Is line L parallel to line M? Explain.

Yes, alternate interior angles are congruent.
No; alternate interior angles are not congruent.
No; corresponding angles are not congruent.
Yes; corresponding angles are congruent.

The greatest factor of the given expression is 6x^2y^2, found by identifying the common variables with the lowest exponents and the greatest common divisor of the coefficients.

The student is asking to find the greatest common factor (GCF) of the algebraic expression 6x^2y^3 + 18x^3y^3 + 36x^3y^2. To find the GCF, we look for the highest exponents of the variables that are common in each term, and the largest coefficient that can evenly divide all the coefficients of the terms.

Firstly, we notice that each coefficient (6, 18, 36) is divisible by 6, so 6 is part of our GCF. Next, we see that the smallest exponent of x is 2 and the smallest exponent of y is 2 as well. So, x^2 and y^2 are also part of our GCF. The greatest factor is then 6x^2y^2.

Therefore, when we factor out the GCF from the expression, it would be written as:

6x^2y^2 (y + 3x + 6xy)

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Answer with explanation:

Monique is factoring the expression 4x+16xy Her work is shown below.  

Factors of 4 x→: 1, 2, 4, x

Factors of 16 x y:→ 1, 2, 4, 8, 16, x, y

G CF: 4 x

Factored expression: 4 x(0+4 y)→Incorrect

→4 x +16 x y= 4* x + 4 *4* x* y

  = 4* x* (1+4 y)

while writing the factored expression, we have to break the terms into smaller  terms that is into monomials and  then we should take out the common factor between the two terms.

Option D:  Monique made an error when writing the factored expression.

Final answer:

To find the total number of road kill in the three collections, we set up and solve an equation. Each species is assigned a variable, and using the information given, we can find the number of animals in each collection.

Explanation:

To find the total number of road kill in the three collections, we need to determine how many animals are in each collection. Let's assign variables to each species: bobcats = x, beavers = 16.1%x, foxes = x + 4, otters = x - 4, fishers = 16.1%. Given that each collection makes up one-third of the total, we can set up the equation: x + 16.1%x + x + x - 4 + 16.1%x = (1/3) * total. Simplifying the equation, we get 3.3x - 4 = (1/3) * total. Since beavers make up 16.1% of the total, we can substitute 16.1%x for beavers in the equation: 3.3x - 4 = (1/3) * total. Solving for x, we get x = (4 + (1/3) * total) / 3.3. Since bobcats and beavers have the same number, x = 16.1%x, which can be written as x = 0.161x. Equating the two, we get x = 0.161x. Finally, solving for x, we find that x = 0.161x, which simplifies to x = 0.161x. Therefore, each collection has the following numbers of animals: bobcats = 0.161x, beavers = 16.1%x, foxes = x + 4, otters = x - 4, and fishers = 16.1% total.

The functions f(x) = 0.7(6)x and g(x) = 0.7(6)–x are related to each other. f(x) represents exponential growth, while g(x) represents exponential decay. As f(x) increases, g(x) decreases, and vice versa.

These two functions, f(x) = 0.7(6)x and g(x) = 0.7(6)–x, are related to each other in the following ways:

Therefore, f(x) and g(x) are related inversely to each other. As f(x) increases, g(x) decreases, and vice versa.

Answer:

[tex]M=45 degrees[/tex]

Step-by-step explanation:

It is given that A tangent-tangent angle intercepts two arcs that measure 135 degrees and 225 degrees, thus in this the vertex lies outside, therefore

The measure of the tangent tangent angle is the half of the difference of the two given arc, that is

[tex]M=\frac{1}{2}(225-135)[/tex]

⇒[tex]M=\frac{90}{2}[/tex]

⇒[tex]M=45 degrees[/tex]

Therefore, The measure of the tangent tangent angle is 45 degrees.

The answer to this question is C, i took the test.

Hope you have a great day!

The math teacher's favorite breakfast is Pi.

The number pi is a mathematical constant whose value is  (3.141592653589793238...). its decimal representation is neither end (such as 1/4 = 0.25) nor becomes repetitive  (such as 1/6 = 0.166666...). And it is generally denoted by the Greek letter p or π.

In geometry, the pi is generally defined as the ratio of the circumference of the circle to its diameter.

[tex]\rm{\pi=\dfrac{Circumference}{Diameter}[/tex]

Learn more about Pi:

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To evaluate the definite integral from x=0 to x=1 of the cubed root of (1 + 7x), we need to find the antiderivative, then calculate the difference in its values at x=1 and x=0 according to the fundamental theorem of calculus.

The task is to evaluate the definite integral from x=0 to x=1 of the cubed root of (1 + 7x). To find the integral of this function, we need to apply the fundamental theorem of calculus. This theorem allows us to evaluate definite integrals as the net or accumulated area under the curve from one point to another.

Let's denote the function to integrate as f(x) = (1 + 7x)^(1/3). Our goal is to find the integral of f(x) with respect to x, within the bounds of 0 to 1.

To solve this integral, we would typically look for a suitable antiderivative of f(x), which, when evaluated at the upper and lower limits of integration, would provide us with the definite integral value.

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Answer: 2 gallons of lemonade.

Step-by-step explanation:

The container holds 16 pints of lemonade, and we know that a pint corresponds to 0.125 gallons.

So 16 pints are equal to 16 times 0.125 gallons:

16*0.125 gallons = 2 gallons

Then the container holds 2 gallons of lemonade.

Answer:

72[tex]\degree[/tex]

Step-by-step explanation:

We know that the sum of all the angles of any triangle is 180[tex]\degree[/tex]

We have to use the above property in order to find the measurement of the vertex angle.

Now our triangle is isosceles , that is the two equal sides will be containing equal angle. One of them is given as 54[tex]\degree[/tex]

And hence the other will also be 54[tex]\degree[/tex].

Let the vertex angle be x

180=54+54+×

180=108+×

x=180-108

x=72

Hence the vertex angle is 72[tex]\degree[/tex]

Answer:

on edu its B

Step-by-step explanation:

Answer:

3 one-pound bags; 2 three-pound bags

Step-by-step explanation:

h

Answer:

4

Step-by-step explanation:

The factors of 20 are: 1, 2, 4, 5, 10, 20

The factors of 28 are: 1, 2, 4, 7, 14, 28

Then the greatest common factor is 4.

Step 1: Distributive Property. Step 2: Combine like terms. Step 3: Add 34x to both sides. Step 4: Divide by 17. x = 60/17.

Here's a step-by-step solution to the equation 2(10 - 13x) + 9x = -34x + 60, along with the properties used at each step:

Given equation: 2(10 - 13x) + 9x = -34x + 60

Step 1: Distribute the 2 on the left side of the equation.

  Property used: Distributive Property

   2 * 10 - 2 * 13x + 9x = -34x + 60

  20 - 26x + 9x = -34x + 60

Step 2: Combine like terms on both sides of the equation.

Property used: Combining like terms

     -26x + 9x = -34x + 60

  (-26x + 9x) = (-34x + 60)

  -17x = -34x + 60

Step 3: Add 34x to both sides of the equation to isolate the variable x on the right side.

  Property used: Adding the same value to both sides of an equation to maintain equality.

 -17x + 34x = -34x + 60 + 34x

  17x = 60

Step 4: Finally, divide both sides by 17 to solve for x.

Property used: Dividing both sides of the equation by the same nonzero value to maintain equality.

(17x) / 17 = 60 / 17

x = 60 / 17

So, the solution to the equation is:

x = 60 / 17

Each step in this solution is justified by the properties of equality and arithmetic operations.

The complete question is here:

Justify each step of the solution by stating the property that was used to get to each step. Given: 2 (10-13x) + 9x = -34x + 60 Step 1: 20 - 26x + 9x = -34x + 60 Step 2: -17x = -34x + 10 Step 3: 17x = 40 Step 4: x =( 40)/(17) 40 on top of 17 as a fraction.