2. Theorem 2-10 states that through a point not on a line, there

is one and only one line parallel to the given line. How does this

justify the construction of the line through C that is parallel to

the line AB?

Answers

Answer 1

When two or more lines are parallel to each other, this implies that they do not meet even extending them till infinity. So the statement justifies the construction because only one line through point C can be constructed to be parallel to AB.

When a parallel line is constructed through a point to a given line, this is the only parallel line that can be drawn to the given line. Parallel lines are lines that will not meet at any point. Thus, only one parallel line can be constructed through a point not to a given line.

The construction of a line through C that is parallel to line AB is justified by the given statement in the theorem since this is the only parallel line to line AB that can be drawn through the point C. Any other line through C would intersect or meet line AB at a point when extended, thus would not be parallel to the given line.

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Related Questions

When William had one cat, he needed to serve 1/8 of a can of cat food each day. Now that William has adopted a second cat, he needs to serve a total of 2 7/8 cans each day. How much extra food is needed to feed the second cat?

Answers

2 7/8 - 1/8 = 2 6/8 cans of cat food

PLS HELP ASAP THANKS ILL GIVE BRAINLKEST THANKS

Answers

Answer:

1

Step-by-step explanation:

it means from Virginia to Florida you will drive more than 7 hours

Six apples and three oranges cost $3.36. Two apples and five oranges cost $3.04. Find the cost of one apple and the cost of an orange.

Answer and step-by-step explanation pls!!

Answers

Answer:

$0.8

Step-by-step explanation:

let x represent the price of apples

let y represent the price of oranges

6x+3y=3.36—eqn 1

2x+5y=3.04—eqn 2

Multiply eqn 2 by 3

3(2x+5y=3.04)=6x+15y=9.12

Subtract eqn 2 from 1

6x+3y=3.36

-{6x+15y=9.12}

-12y=-5.76

y=0.48

plug y=0.48 into eqn 1

6x+3(0.48)=3.36

6x=3.36-1.44

x=1.92/6=0.32

That is, an apple costs $0.32 and an orange costs $0.48

Therefore the cost of an orange and an apple=$0.48+$0.32=$0.8

Answer:

apple: $0.32orange: $0.48

Step-by-step explanation:

Let x and y represent the costs of 1 apple and 1 orange, respectively. The two cost figures tell us ...

  6x +3y = 3.36

  2x +5y = 3.04

We note that all of the numbers in the first equation are divisible by 3, so we can divide by 3 to reduce it to ...

  2x +y = 1.12

Subtracting this from the second equation gives ...

  (2x +5y) -(2x +y) = (3.04) -(1.12)

  4y = 1.92 . . . . . . . simplify

  y = 0.48 . . . . . . . divide by 4

Then the cost of an apple can be found from our reduced equation:

  2x +0.48 = 1.12 . . . substitute for y

  2x = 0.64 . . . . . . . . subtract 0.48

  x = 0.32 . . . . . . . . . divide by 2

The cost of one apple is $0.32; the cost of one orange is $0.48.

_____

Additional comment

The method of solution we used here is called "elimination," because the x-variable was eliminated from the combined equations. There are numerous other methods available for solving a system of linear equations. Most graphing calculators have features for graphing and for reducing matrices that will solve these for you. All you need to do is enter the equations.

70% of Hassan's collection of goldfish died. if he has 60 survivors, how many did he have originally?​

Answers

Hassan originally had 200 goldfish

Step-by-step explanation:

Multiply 60 by 100, which will get you 6,000, then divide by 30 to get 200. The 100 is for the total percentage, the 30 is the percentage left.

Answer:

200goldfish

Step-by-step explanation:

since 30percent(100_70)is60 what about 100percent

100percent/30percent multiplied by 60goldfish=200

Therefore the answer is 200goldfish

Shawn has 325 dollars if shawn uses only hundreds tens and ones write the number of each kind of bill that shawn has NEEDS TO BE ANSWERED ASAP

Answers

Answer:

3 hundreds, 2 tens, 5 ones

solving linear systems graphically .

Answers

Answer:

D- points on one side of one of the lines

Step-by-step explanation:

I may be wrong but I believe I am correct

Slope - Part 1
What is the slope of this line?
Enter your answer as a whole number or a fraction in simplest
form in the box
Please hurry!!

Answers

Answer:

-1

Step-by-step explanation:

We can use the slope formula to find the slope

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

Using the points on the line  (-2,0) and (0,-2)

m = ( -2-0)/(0- -2)

   = (-2-0)/(0+2)

   -2/2

   -1

Help again pls I think it’s D and A or am I wrong some one pls tell me thank you

Answers

It’s A and E, it can’t be D because of this reason.
x-2=4
+2=+2
x=6

You always need to do the opposite of the numbers around the variable so that the numbers cancel out for the variable to be alone.

A Web site charges $0.99 to download a game and a $12.49 membership fee. Write an expression that gives the
total cost in dollars to download g games. Then find the cost of downloading 6 games.

Answers

Answer:

Part A (Equation): C(g) = 0.99g + 12.49

Part B: Total cost of 6 games = $18.43

Step-by-step explanation:

Given the $0.99 charge to download a game, and a membership fee of $12.49:

Part A: Find the Equation of Total Cost, C, and Number of Games (g)

A cost function (or equation) that represents the total cost (C ), in dollars, to download g number of games is:  

C(g) = 0.99g + 12.49

where:

0.99 (cost per downloaded game) = represents the rate of change (or slope). This means that the total cost increases by $0.99 for every game that is dowloaded.  12.49 (membership fee) = the initial value or flat fee (y-intercept).

Part B:  Find the cost of downloading 6 games:

To find the cost of downloading 6 games C(6), substitute the value of g = 6 into the equation:

C(g) = 0.99g + 12.49

C(6) = 0.99(6) + 12.49

C(6) = 5.94 + 12.49

C(6) = 18.43

Therefore, it costs $18.43 to download 6 games.

Sally collected 30.4 pounds of cans to recycle and plans to collect 2.1 more pounds each week. In this situation, what is the value of the y-intercept?​

Answers

The y-intercept is the intital value where the equation begins.

Because Sally initially started at 30.4 pounds, the y-intercept is 30.4.

1. John is going to join a gym. He must pay a one-time membership fee of $75 and a monthly fee of $30. Let m = the number of months John has his membership. Write an expression to represent this situation How much will John pay for 6 months of membership?

2. Madison is having a party. She went to the store and bought a cake for $18.50 and 20 balloons. Her total bill was $63.50. How much did each balloon cost if they all cost the same? Write and solve an equation. Please look over these again. Webmail your answers to get your points back.

Answers

John's membership in the gym and Madison's party are illustrations of linear equations.

1. John's equation

The given parameters are:

[tex]\mathbf{Base = 75}[/tex]

[tex]\mathbf{Monthly = 30}[/tex]

The monthly expression is:

[tex]\mathbf{f(m) = Base + Monthly \times m}[/tex]

So, we have:

[tex]\mathbf{f(m) = 75+ 30 \times m}[/tex]

[tex]\mathbf{f(m) = 75+ 30m}[/tex]

For 6 months, we have:

[tex]\mathbf{f(6) = 75+ 30 \times 6}[/tex]

[tex]\mathbf{f(6) = 255}[/tex]

Hence, the expression that represents the situation is [tex]\mathbf{f(m) = 75+ 30m}[/tex], and the amount for 6 months of membership is $255

2. Madison's party

The given parameters are:

[tex]\mathbf{Cake = 18.50}[/tex]

[tex]\mathbf{Balloon = 20}[/tex]

[tex]\mathbf{Total = 63.50}[/tex]

Let n represent the cost of each balloon.

So, the equation is:

[tex]\mathbf{Cake + Balloon \times n = Total}[/tex]

This gives:

[tex]\mathbf{18.50 + 20 \times n = 63.50}[/tex]

Subtract 18.50 from both sides

[tex]\mathbf{ 20 \times n = 45}[/tex]

Divide both sides by 20

[tex]\mathbf{ n = 2.25}[/tex]

Hence, the expression that represents the situation is [tex]\mathbf{18.50 + 20 \times n = 63.50}[/tex], and the cost of each balloon is $2.25

Read more about linear equations at:

https://brainly.com/question/11897796

Someone could help me with problem 3-76 (b) pls

Answers

Answer:

ok so you see the equation at the top... you are going to "plug in" the number in the "in" row to get the "out number

Step-by-step explanation:

example

in: 4

-2(-4)+1

8+1

9

so for the out row under -4 you would put 9

-2(-3)+1

6+1

7

so for the out row under 3 you would put 7

Answer:

...

Step-by-step explanation:

the bill from your electrician was $198. he worked for 3 hours. the cost for materials was $33. how much did the electrician charge you per hour

Answers

Answer:

Answer is 66

Step-by-step explanation:

divide 198 by 3 and you get 66

Hope this helps!

solve for X in the figure below

Answers

[tex]\\ \sf\longmapsto 4x+12+90=180[/tex]

[tex]\\ \sf\longmapsto 4x+102=180[/tex]

[tex]\\ \sf\longmapsto 4x=78[/tex]

[tex]\\ \sf\longmapsto x=19.7[/tex]

how do u add and subtract rational numbers

Answers

Answer:

ration number such as 2 and 3

2 plus 3 is 5

3 minus 2 is 1

3 by 5 plus 2 by 5 is 5 by 5 which is 1

3 by 5 plus 2 by 4 take lcm and add the numerator .

Can someone help me with 1. ?

Answers

Make a table of each equation.

Find the point where the two lines end? or meet?

Jenny drove 335 miles in 5 hours at the same rate how long would it take her to drive 871 miles?

Answers

Answer: x = 13 hours

Step-by-step explanation:

335 miles/5 hours = 67 mi/hr

(67 mi/hr)x = 871 miles

x = 13 hours

Here is the problem: (Picture)

Answers

Answer:

c

Step-by-step explanation:

Graph the function f(x)=1/2x+1

Answers

Answer:

See attached graph.

Step-by-step explanation:

find equation of a line containing (3,-4) and having a slope of -2. if this line contains the points(a, 8) and (5,b) find a and b

i will give brainlest for the best answers with best explanation ​

Answers

Answer:

a = - 3, b = - 8

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - 2 , then

y = - 2x + c ← is the partial equation

To find c substitute (3, - 4 ) into the partial equation

- 4 = - 6 + c ⇒ c = - 4 + 6 = 2

y = - 2x + 2 ← equation of line

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

Substitute (a, 8 ) into the equation and solve for a

8 = - 2a + 2 ( subtract 2 from both sides )

6 = - 2a ( divide both sides by - 2 )

- 3 = a

Substitute (5, b ) into the equation and solve for b

b = - 2(5) + 2 = - 10 + 2 = - 8

SOMEONE PLS HELP ME!!!

Answers

Answer:

refer to the picture attached for steps

Given that (x-1) is a factor of p(x)=x^3+2x^2-x-2,factorize p(x) completely ​

Answers

Answer:

Step-by-step explanation:

Where are the factors? The number of terms? Where are the constants? Where are the confficients

3x-5y+15

Answers

Answer:

given the expression  4x - 2y + z + 5 we see three terms of the expression:  4x, -2y, +z , 5.

Terms are made of two things, a coefficient and a variable.

coefficient       variable

     4                 x

    -2                 y

   +1                 z

   +5                 no variable exists in this term so it is a special term called a constant.

Coefficients can be +/-, fractions, decimals, whole numbers, etc.

In equations the coefficient is often shown as a letter such as

ax + by + 3.

This means (a times x) plus (b times y) plus 3

fractional coefficients looks like this example:   x/4  + y/2  - z/3

the coefficient for x is 1/4, the coefficient for y is 1/2 and the coefficient for z is -1/3Step-by-step explanation:

An item is on sale for 30% What would the new cost be if the item was originally $275

Answers

Answer:

$192.5

Step-by-step explanation:

$275÷10=27.5

27.5×3=82.5

275-82.5=192.5

how do you turn radius into cm​

Answers

Answer:

depending on the question I suggest only converting at the end

sorry if it doesn't help

by the way a cm needs to be times by 100 to become a meter

I HAVE A SEMICIRCLE WITH A DIAMETER 16cm. How do I find the perimeter of the SEMICIRCLE

Answers

Answer:

Perimeter of Semicircle

The perimeter of a semicircle is the sum of the half of the circumference of the circle and diameter. As the perimeter of a circle is 2πr or πd. So, the perimeter of a semicircle is 1/2 (πd) + d or πr + 2r, where r is the radius.21-Oct-202

Answer:

Perimeter is 41.1327 centimeters

Step-by-step explanation:

The perimeter of a semi-circle is the circumference of the full circle plus the length of the diameter.

To find the circumference of a circle, just multiply the diameter by pi:

[tex]c=\pi\times d\\c=\pi\times 16\\c=50.2655[/tex]

Now, add the diameter to half of it:

[tex]p=\frac{c}{2}+d\\p=\frac{50.2655}{2}+16\\p=25.1327+16\\p=41.1327[/tex]

Are the ratios 17:10 and 2:1 equivalent?

Answers

Answer:

No, they don't have the same value

Step-by-step explanation:

Are the ratios 17:10 and 2:1 equivalent?

17 : 10 = 1.7

2:1      = 2

The average bedroom is an apartment is approximately 16x10

Answers

Answer:

Bro what to find with this

Answer:

 which would mean it would  have the area  of   160 square feet  

Step-by-step explanation:

The Batpod and The Falcon Cycle are traveling down the
highway. That Batpod can travel at a speed of 4 miles
per minute; while the Falcon Cycle can double that at a
speed of 8 miles per minute. If Falcon gives Batman a 6
minute head start. How long will Batman have traveled
before Falcon catches him?


I need help so I can turn in my Packet?!?!?

Answers

Answer:

3/2 minutes or 1.5 minutes

Step-by-step explanation:

We want to know when the two following equations will be equal, so we can set them equal to each other

(x = time passed)

Falcon

\/

8x = 4x + 6

         /\

   Batman

8x = 4x + 6 -> 4x = 6 -> x = 6/4 -> x = 3/2

We can also graph it, see attatched

Have a nice day! - also, lol, the different car names

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Harmony used discarded paper to make notepads for her friends she folded 5 letter size pieces of paper 3 times then cut along the lines then she would stack the smaller note papers and staple them together how long one notepad last if someone wrote 10 notes per day

Answers

Answer:

Answer is 5

Step-by-step explanation:

I don't what the problem is ;-; not sure

5x3-x=10

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