The graph shows the relationship between the distance a truck can travel and the amount of gasoline used. (5,35) What is the unit rate for the distance traveled to the amount of gasoline used? (1,7) Enter your answer in the box. mpg

Final answer:

A bisector cuts a line segment or angle into two equal parts, while a perpendicular bisector not only does that but also intersects the line segment at a right angle.

Explanation:

In mathematics, a bisector is a line segment or line that divides an angle or segment into two equal parts. It cuts the angle or segment into two congruent angles or segments. For example, if you have a line segment AB and its bisector is a line segment CD, then CD divides AB into two congruent segments AC and CB.

A perpendicular bisector is a type of bisector that not only divides a line segment into two equal parts, but it also intersects the line segment at a right angle (90 degrees). So, in addition to being equidistant from the two endpoints of the line segment, the perpendicular bisector is perpendicular to the line segment as well.

The change in the width of the beachfront from low to high tide is 102 feet, and the distance from the ocean to the homes at high tide is 248 feet.

a. To find the change in width from low to high tide, we multiply the rate of change (-17 feet/hour) by the time it takes for the ocean to move from low to high tide (6 hours).

So, -17 feet/hour * 6 hours = -102 feet. Therefore, the width of the beachfront decreases by 102 feet from low to high tide.

b. At high tide, the distance from the ocean to the homes is the sum of the original distance (350 feet) and the change in width during the tide change (-102 feet), resulting in 350 feet + (-102 feet) = 248 feet.

Final answer:

The sum of 60 and 84 expressed as a product of their Greatest Common Factor is 144. You determine this by first finding the GCF, which is 12, and then adding the other factors (5 and 7) together and multiplying by the GCF.

Explanation:

To find the sum of the numbers 60 and 84 as a product of their Greatest Common Factor (GCF), you first need to calculate the GCF of the two numbers. The GCF of 60 and 84 is 12. You can divide each number by 12 to find the other factors, which are 5 for 60 and 7 for 84. Therefore, the sum of the numbers can be expressed as the product of their GCF and the sum of these other factors:

60 + 84 = (12 × 5) + (12 × 7)

GCF × (sum of other factors) = 12 × (5 + 7)

Now you can add the other factors:

5 + 7 = 12

Then multiply by the GCF:

12 × 12 = 144

So, the sum of the numbers expressed as a product of their GCF is 144.

Converting Sales Tax Rates and Sorting by Rate

Convert Fractions to Decimals:

Hamilton: 9/160 = 0.05625

Oakland: 5.75% = 5.75 / 100 = 0.0575

Green: 5 7/8% = 47/8 / 100 = 0.05859375

Campbell: 11/200 = 0.055

2. Sort Countries by Tax Rate:

1. Campbell: 0.055

2. Hamilton: 0.05625

3. Oakland: 0.0575

4. Green: 0.05859375

Therefore, the countries sorted from least to greatest tax rates are:

1. Campbell (0.055%)

2. Hamilton (0.05625%)

3. Oakland (0.0575%)

4. Green (0.05859375%)

The function is increasing in:

                  x< -1

and it is decreasing in:

            x > -1

and nowhere constant.

To solve this problem, the two consecutive odd integers are defined as x and x+2. A mathematical equation is created according to the problem conditions and solved. The consecutive odd integers are found to be 81 and 83.

Let's define the two consecutive odd integers as x (the smaller) and x+2 (the larger). Given the condition from the question that the sum of the smaller integer and three times the larger integer is 330, we can form the equation x + 3*(x+2) = 330.

We'll simplify that equation, which gives us: x + 3x + 6 = 330, and combining like terms, we get 4x + 6 = 330. We can solve for x by subtracting 6 from both sides and then dividing both sides by 4, which results in x = 81. Given that x represents the smaller odd integer, the larger integer would be x + 2 or 83.

So, the two consecutive odd integers fulfilling the conditions given are 81 and 83.

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The two consecutive odd integers such that the sum of the smaller and 3 times the larger is 330 are 81 and 83.

Denote the smaller odd integer as x and the larger consecutive odd integer as x + 2.

According to the problem, the sum of the smaller integer and 3 times the larger integer is 330. So, we have the equation:

x + 3(x + 2) = 330

Now, solve for x :

1. Distribute the 3 on the left side:

x + 3x + 6 = 330

2. Combine like terms:

4x + 6 = 330

3. Subtract 6 from both sides to isolate terms with x:

4x = 324

4. Divide both sides by 4 to solve for x:

[tex]\[ x = \frac{324}{4} \]\[ x = 81 \][/tex]

So, the smaller odd integer x is 81. Now find the larger consecutive odd integer:

x + 2 = 81 + 2 = 83

Therefore, the two consecutive odd integers are 81 and 83.

To verify:

- The sum of the smaller integer and 3 times the larger integer:

[tex]\[ 81 + 3 \cdot 83 = 81 + 249 = 330 \][/tex]

The verification confirms that the solution is correct.

So, the two consecutive odd integers such that the sum of the smaller and 3 times the larger is 330 are 81 and 83.

The required answer of the given expression is 8/3.

Simplification generally means finding an answer for the complex calculation that may involve numbers on division, multiplication, square roots, cube roots, plus and minus.

The given expression is,

7/3 + 3(2/3 − 1/3)²

Solving the bracket,

= 7/3 + 3{(2− 1)/3}²

solving the fraction,

= 7/3 + 3(1/3)²

solving the square,

= 7/3 + 3(1/9)

= 7/3 + 1/3

adding them we get,

= 8/3

which is the required answer of the given expression.

Thus, the required answer of the given expression is 8/3.

To learn more about simplification, here:

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The number 0.912912 can be written in bar notation as 0.912, with a bar over 912 to indicate the repeating decimals. This method is commonly used in mathematics to represent repeating decimals.

To rewrite the number 0.912912 using bar notation, consider the part of the decimal that repeats. In this case, the repeating section is 912. Therefore, the number can be written as 0.912 where the 912 has a bar over it to represent the fact that it repeats. Bar notation is a way in mathematics to represent repeating decimals. The bar, or vinculum, shows which numbers repeat in the decimal. For this number, 0.912 with a bar over 912 is the way it would be written in bar notation.

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Answer:

#1)   4 1/5

#2)  7 1/2

#3)  8 4/5

#4)  18 1/2

#5)  10 1/2

Step-by-step explanation:

In order to convert to a mixed number, place the numbers to the right of the decimal over 10. Reduce the fraction.

I hope this helped!