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satela [25.4K]
3 years ago
6

If Smith is guilty, then Jones is innocent. If Jones is innocent, then Smith is guilty. Write each biconditional statement in ex

ercises 17 and 18 as two separate statements a conditional statement and its converse
Mathematics
1 answer:
Volgvan3 years ago
6 0

Answer:

The required biconditional statement is: If Smith is guilty, if and only if Jones is innocent.

Step-by-step explanation:

From the provided statement.

The statement is: If Smith is guilty, then Jones is innocent.

The converse is: If Jones is innocent, then Smith is guilty.

The combination of a conditional statement and its converse is called biconditional statement.

The biconditional statement contains if and only if phrase between two part of the statement.

Which means the statement and converse both are true.

Therefore, the required biconditional statement is: If Smith is guilty, if and only if Jones is innocent.

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The hypotenuse of a right triangle is 15 inches. One of the legs is 3 inches more than the other. Find the length of the two leg
Crank
Let x = one of the legs.

Then, the other leg = x + 3.

Ed will use the Pythagorean Theorem to find the hypotenuse.

So, let a = x one leg. Let b= x + 3 the other leg. And, let c = 15 the hypotenuse.

The Pythagorean Theorem is:

c^2 = a^2 + b^2, where a and b are the legs and c is the hypotenuse.

We have:

15^2 = x^2 + (x + 3)^2

225 = x^2 + x^2 + 6x + 9

Rearranging:

2x^2 + 6x - 216 = 0

Divide by 2:

x^2 + 3x - 108 = 0

Solve by factoring:

(x - 9)(x + 12) = 0

So, x = 9 and x = -12. (x = -12 is not a valid answer.)

x = 9

x + 3 = 12

Conclusion: The legs of the right triangle are 9 inches and 12 inches.

Eddie-G…
3 0
3 years ago
Line AB contains (0, 4) and (1, 6) Line CD contains points (2, 10) and (−1, 4). Lines AB and CD are
vlada-n [284]

Answer  

Option (A) is correct .

Reason

The formula for the slope.

Slope = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}

As given

Line AB contains (0, 4) and (1, 6) .

put in the slope formula

Slope = \frac{6 - 4}{1 - 0}

Slope = \frac{2}{1}

Slope of the AB is 2.

As given

Line CD contains points (2, 10) and (−1, 4).

put in the slope formula

Slope = \frac{4 - 10}{-1 -2}

Slope = \frac{-6}{-3}

Slope = 2

Slope of the CD is 2.

As the slope of the  AB contains (0, 4) and (1, 6) Line CD contains points (2, 10) and (−1, 4) is 2 .

Therefore the option (A) is correct i.e the lines are parallel because the slopes are the same.

5 0
3 years ago
Read 2 more answers
2/5 of house household own pets . Of the household pets 1/3 have cats. What is the fraction of the household own cats
fredd [130]

Fraction of household owning pets = \frac{2}{5}

Fraction \; of \; household \; owning \; cats \; \\\\=\; \frac{1}{3} \; of\; Fraction \; of\; household\; owning \; pets \\\\=\frac{1}{3}  \times\frac{2}{5}  \\ \\Multiply \; numerator\; with\; numerator\; and\; denominator\; with\; denominator\\\\=   \frac{1 \times 2}{3 \times 5}= \frac{2}{15}

Conclusion:

The fraction of the household own cats is <em>two-fifteenth </em>

4 0
3 years ago
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Melissa reserves another rectangular patch in her vegetable garden for growing bell peppers. Since the space that she can reserv
Otrada [13]

Answer:

Quadratic, 16, 18, 6

Step-by-step explanation:

Did this assignment myself

7 0
3 years ago
The sum of two consecutive even numbers is 54 Find the numbers?
pogonyaev

Answer:

26 and 28

Step-by-step explanation:

1st integer = x

2nd integer = x + 2

 

x + x + 2 = 54

2x + 2 = 54

2x = 52

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The 1st integer is 26.

The 2nd integer is 28.

 

 

Let's add these numbers.

 

26 + 28 = 54

     54  =  54

5 0
3 years ago
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