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:

C

Step-by-step explanation:

use Pythagorean theorem

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

c is the longest side

if [tex]a^{2}[/tex] + [tex]b^{2}[/tex] > [tex]c^{2}[/tex] then it's acute (greater than)

if [tex]a^{2}[/tex] + [tex]b^{2}[/tex] < [tex]c^{2}[/tex] then it's obtuse   (less than)

if they are equal, then its a right triangle

[tex]6^{2}[/tex] + [tex]10^{2}[/tex] = [tex]12^{2}[/tex]

36 + 100 = 144

136 = 144

136 < 144   obtuse

Answer 2

The correct classification 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 side lengths, 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 triangle inequality theorem, the given side lengths do form a valid triangle.

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

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

[tex]c^2 = a^2 + b^2 - 2ab cos(C)[/tex]

In this case, the side lengths 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 cosine function is negative for angles between 90 and 180 degrees, we know that angle C is obtuse.

Therefore,

The correct classification for this triangle is:

obtuse, because 6² + 10² < 12²

Learn more about triangles here:

https://brainly.com/question/25950519

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Related Questions

An angle in standard position measures 5п 8 radians. In which quadrant does the terminal side of this angle lie? O Quadrant I II Quadrant Quadrant IIT Quadrant IV​

Answers

Answer:

I've attached a picture of a unit circle with the quadrant labeled.

Calculate the degree of 5п 8 radians:

[tex]\frac{5\pi }{8} =\frac{5*180}{8} =\frac{900}{8} =112.5[/tex]

Locate the general location of 112.5° on the unit circle:

It's between 120°([tex]\frac{2\pi }{3}[/tex]) and 90°([tex]\frac{\pi }{2}[/tex]).

Find the quadrant it lies in:

Quadrant II

Region A has a total of 81,218,576 acres. Estimate the number of acres owned by the government in Region A. Choose the correct estimate below.

Answers

Answer:

See Explanation

Step-by-step explanation:

Given

[tex]Region\ A = 81218576[/tex]

Required

The acres owned by the government

The question is incomplete as the proportion (p) owned by the government is not given.

However, the formula to use is as follows:

[tex]Govt = p * Region\ A[/tex]

Assume the proportion is 28%, the equation becomes

[tex]Govt = 28\% * 81218576[/tex]

[tex]Govt = 22741201.28[/tex]

The acres owned by the government will be 22741201.28

In the graph increasing, decreasing, or constant?

Answers

The graph is increasing

Answer:

Step-by-step explanation:

slope>0 so graph is increasing.

Determine the length of AC.

32 units
35.2 units
38.5 units
10.3 units

Answers

Answer:

38.5

Step-by-step explanation:

b^2= 29^2+20^2-2×20×29× Cos 102

b^2=841+400-1160 (-0.2079)

=1241- 241.164

b^2=1482.164

b= square root of 1482.164

AC = 38.5

Using the number line below, draw a box and whisker plot for the following data: 12,18,18,20,22,22,25,26,30,30,32,32,35,35,38,49,42

Answers

Answer:

Step-by-step explanation:

Population size: 17

Median: 30

Minimum: 12

Maximum: 49

First quartile: 21

Third quartile: 35

Interquartile Range: 14

Outliers: none

Helpppp someone please

Answers

Given:

The graph of system of inequalities.

To find:

The system of inequalities.

Solution:

From the given graph it is clear that the shaded region is lies below the line y=10 and the boundary line y=10 is a solid line. So, the sign of inequality must be [tex]\leq[/tex].

[tex]y\leq 10[/tex].

The shaded region lies on the right side of the y-axis. So, [tex]x\geq 0[/tex].

Another boundary line passes through the point (0,1) and (1,2). So, the equation of the line is:

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

[tex]y-1=\dfrac{2-1}{1-0}(x-0)[/tex]

[tex]y=1(x)+1[/tex]

[tex]y=x+1[/tex]

The boundary line [tex]y=x+1[/tex] is a dotted line and the shaded region lies above the boundary line, so the sign of inequality must be [tex]>[/tex].

[tex]y> x+1[/tex]

So, the required system of inequalities is:

[tex]y> x+1[/tex]

[tex]y\leq 10[/tex]

[tex]x\geq 0[/tex]

Therefore, the correct option is B.

What is the value of the expression below
(-64)^2/3

Answers

Answer:

16

Step-by-step explanation:

[tex](-64)^2/3[/tex]

64 = [tex]2^{6}[/tex]

[tex]2^{6} ^{\frac{1}{3} } ^{2}[/tex]

[tex]2^{ 2^{2} }[/tex]

[tex]2^{4}[/tex]

16

translate the sentence into an equation

three more than the quotient of a number and 2 is 9

Answers

Answer:

Well the correct answer is 9=2+(x/3) or

(3/x)+2=9

Expand the following using the Binomial Theorem and Pascal’s triangle (2x − 3y)^4

Answers

Answer:

Step-by-step explanation:

Binomial Expansion:

[tex](2x-3y)^4 \\\\= 4C_0(2x)^4 (-3y)^0 + 4C_1(2x)^3 (-3y)^1 + 4C_2(2x)^2(-3y)^2 \\\\+ 4C_3(2x)^1 (-3y)^3 + 4C_4(2x)^0 (-3y)^4\\\\=16x^4 + 4(8x^3)(-3y) + 6(4x^2)(9y^2) + 4(2x)(-27y^3) + 81y^4\\\\=16x^4 - 96x^3y + 216x^2y^2-216xy^3 +81y^4[/tex]

Pascal's Triangle:

  Zero row                        1

 First row                  1                 1

 Second row          1           2             1

 Third  row         1         3              3          1

 Fourth row    1       4            6           4          1

Solve the given differential equation by finding, as in Example 4 from Section 2.4, an appropriate integrating factor. y(6x y 6) dx (6x 2y) dy

Answers

Answer:

[tex]\mathbf{6xe^xy+y^2e^x = C}[/tex] which implies that C is the integrating factor

Step-by-step explanation:

The correct format for the equation given is:

[tex]y(6x+y +6)dx +(6x +2y)dy=0[/tex]

By the application of the general differential equation:

⇒ Mdx + Ndy = 0

where:

M = 6xy+y²+6y

[tex]\dfrac{\partial M}{\partial y}= 6x+2y+6[/tex]

and

N = 6x +2y

[tex]\dfrac{\partial N}{\partial x}= 6[/tex]

[tex]f(x) = \dfrac{1}{N}\Big(\dfrac{\partial M}{\partial y}- \dfrac{\partial N}{\partial x} \Big)[/tex]

[tex]f(x) = \dfrac{1}{6x+2y}(6x+2y+6-6)[/tex]

[tex]f(x) = \dfrac{1}{6x+2y}(6x+2y)[/tex]

f(x) = 1

Now, the integrating factor can be computed as:

[tex]\implies e^{\int fxdx}[/tex]

[tex]\implies e^{\int (1)dx}[/tex]

the integrating factor = [tex]e^x[/tex]

From the given equation:

[tex]y(6x+y +6)dx +(6x +2y)dy=0[/tex]

Let us multiply the above given equation by the integrating factor:

i.e.

[tex](6xy+y^2 +6y)dx +(6x +2y)dy=0[/tex]

[tex](6xe^xy+y^2 +6e^xy)dx +(6xe^x +2e^xy)dy=0[/tex]

[tex]6xe^xydx+6e^xydx+y^2e^xdx +6xe^xdy +2ye^xdy=0[/tex]

By rearrangement:

[tex]6xe^xydx+6e^xydx+6xe^xdy +y^2e^xdx +2ye^xdy=0[/tex]

Let assume that:

[tex]6xe^xydx+6e^xydx+6xe^xdy = d(6xe^xy)[/tex]

and:

[tex]y^2e^xdx +e^x2ydy=d(y^2e^x)[/tex]

Then:

[tex]d(6xe^xy)+d(y^2e^x) = 0[/tex]

[tex]6d (xe^xy) + d(y^2e^x) = 0[/tex]

By integration:

[tex]\mathbf{6xe^xy+y^2e^x = C}[/tex] which implies that C is the integrating factor

3( − 3) − 5 >− 3 − 6
(show your work)

Answers

Answer:

x > 3

Step-by-step explanation:

3x-9-5x > -3x - 6

3x-5x+3x > -6+9

x > 3

A savings account for a car is set up with an initial balance of $3000, and 125 is added every
month (no other transactions occur on the account).
1. Write the expression:
2. Write the equation equal to the $5,000 car goal:
3. M=
4. How long will it take:

Answers

Answer:

1) 3000 + 125m

2) 3000 + 125m = 5000

3) M= 16

4) It would take 16 months

Step-by-step explanation:

Okay so no since there are no other transaction and you already have a balance of 3000 with a monthly Fee of 125 the equation shpuld be like this.

So every month you add 125,we dont know how much months we have to pay so we can use the variable given to us in this case “M”. So your base expression should look like this,

3000 + 125m (3000 base fee that doesnt change, and 125 every month fee)

Then it asked us to put it as the final balance as 5000, so using the base expression we can do this

3000 + 125m = 5000

Now to solve it you would solve it like any other equation

5000-3000=2000

2000=125m

2000/125= 16

Okay so m = 16

M in this case stands for months so the final answer would be it would take 16 months to reach the final balance of 5000

Shirley buys fiction books for $20 each, and then marks up by 25% to
resell. What is the markup in dollars?

Answers

Answer:

$5

Step-by-step explanation:

Find the markup by finding 25% of 20:

20(0.25)

= 5

So, the markup is $5

a. 32
b. 44
c. 22
d. 8

Answers

Answer:

sorry I don't know

Step-by-step explanation:

.........

Determine whether each sequence is arithmetic or geometric. Sequence 1: –10, 20, –40, 80, ... Sequence 2: 15, –5, –25, –45, ...
A. Sequence 1 is arithmetic and Sequence 2 is geometric.
B. Both sequences are geometric.
C. Sequence 2 is arithmetic and Sequence 1 is geometric.
D. Both sequences are arithmetic.
sequence 2 may be arithmetic because -20 but I can't find out what sequence 1 is

Answers

Answer:

Step-by-step explanation:

C-10,20,-40,80,...[tex] u_{n+1}=(-2)*u_{n}[/tex]. is geometric1

What is the quotient of 23 and 56?

Answers

Answer:

0.410714

Step-by-step explanation:

Dividend ÷ Divisor = Quotient

Is the function g(x)= –5x+4 linear or nonlinear

Answers

linear, since the variable isnt to a power (squared or cubed or anything), its highest power is 1, which makes the function linear

Help
Find the volume of this cone.
Use 3 for TT.

Answers

Answer:

[tex]180ft^{3}[/tex]

Step-by-step explanation:

Volume of a cone:

[tex]V=\pi r^{2} \frac{h}{3}[/tex]

Take [tex]\pi[/tex] as 3, as mentioned in the question

'r' is 'radius' ⇒ {diameter is given so divide by 2: 12/2 = 6}

'h' is 'height'

[tex]V=(3)(6)^{2} (\frac{5}{3} )[/tex]

[tex]V=(3)(36)(\frac{5}{3} )[/tex]

[tex]V=108(\frac{5}{3} )[/tex]

{multiply 108 with 5 and then divide the answer by 3}

[tex]V=108[/tex] × [tex]5[/tex]

[tex]V=540[/tex]

[tex]V=540/3[/tex]

[tex]V=180ft^{3}[/tex]

it is 180ft3 definitely do that one

Find the total number of outcomes in each experiment. Write your answers on a sheet of paper.

1. tossing a coin
2. tossing 3 coins
3. rolling a die 10 times
4. rolling two dices
5. pressing a number key on a calculator
6. picking a card from a regular deck of cards
7. choosing a letter from the English alphabet
8. choosing a letter from the word OUTCOME
9. choosing a letter from the word PREDICTION
10. picking a crayon from a box with 36 crayons of different colors

Answers

Answer:

Step-by-step explanation:

In each option you need to find the number of outcomes of a single event and then multiply that by the number of times that event takes place.

1. 2 outcomes (heads and tails)

2. 6 outcomes (2 outcomes * 3 tosses)

3. 60 outcomes (6 outcomes per die * 10 rolls)

4. 12 outcomes (6 outcomes per die * 2 rolls)

5. 10 outcomes (10 numbers on the pad)

6. 52 outcomes (52 cards in a regular deck)

7. 32 outcomes (32 letters in the alphabet)

8. 7 outcomes (7 letters to choose from)

9. 10 outcomes (10 letters to choose from)

10. 36 outcomes (36 crayons to choose from)

alguien que me ayude porfavor !!!!!

Answers

Es 10 miles per minute

The graph of g(x) = |x - h1 + k is shown on the
coordinate grid. What must be true about the signs of h
and k?

Answers

Answer:

Step-by-step explanation:

D.The sign of h must be negative and the signal of k must be positive *it’s for sure the answer.

Answer:

D.The sign of h must be negative and the signal of k must be positive EDGE 2021

I really need some help with this question also.

A) 2/5

B) 3/5

C) 11/25

D) 14/25

Answers

the answer to this problem is B 3/5

find missing side of triangle, help!

Answers

Answer:

2√10 km

Step-by-step explanation:

By Pythagoras theorem,

x^2 + 9^2 = 11^2

x^2 + 81 = 121

x^2 = 121 - 81

x^2 = 40

= 4 x 10

x^2 = 2^2 x 10

x = 2√10 km

help please (ignore my answer i just put whatever)

Answers

Answer:the awnser would b 2

Step-by-step explanation: it’s telling you if you look at the triangle from ABC it’s 54 degrees, but if you look at it from BAC it’s 30 degrees so you can only draw 2 triangles because no other combination is given the only other information we know is the line connecting A and B is 5 in some length which is a line not a triangle it would be a triangle thou if lines BC and AC were given. Long story short it’s B) 2

I need help ASAP !!!!

Answers

The last option because the range is the input values

please help asap
Find the volume of this cone.
Use 3 for TT.
5in
V =

Answers

Answer:

V=πr2h /3

V=πr2h /3=π·2.52·8 /3≈52.35988

so the volume is 52.36 inches

Using the formula for the area of a triangle, , write an expression for the area of ΔABC. Base your answer on the work you did in parts G through I. Show your work.

Answers

Answer:

[tex]Area = \frac{1}{2} * AC * D[/tex]

Step-by-step explanation:

From the complete question, we have:

Length D to be perpendicular to side AC

So, the area of the triangle is:

[tex]Area = \frac{1}{2} * Base * Height[/tex]

Since:

Length D is perpendicular to side AC

Then:

[tex]Base = AC[/tex]

[tex]Heigjt =D[/tex]

So:

[tex]Area = \frac{1}{2} * AC * D[/tex]

i'm kinda confused in this question, please help me.

Answers

Answer:

there you go

Step-by-step explanation:

angle DOB is 60 degree.

Answer:

see explanation

Step-by-step explanation:

Given ∠ DOC = 90° then

∠ DOB = 90 - p and

Since AOB is a straight angle , then

4p + 90 - p = 180

3p + 90 = 180 ( subtract 90 from both sides )

3p = 90 ( divide both sides by 3 )

p = 30

4p = 4 × 30 = 120

Then

∠ DOB = 180° - 4p = 180° - 120° = 60°

P(x) is a polynomial. here are a few values of p(x).
P(-5) = - 2
P(-3) = 6
P(3) = 7
P(5) = -1
What is the remainder when P(x) is divided by (x+5)?
What is the remainder when P(x) is divided by (x-3)?

Answers

Given:

Values of a polynomial P(x).

[tex]P(-5)=-2[/tex]

[tex]P(-3)=6[/tex]

[tex]P(3)=7[/tex]

[tex]P(5)=-1[/tex]

To find:

The remainder when P(x) is divided by (x+5).

The remainder when P(x) is divided by (x-3).

Solution:

If a polynomial P(x) is divided by (x-a), then the remainder is P(a).

If the polynomial P(x) is divided by (x+5), then the remainder is P(-5).

[tex]P(-5)=-2[/tex]

Therefore, the remainder is -2 when P(x) is divided by (x+5).

If the polynomial P(x) is divided by (x-3), then the remainder is P(3).

[tex]P(3)=7[/tex]

Therefore, the remainder is 7 when P(x) is divided by (x-3).

Determine the area of the triangle.
90.6 square units
50.1 square units
94.2 square units
106.0 square units

Answers

Answer:

94.2 square units.

I got 94.09 but that seems to be the closer answer.

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