Complete the following indirect proof (proof by contradiction).
Given: Adjacent angles LA and ZB, formed by the intersection of two lines
Prove: At least one of the angles LA and B has measure 90° or greater

Complete The Following Indirect Proof (proof By Contradiction).Given: Adjacent Angles LA And ZB, Formed

Answers

Answer 1

First, we assume that this conclusion is false. In other words, we assume that the contrary statement "none of the two angles has measure [tex]90^{\circ}[/tex] or greater" is true.

The assumption is equivalent to the following two statements:

(1) [tex]m\angle A\text{ } \boxed{ < 90^{\circ}}[/tex]

(2) [tex]m\angle B\text{ } \boxed{ < 90^{\circ}}[/tex]

Using (1) and (2) and the addition properties of inequalities, we conclude that [tex]m\angle A+m\angle B \text{ } \boxed{ < } \text{ } 180^{\circ}[/tex].

On the other hand, two adjacent angles form a linear pair. Thus, the last statement contradicts the Linear Pair Property, which states that for a linear pair of angles [tex]\angle A[/tex] and [tex]\angle B[/tex], [tex]m\angle A+m\angle B \text{ } \boxed{=} \text{ } 180^{\circ}[/tex].

Therefore, the assumption made is false, and the statement "at least one of the angles [tex]\angle A[/tex] and [tex]\angle B[/tex] has measure [tex]90^{\circ}[/tex] or greater" is true.


Related Questions

Hellooooooooooooooooooooo

Answers

Answer:

Hi.

Step-by-step explanation:

Heya. How you doing?

Plz help me well mark brainliest if correct!!

Answers

Answer:

C

Step-by-step explanation:

There is no class at 8:30 at studio B

Find (f/g)(x). f(x)=/x^2-1 g(x)=/x-1

Answers

Answer:

[tex](\frac{f}{g})(x) = \sqrt{x + 1}[/tex]

Step-by-step explanation:

Given

[tex]f(x) = \sqrt{x^2 - 1[/tex]

[tex]g(x) =\sqrt{x - 1[/tex]

Required

Find [tex](\frac{f}{g})(x)[/tex]

[tex](\frac{f}{g})(x)[/tex] is calculated as:

[tex](\frac{f}{g})(x) = \frac{f(x)}{g(x)}[/tex]

This gives:

[tex](\frac{f}{g})(x) = \frac{\sqrt{x^2 - 1}}{\sqrt{x - 1}}[/tex]

Apply difference of two squares on the numerator

[tex](\frac{f}{g})(x) = \frac{\sqrt{x - 1}*\sqrt{x + 1}}{\sqrt{x - 1}}[/tex]

[tex](\frac{f}{g})(x) = \sqrt{x + 1}[/tex]

A 200-foot cable weighing 800 pounds is hanging from a winch 200 feet above ground level.
(a) How much per foot does this cable weigh? if a piece of this cable is A.x long, what is the weigh of this piece?
(b) Find the work (in ft-lb) done in winding up the cable when there is a 400- pound load attached to the end of the cable.

Answers

Answer:

4 pd / ft

140000 ft/pd

Step-by-step explanation:

Total Weight of cable = 800 pounds

Length of cable = 200 feets

Weight per foot = Total weight / length = 800 / 200 = 4 pounds per foot

Weight of piece will be :

Weight of cable - weight per foot * x

800 - 4x

Workdone with 300 pound load attached :

∫f(x)

f(x) = (800+300 - 4x) = 1100 - 4x

∫1100 - 4xdx at 200 to 0

Integrating the above

1100x - 4/2x² at x = 200 to 0

1100x - 2x²

1100(200) - 2(200²) - 1100(0) + 2(0^²))

(220000-80000) - 0 + 0

140000 ft/pd

Solve the following inequality algebraically: 1<3x-2<4

Answers

Answer:

1<x<2

Step-by-step explanation:

Let's solve your inequality step-by-step.

1<3x−2<4

1+2<3x−2+2<4+2 (Add 2 to all parts)

3<3x<6

3/3<3x/3<6/3   (Divide all parts by 3)

1<x<2

Answer:

1<x<2

Solve for x.
7x + 9
9x - 19
= X

Answers

Answer:

14

Step-by-step explanation:

7x+9= 9x-19

-2x= -28

x= 14

they are corresponding angles

Answer:

x = 14

Step-by-step explanation:

the angles are corresponding.

corresponding angles theorem states that when two parallel lines are cut by a transversal , the resulting corresponding angles are congruent.

therefore:

7x + 9 = 9x -19

9 = 2x - 19

28 = 2x

14 = x

Can y’all help me on question 21?!

Answers

Answer:

24

Step-by-step explanation:

96 divided by 4 = 24

Answer is a) 24

You can solve this by doing guess and check.

So 4x24 = 96



A rectangular prism has the dimensions shown. What is the total area of the prism?

170 cm 2
270 cm 2
310 cm 2
120 cm 2

Answers

Answer:

310 cm 2

Step-by-step explanation:

Combine the like term to create an equivalent expression:
-k - (-8k)

Answers

Answer:

7k

Step-by-step explanation:

10.) 1 and 2 in this diagram are___
a. Complementary
b. Supplementary
c. Congruent
d. Vertical angle

Answers

Answer:

A

Step-by-step explanation:

they are complementary, they add to 90

A data set that is normally distributed has a mean of 128 and standard deviation of 6.2. What is the Z-score,
rounded to the nearest hundredth, for a data value of 143

Answers

Answer:

2.42

Step-by-step explanation:

Given:

μ = 128σ = 6.2x = 143

Z-score is:

z = (x - μ)/σ = (143 - 128)/6.2 ≈ 2.42 (rounded to the nearest hundredth)

how many numbers did bill wrote if he wrote all the natural numbers between w and v not including w and v

Answers

Answer:

v - w - 1

Step-by-step explanation:

Try an experiment with a small, specific set of numbers like:

4, 5, 6, 7, 8, 9, 10   w = 4 and v = 10.

There are 5 numbers in the list, not counting the first and last.  Is this related to the difference between v and w?  v - w = 6, one more than 5.

The number of natural numbers between  w  and  v, not including  w  and  v, is v - w - 1.

Tina paid for6 hours of canoeing and 1 life jacket rental with two twenty dollar bills. How much change did Tina get back

Answers

The amount of change that Tina got back would be = $10

How to calculate Tina's change after the bills payment?

The amount of hours Tina spent in canoeing = 6 hours

The amount paid per hour for canoeing = $4

Therefore the total amount spent on canoeing = 6×4 = $24

The cost of the life jacket = $6

Therefore the total amount Tina spent = total amount spent on canoeing + cost of the life jacket.

That is; 24+6 = $30

The change Tina will receive from the two twenty dollars bills = (2×20) - 30

= 40-30 = $10

Learn more about addition here:

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A flowerpot has a diameter of 15 centimeters. Which expression can be used to find its circumference, C , in centimeters?

DO NOT ANSWER IF YOU DO NOT KNOW THE ANSWER! Whoever answers correctly will get Brainliest! :)

Answers

Answer:

C.

Step-by-step explanation:

A flowerpot is basically a circle, so you are looking for the circumference of a circle.

Formula: 2 x π x Radius

Tara is considering choosing either anthropology or economics as her college major, and she's wondering how
her SAT scores compare to those of her peers in either major. Tara finds some data on the SAT scores of
anthropology and economics majors at her school. The data is shown in the 2 plots below.
For
majors, the mean SAT score is greater than the median.
The
majors have a greater median SAT score.

Answers

Answer:

for (anthropology) majors, the standard deviation is an approximate measure of spread

The (economics) majors, have a greater standard deviation in SAT scores

The vertices of ABC are A(-3,5), B(-2,3), and C(-5,3). If ABC is reflected across the y-axis to produce the image A'B'C', find the coordinate of the vertex C'.

Answers

Answer:

[tex]C' =(5,3)[/tex]

Step-by-step explanation:

Given

[tex]A = (-3,5)[/tex]

[tex]B = (-2,3)[/tex]

[tex]C = (-5,3)[/tex]

Reflection across y-axis

Required

Find C'

For reflection across y-axis, the rule is:

[tex](x,y) \to (-x,y)[/tex]

So, the image of C is:

[tex](-5,3) \to (-(-5),3)[/tex]

[tex](-5,3) \to (5,3)[/tex]

Hence:

[tex]C' =(5,3)[/tex]

Solve for x:
please help me

Answers

Answer:

88 is the correct answer.

please mark brainliest

Answer:

88

Step-by-step explanation:

since a straight line is 180

180-92=88

Which of the following is equivalent to 5/20 ? *
Mark only one oval.

2/10
10/30
5/10
1/4

Answers

1/4. Because if you divide it by both the numerator AND denominator by five (the numerator) you get 1/4

Mrs. Dern's class is preparing to write reports on the United States. Students must draw from a box the state that they will be assigned to. When it is Jake's turn to draw, there are three western states, one southern state, five midwestern states, and some eastern states remaining in the box. If the probability of drawing an eastern state is 1/2, how many eastern states are in the box?​

Answers

Answer:

9

Step-by-step explanation:

Add all the states provided which is 9 since it said 1/2 chance answer is 9

Please help me with this will mark brainlist

Answers

Answer:

[tex]\frac{x}{3} +5[/tex]

Step-by-step explanation:

5 more than means "+ 5"

quotient means fraction so x is the numerator and 3 is the denominator

[tex]\frac{x}{3} +5[/tex]

© Express the ratio below in its simplest form.
2.5 : 3.5​

Answers

1 : 1.4 is the answer

Answer:

5:7

Step-by-step explanation:

Which expression is equivalent to 10 ?
0 x²(√²)
Ox2.2
O
**(√)
5
Mark this and retur
Save and Exit
Next
Submit

Answers

The expression 10+(-8) is equivalent to 10 - 8.

What is expression?

Different branches of mathematics exist. The branch of knowledge that deals with numbers and operations is arithmetic. We learned how to add, subtract, multiply, and divide two or more numbers through arithmetic.

Shapes and how they are created with various tools, such as a compass, ruler, and pencil, are the focus of geometry. Another fascinating area of study is algebra, which helps us communicate the numerical and alphabetic aspects of daily life (variables).

Any mathematical statement made up of numbers, variables, and an operation between them is called an expression or an algebraic expression. As an illustration, the expression 4m + 5 consists of the terms 4m and 5, as well as the variable m, all of which are separated from one another by the arithmetic sign +.

Learn more about expression

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Full question

What expression is equivalent to 10-8?

Help me again pleaseeeeeeeeee

Answers

Answer:

0.2 recurring I the same as 2/9

Step-by-step explanation:

x=0.2222

10x=2.2222

10x-x=9x

9x=2

divide both sides by 9

9x÷9=x

2÷9=2/9

Hope it helps:)

x -3y = -5
-x +3y = 0

Answers

9514 1404 393

Answer:

  no solution

Step-by-step explanation:

The equations are inconsistent. They have NO SOLUTION.

__

Add the two equations and you get ...

  0 = -5 . . . . . . False

No values of the variables will make this be true.

i am a 5 digit number,my ones place digit is of no use as i, i still remain same without it . my ten's and hundreds place digits are mirror images. my thousand place digit are half of 2nd, my 10thousand digit is 3 more than my ones place , who am i ?​

Answers

Answer:

The 5 digit number is 34880

Step-by-step explanation:

Let the five digit number be represented by "abcde".

We are told that 1 place digit number is of no use and the 5 digit number will remain the same without it.

This means that e = 0

The tens and hundreds digit are d and c respectively. We are told that they are mirror images of each other.

Thus, d = c = 8. Since 8 is the only number from 1 to 10 that can be mirrored and still remain a usable number.

The thousand digit is Half of the second digit.

Thus, b = ½d

b = 8/2

b = 4

We are told the 10thousand digit is 3 more than my ones place. Thus;

a = e + 3

a = 0 + 3

a = 3

We have seen that;

a = 3

b = 4

c = 8

d = 8

e = 0

Thus,the 5 digit number is 34880

If f(x)=2(x)^2+5square root (5+2) complete the following statement f(2)= blank

Answers

The complete statement is f(2) = 8+5√7

What are functions?

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here f(x)=2x²+5√7

Thus f(1) = 2×4+5√7

              = 8+5√7

Hence, The complete statement is f(2) = 8+5√7

Learn more about functions here:

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50 POINTS !!


PLEASE HELP !! ILL GIVE BRAINLIEST TO THE RIGHT ANSWERS.

Answers

Answer:

73

Step-by-step explanation:

48^2 + 55^2 = 5329

square root of 5329 is 73

Answer:73mi

Step-by-step explanation:

What are the zeros of the function g(x) = (x + 6) (x – 4)(x + 2) ?

Answers

9514 1404 393

Answer:

  x in {-6, -2, 4}

Step-by-step explanation:

The zero product rule tells you that a product will be zero if and only if one of the factors is zero. These binomial factors are zero when x has a value that is opposite the constant of the binomial.

  x +6 = 0   ⇒   x = -6

  x -4 = 0   ⇒   x = 4

  x +2 = 0   ⇒   x = -2

The zeros of the function are the x-values -6, -2, and 4.

In ADEF, the measure of ZF=90°, DF = 40, ED = 41, and FE = 9. What ratio
represents the secant of ZE?
E
41
9
D
40

Answers

Answer:

sec(∠F) = [tex]\frac{41}{9}[/tex]

Step-by-step explanation:

In triangle EFD,

m∠F = 90°

Adjacent side of ∠E = EF = 9 units

Opposite side of ∠E = DF = 40 units

Hypotenuse = DE = 41 units

For secant of ∠E ,

sec(∠E) = [tex]\frac{\text{Hypotenuse}}{\text{Adjacent side}}[/tex]

            = [tex]\frac{41}{9}[/tex]

Therefore, [tex]\frac{41}{9}[/tex] is the ratio of secant of ∠F.

Which of the following is not one term? -x^4, 38, 4y/5, -2-x

Answers

Answer:

the correct answer is-2-x

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