Determine whether the given lengths can be sides of a right triangle. Which of the following are true statements. A.The lengths 7, 40 and 41 can not be sides of a right triangle. B.The lengths 12, 16, and 20 can not be sides of a right triangle. C.The lengths 7, 40 and 41 can not be sides of a right triangle.D.The lengths 12, 16, and 20 can be sides of a right triangle. The lengths 7, 40 and 41 can be sides of a right triangle.

Answers 2

Answer:

Given sides 12, 16 and 20 can be the sides of right triangle.

Step-by-step explanation:

Sides of right triangle always follow the Pythagoras theorem.

i.e (base)^2 + (Height)^2 = (Hypotenuse)^2

For the given Lengths 7, 40 and 41

We need to check if

7^2 + 40^2 =41^2 \\or\\ 7^2 + 40^2 \neq41^2

Since \\7^2 + 40^2 = 1649\\and \\41^2 = 1681

That means, \\ 7^2 + 40^2 \neq 41^2

hence 7,40 and 41 can not be the sides of right triangle.

Next,

Given sides 12,16 and 20.

Again follow the similar process used in the above problem.

12^2 + 16^2 =400\\And \\20^2 = 400\\Since 12^2 + 16^2 = 20^2

Therefore given sides 12,16 and 20 can be the sides of right triangle.

AI generated Answer

A. The lengths 7, 40 and 41 can not be sides of a right triangle. C. The lengths 7, 40 and 41 can not be sides of a right triangle. D. The lengths 12, 16, and 20 can be sides of a right triangle. Quick Answer: A and C are true statements. Explanation: In order for three lengths to form a right triangle, the lengths must satisfy the Pythagorean Theorem which states that the sum of the squares of two shorter sides must equal to the square of the longest side. For example, in a right triangle with sides 7, 40, and 41, 72 + 402 ≠ 412, so it does not satisfy the Pythagorean Theorem and therefore cannot be a right triangle. Similarly, 122 + 162 = 202, thus for the lengths 12, 16 and 20, they can form a right triangle.

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The two triangles are similar. What is the value of x? Enter your answer in the box. x = Two right triangles, one smaller than the other, back to back, so that their right angles form a straight angle. The two acute angles along the straight angle are congruent to each other. The overlapping part of the legs is labeled 8. The part of the overlapping side that extends above the smaller triangle is labeled 6. The leg of the smaller triangle that is a ray of the straight angle is labeled 2 x minus 2. The leg of the larger angle that is a ray of the straight angle is labeled 3 x.

Answer:

x = 7

Step-by-step explanation:

For better understanding of the solution see the attached figure :

Given : AD = 6 units , BD = 8 units, m∠ABC = m∠DBE = 90° and               ∠DEB ≅ ∠ACB

Now, AB = AD + BD

               = 8 + 6 = 14 units

In ΔABC and ΔDBE,

∠DBE = ∠ABC ( Each of 90° )

∠DEB = ∠ACB ( Both angles are congruent to each other )

So, By using AA postulate of similarity of triangles , ΔABC ~ ΔDBE

So, proportion of the corresponding sides will be equal.

\implies \frac{AB}{DB}=\frac{BC}{BE}=\frac{AC}{DE}\\\\\implies \frac{AB}{DB}=\frac{BC}{BE}\\\\\implies \frac{14}{8}=\frac{3\cdot x}{2\cdot x-2}\\\\\implies 28\cdot x-28=24\cdot x\\\implies 4\cdot x=28\\\implies x=7

Hence, x = 7

answer img

The two triangles are similar. The value of x is 7.

Given information:

Two right triangles, one smaller than the other, back to back, so that their right angles form a straight angle.

The two triangles are similar.

The overlapping part of the legs is labeled 8. The part of the overlapping side that extends above the smaller triangle is labeled 6. The leg of the smaller triangle that is a ray of the straight angle is labeled 2x-2. The leg of the larger triangle that is a ray of the straight angle is labeled 3x. See the figure attached for more information.

The ratio of sides of triangles will be equal.

The ratio of the height of two triangles will be equal to the ratio of the base of them.

So, the value of x can be calculated as,

\dfrac{2x-2}{3x}=\dfrac{8}{8+6}\\\dfrac{2x-2}{3x}=\dfrac{4}{7}\\14x-14=12x\\2x=14\\x=7

Therefore, the value of x is 7.

answer img
Which statement best describes the difference between these versions? The radio adaptation's tone is more urgent than the novel's tone. The radio adaptation's tone is more academic than the novel's tone. The radio adaptation's tone is more peaceful than the novel's tone. The radio adaptation's tone is more friendly than the novel's tone.

The answer is A, The radio adaptation's tone is more urgent than the novel's tone.

The statement which best describes the difference between these versions is:

Option A

  • The radio adaptation's tone is more urgent than the novel's tone.

Orson Welles and his Mercury Theater froze a great many radio audience members with their innovative creation of War of the Worlds. It's the most popular radio dramatization ever, and it caused the news by professing to be the information.

Radio Drama blossoms with solid stories. Regardless of whether you're composing a misfortune, a parody or a play to change the world, an extraordinary storyline will keep your crowd tuning in.

In any case, don't make the story excessively convoluted with such a large number of topics, characters and plotlines, or the audience will get confounded.

These were absolutely acoustic exhibitions that passed on sensational stories and were communicated live or disseminated through sound media, like CDs and tape. With no visual components, radio dramatizations depended only on discourse, music, and audio effects to convey their accounts.

In "There’s a Man in the Habit of Hitting Me on the Head with an Umbrella," the tendency of the narrator to accept the absurd as ordinary is known as _____. Select all that apply. magical realism authorial reticence extended metaphor stream of consciousness

Answer:

The correct answers are "magical realism" and "authorial reticence".

Explanation:

Magical realism is a style of fiction writing that takes aspects of the everyday world and adds magical elements as if they were ordinary. The concept of authorial reticence is related to magical realism, as it refers to the lack of an opinion about the accuracy and credibility of events such as the magical elements in a story. Therefore, the narrator accepting absurds as ordinary in "There’s a Man in the Habit of Hitting Me on the Head with an Umbrella" is known as magical realism or authorial reticence.

Answer:

Magical Realism and Authorial Reticence

Explanation:

Odyssey mentions these two specifically in their lesson involving this story. It was correct on my test.

Todd has 3/4 of an apple left from breakfast. His sister ate 1/8 of what was left.How much of the apple is left?

Answer:

5/8

Step-by-step explanation:3/4=6/8 6/8-1/8=5/8

Answer:

5/8 apple

Step-by-step explanation:

To solve this problem subtract 1/8 from 3/4. Make both fractions have common denominators by multiplying 3/4 by 2/2.

  • 3/4 * 2/2 = 6/8

Subtract 1/8 from 6/8.

6/8 - 1/8 = 5/8

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