Triangle ABC has vertices at A(-4, -2), B(1, 7) and C(8, -2)

A) Determine the exact value of the area of Triangle ABC.

B) Determine the perimeter of Triangle ABC to the nearest tenth.

Triangle ABC Has Vertices At A(-4, -2), B(1, 7) And C(8, -2)A) Determine The Exact Value Of The Area

Answers

Answer 1

Answer:

a). Area = 54 square units

b). Perimeter = 33.7 units

Step-by-step explanation:

Vertices of the triangle ABC are A(-4, -2), B(1, 7) and C(8, -2).

(a). Area of the triangle ABC = [tex]\frac{1}{2}[x_{1}(y_{2}-y_{3})+x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2})][/tex] (Absolute value)

By substituting the values from the given vertices,

Area = [tex]\frac{1}{2}[(-4)(7+2)+(1)(-2+2)+8(-2-7)][/tex]

        = [tex]\frac{1}{2}[-36+0-72][/tex]

        = [tex]\frac{1}{2}(-108)[/tex]

        = (-54) unit²

Therefore, absolute value of the area = 54 square units

(b). Distance between two vertices (a, b) and (c, d)

        d = [tex]\sqrt{(a-c)^{2}+(b-d)^2}[/tex]

     AB = [tex]\sqrt{(-4-1)^{2}+(-2-7)^{2}}[/tex]

           = [tex]\sqrt{106}[/tex]

           = 10.295 units

     BC = [tex]\sqrt{(1-8)^2+(7+2)^2}[/tex]

           = [tex]\sqrt{130}[/tex]

           = 11.402 units

     AC = [tex]\sqrt{(-4-8)^2+(-2+2)^2}[/tex]

           = 12 units

     Perimeter of the triangle = AB + BC + AC = 10.295 + 11.402 + 12

                                                                          = 33.697

                                                                          ≈ 33.7 units


Related Questions

it’s multi choice please help me out thankyou so much

Answers

Answer:

Yes

Step-by-step explanation:

If you look at the angle they're the same which gives you one hint.  Then both side lengths are also equal making both triangles congruent.

This follows SAS( Side-Angle-Side)

Answer:

yes is the correct answer

Step-by-step explanation:

Martha has $10,000 saved and wants to attend a college with a current tuition of $10,000 a year. She will graduate from high school in five years. Roughly how much more will Martha need to save for one-year's tuition to account for an annual rate of inflation of 3%?

Answers

Answer:

$1,592.74

Martha will need to pay $1,592.74 more

Step-by-step explanation:

Using the compound interest/inflation formula;

A = P(1+r)^(t)

Where;

A = final value

P = initial value = $10,000

r = inflation rate = 3% = 0.03

t = time = 5 years

Substituting the values;

A = $10,000(1+0.03)^(5)

A = $11592.740743

A = $11,592.74

How much more will Martha need to save;

C = final value - initial value = A - P

C = $11,592.74 - $10,000

C = $1,592.74

Martha will need to pay $1,592.74 more

Answer:

1,590.00

Step-by-step explanation: I took the test

Please answer correctly !!!!!!!! Will mark brainliest !!!!!!!!!!!!

Answers

Answer:

1/5 = 0.2

Step-by-step explanation:

(0,3) and (5,4)

average rate of change is slope

formula for slope =  [tex]\frac{y2-y1}{x2-x1}[/tex]

so [tex]\frac{4-3}{5-0} = \frac{1}{5}[/tex]

Factorise polynomials 15^2p-7p

Answers

Answer:

p ( 15p - 7)

Step-by-step explanation:

15 p^2 - 7p

The only common term is p so factor out p

p ( 15p - 7)

____________________________

15p^2-7p

take the common,

Ans: p(15p-7)

hope it helps

Good luck on your assignment

__________________________

Can the side lengths of 8, 9, and 12 form a triangle?
Yes
No




Please help help help :(

Answers

the answer is no:))))))))

Yes, with sides 8,9 and 12 triangles can be formed.

What is the triangle?

Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees.

From the triangle property, the sum of the two sides of the triangle should be greater than the third side.

From the given data the sum of the two sides is greater than the third side.

8 + 9 > 12

17 > 12

Hence, with sides 8,9 and 12 triangles can be formed.

To know more about triangles follow

https://brainly.com/question/17335144

#SPJ2

Find the value of (3 + 4)²·

Answers

Answer:

( 3 +4)² = 7² = 49

Hope this helps.

Answer:

49

Step-by-step explanation:

Follow the PEMDAS rule.

P- Parenthesis

E- Exponents

M- Multiplication

D- Division

A-Addition

S-Subtraction

Following this rule, you would add 3+4, which gets you 7.

Then, you would multiply 7 by 7, as that is what the exponent, two suggests

7x7 = 49.

thus,

(3 + 4)² = 49

Clara goes mini golfing. She pays $7.50 for an admission ticket and $6.25 for each round she golfs. The total amount Clara pays for admission and the number of rounds she golfs is $26.25. Which equation can be used to determine the number of rounds, x, that Clara golfs?

6.25x + 7.50 = 26.25

6.25x - 7.50 = 26.25

7.50x + 6.25 = 26.25

7.50x - 6.25 = 26.25

Answers

Answer:

6.25x + 7.50 = 26.25

Step-by-step explanation:

Given that

The admission fee is = $7.50

Each round costs = $6.25

Total money Clara paid = $26.25

The computation of equation can be used to determine the number of rounds, x, that Clara golfs is shown below:-

we assume the number of rounds = x

Here, We can denote this equation in the following form

[tex]6.25x+7.50=26.25[/tex]

Therefore with the help of above equation we can now find out the x value

[tex]6.25x=26.25-7.50[/tex]

[tex]=> 6.25x=18.75[/tex]

[tex]=> x = 3[/tex]

So, Clara played 3 rounds of golf.

Determine the length of MN to the nearest tenth of a centimetre.





Select one or more:
a. 3.0 cm
b. 4.0 cm
c. 2.8 cm
d. 2.1 cm

Answers

Answer:

  b.  4.0 cm

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that the ratio of the adjacent side to the hypotenuse is given by the cosine of the angle:

  Cos = Adjacent/Hypotenuse

  cos(35°) = NL/NK

  NL = NK·cos(35°)

__

Similarly, it reminds you that the ratio of the opposite side to the hypotenuse is given by the sine function:

  Sin = Opposite/Hypotenuse

  sin(53°) = NM/NL

  NM = NL·sin(53°)

Substituting from the first triangle, we have ...

  NM = NK·cos(35°)·sin(53°)

  NM = (6.1 cm)(0.81915)(0.79864)

  NM ≈ 3.991 cm

  MN ≈ 4.0 cm

-In the term, 3x^5 , the number 5 is called ?

Answers

Answer:

Step-by-step explanation:

power i guess

Answer:

Exponent, Power or Indices

Step-by-step explanation:

The number is called Exponent, Power or Indices

Please answer ASAP !!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!

Answers

16 is the correct answer

Paul needs to find 310% of 72%. which expression should he use?

Answers

Answer:

2.232, or 223.2%

Step-by-step explanation:

(3.1)(0.72)

Answer:

B

Step-by-step explanation:

i took the test and got it right

PLSS HELP ME THXS YOUUUUU!!!!!

Answers

Answer: Point A

Air pressure is essentially the weight of the air pressing down; it's greatest when there's the most air above, so at the lowest point, which is point A, elevation 1000 feet.

what is the slope line of m (0,6),(3,0)

Answers

Answer:

slope= y²-y¹

x²-x¹

0-6

3-0

-6

3

= -2

Multiple choice easy question! Please help!!!! Question in photo.

Answers

Answer:

B. -5.5 + (-8.3)

Step-by-step explanation:

The plus sign is basically just saying to add the two negatives just like how you would have added the negatives without the sign.

ANSWER B. -5.5 + (-8.3)

An isosceles triangle in which the two equal sides, labeled a, are longer than the base, labeled b.
This isosceles triangle has two sides of equal length, a, that are longer than the length of the base, b. The perimeter of the triangle is 15.7 centimeters. The equation 2a + b = 15.7 models this information.

If one of the longer sides is 6.3 centimeters, which equation can be used to find the length of the base?

Answers

The side labeled "a" is made the longer side. These are the two congruent sides. So a > b.

We are told that the longer side is 6.3, so a = 6.3, meaning that

2a+b = 15.7

2(6.3)+b = 15.7

12.6+b = 15.7

b = 15.7-12.6

b = 3.1

The triangle has sides of: 6.3, 6.3, 3.1

The perimeter is 6.3+6.3+3.1 = 15.7

Going back to the question "which equation can be used to find the length of the base?", it sounds like either you were given a list of multiple choice answers, or you just fill in the blank. If multiple choice, then try to see which answer matches with what I wrote above. If fill in the blank, then I would just enter either 2(6.3)+b = 15.7 or 12.6+b = 15.7

Answer:

2(6.3)+b = 15.7 or 12.6+b = 15.7

Step-by-step explanation:

A prism has a trapezoid as its base whose area is 140 square centimeters. A cylinder with the same height has a radius of 6 centimeters. How much larger, to the nearest cubic centimeter, is the volume of the prism than the volume of the cylinder?

Answers

Answer:

difference in volume = 26.96h cm³

Step-by-step explanation:

The volume of a prism is the product of the base area and the height. A trapezoid prism has a trapezium as the base shape. Therefore,

volume of a trapezoid prism = area of a trapezium × height

area of the base(trapezoid) = 140 cm²

Volume = 140h

Volume of a cylinder = πr²h

where

r = radius

h = height

volume = πr²h

volume = π × 6² × h

volume = 3.14 × 36 × h

volume = 113.04h

To know how much larger the volume of the prism is than the volume of the cylinder we have to take the difference of the volume.

Recall the height are the same

difference in volume = 140h - 113.04h

difference in volume = 26.96h cm³

Help!
Suppose that a biologist is watching a trail known for wildebeest migration. During the first minute, 24 wildebeests migrated past the biologist on the trail. Each minute, the number of wildebeests per minute increased by 3.

How many wildebeests migrated past the biologist during the first 20 minutes?

Enter your answer in the box.

Answers

Step-by-step explanation:

first minute = 24 wildebeest

by 20 min = (20 × 3) + 24 = 84 wildebeest

URGENT!!! JUST NEED THESE 3!!! WILL GIVE BRANLIEST!!!
1. What is the measure of angle x? IMAGE 1 TO THE RIGHT SIDE IT IS 23 DEGREE AND TO THE LEFT IT IS 10 DEGREE
A) 100°
B) 147°
C) 60°
D) 33°
2. What is the measure of angle EGH? IMAGE 2
A) 102°
B) 38°
C) 78°
D) 26°
3. Find the value of x. IMAGE 3
A) 9.14
B) 15.2
C) 5.58
D) 10

Answers

Answer:

B.

A.

D.

Step-by-step explanation:

1.) Do 10 + 23 + x = 180. x = 147 Triangles add to 180, remember this or fail

2.) Do 64 + 38 + x = 180 to find the missing ∠G. G = 78

Now, a line is equal to 180 degrees. Remember this or you will fail. Do 180 - 78 to get your missing angle. 102 degrees

3.) Adjacent angles add up to equal 180, this is a very simple geometry concept. Remember it. 5x + 3 + 12x + 12 = 180

17x + 15 = 180

Subtract 15 from both sides to get 17x = 165

Divide both sides by 17 to get your x value of about 10

Directions: Find the value of x.

Answers

Answer:

x=14

Step-by-step explanation:

We know JNK+KNI must equal 180 because it is half of a circle.

31+9x+23=180

9x=126

x=14

If PQRS is a rhombus, which statements must be true? Check all that apply.

Answers

Answer:

Options (B), (C) and (F) are correct.

Step-by-step explanation:

Properties of a rhombus,

1). All sides of a rhombus are equal in measure.

2). Both the diagonals of a rhombus are the perpendicular.

3). Diagonals bisect the vertex angles.

By these properties of a rhombus,

Option (B): PR is perpendicular to QS.

Option (C): ∠QPR ≅ ∠SPR

Option (F): PQ ≅ QR

Therefore, options (B), (C) and (F) are correct.

Answer:

B, C, F, and E are all correct.

Step-by-step explanation:

Please help me with my question!!

Answers

We know that the area of each tile is 3 1/2in^2

All we need to do is divide.

210 / 3.5 = 60

So, she will need 60 tiles to cover the entire bathroom floor.

Best of Luck!

Find the third side in simplest radical form

Answers

Answer: 8[tex]\sqrt{2}[/tex]

Step-by-step explanation:

8^2 + 8^2 = c^2

64 + 64 = c^2

128=c^2

[tex]\sqrt{128}[/tex]  

[tex]\sqrt{4 * 32}[/tex]  

2[tex]\sqrt{4 * 8 }[/tex]

2* 2 [tex]\sqrt{4 * 2}[/tex]

4 * 2[tex]\sqrt{2}[/tex]

8 [tex]\sqrt{2}[/tex]

Find the slope of the line will make brainiest
y= -3x +1


Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Answers

Answer:

-3

Step-by-step explanation:

if ay=bx+c , then the slope is b/a

I have 1*y=-3*x+1, the slope is -3/1=-3

Or

the slope is y2-y1/x2-x1

if x1=1 ,y1= -3*1+1=-3+1=-2

  x2=2, y2=-3*2+1=-6+1=-5

the slope is (y2-y1)/(x2-x1)=(-5+2)/1=-3


Which is not a characteristic of the linear parent function?
A. It goes through the origin.
B. The domain is all real numbers.
C. It has a slope of 1.
D. The range is positive real numbers (y > 0).​

Answers

Answer: D

Step-by-step explanation:

Can someone please help me with my homework.

Answers

Answer:

Step-by-step explanation:

a = 22 cm

b = 12 cm

h = 8 cm

[tex]Area=\frac{(a+b)*h}{2}\\\\=\frac{(22+12)*8}{2}\\\\=\frac{34*8}{2}\\\\=34*4[/tex]

= 136 cm²

Here is a pattern made from sticks:
a) How many sticks would be in pattern number 6?
Answer: 32
b) How many sticks would be in pattern n?
Answer: ____

Answers

The answer is 5n+2.

Example:
6x5= 30
30+2=32

 Recursive formula of an arithmetic sequence is given by the expression,

                          [tex]T_n=a+(n-1)d[/tex]

                 Where, [tex]T_n=[/tex] nth term

                              [tex]a=[/tex] First term of the sequence

                              [tex]n=[/tex] Number of term

                              [tex]d=[/tex] Common difference

Therefore, number of sticks in the 6th pattern are 32.

                   And number of sticks in the nth pattern are [tex]T_n=5n+2[/tex]

From the picture attached,

Number of sticks in 1st pattern = 7

Number of sticks in 2nd pattern = 12

Number of sticks in 3rd pattern = 17

Sequence formed is 7, 12, 17..... nth term

This sequence has a common difference of 5 in each successive term so it will be an arithmetic sequence.

Therefore, nth term of the sequence will be,

       [tex]T_n=a+(n-1)d[/tex]

       [tex]T_n=7+(n-1)5[/tex]

       [tex]T_n=5n+2[/tex]

If [tex]n=6,[/tex]

       [tex]T_n=7+(6-1)5[/tex]

       [tex]T_n=7+25[/tex]

       [tex]T_n=32[/tex]

Learn more,

https://brainly.com/question/1606280

Ky buys three tshirts originally priced at 49.96the stores discount applys 7.1 tax

Answers

Answer:

42

Step-by-step explanation:

49-7=42

f(x) = 20(1.5)x. Let your dependent variable in the function be y. Write the function that models the independent variable in terms of y, using logarithms.

Answers

Answer:

[tex]x=log_{1.5}(\frac{y}{20})[/tex]

Step-by-step explanation:

Considering the function:

[tex]f(x) = 20\, (1.5)^x[/tex]

The independent variable is "x" and we are asked to model it in terms of the variable "y":

[tex]f(x) = 20\, (1.5)^x\\y=20\, (1.5)^x[/tex]

Then, in order to solve for x (which resides in the exponent), we need to use the logarithm function.

Since the base of the exponent is 1.5, we need to use the logarithm base 1.5, to lower that exponent "x":

[tex]y=20\, (1.5)^x\\\frac{y}{20} =(1.5)^x\\log_{1.5}(\frac{y}{20}) =x\\x=log_{1.5}(\frac{y}{20})[/tex]

Which of the following choices will simplify (8 − 5)2 + + 4

Answers

Answer:

10

Step-by-step explanation:

(8-5)2 + 4, let's start with the first step, the parentheses.

(8-5)=3 , then we multiply by 2, so (3)*2 which equals 6. 6+4=10!

Hope this helps! :)

Answer: the answer is 19

Step-by-step explanation:

i just got this question and got it right!

which graph represents a quadratic function with a vertex at (0,0)

Answers

Answer:

parabola On a coordinate plane, a parabola opens up. It goes through (negative 5, 6), has a vertex of (0, 0), and goes through (5, 6). On a coordinate plane, a parabola opens up.

Step-by-step explanation:

Answer: C) the third graph

Step-by-step explanation: i got 100% on my quiz, hope this helps!!

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