MATHEMATICS COLLEGE

Analyze the biconditional statement below and complete the instructions that follow.A polygon is a pentagon if and only if it has five sides.

Express the given biconditional as the conjunction of two conditionals.

A.
If it is a pentagon, then it has five sides. If it is a polygon, then it is a pentagon.
B.
If it is a pentagon, then it is a polygon. If it is a polygon, then it is a pentagon.
C.
If it is a pentagon, then it is a polygon. If it is a polygon, then it has five sides.
D.
If it is a pentagon, then it has five sides. If the polygon has five sides, then it is a pentagon

Answers

Answer 1
Answer:

Answer:

D.  If it is a pentagon, then it has five sides. If the polygon has five sides, then it is a pentagon

Step-by-step explanation:

Given statements;

      A polygon is a pentagon if and only if it has five sides.

  • From the statement we see that a pentagon has 5 sides.
  • A body of this structure with 5 sides can be classified as a polygon.

Therefore, this bi-conditional statement is premised on two "if"s,

    If it is a pentagon then we are dealing with a body with 5 sides.

   And if such body has five sides, it is a polygon called pentagon

The correct option is D

Choice A, B and C are logically flawed.

A.  If it is a pentagon, then it has five sides. If it is a polygon, then it is a pentagon.

The emboldened part we do not know.

B.  If it is a pentagon, then it is a polygon. If it is a polygon, then it is a pentagon

 The emboldened part is flawed.

C. If it is a pentagon, then it is a polygon. If it is a polygon, then it has five sides.

We do not know if all pentagons have 5 sides.

Answer 2
Answer:

Final answer:

The conjunction of two conditional statement for the biconditional 'A polygon is a pentagon if and only if it has five sides' is 'If it is a pentagon, then it has five sides' and 'If a polygon has five sides, then it is a pentagon'.

Explanation:

The given biconditional statement 'A polygon is a pentagon if and only if it has five sides' can be split into two conditional statements as follows: 'If it is a pentagon, then it has five sides' and 'If a polygon has five sides, then it is a pentagon'.

These two separate conditional statements show both possible directions of the biconditional statement. Option D correctly represents these two conditions as the conjunction of two conditional statements.

Learn more about Biconditional Statements here:

brainly.com/question/35695050

#SPJ2

Related Questions

I really need help I posted this question 3 times and no answers, can someone help I even put extra points and ill give brainliest <333
1. Line L passes through point (-1, 2) and (-3,-2) on a coordinate plane. LineM passes through the points (1.1) and (-1, W). For what value of W will makeline L and line M parallel.
If f(x)=2x-3 find the following f(7)=f(-2)=f(-4)=
A builder needs to tile a 7-foot by8-foot room with one-foot square tiles. How many tiles will she need? 56 tiles 15 tiles 30 tiles
Multiply the polynomials 3(x+7) (show work pls)

The function f(x) = 2x2 + 3 represents the rate of a boat traveling with the current in miles per hour. The function g(x) = x + 2 represents the time the boat traveled in hours. Solve (f • g)(2), and interpret the answer.

Answers

\boxed{(f\cdot g)(2)=44}

Explanation:

Here we have two functions, namely:

f(x)=2x^2+3 \n \n \n g(x)=x+2

So here we need to perform the product of two functions and evaluate this new function for x=2. So:

f(x)=2x^2+3 \n \n g(x)=x+2 \n \n \n (f\cdot g)(x)=(2x^2+3)(x+2) \n \n (f\cdot g)(2)=(2* 2^2+3)(2+2) \n \n \boxed{(f\cdot g)(2)=44}

Learn more:

Rigid transformations:brainly.com/question/13653482

#LearnWithBrainly

Answer:

C.(f • g)(2) = 44, the distance in miles the boat traveled

Step-by-step explanation:

Raj recorded the scores of six of his classmates in the table.Math Scores
98
76
100
88
82
70

What is the range of their test scores?

Answers

The answer is 30. Range: largest number - smallest number = range

A die is rolled twice.What is the probability that the first roll was a 6 and the second roll was an odd number?

Answers

Answer:

1/12

Step-by-step explanation:

1/6 * 3/6 (First roll has a one in 6 chance, second 3 in 6)

1*3 / 36 =

3 / 36 =

1/12

A plane leaves the airport in galisteo and flies 170 km at 68 degrees east of north; then it changes direction to fly 230 km at 36 degrees south of east, after which it makes an immediate emergency landing in a pasture. When the airport sends out a rescue crew, in which direction and how far should this crew fly to go directly to this plane?

Answers

Answer:

4.68° south east 317.36 km

Step-by-step explanation:

We can find the angle between the two distances (vectors) because according to the diagram, we can draw two right triangles between them.

The complement of the 36 degree angle is 54 (90-36=54), and the complement of the 68 angle is 22, (90-68=22) the sum of 22 and 54 is 76. So the angle between the two distances is 76.

Then we apply the cosine law

b^(2) =a^(2) +c^(2) -2*a*c*cosB\n \nb^(2) =230^(2) +170^(2) -2*230*170*cos(76)\n\nb=\sqrt{230^(2) +170^(2) -2*230*170*cos(76)} \n\nb=317.36 km

then we apply the sin law

(sin(C))/(c) =(sin(B))/(b) \n\nsin(C)=c*(sin(B))/(b)\n\nsin(C)=170*(sin(76))/(317.36)\n\nsin(C)=0.52\n\narcsin(0.52)=C=31.32\n\n

and because in any triangle, the sum of the inside angles is equal to 180

180=76+31.32+68+y\n\ny=180-76-31.32-68\n\ny=4.68^(o)

180= 76+C+(68+Y)

y=180-76-C-68

So the emergency plane has to travel 317.36 km, 4.68° southeast.

Help please points and brainlest!!

Answers

Answer:

0.20m + 650 < 755

Step-by-step explanation:

So you know that m is the total amount of miles that he travelled, so the cost of these miles would have been 0.20m. The total also included 650 and it has to be less than 755. Thus the equation would be 0.20m + 650 < 755 which means that the sum of 0.20m (cost of miles) and 650 (night cost) is less than (< means less than something else on the right) 755.

A circle has a radias of 12in. The diameter of the circle is _____in. In order to find the area of the circle, use the formula ____ The area of the circle is ____Thanks

Answers

Answer:

Step-by-step explanation:

The diameter of the circle is twice the radius, so the diameter of the circle is 2 x 12 inches = 24 inches.

To find the area of the circle, we can use the formula A = πr^2, where A is the area of the circle and r is the radius.

So, for this circle, A = π(12 inches)^2 = 144π square inches.

Therefore, the diameter of the circle is 24 inches, the formula to find the area of the circle is A = πr^2, and the area of the circle is 144π square inches.

Answer: 144 pie square inches!

Step-by-step explanation:

1st blank : is 24 square inches since the radius which is half the diameter is 12 square inches we can easily know that the diameter would be 24 square inches!

2nd blank : pie r squared is the formula! for all areas of the circles! the total length in other words the circumference of the circle would be 2 pie r basically multiplying 2 and pie and the radius.

3rd blank : the area of the circle is 144 pie (square inches)!
Other Questions
A digital camcorder repair service has set a goal not to exceed an average of 5 working days from the time the unit is brought in to the time repairs are completed. A random sample of 12 repair records showed the following repair times (in days): 5, 7, 4, 6, 7, 5, 5, 6, 4, 4, 7, 5.(a) H0: μ ≤ 5 days versus H1: μ > 5 days. At α = .05, choose the right option. Reject H0 if tcalc > 1.7960 Reject H0 if tcalc < 1.7960b. Calculate the Test statistic.c-1. The null hypothesis should be rejected.i. TRUEii. FALSEc-2. The average repair time is longer than 5 days.i. TRUEii. FALSEc-3 At α = .05 is the goal being met?i. TRUEii. FALSE
Complete the following proof
A pet store has 32 dogs. The owner gives 2 treats to each dog until she has no treats left over. How many treats did she have?
P(q ÷ 3 - p ); use p = -6, and q= -3