Mathematics High School

If two lines are parallel, then
corresponding angles are congruent. i

Answers

Answer 1

Answer: Choice B)

If corresponding angles are not congruent, then the lines are not parallel.

==================================================

Explanation:

The given conditional is in the form "If P, then Q"

where,

P = two lines are parallelQ = corresponding angles are congruent

The P and Q are placeholders for those definitions shown above. So we'll simply do a "search and replace" to replace P and Q with those phrases. We do this shortening so that we can do logical operations.

Specifically, we'll do two things:

Swap the positions of P and QPlace a "not" before each letter after the swap

We go from the format "if P, then Q" to "if not Q, then not P". Those two formats are equivalent in truth value. This is known as the contrapositive.

In terms of the problem at hand, the phrase "if not Q, then not P" becomes "If corresponding angles are not congruent, then the lines are not parallel"

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

In short, we swap each part of the original "if ..., then ..." statement, and stick "not"s in there to negate each piece.

Answer 2

Option B is correct, if corresponding angles are not congruent then the lines are not parallel.

What is Mathematical Reasoning?

In mathematics, reasoning involves drawing logical conclusions based on evidence or stated assumptions

The given statement is "If two lines are parallel, then corresponding angles are congruent."

Let us consider p as two lines are parallel,

q as corresponding angles are congruent.

If p is true then q should be true

or else if p is false then q also should be false

if P, then Q" to "if not Q, then not P". Those two formats are equivalent in truth value

This is known as the contrapositive.

"If two lines are parallel, then corresponding angles are congruent." is equivalent to if corresponding angles are not congruent then the lines are not parallel.

Hence, option B is correct, if corresponding angles are not congruent then the lines are not parallel.

To learn more on Mathematical reasoning click:

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Related Questions

Jenny earned 100 of a possible 144 points on a test. She lost 2 points for each incorrect answer. How
many incorrect answers did she have?
The equation is
There are
incorrect answers.

Answers

Answer: She had 22 incorrect answers

Step-by-step explanation: You divide 44 by 2.

Graph each pair of ordered pairs. Then find the distance between the points. Round to the nearest tenth if necessary.

1. (4, 3), (1, –1)

Answers

Attached below.......

Can someone help me pls

Answers

Answer: Angle B is 27 degrees

Step-by-step explanation:

All angles in a triangle must add up to 180 degrees so if two angles 63 and 90 add up to 153 then the last number added to 153 (x+153)=180 so 27 degrees

Answer:

Angle B is 27°

Step-by-step explanation:

90°-63°=27°

A car drives 120 miles at a speed of 40 mph. How long did it take?

Answers

Answer:

3 hours

Step-by-step explanation:

Answer:

3 hours

Step-by-step explanation:

120/40=3

x + 2y = 10
-6x + 5y = -9
- what is the solution using substitution

Answers

X+2Y=10
X=10-2Y

-6X+5Y= -9
-6(10-2Y)+5Y= -9
-60+12Y+5Y= -9
17Y= -9+60
17Y=51
Y=3

X=10-2Y
X=10-2•3
X=10-6
X=4

HELP PLEASE!!!
This meal costs $14.00.
A 7% sales tax is applied, followed by an automatic tip of 18%.
What is the total with tax and tip?

Answers

Answer:

17.6764$

Step-by-step explanation:

14 * 1.07 = 14.98$

14.98$ * 1.18 = 17.6764$

The tax is $0.98 and tip is $2.52

what is Unitary Method?

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Original Cost = $14

Tax = 7%

So, Price after tax = 14 + 7% of 14

= 14 + 0.98

= $14.98

and, after 18% tip = 14 + 18% of 14

= $16.52

Hence, the tax is $0.98 and tip is $2.52

Learn more about Unitary Method here:

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A teacher is planning a class trip to the aquarium. The aquarium requires 2
chaperones for every 15 students. The teacher plans accordingly and orders a
total of 85 tickets. How many tickets are for chaperones, and how many are for
students? Use the table to help you solve.
Use a table.
(Fill rows as needed.)
kids
chaperones
total
15
2
17

Answers

Answer:

The aquarium requires 2 chaperones for every 15 students. The teacher plans accordingly and orders a total of 85 tickets. How many tickets are for chaperones, ...

Step-by-step explanation:

Continue to name one point that is a solution to the
inequality and one point that is not a solution.

y ≤ 3x + 4

Answers

Answer:

y≤6x+8

Step-by-step explanation:

Given function:

y≤3x+4

This means:

variable stays same

if y=7 then x=1 and if y=14 then x can be 2 or 3.

we can also think as:

y≤6x+8

what we did:

double the number: 3x+4 · 2 = 6x+8

Therefore, another equation for y≤3x+4 would be y≤6x+8.

Can a triangle have two obtuse angles? please Justify your answer.

Answers

Answer:

No, a triangle cannot have 2 obtuse angles. The definition of an obtuse angle is an angle with a measure that is greater than 90°.

Step-by-step explanation:

Answer:

No, because if the triangle have two obtuse angles i.e., more than 90° angle, then the sum of all three angles of a triangle will not be equal to 180°.

Step-by-step explanation:

2/3x-3=19. Help? solve X

Answers

Answer:

x=33

Step-by-step explanation:

Answer: x=33

Step-by-step explanation:

2/3x-3=19

+3 +3

2/3x=22

Divide by 2/3 on each side

x=33

Kan buys 35pound of mixed nuts for $ 3.50. At this rate, how many pounds of mixed nuts can he buys for $15?

Answers

Answer:

i think its 150 pounds if i wrong im super sorry

Step-by-step explanation:

Annabelle has 56 1 cm³ what are the dimensions of the rectangle Langer prism Annabelle could build with all the cubes

Answers

Answer:

The six possible rectangular prisms Anabelle could build are;

W = 1, B = 1, L = 56

W = 1, B = 2, L = 28

W = 1, B = 4, L = 14

W = 2, B = 2, L = 14

W = 1, B = 7, L = 8

W = 2, B = 4, L = 7

Step-by-step explanation:

The number 1 cm³ Annabelle has = 56

The dimensions volume of the cubes Annabelle could build with the 1 cm³ = 56 cm³

The volume of rectangular prism, V = L × B × W

∴ For the rectangular prism, V = 56 cm³ = L × B × W

Therefore, the possible dimensions of the prism are three factors of 56, including;

1, 2, 4, 7, 8, 14, 28, 56

The combination of 3 factors of 56 that can be multiplied together to give 56 and therefore, the possible rectangular prisms includes;

W × L × B = A

1) 1 × 1 × 56 = 56

2) 1 × 2 × 28 = 56

3) 1 × 4 × 14 = 56

4) 2 × 2 × 14 = 56

5) 1 × 7 × 8 = 56

6) 2 × 4 × 7 = 56

There are therefore 6 possible rectangular prisms Annabelle could build

please help asap!!!!

Answers

Answer:

2,145.612

Step-by-step explanation:

Read the file upload!

Sarah went to lunch with 4 friends. The total bill was $125.68 and they had coupon for $20 off. How much did each person pay?

Answers

$21.13 you do $125.68-$20=... then divide the answer ___ /by 5!

PLEASE HELP ME OMG I WILL LOVE U FOREVER

Answers

Answer:

Extreme points of [tex](3-x)^{2}[/tex] (6-x) : Minimum (3,0), Maximum (5, 4)

I hope that helps hshshs :)

PLEASE HELP MEEEE
Which of the following equations will produce the graph shown below?

Answers

Answer:

A. 6x^{2}+6y^{2}=144

Step-by-step explanation:

which function is shown in the table? (see image)

Answers

A is the answer the answers of f(x) are being multiplied by 3

quotient 2 divided by 2 3

Answers

Answer: 11.5

Step-by-step explanation:

The list price on a winter coat is $84. It is being sold at a 23% discount. What is the sale price of the coat?
A)$64.68
B)$61.32
C)$47.48
D)$22.68

Answers

Answer:

A) $64.68

Step-by-step explanation:

Note that 23% = 23/100 = 0.23

First, multiply $84 with 0.23:

84 x 0.23 = 19.32

Next, subtract 19.32 from the total cost:

84 - 19.32 = 64.68

A) $64.68 is your answer.

Answer:

A)$64.68

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

7. Find the missing length. A. 36 B. 48 C. 49 D. 80

Answers

Answer:

A. 36

Step-by-step explanation:

100-64= 36

PLS HELP
What is the area, in square of the parallelogram below?

Answers

Answer:

35 square units

Step-by-step explanation:

Area of the parallelogram = 7*5 = 35 square units

please help
ill mark as the brainliest

Answers

180-130=50 so we know y=50 degrees now we need to add 50+68=118 degrees we know that all angles in a triangle add up to 180 degrees so we subtract 118 from 180 which gives us 62 so x=62 degrees

In ΔMNO, the measure of ∠O=90°, the measure of ∠N=48°, and NO = 73 feet. Find the length of MN to the nearest tenth of a foot.

Answers

Answer:109.1 feet

Step-by-step explanation:

What function uses the ADJACENT and the HYPOTENUSE?

\text{SOH-CAH-TOA}

SOH-CAH-TOA

\cos N = \frac{\text{adjacent}}{\text{hypotenuse}}=\frac{73}{x}

cosN=

hypotenuse

adjacent

\cos 48=\frac{73}{x}

cos48=

x\cos 48=73

xcos48=73

Cross multiply.

\frac{x\cos 48}{\cos 48}=\frac{73}{\cos 48}

cos48

xcos48

cos48

Divide each side by cos 48.

x=\frac{73}{\cos 48}=109.0968\approx 109.1\text{ feet}

cos48

=109.0968≈109.1 feet

Type into calculator and roundto the nearest tenth of a foot.

Can someone help me on this plzzz

Answers

The answer is 20 y=9 times that and y= 9 times that also u subtract and then u get 20.

Point form:(1,7) equation form: x=1,y=7

If p:q = 34 :2 and p:r = 13 : 12, find the ratio of p:q:r

Answers

Answer:

p:q:r = ?

p:q = 13/2

p:r = 34/12

= 17/6

p:q:r = 221:34:78

Step-by-step explanation:

Determine the vertical asymptotes and holes for the graph of the equation below.

y=[tex]\frac{x+7}{x^2+8x+7}[/tex]

Please show all steps to solve!

Answers

Since x ² + 8x + 7 = (x + 7) (x + 1), we have for x ≠ -7,

y = (x + 7) / (x ² + 8x + 7) = 1/(x + 1)

so y is undefined at x = -1, indicating a vertical asymptote, and there is a hole/removable discontinuity at x = -7. Then the answer is D.

Alex bought a new skate board at 20% discount. He paid $72. What percent of the original price did he pay?

Answers

Answer:

Step-by-step explanation:

Alex bought a new skate board at 20% discount. He paid $72. What percent of the original price did he pay?

Step 1

We find the original price

= Percent Discount × Original price =

= 20% × Original price = $72

= 0.2 × x = $72

x = $72/0.2

x = 360

ANSWER FAST PLEASE

Which of the following is not an example of a Mixed Number?
A. 5 1/4
B. -3.85
C. 16/8
D. 27 2/3

Answers

Answer:16/8

Step-by-step explanation:

I need to show my work ASAP

Answers

Answer:

intergers

square root of 14 = 3.74

integer is 4

nearest tenth is 3.7

square root of 90 =9.49

interger = 9

nearest tenth =9.5

square root of 175 =13.23

interger =13

nearest tenth =13.2

Plz, answer this question plz!

Answers

Answer:d

Step-by-step explanation:

Answer: C. 2/3

Step-by-step explanation:

Take the number of times the coin was flipped on heads (12)

and the total number of times the coin was flipped (18)

make it a fraction

12/18

reduce the fraction by dividing both numbers by 6

2/3

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If two lines are parallel, then corresponding angles are congruent. i

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If two lines are parallel, then
corresponding angles are congruent. i