MATHEMATICS HIGH SCHOOL

Which classification best represents a triangle with side lengths 6 cm, 10 cm, and 12 cm?acute, because 62 + 102 < 122
acute, because 6 + 10 > 12
obtuse, because 62 + 102 < 122
obtuse, because 6 + 10 > 12

Answers

Answer 1
Answer:

The correctclassification for this triangle is:

obtuse, because 6² + 10² < 12²

Option C is the correct answer.

What is a triangle?

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

To determine the classification of a triangle based on its sidelengths, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, we have a triangle with side lengths of 6 cm, 10 cm, and 12 cm. Checking the sum of the lengths of each pair of sides, we have:

6 + 10 = 16 > 12

6 + 12 = 18 > 10

10 + 12 = 22 > 6

Since all three pairs satisfy the triangleinequalitytheorem, the given side lengths do form a valid triangle.

Next, we can use the lawofcosines to determine the measure of the largest angle in the triangle, which will allow us to classify it.

The lawofcosines states that, for a triangle with side lengths a, b, and c, and the angle opposite c denoted as C, we have:

c^2 = a^2 + b^2 - 2ab cos(C)

In this case, the sidelengths are a = 6 cm, b = 10 cm, and c = 12 cm. Substituting these values into the formula and solving for cos(C), we get:

cos(C) = (6² + 10² - 12²) / (2 x 6 x 10)

cos(C) = -1/5

Since the cosinefunction is negative for angles between 90 and 180 degrees, we know that angle C is obtuse.

Therefore,

The correctclassification for this triangle is:

obtuse, because 6² + 10² < 12²

Learn more about triangles here:

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Answer 2
Answer:

Answer:

C

Step-by-step explanation:

use Pythagorean theorem

a^(2) + b^(2) = c^(2)

c is the longest side

if a^(2) + b^(2) > c^(2) then it's acute (greater than)

if a^(2) + b^(2) < c^(2) then it's obtuse   (less than)

if they are equal, then its a right triangle

6^(2) + 10^(2) = 12^(2)

36 + 100 = 144

136 = 144

136 < 144   obtuse

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A circular track has a circumference of 1/4 mile. What is the radius?

Answers

The formula for circumference is C = 2 \pi r. We know the circumference and therefore we can plug that into the formula and solve for the radius.

(1)/(4) = 2 \pi r

Lets divide by 2 first.
(1)/(8)= \pi r

Next, lets divide by pi.
(1)/(8 \pi)= r
Thus the answer is (1)/(8 \pi) of a mile, which is approximately (1)/(25.13) of a mile.

Find the geometric mean of 125 and 5..

Answers

The geometric mean of two numbers is the square root of their product.
GM = √( 125 · 5 ) = √ 625 = 25
Answer:
The geometric mean of 125 and 5 is 25. 

Answer:

The geometric mean of 125 and 5 is, 25

Step-by-step explanation:

Geometric mean(GM) of two number is given by:

GM = √(ab)

As per the statement:

Given two numbers i.e 125 and 5

then by definition we have;

GM = √(125 \cdot 5)

⇒GM = √(625)

⇒GM = √((25)^2)

⇒GM = 25

Therefore, the geometric mean of 125 and 5 is, 25

Charlie solved an equation, as shown below:Step 1: 5x = 30
Step 2: x = 30 – 5
Step 3: x = 25

Part A: Is Charlie's solution correct or incorrect? If the solution is incorrect, explain why it is incorrect and show the correct steps to solve the equation. (6 points)

Part B: How many solutions will this equation have? (4 points)

Answers

Part A:  Charlie's answer is incorrect. Part B: There is only 1 solution for this equation.

What is a linear equation?

A linear equation is an equation that has the variable of the highest power of 1.

The standard form of a linear equation is of the form Ax + B = 0.

Charlie solved an equation;

Step 1: 5x = 30

Step 2: x = 30 – 5

Step 3: x = 25

Part A:  Charlie's answer is incorrect.

In step 2 of Charlie's answer he subtracted 5 from each side. Since 5x is multiplication so, he must divide each side by 5 to get x by itself.

Step 1:  5x = 30

Step 2:  x = 30/5

Step 3:  x = 6

Part B: There is only 1 solution for this equation.

Learn more about linear equations;

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Part A:  Charlie's answer is incorrect
In step 2 of Charlie's answer he subtracted 5 from each side.  Since 5x is multiplication, he must DIVIDE each side by 5 to get x by itself.  The problem should have worked out like this...

Step 1:  5x = 30
Step 2:  x = 30/5
Step 3:  x = 6

Part B:  There is only 1 solution for this problem.

Many of the constructions that the Greeks thought impossible were later proven impossible in the 18th and 19th centuries.A. True
B. False

Answers

Answer:

True

Step-by-step explanation:

Types of proof:

You can use contradiction Or You can use decent.

Types of Dis-Proof:

You can use a counterexample Or You can use logical contradiction.

Note To Moderators:

Please don't delete this answer because I want to help everyone that I can during school hours.

Answer: true

Step-by-step explanation:

I did the the test and. got it correct

What is the quotient written in scientific notation? 2x10^21 -------- 8x10^3 A)2.5x10^17 B)2.5x10^6 C)0.25x10^18 D)0.25x10^7

Answers

Have a good day :).......

Expand (2x-3y+3)^2

PLEASE HELP!!

Answers

Answer:

Step-by-step explanation:

(x+ y + z)² = x² +y² + z² + 2xy +2yz + 2zx

Here, x = 2x   ; y = -3y  & z = 3

(2x - 3y + 3)² = (2x)² + (-3y)² + 3² + 2(2x)(-3y) + 2(-3y)3 + 2*3*(2x)

                    = 4x² + 9y² + 9  - 12xy - 18y + 12x

Answer:

4x² + 9y² + 12x - 18y - 12xy + 9

Step-by-step explanation:

Given

(2x - 3y + 3)² = (2x - 3y + 3)(2x - 3y + 3)

Each term in the second factor is multiplied by each term in the first factor, that is

2x(2x - 3y + 3) - 3y(2x - 3y + 3) + 3(2x - 3y + 3)

Distribute the 3 parenthesis

= 4x² - 6xy + 6x - 6xy + 9y² - 9y + 6x - 9y + 9 ← collect like terms

= 4x² + 9y² + 12x - 18y - 12xy + 9
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