1. Refer to the equation 2x − 6y = 12.
(a) Create a table of values for at least 4 points. Show your work.
(b) Use the table of values to graph the line.

Joe was given  $329 for an overnight trip because he drove a distance of 220 miles

Given Data

The Mathematical relation for this scenario is

Total amount = Amount Receive+ 0.7*Distance driven

let the distance driven be x

Substituting our given data into the relation we have

329= 175+ 0.7*x

329-175 = 0.7x

154 = 0.7x

divide both sides by 0.7

x = 154/0.7

x = 220miles

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Answer:

205000

Step-by-step explanation:

Given :  253,495 - 48,617

To Find : What is rounding and estimate

Solution:

To Estimate a difference by rounding.

1 ) Round each term that will be subtracted

2 )Subtract the rounded numbers

Round off of 253,495 = 253000

Round off of 48,617 = 48000

So,  253000 - 48000 = 205000

Hence The rounding and estimate 253,495 - 48,617= 205000

6/7 because if you divide 30/35 by 5 it will leave at 6/7

3.2(2.3) - 4.8

Simplify.

(3.2 × 2.3) - 4.8

Simplify.

(7.36) - 4.8

Simplify.

2.56

Hope this helped. :)

its not d its the +2 one

By setting up a proportion based on the similar triangles created by the streetlight and the building, we can find that Melanie is standing 48 feet away from the building.

To solve the problem of determining how far Melanie is standing from the building using the shadows, we can use similar triangles. We are given a 25-foot streetlight that casts a 20-foot shadow and a 60-foot tall building. The goal is to find the length of the shadow cast by the building, which will tell us how far Melanie is from the building.

By setting up a proportion based on the similar triangles, we have:

Therefore, Melanie is standing 48 feet away from the building.

The least common denominator of 5/6 and 7/9 is 18. This results in equivalent fractions of 15/18 for 5/6 and 14/18 for 7/9.

To find the least common denominator (LCD) of the fractions 5/6 and 7/9, we first find the least common multiple (LCM) of the two denominators, 6 and 9. The LCM of 6 and 9 is 18.

Next, we convert each fraction to an equivalent fraction with the LCD as the new denominator. We multiply the numerator and denominator of 5/6 by 3 to get 15/18. Similarly, we multiply numerator and denominator of 7/9 by 2 to obtain 14/18.

So the fractions 5/6 and 7/9, when written with their LCD, are 15/18 and 14/18, respectively.

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The correct option is d. 8 oz. can of juice is most convenient to meet this requirement.

First, let's convert 240 milliliters to ounces because the answer choices are in ounces.

1 milliliter is approximately equal to 0.0338 ounces.

So, 240 milliliters is approximately \( 240 \times 0.0338 \) ounces, which is about 8.112 ounces.

Now, let's examine the options:

a. 5 oz. can of juice: Not enough juice. It's less than the required 8.112 ounces.

b. 4 oz. can of juice: Not enough juice. It's less than the required 8.112 ounces.

c. 12 oz. can of juice: More than enough juice. It's more than the required 8.112 ounces.

d. 8 oz. can of juice: Exactly the amount needed. It matches the required 8.112 ounces, which is the closest to the calculated amount of 8.112 ounces.

Therefore, the 8 oz. can of juice is the most convenient option to meet the requirement of having 240 milliliters of juice every 2 hours.

Answer: 40%

Step-by-step explanation:

Given : Katie is selling lemonade for $1.50 per cup she decides to put them on sale for $0.90 .

i.e. Original price=  $1.50     ;    Price after discount= $0.90

Then, the Discount amount= Original price-Price after discount

= $1.50- $0.90=$0.60

Now, the  percent discount will be :-

[tex]\dfrac{\text{\text{Discount amount}}}{\text{original price}}\times100\\\\=\dfrac{0.60}{1.50}\times100=40\%[/tex]

Hence, the required answer = 40%

The correct equation for the distance Tran drove at a constant speed of 55 mph is B. d = 55t.

In this equation:

"d" represents the distance in miles that Tran drove.

"t" represents the time in hours.

So, the distance "d" is equal to Tran's constant speed of 55 mph multiplied by the time "t" in hours, which is why the equation is written as d = 55t.

Option D is not the correct equation because it has the variables and constants in the wrong order.

The correct order is distance (d) on the left side of the equation, followed by the constant speed (55) and then the time (t) on the right side of the equation.

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Answer:

Rational

2. Irrational

3. Irrational

4. Irrational

5. Rational

Step-by-step explanation:

To solve the equation 5x(x+6) = -50 by completing the square, we first isolate the quadratic term and then add the square of half the coefficient of x to both sides of the equation. Taking the square root gives us the solution x = -3 + i and x = -3 - i.

To solve the equation by completing the square, we first need to isolate the quadratic term on one side of the equation. So, let's distribute the 5x to get 5x^2 + 30x = -50. Next, we move the constant term to the other side and divide the equation throughout by the leading coefficient to get x^2 + 6x + 10 = 0.

Now, we can complete the square by adding the square of half the coefficient of x (which is 3) to both sides of the equation. This gives us (x + 3)^2 + 10 - 9 = 0, which simplifies to (x + 3)^2 + 1 = 0.

Taking the square root of both sides, we get x + 3 = ±√(-1), which means x = -3 ± i. Hence, the solution to the equation is x = -3 + i and x = -3 - i.

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