Nathan uses 1/18 of a gallon of milk each time he eats a bowl of cereal.Nathan has used 8 gallons of milk for cereal in one year.how many bowls of cereal did he eat?

Yes, Ranger was right that expression 8x-20 can be simplified further as 4(2x-5).

The given expression is 8x-20.

Ranger says the expression is not in its simplest form. He thinks the two terms need to be combined.

Yes Ranger is correct, the given expression can simplified further.

That is, 8x-20

Factors of 8x and 20 are

8x=2×2×2×x

20=2×2×5

So, the common term is 4

Now, 8x-20=4(2x-5)

Yes, Ranger was right that expression 8x-20 can be simplified further as 4(2x-5).

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Answer: y = -2x + 13.

Step-by-step explanation:

To find the equation of a line that passes through the points (4,5) and (2,9), we can follow these steps:

1. First, let's determine the slope of the line using the formula: slope (m) = (change in y) / (change in x). We can choose any point as (x1, y1) and the other point as (x2, y2) to calculate the slope.

Using (4,5) as (x1, y1) and (2,9) as (x2, y2):

slope (m) = (5 - 9) / (4 - 2) = -4 / 2 = -2

2. Now that we have the slope (-2), we can use the point-slope form of a line to find the equation. The point-slope form is given by: y - y1 = m(x - x1), where (x1, y1) is one of the given points and m is the slope.

Using (4,5) as (x1, y1) and -2 as the slope (m):

y - 5 = -2(x - 4)

3. Simplifying the equation further, we get:

y - 5 = -2x + 8

4. To obtain the equation in slope-intercept form, we can isolate y by adding 5 to both sides:

y = -2x + 8 + 5

y = -2x + 13

Therefore, the equation of the line that passes through the points (4,5) and (2,9) is y = -2x + 13.

Final answer:

The equation of the line that passes through the points (4,5) and (2,9) is y = x + 1.

Explanation:

To find the equation of the line that goes through the two given points (4,5) and (2,9), we can use the slope-intercept form of a linear equation, y = mx + b.

First, we need to calculate the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the values from the points, we get:

m = (9 - 5) / (2 - 4) = -2 / -2 = 1.

Next, we can substitute the slope and one of the given points into the equation to solve for the y-intercept (b).

Using the point (4,5):

5 = (1)(4) + b

b = 5 - 4 = 1.

Therefore, the equation of the line is y = x + 1.

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Using the Corresponding Angles Theorem, Vertical Angles Theorem, and the Transitive Property of Congruence, we can prove that alternate exterior angles (e.g, <4 and <5) are congruent by the alternate exterior angles theorem.

Recall:

• Alternate exterior angles are angles that lie outside the two lines that is cut across by a transversal but on opposite sides along the transversal.
• Examples of alternate exterior angles are <2 and <7; <4 and <5 as shown in the figure attached below.

If we are given that in the diagram attached below, the following are theorems and definitions we can use to prove that (alternate exterior angles).

Statement 1:

Reason: Corresponding Angles Theorem

The corresponding angles theorem states that when two parallel lines (lines m and n) are intersected by a transversal line (line w), the two corresponding angles formed (e.g. <4 and <8) are congruent.

Statement 2:

Reason: Vertical Angles Theorem

The Vertical Angles Theorem states that the opposite vertical angles (e.g. <8 and <5) formed when two lines (lines n and w) intersect are congruent to each other.

Statement 3:

Reason: Transitive Property of Congruence

The Transitive Property of Congruence states that if a = b; and b = c; then a = c.

Therefore, using the Corresponding Angles Theorem, Vertical Angles Theorem, and the Transitive Property of Congruence, we can prove that alternate exterior angles (e.g, <4 and <5) are congruent by the alternate exterior angles theorem.

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Angle 1 is 112

Angle 2 is 68

Angle 3 is 90

Angle 4 is 90

Angle 5 is 22

Angle 6 is 158

Answer:

1) Reflection

2) Translation

3) Dialation

4) Translation (Hard to see, If it has gotten biggeror smaller, it is dialation)

5) Reflection