Kendall recently received a job offer which required him to move his house full of furniture across the country from Columbia, South Carolina, to Riverside, California. To manage his moving expenses, Kendall kept track of the amount of gasoline used by the moving truck he rented. The truck used 109 gallons of gas to drive 1,092 miles from Columbia to Des Moines, Iowa. On the next leg of the drive, the truck used 67 gallons of gas to drive 671 miles from Des Moines to Denver, Colorado. Finally, he used 99 gallons of gas to drive 985 miles from Denver to Riverside, California. Using x to represent the number of miles and y to represent the number of gallons, create a table of values to represent this relation.

Answer:

(C) Base angle theorem

Step-by-step explanation:

Given: JKLM is an isosceles trapezoid, KL ∥ JM  

Prove: KM ≅ JL

Proof:

Statements                                                                 Reasons

1. JKLM is an isosceles trapezoid, KL ∥ JM               Given

2. JK ≅ LM                                                definition of isosceles trapezoid

3.  KL ≅ KL                                                          reflexive property

4. ∠JKL ≅ ∠MLK                                          Base angle theorem (base=LK)

5. △JKL ≅ △MLK                                                       SAS rule

6. KM ≅ JL                                                                  CPCTC  

Hence proved.

therefore, option C is correct.

The missing reason for statement 4, is: C. base angles theorem.

The base angle theorem states that the two base angles in an isosceles triangle that are opposite the congruent sides are equal in measure or congruent.

Thus, ∠JKL and ∠MLK are base angles of the identified isosceles triangle, therefore, the missing reason for statement 4, is: C. base angles theorem.

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The Difference between Rational numbers and Irrational numbers are given as follows

Rational numbers =   A number of the form [tex]\dfrac{p}{q}[/tex]  when [tex]q\neq 0[/tex] is called as a Rational number

Example = Any fraction of the form p/q such as 2/3 , -3/11 and 5/12

Irrational number =  A number that can not be expressed in the form of [tex]\dfrac{p}{q}[/tex]  or nor it can be represented as a recurring  decimal form then it is called as Irrational number

These are of the form [tex]\sqrt[n]{x}[/tex] where we can not simplify positive integer x

Example = [tex]\sqrt{2}[/tex] ,  [tex]\sqrt{3}[/tex] ,[tex]\sqrt[3]{5}[/tex]

These both types of numbers belong to the category of Real numbers as they fall on Real number line.

Rational numbers  with denominators = 1 are called as Integers

Surds are the categories of Irrational numbers  are

Surds  are the values of square root of any positive number that can not be simplified further to a whole number

Some examples of Surds are [tex]\sqrt{2}[/tex] and [tex]\sqrt{3}[/tex]

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Answer:

the best estimate of the  current price is $39.99

Step-by-step explanation:

Hello, I think I can help you with this,

You can solve this by using a rule of three

Step one

if

$31 ⇔100%

x?   ⇔129%

the relation is

[tex]\frac{31}{100}=\frac{x}{129}}\\now, solve\ for\ x\\x=\frac{129*31}{100} \\x=\frac{3999}{100}\\ x=39.99\\[/tex]

the current price is $39.99

I hope it helps, have a fantastic day-

Answer:

Positive integer

Step-by-step explanation:

An integer is a collection of positive and negative number and zero

Positive Numbers:  Positive number are the numbers which have positive sign. For example 4, 9 or which which represents positivity like gain , increase, profit etc

Negative numbers: Negative number are the numbers which have negative sign. For example -4, -9 or which which represents negativity like loss , decrease etc

Zero is neither a negative number nor a positive number.

13 yard is a positive because there is a gain , which represent positivity.

We can also write + 13 yard.

Hence, the correct answer is it is a positive integer

To solve this problem, we simply have to use ratio and proportion. We know that for every 5 cm, we have 1 m therefore the factor to use is:

5 cm / 1 m

SO for a table length of 1.4 m, the model length should be:

model = (5 cm / 1 m) * 1.4 m

model = 7 cm

Answer:

7 cm

To divide 3,050 by 10 to the second power, simply move the decimal point two places to the left, resulting in the answer 30.50.

When dividing by powers of 10, you simply need to move the decimal point to the left by the number of zeros in the exponent. In this case, the exponent is 2, so you would move the decimal point two places to the left.

Therefore, 3,050 divided by 10 to the second power is equal to 30.50.

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The equation 6+7+7+6 demonstrates the Commutative Property of addition, which states that the order of addition does not affect the sum.

The property shown by the equation 6+7+7+6 is the Commutative Property of addition. This property states that the order in which two numbers are added does not affect the sum. In other words, A+B = B+ A. Specifically here, the numbers 6 and 7 are added together in an order that can be rearranged without changing the result, indicating the commutative nature of their addition. To visualize:

Both expressions yield the same sum, showing the commutative property.

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Hey there! You answer is x - (-17) . I hope this helped! Your fellow Brainly user, GalaxyGamingKitty.

Answer:

A. 4r = v

Step-by-step explanation:

the amount of salad Reagan ate is r.

If Olivia ate 4 times as much salad as Reagan, then she ate r amount multiplied by 4:

4r

Thus, the equation than can be used to describe the amount of salad for Olivia is:

4r = v

This is because this equation tells us that 4 times the amount of salad Reagan ate (4r) is equal to what Olivia ate (v)

8/4 = 2 caps per ball of wool

 so 6/2 = 3 balls of wool are needed.

4/8 = x/6

8x/24

x = 24/8 = 3

Malcom will need 3 balls of wool to make 6 caps.

Understanding Wool to Caps Ratio

To determine how many balls of wool Malcom will need to make 6 caps, we will use a ratio table. We know that 4 balls of wool can make 8 knitted caps. We can set up a ratio table to find the number of balls needed for any number of caps.

Step-by-Step Explanation:

Step 1: Establish the known ratio: 4 balls of wool : 8 caps

Step 2: Simplify the ratio: (4 balls of wool) / (8 caps) = 1 ball of wool : 2 caps

Step 3: Determine the number of balls of wool needed for 6 caps using the simplified ratio. If 1 ball of wool makes 2 caps, then:

Step 4: Calculate: (number of caps) / (caps per ball) = 6 caps / 2 caps per ball = 3 balls of wool

Therefore, Malcom will need 3 balls of wool to make 6 caps.

The solution of the given equation xy-7y=49 for y is y = 49/(x-7) for all values of x not equal to 7.

To solve the equation xy-7y=49 for y, first we can factor out y from the left side of the equation which gives us y(x-7)=49.

Then we can isolate y by dividing both sides of the equation by (x-7).

This gives us y = 49/(x-7).

This solution assumes that x is not equal to 7 because division by zero is undefined.

Hence, the solution is y = 49/(x-7) for x ≠ 7.

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All I can say is that the answer is 6 because this needs paper to draw a bar diagram

The value of the unknown number is 36. 2 1/9 of 36 is 76.

Given the parameter:

2 1/9 of what number is 76?

To solve for the unknown value, first, convert the mixed fraction to an improper fraction:

2 1/9 = ( 9×2 + 1 )/9 = 19/9

Now, we set up the equation:

Let 'x' represent the unknown number:

19/9 of x is 76

19/9 × x = 76

Solve for x:

19x/9 = 76

19x = 9 × 76

19x = 684

x = 684/19

x = 36

Therefore, the value of x is 36.

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Final answer:

To find the quadratic equation that models the depth of the Pythagorean Sea, we apply given conditions to the standard form y = ax^2 + bx + c. Solving for coefficients, we then identify the vertex of the parabola to find the deepest point of the sea. Finally, we calculate the depth at this point by substituting the vertex into the equation.

Explanation:

Finding the Particular Quadratic Equation and Depth of the Sea

To find the particular quadratic equation for the depth of the Pythagorean Sea as a function of its width, we can begin by assuming the standard form of the equation:

y = ax^2 + bx + c,

where y represents the depth in meters, and x is the horizontal distance from the shore in meters. Given that the sea's width is 1000 meters and at 200 meters from the shore the depth is 20 meters, we can establish some conditions.

By substituting these conditions into the equation, we can solve for a and b to determine the complete equation. Once we have the equation, the depth's maximum (the deepest part of the sea) will occur at the vertex of the parabola, which is at x = -b/(2a).

Once we find the deepest point, we can calculate its depth by substituting back into the equation.

Answer:

equation: y = 0.0005x²

maximum depth: 500 m

Step-by-step explanation:

Equation for a quantity that changes quadratically with another quantity:

y = kx²

where x = width, and y = depth.

For x = 200, y = 20.

20 = k(200²)

k = 20/(40000)

k = 0.0005

The equation is

y = 0.0005x²

The width is 1000 m.

For 1000 m, x = 1000

y = 0.0005x²

y = 0.0005(1000²)

y = 500

Answer:

equation: y = 0.0005x²

maximum depth: 500 m