solve each system of linear equations by adding or subtracting

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.

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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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.

Answer: the answer is 20

Step-by-step explanation:

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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Jeandre is correct because the absolute value of a number represents its distance from zero on a number line. Both |3| and |-3| are three units away from zero, therefore they have the same value of 3.

Jeandre is correct when he says that |3| equals |-3|. In mathematics, the absolute value of a number is the distance of that number from zero on a number line, regardless of direction. Both 3 and -3 are three units away from zero. Therefore, the absolute value of 3 is 3, and the absolute value of -3 is also 3.

To visualize this on a number line: if you start at zero and move three units to the right, you reach +3. If you move three units to the left of zero, you reach -3. Since absolute value is concerned with distance only and not direction, both |3| and |-3| represent a distance of 3 units from the origin, hence both have a value of 3.

The equals sign is used to indicate that both expressions are the same in value. Additionally, the rules of algebraic signs help to understand that the negative sign indicates direction on a number line, but does not affect the absolute value.

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

Answer:

a. [tex]9\frac{3}{4}[/tex], from which he can make 9 loaves.

b. [tex]\frac{3}{4}[/tex] is the remaining part.

Step-by-step explanation:

Givens

To find then number loaves that Paul can make, we just need to divide the number of cups of raising he has, and the cups of raisins need it according to the recipe.

[tex]3\frac{1}{4} \div \frac{1}{3}[/tex]

But, we first need to transform the mixed numero into a fraction, then we solve

[tex]3\frac{1}{4} \div \frac{1}{3}=\frac{13}{4} \div \frac{1}{3}=\frac{13}{4} \times \frac{3}{1}= \frac{39}{4}[/tex]

If we divide this fraction, we obtain a mixed number, becuase the division is not exact

[tex]\frac{39}{4}= 9\frac{3}{4}[/tex]

So, Paul can make [tex]9\frac{3}{4}[/tex] number of loaves. But, he cannot make an incomplete loaf, that means Paul can only make 9 loaves, and the remaining is 3/4, that's the "excess". You can get this answer by subtracting

[tex]9\frac{3}{4} - 9= \frac{39}{4}-9=\frac{39-36}{4}=\frac{3}{4}[/tex]

Therefore, the answers are

a. [tex]9\frac{3}{4}[/tex]

b. [tex]\frac{3}{4}[/tex]

Answer:

Slope is 15 and y-intercept is 35.

Step-by-step explanation:

Given : The lake side marina charges a $35 rental fee for a boat in addition to charging $15 an hour for usage.

The total cost y of renting a boat for x hours can be represented by the equation [tex]y=15x+35[/tex]

To find : Graph the equation and interpret the slope and the y-intercept?

Solution :

The general slope form is [tex]y=mx+c[/tex]

where, m is the slope and c is the y-intercept.

On comparing the equation [tex]y=15x+35[/tex]

The slope is m=15.

The y-intercept is c=35.

Now we plot the equation [tex]y=15x+35[/tex] in graphing tool.

The equation is in green line passing thorough (35,0) and (-2.333,0).

Refer the attached figure below.

Answer:

y=15x+35

Step-by-step explanation:

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.

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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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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Answer:

Step-by-step explanation:

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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.

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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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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Answer:

42.9

Step-by-step explanation:

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.