Balance the equation

Answer: The correct answer would be B!

Step-by-step explanation:

To find a fraction equivalent to 1/3 using the LCD, multiply the numerator and denominator by the same whole number that gives the LCD as the new denominator.

To find a fraction that is equivalent to 1/3 using the LCD (Least Common Denominator), we need to find a fraction with the same value but different numerator and denominator. The LCD of 1/3 is 3, so we can multiply the numerator and denominator by any whole number that gives us 3 as the new denominator. For example, multiplying both the numerator and denominator by 2, we get 2/6, which is equivalent to 1/3.

Final answer:

To find an equivalent fraction to 1/3 using the LCD, the fraction itself is already equivalent to 1/3.

Explanation:

To find a fraction equivalent to 1/3 using the least common denominator (LCD), we need to identify the LCD of 1/3. The LCD is the least common multiple of the denominators of the given fractions. In this case, the LCD is 3. Now, we need to express 1/3 with a denominator of 3. To do this, we multiply both the numerator and denominator by 1, resulting in 1/3 × 1/1 = 1/3. Therefore, 1/3 is already equivalent to 1/3.

The coordinates are (5,4) and (9,3)

Remember that the x axis comes before the y axis when plotting down the points. I made this simple mistake with these coordinates reversed and got it wrong with putting the y axis before the x axis.

The graph of the equation of line y = - 14x + 74 is shown in figure.

What is Equation of line?

The equation of line in point-slope form passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The equation of line is,

y - 4 = - 14 (x - 5)

Now,

The simplify the equation of line as;

y - 4 = - 14 (x - 5)

y - 4 = - 14x + 70

Add 4 on both side, we get;

y - 4 + 4 = - 14x + 70 + 4

y = - 14x + 74

Thus, By comparing the slope form of the equation of line y = mx + b we get;

The slope of the line m = - 14

And, The y - intercept = 74

So, The graph of the equation of line y = - 14x + 74 is shown in figure.

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The solution of the operations of the fractions are found as below.

Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.

4. [tex]\frac{3}{4}[/tex] + [tex]\frac{1}{2}[/tex]

Make the denominator equal.

1/2 is equal to (1×2) / (2×2) = 2/4

[tex]\frac{3}{4}[/tex] + [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{4}[/tex] + [tex]\frac{2}{4}[/tex] = [tex]\frac{3+2}{4}[/tex] = [tex]\frac{5}{4}[/tex]

5. 2 [tex]\frac{3}{8}[/tex] + 1 [tex]\frac{1}{8}[/tex]

This in the form of mixed fraction.

Convert it into improper fraction first.

2 [tex]\frac{3}{8}[/tex] = (2 × 8 + 3) / 8 = 19/8

1 [tex]\frac{1}{8}[/tex] = (1 × 8 + 1) / 8 = 9/8

2 [tex]\frac{3}{8}[/tex] + 1 [tex]\frac{1}{8}[/tex] = 19/8 + 9/8 = 28/8 = 7/2

6. 5 [tex]\frac{2}{5}[/tex] - 3 [tex]\frac{7}{10}[/tex]

5 [tex]\frac{2}{5}[/tex] = (5 × 5 + 2) / 5 = 27/5

3 [tex]\frac{7}{10}[/tex] = (3 × 10 + 7) / 10 = 37/10

5 [tex]\frac{2}{5}[/tex] - 3 [tex]\frac{7}{10}[/tex] = 27/5 - 37/10

              = 54/10 - 37/10

              = 17/10

7. 5 [tex]\frac{1}{2}[/tex] × [tex]\frac{3}{11}[/tex]

5 [tex]\frac{1}{2}[/tex] = 11/2

5 [tex]\frac{1}{2}[/tex] × [tex]\frac{3}{11}[/tex] = [tex]\frac{11}{2}[/tex] × [tex]\frac{3}{11}[/tex]

            = 3/2

8. [tex]\frac{5}{6}[/tex] ÷ [tex]\frac{1}{3}[/tex]

When dividing two fractions, the second term becomes reciprocal and the operation becomes multiplication.

[tex]\frac{5}{6}[/tex] ÷ [tex]\frac{1}{3}[/tex] =  [tex]\frac{5}{6}[/tex] × [tex]\frac{3}{1}[/tex] = 5/2

Hence the solutions are found.

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Final answer:

To find the area of a window that measures 3 yards by 3/4 yard, multiply the length by the width. The area is 9/4 yd² or 2 1/4 yd², which corresponds to answer C.

Explanation:

The area of a rectangle is calculated by multiplying its length by its width. In this case, the window's dimensions are given in yards, and we need to find the area in square yards. We multiply the length (3 yards) by the width (3/4 yard) to find the area.

Area = length × width
Area = 3 yd × 3/4 yd
Area = 9/4 yd² or 2 1/4 yd²

So the correct answer is C. 2 1/4 yd².

To write 0.45 as a fraction, express it as 45/100 then divide by the greatest common divisor, which is 5, to get 9/20 in simplest form.

To write 0.45 as a fraction in simplest form, we can start by recognizing that 0.45 means 45 hundredths, which is the same as 45 over 100. This can be written as:

\\[0.45 = \frac{45}{100}\\]

To simplify the fraction, we look for the greatest common divisor (GCD) that both the numerator (45) and the denominator (100) share. In this case, the GCD is 5. To get a fraction in simplest form, we divide both numerator and denominator by this number:

\\[\frac{45 \div 5}{100 \div 5} = \frac{9}{20}\\]

So, the fraction in simplest form of 0.45 is \(\frac{9}{20}\).

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The question about the number of people who rode the train to work this morning is a statistical question, requiring data collection and analysis to reveal various statistics such as travel behaviors and the relation between ticket class and travel distance.

The question "How many people rode the train to work this morning?" represents a statistical question because it is likely to result in a variety of different answers and requires the collection and analysis of data to provide an accurate response. Statistical questions are concerned with understanding the distributions, trends, and patterns within collected data. In answering such a question, one would typically construct a table or a tree diagram to organize the data collected.

For example, if we wanted to know the percentage of commuters who travel alone to work, we would need to gather data on various modes of transportation, including trains, and analyze how many commuters use each mode alone. This situation could also relate to how many commuters decided to get on the train at each station on a given morning.

Answer:

708 Fahrenheit

Step-by-step explanation:

672 + 36 = 708

You add the 36 because it is a negative number and since you are trying to find the difference, for every negative number you have to add 1.

The difference between the melting and boiling points of mercury, -36 Fahrenheit and 672 Fahrenheit respectively, is 708 degrees Fahrenheit.

To find the difference between two temperatures, you simply subtract the lower temperature from the higher temperature. In this case, we have the boiling point of mercury at 672 degrees Fahrenheit and the melting point at -36 degrees Fahrenheit. So, we subtract -36 from 672 as follows:

672 - (-36) = 708 Fahrenheit.

The difference in temperature between the boiling and melting points of mercury is 708 degrees Fahrenheit.

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Answer:

The correct option is 3.

Step-by-step explanation:

It is given that the Karolyn is arranging her art project, science project, and math project on her desk. The tree diagram below shows the sample space.

According to the tree diagram the elements of sample space are

1. art - math - science

2. art - science - math

3. science - art - math

4. science - math - art

5. math - art - science

6. math - science - art

Total number of possible outcomes is 6.

We need to find the probability that the science project is first. So, the favorable outcomes are

1. science - art - math

2. science - math - art

Total number of favorable outcomes is 2.

The probability of arranging the the science project first is

[tex]P=\frac{\text{Favorable outcomes}}{\text{Total possible outcome}}[/tex]

[tex]P=\frac{2}{6}[/tex]

[tex]P=\frac{1}{2}[/tex]

The probability of arranging the the science project first is 2/6 or it can be written as 1/3. Therefore the correct option is 3.

since the fence will be 3 sides, the length would be length minus 2 widths

 so length = 1200 - 2x

 area = length x width

 width is x

area = (1200-2x)*x

= 1200x -2x^2

 after doing the calculations x = 600 meters, width = 300 meters

Answer:

6w

Step-by-step explanation:

They are basically asking you to multiply 6 and w, which is 6w

Answer:

0.6484

Step-by-step explanation:

They would always be coplanar.

Hope this helps!