Mathematics High School

HELP PLEASE
find the area of the polygon with the given vertices P(1,1), Q(-2,1), R(-1,-4)

Answers

Answer 1

Answer:

Area = 7.5

Step-by-step explanation:

Answer 2

The area of the triangle bounded by vertices P(1,1), Q(-2,1), and R(-1,-4) will be 7.5 unit square.

What is a triangle?

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

There are many types of triangles such that right-angle triangles, equilateral triangles, and much more.

Given the triangle with  vertices P(1,1), Q(-2,1), R(-1,-4)

Length between two coordinates (x₁,y₁) and (x₂,y₂) is given by

[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]

By using this formula

PQ = 3 , QR = 5.099 and PR = 5.385

Now,

The area of a triangle with  all three sides is given by

A = [tex]\sqrt{S(S - A)(S - B)(S - C)}[/tex] where A,B and c are sides and s = (A + B + C)/2

So,

S = (3 + 5.099 + 5.385)/2 = 6.742

Now,

A = [tex]\sqrt{6.742(6.742- 3)(6.742 - 5.099)(6.742 - 5.385)}[/tex]

A = 7.499 ≈ 7.5

Hence "The area of the triangle bounded by vertices P(1,1), Q(-2,1), and R(-1,-4) will be 7.5 unit square".

For more about triangles,

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Related Questions

Solve the equation for y.
10x -4y = -20

Answers

Answer:

y=5+5/2x

Step-by-step explanation:

Simplify (3x – 5) + (5x + 1).

Answers

Answer:

(-2x - 6)

Step-by-step explanation:

The given expression is ( 3x - 5 ) - ( 5x + 1 )

We have to simplify the given expression

First we will open the bracket having negative notation outside.

( 3x - 5 ) - 5x - 1

3x - 5 - 5x - 1

Now we will collect the similar terms together.

3x - 5x - 5 -1

-2x - 6

So the simplified form of the expression is (-2x - 6)

Answer:

8x - 4

Step-by-step explanation:

queifnsldnalbdejsjsbsjas

In the context of this graph, what do the slope and y-intercept mean?


Help me for a brainliest

Answers

We’re are the answer choices

brainliest if correct1+1​

Answers

Answer:

11

Step-by-step explanation:

:>

Answer:

1+1=2 is the answer

Step-by-step explanation:

mark me as brainlist

ahhahanvm? shushaha bruh what do i do

Answers

Uh I’m not even gonna question it but thanks for the free points ig? Lol

\u gotta ask ur question

Step-by-step explanation:

They will rest after they hike `2` miles. Then they will hike the remaining `1.75` miles to the lookout. The trail the hikers will use to return from the lookout is `0.5` miles shorter than the trail they will use to go to the lookout. Each hiker will bring `0.25` gallons of water for each mile to and from the lookout. What is the total amount of water each hiker will need to carry?

Answers

Answer:

1.75 gallons

Step-by-step explanation:

First, we need to calculate how far the hike is going up the trail. They first hike 2 miles and then another 1.75 miles after resting so...

2 + 1.75 = 3.75 miles

The trail is 3.75 miles long, the question states that the return path is 0.5 miles shorter, therefore...

3.75 - 0.5 = 3.25 miles

Leaving us with a total hiking distance of

3.75 + 3.25 = 7 miles.

Since each hiker will carry 0.25 gallons for each mile we simply need to multiply this amount by the total number of miles in the hike.

7 * 0.25 = 1.75 gallons

Finally, we can see that each hiker will carry a total of 1.75 gallons of water for the entire hike.

Use the sine rule to calculate BC :)

Answers

Answer:

BC≈12.2

Step-by-step explanation:

As we know

24/sin(100°)=BC/sin(30°)

BC=sin(30°)×24/sin(100°)

BC=1/2×24/sin(100°)

BC=12/sin(100°)

BC=12.2 (approximately)

Answer:

BC≈12.2

Step-by-step explanation:

Hope this helped have an amazing day!

Solve the equation

9x^2 - 64= 0

9x^2 + 64= 0

Answers

Answer:

x1= - 8/3 , x2= 8/3

Step-by-step explanation:

PLEASEE HELPP ASAPP!!

Solve: -35/-7

A: 7
B: -7
C: 42
D: -42

Answers

Answer:

D.

Step-by-step explanation:

You see, this is simple division. Let's divide it.

-35/-7 = -42

_____________________

Don't let the other options confuse you. negative dividing is just the same as regular, just negative ^^

What is the value of 7 in 46.897

Answers

Answer:

If your asking its place value its Thousandths

Step-by-step explanation:

.1 is tenths

.01 is hundredths

.001 is thousandths

5. The price of a new gym bag is $37.00 plus 8% sales tax. What is the sales tax on this gym
bag in dollars and cents?

Answers

Answer:

$25.00 which is $24.50

Step-by-step explanation:

Changes made to your input should not affect the solution:

(1): Dot was discarded near "x.s".

(2): "37." was replaced by "(37/1)".

Unauthorized use of the imaginary unit "i" or syntax error in complex arithmetic expression

I need some help with MORE math if you could answer that would be great.

Answers

Answer:

bbbbbb

Step-by-step explanation:

:)

Answer:

D. [tex]\frac{81}{m^{7}}[/tex]

Step-by-step explanation:

[tex](3m^{-4})^{3}(3m^{5})[/tex]

[tex]\frac{81m^{5}}{m^{12}}[/tex]

[tex]\frac{81}{m^{7}}[/tex]

i will mark you as brianilest The school band sold T-shirts to raise money for an upcoming trip. The band sold 400 T-shirts on Saturday and on Sunday, it will sell 30 percent of that amount. Which statements are true about the number of T-shirts that the band will sell on Sunday? check that all apply A. the answer will be less than 400 because 30 is less than 100 B. The answer will be greater than 400 because 300 percent is greater than 100 C. (100)(4)=400 so 30 (4) is the number of T-shirts the band will sell on Sunday. D. The band will sell 430 T-shirts on Sunday or E. The band will sell 120 T-shirts on Sunday.

Answers

Answer:

A and E

Step-by-step explanation:

A is correct because if you have less than 100 percent of something then the value will be less than the original value.

E is correct because 30 percent of 400 is 120 so the band will sell 120 t-shirts on Sunday.

Helpppppppppppppphxhxhxhxhx

Answers

Answer:

C  [tex]\frac{48}{70}[/tex]

Step-by-step explanation:

Option C - [tex]\frac{48}{70}[/tex] is incorrect because when multiplying the numerator and denominator of the fraction [tex]\frac{7}{10}[/tex] by 7, you’re suppose to get [tex]\frac{49}{70}[/tex].

What set of transformations could be applied to rectangle ABCD to create A'B'C'D'?

Answers

Answer: C :>

Step-by-step explanation:

Answer:

the answer is number 3

Betsy works from 6:00 AM to 12:00 PM, takes an unpaid lunch break from 12:00 PM to 1:00pm, then works from 1:00 PM to 3:30 PM. How many hours did Betsy work?

Answers

Answer:

9 hours and 30 mins

Step-by-step explanation:

Betsy works for about 9 hours 30 minutes daily.

What are mathematics operations?

A mathematical operation is a function that converts a set of zero or more input values (also called "b" or "arguments") into a defined output value. The number of operands determines the operation's arity. Most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive and multiplicative inverses.

• Zero-arity operations, or nullary operations, are constants, and mixed products are arity three operations, or ternary operations.

Calculating time of Betsy total work for getting paid :

Betsy Working from 6:00 AM to 12:00 PM =  6 hour

Betsy takes an unpaid lunch break from 12:00 PM to 1:00pm = 1 hour

Betsy Working from  1:00 PM to 3:30 PM =  2.5 hour

Now adding-up all the time = 6 + 1 +  2.5 hour = 9.5 hours or 9 hours 30 minutes.

Therefore,  Betsy works for about 9 hours 30 minutes daily.

Read more about mathematics operations at:

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Mrs. Rodriquez has 24 students in her class. Ten of the students are boys. Jeff claims that the ratio of boys to girls in this class must be 5:12. What is Jeff’s error and how can he correct it?

Answers

Answer:

See Below

Step-by-step explanation:

Total no of students = 24

No of boys = 10

So, no of girls = 24 - 10 = 14

Ratio of boys to girls = 10/14 = 5/7 = 5 : 7

So the ratio of boys to girls should be 5 : 7 and not 5 : 12

It is 49,280 yards from Topeka to Tonko. How many miles
is this?

Answers

Answer:

Step-by-step explanation:

1 yard = 0.000568 miles

49280 yards = 28 miles

1 mile = 1,760 yards

Divide total feet by 1760

49,280 / 1760 = 28 miles.

I need quick help pls!!!

Answers

Answer:

It's the second one. 2/3 and 2/6

PLS I NEED HELP ASAP

Answers

Answer:

Answer C

.....,.................

Can somebody plz answer this math problem correctly thanks!

WILL MARK BRAINLIEST :D

Answers

Answer:

Ellen and Blake answered 20 questions correctly since Ellen had 0.8 correct and that is 80% same with Blake

Stephen scored a .84 or an 84%

I hope this helps :)

Step-by-step explanation:

plz mark B R A I N L I E S T

Answer:

Stephen: 21

Ellen: 20

Blake: 20

Step-by-step explanation:

If youre looking for more in depth answers:

Stephen received a 21 / 25 (84%)

Ellen received a 20 / 25 (80%)

Black received a 20 / 25 (80%)

plzzz help me with this ​

Answers

Ok, to prove the two triangles, we need reasoning:

1) the side AC is common (as you can see, both triangles share the side AC)

2) angle DCA is equal to angle BAC (this is due to alternate angles)

3) angle BCA is equal to angle DA (again, this is due to alternate angles)

need a quick answer please

Answers

Answer:

5

Step-by-step explanation:

The answer would be 62 if it requires another 32 and explanation
Bababoey

Which expression is equivalent to (q^4)^-3/q^-15 for all values of q where the expression is defined?

Answers

Answer: (h)q^3

Step-by-step explanation:

2. Ashley had a summer lemonade stand where she sold small cups of lemonade for $1.25 and large
cups for $2.50. If Ashley sold a total of 155 cups of lemonade for $265, how many cups of each
type did she sell?

Answers

Answer:

[tex]\boxed {\boxed {\sf 98 \ Small \ Cups}}\\\\\boxed {\boxed {\sf 57 \ Large \ Cups}}[/tex]

Step-by-step explanation:

Let's make a system of equations.

First, define the variables.

Let s= small cups and g= large cups

Next, make 2 equations. 1 for the money and 1 for the number of cups.

Money

A small cup costs 1.25 and a large cup costs 2.50. The total money made is 265. 1.25s+2.50g=265

Number

A total of 155 cups of lemonade were sold. The sum of small cups and large cups sold will equal 155. s+g=155

Here is our system of equations:

[tex]1.25s+2.50g=265 \\s+g=155[/tex]

Now, solve. Let's isolate a variable in the 2nd equation, so we can plug it in after.

Subtract g from both sides of the equation. s+g=155 s+g-g=155-gs=155-g

Now we know that s is equal to 155-g. We can substitute (155-g) in for s in the first equation.

[tex]1.25s +2.50g=265[/tex]

[tex]1.25(155-g)+2.50g=265[/tex]

Distribute the 1.25

1.25(155-g)= (1.25*155)+ (1.25*-g)= 193.75-1.25g

[tex]193.75-1.25g+2.50g=265[/tex]

Work to isolate the variable. Subtract 193.75 from both sides of the equation and combine like terms on the left.

[tex]193.75-1.25g+2.50g=265-193.75[/tex]       (Subtract 193.75)

[tex]-1.25g+2.50g=265-193.75[/tex]      

[tex]1.25g=71.25[/tex]      (Combine like terms).

1.25 and g are being multiplied. The inverse of multiplication is division. Divide both sides by 1.25

[tex]1.25g/1.25=71.25/1.25\\g=71.25/1.25\\g=57[/tex]

Now we know that 57 large cups were sold. Plug 57 back into the original second equation to find the small cups.

[tex]s+g=155[/tex]

[tex]s+57=155[/tex]

Subtract 57 from both sides of the equation to isolate the variable, s.

[tex]s+57-57=155-57\\s=155-57\\s=98[/tex]

Ashley sold 57 large cups and 98 small cups.

small cup she sold = x = 98

large cup she sold = y =57

Solve each system to find the answer

Answers

Given:

The system of equations is

[tex]5g+4k=10[/tex]

[tex]-3g-5k=7[/tex]

To find:

The solution of given system of equations.

Solution:

We have,

[tex]5g+4k=10[/tex]        ...(i)

[tex]-3g-5k=7[/tex]         ..(ii)

Multiply (i) by 5 and (ii) by 4.

[tex]25g+20k=50[/tex]        ...(iii)

[tex]-12g-20k=28[/tex]         ..(iv)

Adding (iii) and (iv), we get

[tex]25g-12g=50+28[/tex]

[tex]13g=78[/tex]

Divide both sides by 13.

[tex]g=\dfrac{78}{13}[/tex]

[tex]g=6[/tex]

Put g=6 in (i).

[tex]5(6)+4k=10[/tex]

[tex]30+4k=10[/tex]

[tex]4k=10-30[/tex]

[tex]4k=-20[/tex]

Divide both sides by 4.

[tex]k=-5[/tex]

So, the solution of the system of equation is (6,-5).

Therefore, the correct option is A.

What is the discriminate?

Answers

so it’s basically asking for the difference

Been stuck on this for hours, it's the Law of Sines. 25 POINTS!!

Answers

Answer:

Step-by-step explanation:

(Sin27) / 11 = (sin x) / 15

cross multiply

15 sin27 = 11 sin x

keep in calculator as you divide 15sin27 by 11.

sin x = .6190779542

do sin ^ -1 (.6190779542) (It’s a key on the calculator.)

x = 38.25*

9514 1404 393

Answer:

  38.2°

Step-by-step explanation:

According to the equation you are give, ...

  sin(x)/15 = sin(27°)/11

Multiplying by 15 gives you ...

  sin(x) = 15·sin(27°)/11 ≈ 0.619078

The inverse sine function is used to find the angle x. It may show as sin⁻¹ on your calculator.

  x = arcsin(0.619078)

  x ≈ 38.2°

_____

Additional comment

x is shown in the figure as an acute angle, so that is the value we have chosen. The other angle that has sin(x) = 0.619078 is the supplement of this, or 141.8°. The two solutions are shown in the 2nd and 3rd attachments.

Help me please!!!!!!!

Answers

Answer:

yes

Step-by-step explanation:

that symbol means <= which means x is less than OR equal to  5/2

Ryan also earns money by selling colored watch bands with the watches he sells. The linear expression 100x – 50 models Ryan's additional income. What is the expression that models the new average profit, including the bands? Note: To obtain the new average profit expression, add the linear expression to the original rational expression. Write the new profit expression as one fraction.

Answers

Answer:

Average (additional) income = 100 - 50/x

Step-by-step explanation:

Ryan's additional income = 100x - 50 , where x = quantity of colored watch bands

Ryan's additional average income = Income / Quantity of watches sold

(100x - 50) / x

= 100 - 50/x

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