Triangle A (1, 1), B (4, 4), C (6, 2) is a: Group of answer choicesIsosceles triangle Right triangle Acute triangle None of the other answers are correct Equilateral triangle

Answers

Answer 1

Answer:

Since [tex]AB \neq BC \neq AC[/tex] and [tex]\cos B = 0[/tex], we conclude that given triangle is a right-angled and scalene.

Step-by-step explanation:

First, we determine the lengths of sides [tex]AB[/tex], [tex]BC[/tex] and [tex]AC[/tex] by the Equation of the Line Segment, which is based on the Pythagorean Theorem:

Line segment AB

[tex]AB = \sqrt{(4-1)^{2}+ (4-1)^{2}}[/tex]

[tex]AB = 3\sqrt{2}[/tex]

Line segment BC

[tex]BC = \sqrt{(6-4)^{2}+(2-4)^{2}}[/tex]

[tex]BC = 2\sqrt{2}[/tex]

Line segment AC

[tex]AC = \sqrt{(6-1)^{2}+(2-1)^{2}}[/tex]

[tex]AC = \sqrt{26}[/tex]

And the angles are found by means of the Law of Cosine:, where acute angles exist when [tex]0 < \cos \theta < 1[/tex], whereas obtuse angles exist for [tex]-1 < \cos \theta < 0[/tex].

Angle A

[tex]BC^{2} = AB^{2} + AC^{2} - 2\cdot AB\cdot AC \cdot \cos A[/tex] (1)

[tex]\cos A = \frac{BC^{2}-AB^{2}-AC^{2}}{-2\cdot AB\cdot AC}[/tex]

[tex]\cos A = \frac{8-18-26}{-2\dot (3\sqrt{2})\cdot (\sqrt{26})}[/tex]

[tex]\cos A = 0.832[/tex]

Angle B

[tex]AC^{2} = AB^{2} + BC^{2} - 2\cdot AB\cdot BC\cdot \cos B[/tex] (2)

[tex]\cos B = \frac{AC^{2}-AB^{2}-BC^{2}}{-2\cdot AB\cdot BC}[/tex]

[tex]\cos B = \frac{26-18-8}{-2\cdot (3\sqrt{2})\cdot (2\sqrt{2})}[/tex]

[tex]\cos B = 0[/tex]

Angle C

[tex]AB^{2} = AC^{2}+BC^{2}-2\cdot AC\cdot BC\cdot \cos C[/tex] (3)

[tex]\cos C = \frac{AB^{2}-AC^{2}-BC^{2}}{-2\cdot AC\cdot BC}[/tex]

[tex]\cos C = \frac{18 -26-8}{-2\cdot (\sqrt{26})\cdot (2\sqrt{2})}[/tex]

[tex]\cos C = 0.555[/tex]

Since [tex]AB \neq BC \neq AC[/tex] and [tex]\cos B = 0[/tex], we conclude that given triangle is a right-angled and scalene.


Related Questions

You are a life saver if you help me figure out this problem step by step. I swear my math teacher is trying to make me fail:(

Answers

8.2 the anwser should be then divided by 1.8

make q the subject of 4p=5q-2​

Answers

Answer:

5q = 4p + 2

Step-by-step explanation:

4p = 5q - 2

4p + 2 = 5q - 2 + 2

5q = 4p + 2

A bowl has 2 blue candies and 3 red candies inside it.
The tree diagram shows that the first event tells us the probability of choosing each blue and red candy.
The second event describes the probability of choosing an additional blue and a red candy.
Find the value of x and y

Answers

Answer:

[tex]x = \frac{1}{4} [/tex]

[tex]y = \frac{2}{4} [/tex]

By what percent will the number changed if": it was doubled

Answers

Answer:

what number

Step-by-step explanation:

it took samatha 325 minutes to cook an 18 lb turkey.How many minutes per pound did it take to cook the turkey ?

Answers

Answer:

Below.

Step-by-step explanation:

325/18

= 18.055...   minutes

= 18 minutes to nearest minute.

Can someone help me with 17 20 and especially 21
Only reply if your seriously trying to help me it would be really appreciate

Answers

If I get to a house in a couple hours and then I’ll get a little more money I will let you know that I’m not going out of the house to go to the bank to pick it out or do you want me there or you could do that for you or not and then I will

find the measure of angle R

Answers

Answer:

R=(180-100)/2=40.

Step-by-step explanation:

Answer. Answer: (1) The measure of angle T is 100 degrees --> since no other angle can be equal to 100 degrees (because in this case the sum of the angles will be more than 180 degrees) then the other two angles, R and S, are equal: R=(180-100)/2=40.

PLSSS HELP ILL GIVE BRAINLIEST TO THE RIGHT ANSWER

Answers

Answer:

56

Step-by-step explanation:

The simplest way to do this is to divide 3 by 21 to get 7.  This means that it takes $7 to buy one T-shirt.  If you multiple 8 X 7, you get 56.  This mean that the correct answer is A. $56.00

Hope it helped and have a great day :)

what is this equation factored
49x²-1​

Answers

The answer should be (7x+1)(7x-1)

What is the length of side AB of the triangle?

3
5
Square root of 6
Square root of 13

Answers

Answer:

√13

Step-by-step explanation:

Distance formula

√(4-2)²+(5-2)² = 2²+3² = √4+9 = √13

2x – 5x + 16 = –3(x – 6)

Answers

Answer:

0=2

There are no solutions

Step-by-step explanation:

Answer:

2x – 5x + 16 = – 3(x – 6)

-3x + 16 = - 3x + 18

-3x + 3x + 16 = 18

16 = 18

Thus, This is a False Equation

-TheUnknownScientist


On Claudia's birthday, her parents open a savings account and deposit SS. They also deposit $50 each
year after that on her birthday. The account eams interest at an annual rate of 7% compounded annually
Caudia will make no withdrawals from the account for at least 15 years Complete the table to find how
much Caudla will have in her account at the end of the fifth year. Then compare this amount to the
$290.10 that would be in her account if she had received 5% interest.

Answers

Wacom down straight to logo and and make sure he don’t get up

Which equation represents the line with slope – 2 that
passes through the point (-4, -5)?

Answers

Answer:

D. y+5 = -2(x+4)

Step-by-step explanation:

[tex] \large \boxed{y - y_1 = m(x - x_1)}[/tex]

The equation above is point-slope form where x1 and y1 both are the point that the graph passes through ane m is slope as usual.

We are given the point (-4,-5) and slope of -2. We substitute these values in.

[tex] \large{y - ( - 5) = - 2(x - ( - 4))} \\ \large{y + 5 = - 2(x + 4)}[/tex]

Someone please help me I’ll give out brainliest please dont answer if you don’t know

Answers

Answer:

turtles are vulnerable. so A is your correct answer

Step-by-step explanation:

find the value of x
50 points for all 5 questions.

Answers

Step-by-step explanation:

we have

5x+4=2x+9

5x-2x=9+4

3x=13

x=13/3

Answer:

x = 13/3

Step-by-step explanation:

Now we have to,

→ find the required value of x.

Forming the equation,

→ 2x + 9 = 5x - 4

Then the value of x will be,

→ 2x + 9 = 5x - 4

→ 2x - 5x = -4 - 9

→ -3x = -13

→ x = (-13)/(-3)

→ [ x = 13/3 ]

Hence, the value of x is 13/3.

What is the total surface area of a dog food can which has a diameter of 5 inches and a height of 7
inches?

Answers

Answer:

35.................


What is the slope of AB?
Can anyone help me ??

Answers

Answer:

1/2

Step-by-step explanation:

Point A is (2, 3)

Point B is (6, 5)

To get the slope of a line, first select any two points on that line.

Then, take the difference of the y values, and divide it by the difference of the x values. This is also known as the change in y over the change in x, or rise over run.

[tex]\frac{3-5}{2-6} =\frac{-2}{-4} =\frac{1}{2}[/tex]

1/2 is the slope.

I NEED HELP BADLY PLEASE

Answers

Answer:

m(DE) = 90°

Step-by-step explanation:

Since both circles are equal, therefore, their radius would be equal too.

m<S = 180 - right angle (angles on a straight line)

m<S = 180 - 90 = 90°

m<R = m<S (congruent triangles)

m<R = 90°

m<R = m(DE) (central angle = intercepted arc based on the central angle theorem)

Substitute

90° = m(DE)

m(DE) = 90°

Find the value of y for the given value of x. y=x/3+5;x=6

Answers

Answer: Y= 7, X= 6

Step-by-step explanation:

10 POINTS!!!!!!! write an equation for a line that goes through the point (-3,-4) and has a slope on -2​

Answers

Thats Metal In Ya LungsThats Metal In Ya LungsThats Metal In Ya LungsThats Metal In Ya LungsThats Metal In Ya LungsThats Metal In Ya LungsThats Metal In Ya LungsThats Metal In Ya LungsThats Metal In Ya Lungs

Seventy-five percent, or 15, of the students in
Emily's homeroom class are going on a field trip. Two thirds, or 12, of the
students in Santiago's homeroom class are going on the field trip. Which
class has more students? Justify your answer.

Answers

The answer is in the file below





Bit.xly.com


Hopes this answers your question and helps you

Janice needs 3 gallons of lemonade for a party. She has 4 quarts, 6 pints, and 4 cups of lemonade already made. How many more cups does she need.

Answers


4 quarts is 1 gallon
6 pints is 0.75 gallons
4 cups is 0.25 gallons
if you add all of those you would get 2 gallons
so Janice would need 1 more gallon of lemonade

What is the volume of a rectangular prism with the length of 4.5 ft, the width of 3.5 ft, and the height of 5.5 ft?

Answers

Answer:

The volume would be 86.63 feet squared

Hope this helps!

Mark me brainliest if I'm right :)

. In Paige's class, 13 of the 20 students were born in Texas. Based in the
information, if there are
8010 students at the school, how many students could
be expected to have been
born in Texas?

A.600 students
B.480 students
C.520 students
D.560 students

Answers

Answer:

Road shimmer

Wiggling the vision

Heat heat waves

I'm swimming in a mirror

Road shimmer

Wiggling the vision

Heat heat waves

I'm swimming in a

Sometimes, all I think about is you

Late nights in the middle of June

Heat waves been faking me out

Can't make you happier now

Sometimes, all I think about is you

Late nights in the middle of June

Heat waves been faking me out

Can't make you happier now

Usually I put

Something on TV

So we never think

About you and me

But today I see

Our reflections

Clearly in Hollywood

Laying on the screen

You just need a better life than this

You need something I can never give

Fake water all across the road

It's gone now the night has come but

Sometimes, all I think about is you

Late nights in the middle of June

Heat waves been faking me out…

Answer:490

Step-by-step explanation:

A cylinder has a height of 7 yards and a radius of 14 yards. What is its volume? Use ​ ≈ 3.14 and round your answer to the nearest hundredth.

Answers

The answer to the nearest hundredth, the volume of the cylinder is approximately 4309.28 cubic yards.

To calculate the volume of a cylinder, we can use the formula V = πr²h, where V is the volume, r is the radius, and h is the height.

Radius (r) = 14 yards

Height (h) = 7 yards

Approximation of π = 3.14

Substituting these values into the formula, we have:

[tex]V = 3.14 \times(14^{2} )\times 7[/tex]

First, let's calculate the value of (14²):

[tex]14^{2} = 14 \times 14 = 196[/tex]

Now, substitute the values back into the formula:

[tex]V = 3.14 \times 196 \times 7[/tex]

Next, perform the calculations:

[tex]V = 3.14 \times 1372[/tex]

V ≈ 4309.28

For similar question on cylinder.

https://brainly.com/question/30858645  

#SPJ11

CHRIS
For the field trip this year, use the given information to determine the total
cost for each student and for all 30 students. Transportation costs have
already been paid.
For every 5 students, it would cost:
• $36.25 for admission to the museum, and
• $31.50 for lunch.
What is the total cost, in dollars, for admission and lunch for each student?
What is the total cost, in dollars, for admission and lunch for all 30 students?
1 Student: $
30 Students: $

Answers

Answer:

30 students: $346.5

1 student: $11.55

Step-by-step explanation:

It would cost a total of $57.75 every 5 student so just multiply by 6 to get your amount for 30 students. Then divide by 30 to get the amount per student.

The black trapezoid is a dilation of the green trapezoid. What is the scale factor of the dilation?

A) 1/5
B) 1/3
C) 3
D) 5

Answers

The dilation is by 1/5
Answer: Choice A)  1/5

============================================================

Explanation:

We're told that "The black trapezoid is a dilation of the green trapezoid". This means the black trapezoid is the image, while the green one is the preimage. In other words, the green is the "before" and the black is the "after". The mapping is [tex]\text{green} \to \text{black}[/tex] because of the ordering [tex]\text{preimage} \to \text{image}[/tex]

Since the green figure (preimage) is larger than the black figure (image), the scale factor must be some value k such that 0 < k < 1. That narrows the answer choices between A and B.

Focus on the green trapezoid. The bottom left corner is at (-10,0). The bottom right corner is at (5,0). The distance between these two points is 15 units.

Using the same idea, the distance along the bottom edge of the black trapezoid is 3 units. We can count out the spaces along the bottom, or we can note the two bottom corners are at (-2,0) and (1,0).

------------------------------

So far we found:

The bottom edge of the green trapezoid is 15 unitsThe bottom edge of the black trapezoid is 3 units

These two edges correspond to one another. We divide the values to get the scale factor. We divide the image length over its corresponding preimage length.

scale factor = (image length)/(preimage length)

scale factor = 3/15

scale factor = 1/5

3x + y = -4
3x - 4y = 6​

Answers

Answer:

(-1, -2) or x=-1 y=-2

Step-by-step explanation:

3x+y=-4      (1)

3x-4y=6      (2)

i used the first equation to subtract the second this cancels out the x

and you are left with:

5y=-10

y=-2

plug this back in:

2x+(-2)=-4

2x-2=-4

add 2 to both sides:

2x=-2

x=-1

Solve the system of equations below by graphing them with a pencil and
paper. Enter your answer as an ordered pair.
y=-x+1
y=-2x+ 5

Answers

The first one is

X-intercept: (1,0)
Y intercept: (0,1)

The second one is

X intercept: (5/2,0)
Y intercept: (0,5)

Explanation;

To find the x-intercept, substitute in 0 for Y and solve for X. To find the y-intercept, substitute 0 for X and solve for Y.

Hope this helps :)

Factor the expression completely.
15x2-5x - 10
15x2-5x - 10 =

Answers

Answer:

x=8

Step-by-step explanation:

30-5x-10

-5x+30-10

-5x+40

-5x= -40

divide both sides by -5

-5x/-5= -40/-5

x=8

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