1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Shtirlitz [24]
3 years ago
8

Can someone help me with this proof

Mathematics
1 answer:
maksim [4K]3 years ago
8 0

Step-by-step explanation:

Given :

Given that lines a and b are parallel, angles 1 and 5 are congruent because they are corresponding angles, and angles 1 and 4 are congruent because they are vertical angles

To find : by which property are angles 4 and 5 congruent

Solution :

We know that if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

Also, we know that if two things are equal to the same thing then they are equal to each other . In this case, we can say that if two angles are congruent to a third angle, then they are congruent to each other. As angles 4 and 5 are both congruent to angle 1, they are congruent to each other but angles 4 and 5 are alternate interior angles. So, if parallel lines have a transversal, alternate interior angles are congruent.

You might be interested in
James can jog twice as fast as he can walk. He was able to jog the first 9 miles to his grandmother’s house, but then he tired a
dimulka [17.4K]

Answer:

6 mile/hour

Explanation :



Let the speed of walking of James = x mile/hour


speed of jogging = 2x mile/hour


9/2x + 1.5/x = 2


= > (9 + 3)/2x = 2


= > 12 = 4x


= > x = 3


Average speed of walking = 3 mile/hour


Average speed of jogging = 2 * 3 = 6 mile/hour

5 0
3 years ago
The coldest surface temperature on the Moon is 57 degrees colder than twice the coldest surface temperature on Earth. What is th
german
28.5  is the coldest surface temperature on Earth
5 0
3 years ago
Which graph is the solution of the following systems <br><br> HELP ON ON GRADPOINT
makkiz [27]
I think it is the second one but I’m not for sure I’m really just doing this for points
6 0
3 years ago
A rectangle has a perimeter of 30 inches if the width is 3 times it’s length find it dimension
kakasveta [241]

Answer:

Length = 11.25 and width = 3.75 inches.

Step-by-step explanation:

You must mean that the length is 3 times its width.

If the the width is x then the length is 3x inches.

Perimeter = 2*length + 2*width.

2(3x) + 2x = 30

6x + 2x = 30

8x = 30

x = 3.75.

3x = 11.25.

7 0
3 years ago
Help please!!! I dont understand these questions<br><br><br>currently attaching photos dont delete
Katyanochek1 [597]

Answer:

  1. b/a
  2. 16a²b²
  3. n¹⁰/(16m⁶)
  4. y⁸/x¹⁰
  5. m⁷n³n/m

Step-by-step explanation:

These problems make use of three rules of exponents:

a^ba^c=a^{b+c}\\\\(a^b)^c=a^{bc}\\\\a^{-b}=\dfrac{1}{a^b} \quad\text{or} \quad a^b=\dfrac{1}{a^{-b}}

In general, you can work the problem by using these rules to compute the exponents of each of the variables (or constants), then arrange the expression so all exponents are positive. (The last problem is slightly different.)

__

1. There are no "a" variables in the numerator, and the denominator "a" has a positive exponent (1), so we can leave it alone. The exponent of "b" is the difference of numerator and denominator exponents, according to the above rules.

\dfrac{b^{-2}}{ab^{-3}}=\dfrac{b^{-2-(-3)}}{a}=\dfrac{b}{a}

__

2. 1 to any power is still 1. The outer exponent can be "distributed" to each of the terms inside parentheses, then exponents can be made positive by shifting from denominator to numerator.

\left(\dfrac{1}{4ab}\right)^{-2}=\dfrac{1}{4^{-2}a^{-2}b^{-2}}=16a^2b^2

__

3. One way to work this one is to simplify the inside of the parentheses before applying the outside exponent.

\left(\dfrac{4mn}{m^{-2}n^6}\right)^{-2}=\left(4m^{1-(-2)}n^{1-6}}\right)^{-2}=\left(4m^3n^{-5}}\right)^{-2}\\\\=4^{-2}m^{-6}n^{10}=\dfrac{n^{10}}{16m^6}

__

4. This works the same way the previous problem does.

\left(\dfrac{x^{-4}y}{x^{-9}y^5}\right)^{-2}=\left(x^{-4-(-9)}y^{1-5}\right)^{-2}=\left(x^{5}y^{-4}\right)^{-2}\\\\=x^{-10}y^{8}=\dfrac{y^8}{x^{10}}

__

5. In this problem, you're only asked to eliminate the one negative exponent. That is done by moving the factor to the numerator, changing the sign of the exponent.

\dfrac{m^7n^3}{mn^{-1}}=\dfrac{m^7n^3n}{m}

3 0
3 years ago
Other questions:
  • The area if the of a circle is 111.6 square centimeters. What is the diameter?
    13·2 answers
  • What is the additive inverse ( opposite ) of -50​
    6·1 answer
  • Solve the equation using square roots: 2x²-17 = 15
    15·1 answer
  • Eduardo puts $40 into his piggy bank and plans to add $5 each month. Write an equation to represent this.​
    5·1 answer
  • How many variables are in 4x3 + 2y + 6?
    14·1 answer
  • What is 3 to the 100th power?
    8·2 answers
  • $4.25 for 64 fluid ounces .<br><br> What is the unit rate
    6·2 answers
  • Look at photo (WITH THE PHOTO)
    13·2 answers
  • Simplify the expression
    6·1 answer
  • Yo can y'all help me with this I already did it on another paper. It would be very helpful if it was a step by step explanation
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!