (x-11), but when we substitute x=11 into the expression, we receive 0. However, this leads to an indeterminate form in the original rational expression.

The rational expression given in the question is x^2-121/x+11. If we factorize x^2-121, we'll get (x-11)(x+11), because x^2-121 is a difference of squares. Now, the expression becomes: (x-11)(x+11)/(x+11). We see that (x+11) on numerator and denominator will cancel out each other. This leaves us with (x-11).

Now, let's substitute x=11 in (x-11). We obtain 11-11 which equals 0. So the correct answer is (x-11), but we get 0 when we substitute x=11 into the expression. This actually results in an indeterminate form because the original rational expression becomes a 0/0 form, which points to a situation of undefined or indeterminate form.

https://brainly.com/question/17134322

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