solve the system of linear equations using substitution. Which expression would be eastier to substitute into the other equation, in order to solve this problem?

Final answer:

Mr. Cho has 7 quarters and 14 dollar bills. We find this by setting up an equation considering that he has twice as many dollar bills as quarters and their total value is $15.75. Solving the equation, we find the number of quarters (q) to be 7 and the number of dollar bills to be twice that amount.

Explanation:

Mr. Cho has twice as many dollar bills as quarters, and their total value is $15.75. To find out how many of each he has, let's set up some equations based on this information. Let's call the number of quarters q and the number of dollar bills 2q (since he has twice as many dollar bills as quarters).

Since each quarter is worth $0.25, the total value of the quarters would be 0.25q. The total value of the dollar bills would just be 2q (since each dollar bill is worth $1). The combined value of the quarters and dollars is given as $15.75, so we can set up the following equation:

0.25q + 2q = 15.75

Combining like terms:

2.25q = 15.75

Dividing by 2.25:

q = 15.75 / 2.25

q = 7

Therefore, Mr. Cho has 7 quarters. Since he has twice as many dollar bills as quarters, he has:

2q = 2 * 7 = 14 dollar bills.

In summary, Mr. Cho has 7 quarters and 14 dollar bills.

The product of (-24.98)(-1.29) using  front-end estimation is 20

The correct answer is an option (C)

"It is a way of rounding numbers to estimate sums and differences or product of numbers by rounding. "

For given question,

Ryder used front-end estimation to estimate the product of (–24.98)(–1.29)

We know, to use front end approximation, numbers are rounded to the greatest place value.

(-24.98) is rounded to -20

Here, 4 (4 of -24.98) is rounded here to 0

(-1.29) is rounder to -1

Here, (2 (2 of -1.29) is rounded to 0)

Now we find the product,

(-20) × (-1) = 20

Therefore, the product of (-24.98)(-1.29) using  front-end estimation is 20

The correct answer is an option (C)

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Final answer:

The sequence 12, 144, 1728 is an example of exponential growth, where each term is a product of the previous term by a constant multiplier, which is 12 in this case.

Explanation:

The sequence 12, 144, 1728 shows that each term is 12 times the previous one. This indicates that we are dealing with exponential growth, not a linear sequence. In a linear sequence, a constant number would be added to each term to get the next one, but here we multiply by 12 at each step. Exponential growth is characterized by the fact that quantities increase by a consistent multiplier (in this case, 12) at each interval. So, after n steps in a sequence that starts with a, the formula for the nth term would be a * multiplier^n.

60% of students live within one mile of the school if about 3/5 of the students at Roosevelt Elementary live within 1 mile of the school.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

It is given that:

About 3/5 of the students at Roosevelt Elementary live within 1 mile of the school.

3/5 in percent

= (3/5)x100

= 3x20

= 60 %

Thus, 60% of students live within one mile of the school if about 3/5 of the students at Roosevelt Elementary live within 1 mile of the school.

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Answer:

Step-by-step explanation:

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23 is approximately 25 percent of 92.

To determine the percentage, we need to find what portion of 92 is represented by 23. We can set up a proportion to solve for the percentage.

Let's assume the unknown percentage is 'p'. We can write the proportion as:

23 is to 92 as p is to 100.

This can be expressed mathematically as:

23/92 = p/100

To solve for 'p', we can cross-multiply:

23 x 100 = 92 x p

2300 = 92p

To isolate 'p', we divide both sides of the equation by 92:

2300/92 = p

Simplifying, we find:

25 = p

Therefore, 23 is approximately 25% of 92. This means that 23 is 25% of the whole value of 92. To verify this, we can calculate 25% of 92:

(25/100) x 92 = 0.25 x 92 = 23

Hence, 23 is indeed 25% of 92.

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Mrs. Chang's truck runs at a unit rate of $3.75 per gallon of gas and 24 miles per gallon. These rates are found by dividing the total cost by gallons for the cost rate, and total miles by gallons for the efficiency rate.

To find the unit rates of dollars per gallon and miles per gallon for Mrs. Chang's truck, we can use the ratios provided by the information given. First, to find the cost per gallon of gas, we divide the total amount spent by the number of gallons:

Cost per gallon = Total cost / Number of gallons = $75 / 20 gallons = $3.75 per gallon

To calculate the miles per gallon, we divide the number of miles driven by the number of gallons it took to fill the tank when it was empty again:

Miles per gallon = Total miles driven / Number of gallons = 480 miles / 20 gallons = 24 miles per gallon

By calculating these unit rates, drivers can determine both the price efficiency of their gasoline purchases and the fuel efficiency of their vehicle.

There are 3 students in the class of 27 who neither like video games nor cartoons.

To find the number of students who do not like either video games or cartoons, we first need to understand that some students may like both. According to the data given, 16 students like video games, 20 like cartoons and 12 like both. So, the total liking either or both is 16 (video games) + 20 (cartoons) - 12 (both), which is 24 students. The number of students who do not like either would then be the total number of students in the class minus those who like either or both. Therefore, the number of students who do not like either video games or cartoons is 27 (total students) - 24 (liking either or both) = 3 students.

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To find out how much John and Petra earn altogether per hour, add their hourly earnings. John earns x dollars per hour, while Petra earns $2 per hour more than John. Therefore, the total earnings per hour for both John and Petra would be 2x + 2 dollars.

To find out how much John and Petra earn altogether per hour, we need to add their hourly earnings. John earns x dollars per hour, while Petra earns $2 per hour more than John. So, Petra's earnings per hour would be x + 2 dollars.

Therefore, the total earnings per hour for both John and Petra would be x + (x + 2) = 2x + 2 dollars.

John and Petra's combined hourly earnings are calculated by adding their individual earnings. John earns x dollars, and Petra earns x + 2 dollars, which totals to 2x + 2 dollars per hour for both of them together.

John earns x dollars per hour. Petra earns 2 dollars more per hour than John. To calculate how much they earn altogether per hour, we simply add their hourly earnings.

Let's denote John's hourly earning as x dollars. Since Petra earns 2 dollars per hour more than John, her hourly earning would be x + 2 dollars. The total amount they earn per hour together is the sum of their individual hourly earnings.

Calculating Total Hourly Earnings

So, together they earn 2x + 2 dollars per hour. This is the simplified expression we can use to represent their combined hourly earnings.

The pair of numbers with 4 and 6 as common factors is option D) 36, 48.

To determine which pair of numbers have 4 and 6 as common factors, we need to find the factors of each pair of numbers and see if both 4 and 6 are factors.

A) Factors of 12: 1, 2, 3, 4, 6, 12

  Factors of 18: 1, 2, 3, 6, 9, 18

  Common factors: 1, 2, 3, 6

  Both 4 and 6 are common factors.

B) Factors of 20: 1, 2, 4, 5, 10, 20

  Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

  Common factors: 1, 2, 4

  Both 4 and 6 are not common factors.

C) Factors of 28: 1, 2, 4, 7, 14, 28

  Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

  Common factors: 1, 2

  Both 4 and 6 are not common factors.

D) Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

  Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

  Common factors: 1, 2, 3, 4, 6, 12

  Both 4 and 6 are common factors.

Therefore, the pair of numbers with 4 and 6 as common factors is option D) 36, 48.

The probable question may be:

Which pair of numbers below have 4 and 6 as common factors?

A) 12, 18 B) 20, 24 C) 28, 30 D) 36, 48

To find the number of Koi in the pond after the increase in their population, subtract the number of goldfish from the total number of fish, then add 10% of the remaining fish to find the new number of Koi. The new number of Koi is 0.66g.

To find the number of Koi in the pond after the increase in their population, we need to first calculate the number of goldfish in the pond. If 40% of the fish are goldfish, and the total number of fish is g, then the number of goldfish is 40% of g, which is 0.4g.

Since the rest of the fish are Koi, we can subtract the number of goldfish from the total number of fish to find the number of Koi. The rest of the fish is 100% - 40% = 60% of g, which is 0.6g. After the increase of 10% in the number of Koi, the new number of Koi is 0.6g + (10% of 0.6g).

0.10 * 0.6g = 0.06g, so the new number of Koi is 0.6g + 0.06g = 0.66g.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division. The terms involved in an expression in math are:

Given expression:

4b+7b+5

As. term can be a single constant, a single variable, or a combination of a variable and a constant combined with multiplication or division.

Terms are 4b, 7b, 5

Now, coefficient is a number that is multiplied by a variable in an expression.

coefficient are 4 , 7

As a constant is a fixed numerical value,

So, constant = 4, 7 , 5

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The value hundred place is 282 < 500 thus it will be round as 9372000.

When rounding to the nearest tenth or hundredth, we must consider the unit place. If the number is less than 5, it must be left alone; if it is larger than 5, the tens digit must be rounded up.

Given the digit,

9,372,282

To round to the nearest thousand we need to look at a hundred units value

A hundred units → 282 < 500 thus it will round down or remain as it is.

9,372,282 → 9372000

Hence "The value hundred places is 282 < 500 thus it will be round as 9372000".

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Final answer:

To determine Owen's height at 18, we added his growth each year to his height at age 2, resulting in a total height of 68 ½ inches.

Explanation:

To calculate how tall Owen is on his 18th birthday, we need to add the total amount he grew each year to his height at the age of two. Owen was 34 ½ inches tall on his second birthday. He then grew an average of 2 ½ inches each year for the next 10 years. After that, he grew an average of 1 ½ inches each year for the following 6 years.

Growth from age 2 to 12 (10 years): 2 ½ inches/year × 10 years = 25 inches

Growth from age 12 to 18 (6 years): 1 ½ inches/year × 6 years = 9 inches

Adding this all together:

Initial height at age 2: 34 ½ inches

Total growth from age 2 to 12: 25 inches

Total growth from age 12 to 18: 9 inches

Now, let's add these numbers up to find Owen's height on his 18th birthday:

34 ½ inches + 25 inches + 9 inches = 68 ½ inches

Therefore, Owen is 68 ½ inches tall on his 18th birthday.

Owen's height on his 18th birthday plan is [tex]68\frac{1}{2}[/tex] inches.

The height of Owen is expressed as a mixed number. A mixed number is a number that is made up of a whole number and a proper fraction.

An example of a mixed number is [tex]34\frac{1}{2}[/tex]. 34 is the whole number and [tex]\frac{1}{2}[/tex] is the proper fraction.

The total height of Owen when he was 12 years old = height when he was two years old + (increase in height each of the first 10 years x 10).

[tex]34\frac{1}{2}[/tex] + ([tex]2\frac{1}{2}[/tex] x 10)

[tex]34\frac{1}{2}[/tex] + ([tex]\frac{5}{2}[/tex] x 10)

[tex]34\frac{1}{2}[/tex] + 25

= [tex]59\frac{1}{2}[/tex]

Owen's height when he is 18 years old = Owen's height when he is 12 years old + ( rate of increase x 6)

= [tex]59\frac{1}{2}[/tex] + ([tex]1\frac{1}{2}[/tex] x 6)

= [tex]59\frac{1}{2}[/tex] + ([tex]\frac{3}{2}[/tex] x 6)

 = [tex]59\frac{1}{2}[/tex] + 9

=[tex]68\frac{1}{2}[/tex] inches

Using compatible numbers (numbers that are easy to compute mentally), you can estimate that 474 divided by 9 is approximately 50 by substituting 474 with 450, a number that is easily divisible by 9.

The question is asking you to use compatible numbers to estimate the quotient of 474 divided by 9. Compatible numbers are numbers that are easy to compute mentally. When we look at 474 and 9, one potential set of compatible numbers might be 450 and 9. So, let's divide 450 by 9 to get our estimate.

Step 1: Identify the compatible numbers. Here we can use 450 instead of 474 because it is easily divisible by 9.

Step 2: Perform the division. 450 divided by 9 equals 50.

Therefore, using compatible numbers, we can estimate that 474 divided by 9 is approximately 50.

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By adding the 14 bees in the hive to the 17 bees in the garden, we determine there are a total of 31 bees.

To find out how many bees there are in total, we need to add the number of bees in the hive to the number of bees in the garden. The problem states that there are 14 bees in the hive and 17 bees in the garden. Adding these two quantities together gives us:

14 bees in the hive + 17 bees in the garden = 31 bees in total.

So, there are 31 bees altogether.

Final answer:

To find the total number of bees, you need to add the number of bees in the hive to the number of bees in the garden. The total number of bees is 31.

Explanation:

To find the total number of bees, you need to add the number of bees in the hive to the number of bees in the garden. In this case, there are 14 bees in the hive and 17 bees in the garden.

To find the total number of bees, add the number of bees in the hive and the number of bees in the garden: 14 + 17 = 31.

Therefore, there are 31 bees in total.

Final answer:

To find out how much money Mr. Gaster will have after any number of days, we create an equation based on his initial savings and weekly contributions. For 28 days, the equation is T = ($45 × (28/7)) + $5, which simplifies to T = $185. Therefore, Mr. Gaster will have $185 in his piggy bank after 28 days.

Explanation:

To determine how much money Mr. Gaster will have in any number of days, we need to create an equation that accounts for the initial amount and the weekly savings. Because there are 7 days in a week, Mr. Gaster will save $45 for every 7 days. Therefore, to find the total amount in the piggy bank after a certain number of days (d), we divide the number of days by 7 (to get the full weeks), multiply it by the weekly saving amount, and then add the initial amount.

Forming the Equation

Let T be the total amount, and the equation representing the situation is:
T = ($45 \times \frac{d}{7}) + $5

Solving for 28 Days

To solve for the total amount in 28 days:

T = ($45 \times \frac{28}{7}) + $5

T = ($45 \times 4) + $5

T = $180 + $5

T = $185

Hence, after 28 days, Mr. Gaster will have $185 in his piggy bank.

Answer:

42.9

Step-by-step explanation:

The sum of the interior angles in any quadrilateral is always 360 degrees.

The sum of the interior angles in a quadrilateral is always 360 degrees. This is a fundamental concept in geometry that applies to all quadrilaterals, regardless of their shape. To understand why this is the case, one can consider dividing a quadrilateral into two triangles. Since the sum of the angles in a triangle is always 180 degrees, adding the angles from both triangles within the quadrilateral gives us a total of 360 degrees. This rule is crucial when solving various geometrical problems involving quadrilaterals. For example, if a quadrilateral ABCD has an extended line CE creating two angles on a straight line, angles ACD and ACE would sum up to 180 degrees because angles on a straight line always sum up to 180 degrees.

It is also worth noting that if a quadrilateral has three right angles, the properties of the sides relative to the fourth angle can be determined based on whether that angle is right, acute, or obtuse. These principles are derived from the fundamental properties of angles in polygons and are used to deduce further geometric relationships.