MATHEMATICS COLLEGE

Angle 1 is congruent to angle 2 prove p is parallel to q

Answers

Answer 1

Answer:

You'll need 2 more lines to complete this two column proof.

---------------------

Line 4

For the "statement" portion, you'll say something like $\angle 2 \cong \angle 3$

The reason for this statement is "transitive property"

We're basically combining lines 1 and 3 to form this new line.

The transitive property is the idea that if A = B and B = C, then A = C. We connect the statements like a chain.

---------------------

Line 5

The statement is what you want to prove since this is the last line.

So the statement is $p || q$

The reason is "converse of corresponding angles theorem"

As you can probably guess, this theorem says "If two corresponding angles are congruent, then the lines are parallel".

Answer 2

Answer:

Final answer:

To prove that lines P and Q are parallel based on congruent angles, utilize the geometric understanding that if a transversal intersects two parallel lines, the corresponding angles are congruent. Given that angle 1 is congruent to angle 2, we can infer that the lines forming these angles (P and Q) are parallel.

Explanation:

To prove that the lines P and Q are parallel using the fact that angle 1 is congruent to angle 2, you will utilize the concept of congruent angles. When two parallel lines are intersected by a transversal, the corresponding angles are congruent. Therefore, if we know that angle 1 is congruent to angle 2, we can say the lines forming these angles are parallel.

Here are the steps:

Identify the given congruent angles (angle 1 and angle 2).
Identify the lines that form these angles, which are lines P and Q in this case.
Remember, by the corresponding angles postulate, if a transversal intersects two parallel lines, then the corresponding angles are congruent.
We have given that angle 1 is congruent to angle 2. So, the lines forming these angles, P and Q, are parallel.

This process uses reasoning of the geometry and reviews the core concept of parallel lines and transversals in proving that P is parallel to Q.

Learn more about Geometric Proof here:

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BRAINLIEST AND FIVE STARS TO CORRECT ANSWER

Answers

Note that the first function is f(x) = 4 for x less than 2 and for the second function f(x) = -1 for x greater than or equal to 2

So the limit as x approaches two from the left is 4 and the limit as x approaches 2 from the right is -1.

so looks like you would need the third choice: 4; -1

An architect uses a scale of 3 4 inch to represent 1 foot on a blueprint for a building. If the east wall of the building is 24 feet long, how long (in inches) will the line be on the blueprint?

Answers

The length of the line on the blueprint of the wall will be 18 inches.

What is dilation?

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

There is no effect of dilation on the angle.

An architect uses a scale of 3/4 inches to represent 1 foot on a blueprint for a building.

Then the scale factor of the blueprint will be

Scale factor = 3/4 inches per foot

If the east wall of the building is 24 feet long.

Then the length of the line on the blueprint of the wall will be

Length = 24 feet x scale factor

Length = 24 x (3/4)

Length = 6 x 3

Length = 18 inches

Thus, the length of the line on the blueprint of the wall will be 18 inches.

More about the dilation link is given below.

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Answer:

16 in.

Step-by-step explanation:

We have the ratio

How about let's make this easier. Easier is better, right? Let's get rid of the fraction 2/3. We will do that by multiplying 2/3 by 3 and 1 by 3 to get the equivalent ratio of

Now we need to know how many inches there would be if the number of feet is 24:

Cross multiply to get

3x = 48 so

x = 16 in.

How many numbers are between 0 and 4

Answers

Answer:

infinite rational numbers

Step-by-step explanation:

There are infinite rational numbers between 0 and 4. Now,single decimal value change like 2.34 and 2.35 can change the total value of a rational number. And there are infinite combinations of this decimal value between just two numbers.

Answer:

3 numbers

Step-by-step explanation:

Solve for the given variable: 4. 24 - 9x = -3x

5. 4(5x + 2) + 11 = 18x + 3

6. 3x - 8x = -27 – 13

Show Your Work

Answers

Answer:

4. x=4

5. x=-8

6. x=8

Step-by-step explanation:

It may take one extra step to get to the solution, but this method always works.

1. find the variable term that is smallest or most negative. Subtract all the terms on that side of the equation from both sides of the equation.

2. collect terms

3. divide the equation by the coefficient of the variable

4. add the opposite of the constant

___

4. The most negative variable term is -9x, which is on the left side. Subtracting (24-9x) from both sides of the equation, we have ...

0 = -3x -24 +9x

0 = -24 +6x

0 = -4 +x . . . . . divide by 6

4 = x . . . . . . . . add the opposite of -4

5. The smallest variable term is 18x, on the right. (The variable term on the left is 20x.)

4(5x +2) +11 -18x -3 = 0 . . . subtract the right side

2x +16 = 0 . . . collect terms

x +8 = 0 . . . . . . divide by 2

x = -8 . . . . . . . . add -8

6. All variables are on the left side, so we can just collect terms and divide by the coefficient of the variable.

-5x = -40 . . . collect terms

x = 8 . . . . . divide by -5

If you were to literally follow the steps above, you would recognize that -5x is less than 0x (the x-term on the right side of the equation), so you would subtract the left side, giving ...

0 = 5x -40

0 = x -8 . . . . . divide by 5

8 = x . . . . . . . . add 8

_____

Comment on this solution technique

You will often be told to solve these equations by separating the variable terms from the constant terms. This method actually puts the variable terms and constant terms together (and zero on the other side of the equal sign). The constant is separated from the variable as the last step of this solution process, rather than as one of the first steps. By doing this, we don't have to worry about which variable term or which constant term we're going to mess with.

The only reason for choosing the variable term with the smallest (least) coefficient in the first step is to ensure that the resulting variable coefficient is positive. This tends to reduce errors later on. You can also use that same strategy when solving the equation following the "separate constant terms and variable terms" approach.

2Viviana is ordering carpet

for 16 square rooms in a

hotel. Each room will need

100 square feet of

carpet. What is the

length of 1 room?

Answers

Answer:

Length of a room is 10ft

Step-by-step explanation:

Given

$Rooms = 16$

$Carpet\ Area = 100ft^2$

Required

Determine the length of each room

Here, we'll assume that the carpet will cover each room completely.

If so:

$Carpet\ Area = Length * Length$

$100ft^2 = Length * Length$

$100ft^2 = Length^2$

Take square root of both sides

$√(100ft^2) = √(Length^2)$

$√(100ft^2) = Length$

Take positive square root

$10ft = Length$

$Length = 10ft$

Hence, the length of a room is 10ft

DO NOT ANSWER W/O EXPLANATION PLEASE! NEED WRITTEN SOLUTION.In triangle ABC, an altitude is drawn from vertex C to the line containing AB. The length of this altitude is h and h=AB. Which of the following is true?
I. Triangle ABC could be a right triangle.
II. Angle C cannot be a right angle.
III. Angle C could be less than 45 degrees.

Answers

We have altitude h to side AB and AB=h, i.e. the altitude is congruent to the side it goes to.

That's all kinds of triangles. One way to see them is using two horizontal parallel lines h apart, the bottom one with a base AB=h somewhere on it. Then any C on the top line makes a triangle ABC with altitude h=AB.

Let's go through the choices.

I. ABC could be a right triangle. That's TRUE.

We could have the isoscleles right triangle, C directly above B, so AC is the leg and an altitude, AB=AC and B is the right angle.

II. Angle C cannot be a right angle. That's TRUE.

The biggest angle C can be is when it's over the midpoint of AB, so if AB=2, h=2, and

$AC=√(2^2+1^2)=√(5)$

$C_{\textrm{max}} = 2 \arctan(1/2) \approx 53.13^\circ$

III. Angle C could be less than 45 degrees. That's TRUE.

As long as C stays on our top parallel, we can make it as acute as we like by going farther away from AB.

All true. Hmmm.

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