Round 6,852 to the nearest thousand

The answers to the four mixed number problems  are 2 3/35, 16 7/8, -1 17/24, and 5 7/10, respectively.

These problems involve adding and subtracting fractions and writing the answer as a mixed number, if possible. Let's go through each one step-by-step.

1. 4 2/7 - 2 1/5: First, convert these mixed numbers into improper fractions (4 2/7 = 30/7 and 2 1/5 = 11/5). The common denominator is 35. Rewrite the fractions as 150/35 and 77/35, subtract to get 73/35 which simplifies to '2 3/35'.

2. 5 7/8 + 11/4: Convert these mixed numbers into improper fractions (5 7/8 = 47/8 and 11/4 = 44/4). The common denominator is 8. Rewrite the fractions as 47/8 and 88/8, add to get 135/8 which simplifies to '16 7/8'.

3. 5/8 - 7/3: The common denominator is 24. Rewrite the fractions as 15/24 and 56/24. Subtract to get -41/24 which simplifies to '-1 17/24'.

4. 16/5 + 2 1/2: Convert the mixed number into an improper fraction (2 1/2 = 5/2). The common denominator is 10. Rewrite the fractions as 32/10 and 25/10. Add to get 57/10 which simplifies to '5 7/10'.

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The fraction that is equivalent to -4/6 is 4/-6. so the correct option is C.

To find an equivalent fraction, we need to divide both the numerator and denominator by their greatest common factor.

In this case, the greatest common factor of 4 and 6 is 2.

Dividing -4 by 2 gives -2, and dividing 6 by 2 gives 3.

Since we have given the option as 4 over negative 6

Thus,  -4/6 = 4/-6

Therefore, the fraction equivalent to -4/6 is 4/-6.

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From the sides length of given equilateral triangle,

Length of each side = 21 cm

Given :

In an equilateral triangle , the length of sides are given by

First side:2x-7

Second side:x+y-9

Third side:y+5

All the sides are equal in equilateral triangle .

second side  = third  side length

[tex]x+y-9=y+5\\Subtract \; y \\x+y-y-9=y-y+5\\x-9=5\\x=5+9\\x=14[/tex]

first side =third  side

[tex]2x-7=y+5\\\2(14)-7=y+5\\21=y+5\\21-5=y\\y=16[/tex]

Now we find length of the side

[tex]2x-7\\2(14)-7\\21[/tex]

All sides are equal in equilateral triangle

Length of each side = 21 cm

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The solution of the given system of equations is (1,3) and this can be determined by using the given data.

Given :

The equation of a pink line that passes through the point (0,5) and (2.5,0) is:

[tex]\dfrac{y-5}{x-0}=\dfrac{0-5}{2.5-0}[/tex]

Simplify the above equation.

(y - 5) = -2x

y + 2x = 5   --- (1)

The equation of a blue line that passes through the point (0,4) and (4,0) is:

[tex]\dfrac{y-4}{x-0}=\dfrac{0-4}{4-0}[/tex]

Simplify the above equation.

y - 4 = -x

y + x = 4

y = 4 - x     --- (2)

Substitute the value of 'y' in equation (1).

4 - x + 2x = 5

x = 1

Substitute the value of 'x' in equation (2).

y = 4 - 1

y = 3

Therefore, the correct option is C).

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Final answer:

To find Miguel's average speed, divide the distance to his grandparents' house, 159 miles, by the time it takes, 3 hours, which gives us an average speed of 53 mph.

Explanation:

To calculate Miguel's average speed when driving to his grandparents' house, we use the formula for average speed, which is the distance traveled divided by the time taken to travel that distance. In this case, if Miguel's grandparents live 159 miles away and it takes 3 hours to get there, we divide the distance by the time to find the average speed:

Average speed = Distance ÷ Time

Average speed = 159 miles ÷ 3 hours

Average speed = 53 miles per hour (mph)

Therefore, Miguel's average speed to his grandparents' house is 53 mph.

To divide 19 by 789, we perform long division, considering decimal places and significant figures. A calculator can provide the decimal result, but users should adjust for the correct number of significant figures, especially when working with scientific notation where exponents are subtracted and coefficients are divided.

Dividing 19 by 789 step by step is essentially the process of long division. To divide 19 by 789, we would write 19 as the dividend and 789 as the divisor. Since 19 is smaller than 789, we inherently work with a number less than 1. Therefore, we can apply division by powers of 10 to make the problem more manageable.

We start by considering decimal places and significant figures. For example, if we have 1.9436 and we want to divide it by 1000, we simply move the decimal point three places to the left, resulting in 0.0019436. When we convert ratios to whole numbers, we divide both sides by the smaller amount to simplify the division.

For instance, when calculating 337/217 using a calculator, we obtain a long decimal answer, but we must take into account the significant figures to report the answer accurately. In scientific notation, we subtract exponents during division but divide the coefficients normally.

The Miller's have 3/8 of their income left after setting aside amounts for fixed expenses and savings.

The millers budget 1/2 of their income for fixed expenses and 1/8 of their income for savings. Together, these fractions add up to 1/2 + 1/8 = 5/8 of their income. Calculating what's left of their income involves subtracting the total fraction used (5/8) from the whole (which in terms of fractions, is represented by 1). Hence:

1 - 5/8 = 3/8.

So, the Miller's have 3/8 of their income left after considering fixed expenses and savings.

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Answer:

JUSTIN BIEBER

Step-by-step explanation:

360 ÷ 10 = 36 = 10%

36 ÷ 2 = 18 = 5%

36 + 18 = 54 = 15% = Top-Forty Hits

-

36 × 4 = 144 = 40% = House Music

-

144 + 54 = 198

360 - 198 = 162 = Justin Bieber

But just saying I ❤️  Justin Bieber

Answer: There are 400 white tiles which Ron will need.

Step-by-step explanation:

Since we have given that

Number of rows to cover the counter = 8

Number of tiles to cover each 8 rows = 54 square tiles

So, total number of tiles to cover 8 rows is given by

[tex]8\times 54=432[/tex]

Number of groups on which 4 blue tiles are placed = 8

Total number of blue tiles on 8 groups is given by

[tex]8\times 4=32[/tex]

Remaining are the white tiles so, it is given by

[tex]432-32=400[/tex]

So, there are 400 white tiles which Ron will need.

A double plus fact for 7 is found by using the closest doubles fact to 7 and adjusting one addend slightly, such as 3 + 4 = 7.

A double plus fact for the sum of 7 involves using the concept of doubles in addition. A doubles fact is a simple arithmetic addition where a number is added to itself. For example, 3 + 3 = 6 is a doubles fact.

To create a double plus fact for the sum of 7, we need to consider adding a number to a slightly different number close to a double fact. Here’s a step-by-step approach:

1. Identify the closest doubles fact to 7. In this case, 3 + 3 = 6.

2. Adjust one addend by 1 to reach the sum of 7. So, 3 + 4 = 7.

Therefore, a double plus fact for the sum of 7 is 3 + 4 = 7

The two lines are parallel with equal slopes, will never intersect, and have different y-intercepts, showing a constant vertical distance.

To draw a line through each point using the given slope, we will use the slope-point form of a line equation, which is [tex]\( y - y_1 = m(x - x_1) \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( (x_1, y_1) \)[/tex] is the point through which the line passes.

The slope given is [tex]\( \frac{1}{2} \)[/tex]. We have two points, [tex]\( (-2, 1) \)[/tex] and [tex]\( (4, -2) \)[/tex]. Let's calculate the equation of the line for each point.

For the point [tex]\( (-2, 1) \)[/tex]:

[tex]\[ y - 1 = \frac{1}{2}(x - (-2)) \][/tex]

[tex]\[ y - 1 = \frac{1}{2}(x + 2) \][/tex]

[tex]\[ y = \frac{1}{2}x + 2 \cdot \frac{1}{2} + 1 \][/tex]

[tex]\[ y = \frac{1}{2}x + 2 \][/tex]

For the point [tex]\( (4, -2) \)[/tex]:

[tex]\[ y - (-2) = \frac{1}{2}(x - 4) \][/tex]

[tex]\[ y + 2 = \frac{1}{2}x - 4 \cdot \frac{1}{2} \][/tex]

[tex]\[ y = \frac{1}{2}x - 2 - 2 \][/tex]

[tex]\[ y = \frac{1}{2}x - 4 \][/tex]

Now we have the equations for both lines, plot them on the graph to show the relationship between them. Let's proceed with plotting these lines.

(GRAPH IS GIVEN BELOW)

The graph shows two lines:

1. The red line passes through the point [tex]\((-2, 1)\)[/tex] and has a slope of [tex]\(\frac{1}{2}\)[/tex]. Its equation is [tex]\(y = \frac{1}{2}x + 2\)[/tex].

2. The blue line passes through the point [tex]\((4, -2)\)[/tex] and also has a slope of [tex]\(\frac{1}{2}\)[/tex]. Its equation is [tex]\(y = \frac{1}{2}x - 4\)[/tex].

Observing the two lines on the graph, you can notice the following points:

1. Both lines have the same slope of [tex]\(\frac{1}{2}\)[/tex], which means they are parallel to each other.

2. Because they are parallel, the two lines will never intersect each other.

3. The lines have different y-intercepts, which is consistent with parallel lines that are not coincident.

4. The difference in the y-intercepts 2 for the first line and [tex]\(-4\)[/tex] for the second line) corresponds to the vertical distance between the two lines.