Raj made this argument:

The Triangle Inequality Theorem states that if the lengths of three sides of a triangle are a, b, and c, then a + b > c. For this reason, since a, b, and c are all positive numbers, the square of a + b must be greater than the square of c. However, for a right triangle, the Pythagorean Theorem states that if the lengths of the legs are a and b, and if the length of the hypotenuse is c, then a2 + b2 = c2, not a2 + b2 > c2. Therefore, since the Pythagorean Theorem is known to be correct, and since right triangles should adhere to the Triangle Inequality Theorem, the Triangle Inequality Theorem must be incorrect.

What is wrong with Raj’s argument?
A) The square of a + b is not equal to a2 + b2.
B) One cannot assume that a, b, and c are all positive numbers.
C) It’s not true that right triangles should adhere to the Triangle Inequality Theorem.
D) It’s not true that according to the Triangle Inequality Theorem, a + b > c.

Answer:

90

Step-by-step explanation:

:P

the answer to this question is 37

the answer is c

sorry if im wrong.

Answer:

Renewable electricity

Step-by-step explanation:

Renewable electricity is an option for everybody. Using a small solar panel device can create renewable electricity for your home. Renewable electricity is safer and cleaner.

The renewable source of energy is the generation of energy from naturally extracted resources. These sources are naturally replenishing due to excess consumption and overpopulation.

These renewable sources are virtually inexhaustible. The types of renewable energy sources are: biodiesel, wind, solar, hydropower, and many more.

Renewable electricity is the source of energy upon which the United States must focus its research and development efforts.

Renewable electricity is the most suitable option over which the research and development must focus for making it one of the main sources of energy for the country by the yer 2050.

This can be done by using solar panel devices at homes and factories so that they can generate their own electricity. This will help in saving the electricity supply from the poles.  

To know more about renewable energy, refer to the link:

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ANSWER 1 :

Sample Space ( S )= {B, W, R, G, P}     Option (ii)

Explanation:

There are five types of phone cases. Colors of the phone cases are Black, White, Red, Green, Pink.

One phone case is selecte as random, in this case we have 5 choices to select one phone case at a time.

So, Sample space is S = {B, W, R, G, P}     Option(ii)

Final answer.

Answer 2 :

Probability for student earn grade A = [tex] \frac{7}{12}  [/tex]

Explanation :

There are total 24 students in a class.

All student appeared in a test.

14 students are got grade A

and 10 students are got grade B.

One student choose at random whose grade is A.

Probability for selected grade A student  = (total students of grade A)/(Total number of student in a class)

Probability for selected grade A student  = [tex] \frac{14}{24}  [/tex]

Probability for selected grade A student  =[tex] \frac{7}{12}  [/tex]

Final answer.

It will take almost 2 hours to dig across the garden.

"It is the length of the boundary of the circle."

[tex]c = 2\times \pi \times r[/tex]

"It is the distance covered per unit times."

For given question,

A circular garden has a circumference of 44 yards.

⇒ C = 44

⇒ 2 × π × r = 44

⇒ 2 × r = 14.01 yards

We know, the diameter of the circle is d = 2 × r

This means, the diameter of the circular ground is 14.01 yards.

here, the rate (s) = 7 yards per hour

Using the formula of rate,

[tex]\Rightarrow s=\frac{d}{t}\\\\\Rightarrow 7=\frac{14.01}{t}\\\\ \Rightarrow t= 2.001\\\\ \Rightarrow t\approx 2~~hours[/tex]

Therefore, it will take him almost 2 hours to dig across the garden.

Learn more about the circumference of the circle:

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Answer:

60 feet

Step-by-step explanation:

Multiply the area by 2 to get 1200 feet. then, divide by 20 to get 60. The base of the a-frame is 60 feet.

The value of letter A on the box plot is given by A = 10

A box and whisker plot, often known as a box plot, shows a data set's five-number summary. The minimum, first quartile, median, third quartile, and maximum make up the five-number summary.

here, we have,

we know that,

A box is drawn from the first quartile to the third quartile in a box plot. At the median, a vertical line passes through the box.

It is used when showing the distribution of data points across a selected measure and if the box in a box plot is stretched in one direction or the other, then the data is skewed in that direction.

Given data ,

Let the box plot be represented as Z

Now , the values of the data from the box plot is given by

Z = { 10 , 12 , 15 , 21 , 24 , 30 }

The value of the letter A from the box plot is the first value

where A = 10

Therefore , the value of A is 10

Hence , the box plot is solved

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Answer: 14.6 feet

Step-by-step explanation:

Since, here a ladder which has the length 15 foot  and it is far from the base of the wall by 3.5 feet.

Here L represents the length of the ladder while d  represents the distance of the ladder from the base of the wall. ( shown in figure)

While h represents height that the ladder reaches up the wall.

Thus, L= 15 foot, d= 3.5 foot

Then on applying Pythagoras theorem,

[tex]L^2=d^2+h^2[/tex]

⇒[tex]15^2=3.5^2+h^2[/tex]

⇒[tex]225=12.25+h^2[/tex]

⇒[tex]h^2=21.75[/tex]

⇒[tex]h=14.5859521458[/tex]≈ 14.6 foot

Thus,height that the ladder reaches up the wall= 14.6 foot ( approx)

The square root of 62 lies between the consecutive whole numbers 7 and 8, because 7² is 49 and 8² is 64, and 62 is between these two square numbers.

The student is asking for two consecutive whole numbers between which the square root of 62 lies. First, identify the whole numbers whose square roots are immediately less than and greater than √62. Considering square numbers we know, 7² = 49 and 8² = 64. Since 49 < 62 < 64, the square root of 62 must be between 7 and 8. Therefore, the two consecutive whole numbers are 7 and 8, as √62 is greater than 7 but less than 8.

(0 = 0) is a true statement, it means that the system of equations has infinitely many solutions.

The correct option is (C).

To solve the system of equations using elimination, we'll manipulate one or both equations to eliminate one of the variables, either \(x\) or \(y\). Let's start by using elimination to eliminate \(x\).

Given the system of equations:

[tex]\[ \begin{cases} 3x + 4y = 5 \quad \quad \quad \quad \quad (1) \\21x + 28y = 35 \quad \quad \quad (2)\end{cases} \][/tex]

We can see that if we multiply equation (1) by 7, we can eliminate (x) when we add the equations together:

[tex]\[ 7(3x + 4y) = 7 \times 5 \][/tex]

[tex]\[ 21x + 28y = 35 \][/tex]

Now, we can rewrite equation (1) as:

[tex]\[ 21x + 28y = 35 \quad \quad \quad \quad \quad (3) \][/tex]

Now, we'll subtract equation (2) from equation (3):

[tex]\[ (21x + 28y) - (21x + 28y) = 35 - 35 \][/tex]

[ 0 = 0 ]

Since (0 = 0) is a true statement, it means that the system of equations has infinitely many solutions.

So, the correct answer is option C: Infinitely Many Solutions.

complete question given below:

Use elimination to solve the system of equations given by 3x + 4y = 5 and 21x + 28y = 35.

A. No Solution

B. (5/3, 0)

C. Infinitely Many Solutions

D. (0, 5/4)

Answer:

AC = 12 units.

Step-by-step explanation:

Given  : A triangle ABC with BD is the perpendicular bisector of AC.

To find :  What is the length of AC.

Solution : We have given triangle ABC with BD is the perpendicular bisector of AC.

Bisector : Which cut the line equally in to two part.

So , BD cut AC in  two  equal part AD = DC.

We can write

AC = AD + DC.

Plug the values DC = 6 , AD =DC = 6.

AC = 6 + 6

AC = 12 units.

Therefore , AC = 12 units.