Answers
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 congruentThe 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 swapWe 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.
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.
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Related Questions
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:
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.
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
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 asap!!!!
Answers
Answer:
2,145.612
Step-by-step explanation:
Read the file upload!
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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 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:
Can someone help me on this plzzz
Answers
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
please help
ill mark as the brainliest
Answers
Plz, answer this question plz!
Answers
Answer:d
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
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
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
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:
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
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:
x + 2y = 10
-6x + 5y = -9
- what is the solution using substitution
Answers
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
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:
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
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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
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:
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+4This 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.
quotient 2 divided by 2 3
Answers
Answer: 11.5
Step-by-step explanation:
7. Find the missing length. A. 36 B. 48 C. 49 D. 80
Answers
Answer:
A. 36
Step-by-step explanation:
100-64= 36
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
=
x
73
\cos 48=\frac{73}{x}
cos48=
x
73
x\cos 48=73
xcos48=73
Cross multiply.
\frac{x\cos 48}{\cos 48}=\frac{73}{\cos 48}
cos48
xcos48
=
cos48
73
Divide each side by cos 48.
x=\frac{73}{\cos 48}=109.0968\approx 109.1\text{ feet}
x=
cos48
73
=109.0968≈109.1 feet
Type into calculator and roundto the nearest tenth of a foot.
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.
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
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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
which function is shown in the table? (see image)