A city planner is mapping out some new features for a triangular park. She sketches the park on grid paper. The coordinates of the vertices of the park are (1, 1), (1, 4), and (−3, 4).   The city planner wants to put a flower bed at the centroid of the park. What are the coordinates of the flower bed? (__,__)​

Answers

Answer 1

Answer:

The coordinates of the flower bed are ([tex]-\frac{1}{3}[/tex] , 3)

Step-by-step explanation:

To find the centroid of a triangle, use this rule centroid = ([tex]\frac{x1+x2+x3}{3},\frac{y1+y2+y3}{3}[/tex]), where (x1, y1), (x2, y2), (x3, y3) are the vertices of the triangle

∵ The vertices of the triangle are (1, 1), (1, 4), (-3, 4)

∴ x1 = 1 and y1 = 1

∴ x2 = 1 and y2 = 4

∴ x3 = -3 and y3 = 4

→ Substitute them in the rule above

∵ Centroid = ([tex]\frac{1+1+-3}{3},\frac{1+4+4}{3}[/tex])

∴ Centroid = ([tex]\frac{-1}{3},\frac{9}{3}[/tex])

∴ Centroid = ([tex]-\frac{1}{3}[/tex] , 3)

The coordinates of the flower bed are ([tex]-\frac{1}{3}[/tex] , 3)


Related Questions

Determine the equation of the line given by the graph

A) y-3x+2
B) y=3x-2
C) y=1/3x+2
D) y=1/3-2

Answers

Answer:

y=3x-2

Step-by-step explanation:

Helppp ahhhhhhhh. Plzzzz

Answers

Answer:

15-67X/30X

Step-by-step explanation:

PLEASE HELP!!!!

Which expression is a simplified form of
[tex]3x^{2} - 4x + 5 - x^{2} + 2x - 1[/tex]
[tex]a) \: 2x^{4} - 2x^{2} + 4 \\ b) \: 2x^{4} + 6x^{2} + 4 \\ c) \: 2x^{2} - 2x + 4 \: \: \\ d) \: 4x^{2} - 2x + 4 \: \: [/tex]​

Answers

Answer:  c) 2x² - 2x + 4

Step-by-step explanation:

help plsssssssss. cm.

Answers

It is -2.1 cm

Hope this helps

Does the graph represent a function?

Answers

Step-by-step explanation:

yes dear. .............

the graph does not represent a function because it does not pass the vertical line test

Pweas help....10 points and brainiest and thznks<3

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
A pair of parallel lines are cut by a transversal as shown in the figure. Identify the types of angles created by the transversal.

corresponding angles

vertical angles

alternate interior angles

alternate exterior angles

adjacent angles




angles F and H

angles D and H


angles E and H


angles B and H

Answers

Answer:

F&H are vertical angles, D&H are corresponding angles, E&H are adjacent angles, and B&H are alternate interior angles.

Step-by-step explanation:

Hope this helps. Tell me if you need and explanation.

Answer: F&H are vertical angles, D&H are corresponding angles, E&H are adjacent angles, and B&H are alternate interior angles.

Step-by-step explanation:

Hope this helps. Tell me if you need and explanation.

Solve linear equations

Solve for x

3х – 10 = 16

Answers

Answer:

x=26/3

Step-by-step explanation:

3x-10=16

add 10 to both sides

3x=16+10

simplify

3x=26

divide both sides by 3

x=26/3

Solve for m.
94 = 31 + 7m


Answers

Answer:

M = 9

Step-by-step explanation:

94 = 31 + 7m

63 = 7m

9 = m

Hope this helps. Pls give brainliest.

What is this answer?

Answers

Answer:

X intercepts (-30,0)

Y intercepts (0,-3)

.6(2k - 3) = 3(4k + 5)
Hellppp pleaseee

Answers

Answer:

Step-by-step explanation:

.6(2k-3)=3(4k+5) foil

1.2K-1.8=12k+15 subtract 1.5k from both sides

-1.8=10.8k+15 subtract 15 from both sides

-16.8=10.8k divide by 10.8

k= -1.5

Write an equation in slope-intercept form for the line that passes through the given point and is parallel to the graph of the given equation. (4,-3); y=-5x+8

Answers

Answer:

Step-by-step explanation:

The slope of the line is m = -5

4 is your x1

-3 is your y1

Plug into the equation y - y1 = m(x - x1)

y + 3 = -5(x - 4)

y + 3 = -5x + 20

   -3             -3

y = -5x + 17

Create an equivalent expression without parentheses

-2(3x+4)

Answers

Answer:

-6x - 8

Step-by-step explanation:

-2(3x+4) = -6x - 8

this means the -6x - 8 is equivalent

From 83 hours to 76 hours? And is it a increase or decrease?

Answers

Answer:

decrease

Step-by-step explanation:

Answer:

decrease

Step-by-step explanation:

hi! im quite confused on this. can someone please help me? ill give brainiest if youre correct :)

Answers

Answer:

I believe the answer is D

Step-by-step explanation:

after 3 hours it traveled 120 miles so divide that by the 3 hours and it gives you 40 miles per hour giving you the slope and the y int would be negative 300 because he started 300 miles aways from Denver

Answer:

The answer seems to be D

Step-by-step explanation:

I cannot really confirm but I am most certain it is D.

why wont anybody help me i posted like 5 questons but heres the question :(

Answers

Answer:

i got you fam

Step-by-step explanation:

its b fam because the top x value goes by 1 then 2 and the y value goes from 2 to 4  

To pass a quiz, students need a score of at least 32 points out of a total of 40 points. At least what percent do the students need to pass the quiz

Answers

Answer:

80%

Step-by-step explanation:

Hope this helps :)


rosa and her friends are eating out for dinner. the bill was $30.12. they want to leave a 19% tip.
what is her total cost?

Answers

Answer:

35.84

Step-by-step explanation:

You would take 19% of 30.12$ by doing 30.12x0.19 to get 5.72.

you then add 5.72 to 30.12 to get your total of 35.84$

Determine whether the sets are equal, equivalent, both, or neither.

{apple, orange, pear} and {pear, apple, orange}

A.Neither


B.Equal


C.Both


D.Equivalent

Answers

B equal because they have a match

Jaxon must sell at least 49 rolls of wrapping paper to support the robotics club fundraiser. He has already sold 24 rolls of wrapping paper. Which inequality best represents the number of rolls of wrapping paper Jaxon still needs to sell

Answers

Answer:

x≥25

Step-by-step explanation:

Step one:

given data

Jaxon must sell at least 49 rolls of wrapping paper to support the robotics club fundraiser

We are told that he has already sold 24 rolls of wrapping paper.

Step two:

let x be the number of rolls remaining to be sold,

hence,

x≥49-24

x≥25

Therefore the inequality for the situation is  x≥25

which reads that x must be greater than or equal to 25

I’ll give Brainliest✨

Solve for w

3 - 2w + 4w = 7?

Answers

Answer:

=2

Step-by-step explanation:

Answer:

w= 2

Step-by-step explanation:

3-2w+4w=7. We move all terms to the left: 3-2w+4w-(7)=0,  Then we add all the numbers together, and all the variables: 2w-4=0. After, we move all terms containing w to the left, all other terms to the right: 2w=4, w=4/2

w=2

Find the distance between the points (7,5) and (7,-3)

Answers

Answer:

its eight on the y axis

Step-by-step explanation:

PLEASE HELP ASAP!!!!

Answers

Answer:

The correct Option is Option A

Account B because the principal of Account B is $300 and the principal for Account A is $150

Step-by-step explanation:

Interest earned from Account A = $ 4.50

Interest earned from Account B = $22.50

Time t = 18 months

Interest rate for Account A = 2%

Interest rate for Account B = 5%

We need to find which account has greater principal

The formula used to calculate principal is: [tex]Interest=Principal\times r \times t[/tex]

where r is rate and t is time

Finding Principal for Account A:

Interest earned from Account A = $ 4.50

Time t = 18 months = 1.5 years

Interest rate for Account A = 2% = 0.02

Putting values and finding Principal

[tex]Interest=Principal\times r \times t\\4.50=Principal\times0.02\times1.5\\Principal=\frac{4.50}{0.02\times1.5} \\Principal=\frac{4.50}{0.03} \\Principal=150[/tex]

So, The Principal Amount for Account A = $150

Finding Principal for Account B:

Interest earned from Account B = $ 22.50

Time t = 18 months = 1.5 years

Interest rate for Account A = 5% = 0.05

Putting values and finding Principal

[tex]Interest=Principal\times r \times t\\22.50=Principal\times0.05\times1.5\\Principal=\frac{22.50}{0.05\times1.5} \\Principal=\frac{22.50}{0.075} \\Principal=300[/tex]

So, The Principal Amount for Account B = $300

So, the correct Option is Option A

Account B because the principal of Account B is $300 and the principal for Account A is $150

Plz help me I need help

Answers

I'm not too sure but I think it's option

1. No, because only one angle of the triangle is congruent.

Is the equation y=0.07 + 348 proportional or not

Answers

Answer:

no

Step-by-step explanation:

it does not have any (0,0) value

helllllllllllllllllllllpppppppppppp meeeeeeeeeeeeee

Answers

Answer: I think the answer is x = 4

Step-by-step explanation: 28 = 7x

                                           /7       /7

                                             4   =  x

Write an explicit formula that represents the sequence defined by the following recursive formula



HELP IM TIMED

Answers

Answer:

The explicit formula is a[tex]_{n}[/tex] = 5 - 6n

Step-by-step explanation:

The explicit formula of the arithmetic sequence of the recursive formula

a[tex]_{1}[/tex] = first term; a[tex]_{n}[/tex] = a[tex]_{n-1}[/tex] + d is a[tex]_{n}[/tex] = a + (n - 1)d, where

a is the first termd is the common difference between each two consecutive termsn is the position of the number

∵ The recursive formula is a[tex]_{1}[/tex] = -1 and a[tex]_{n}[/tex] = a[tex]_{n-1}[/tex] - 6

→ Compare it with the formula above

a = -1 ⇒ 1st term

d = -6 ⇒ common difference

→ Substitute them in the form of the explicit formula

∵ a[tex]_{n}[/tex]  = -1 + (n - 1)(-6)

∴ a[tex]_{n}[/tex] = -1 + (-6)(n) - (-6)(1)

∴ a[tex]_{n}[/tex]  = -1 + -6n - (-6)

∴ a[tex]_{n}[/tex] = -1 - 6n + 6

→ Add the like term

a[tex]_{n}[/tex] = 5 - 6n

The explicit formula is a[tex]_{n}[/tex] = 5 - 6n

Tyler has $4.50 in a bank in his bedroom. Each day he adds $1.50 to it. Which equation can be used to find out how many days it will take for Tyler to save $30.00?

a
4.5 + 1.5x = 30.00
b
(4.5 + 1.5)x = 30.00
c
30.00 + 4.5 = 1.5x
d
4.5 × 1.5 × x = 30.00

Answers

Answer:

A

Step-by-step explanation:

2x - 4(x + 1) = 3x
2x - 4x – 4 = 3x
-2x - 4 = 3x
? = ?

Answers

Answer:

-2x-3x=4

-5x=4

x= -4/5

Step-by-step explanation:

Expand and simplify
(x - 5)(x - 2)

Answers

Answer:

=[tex]x^{2}[/tex]−7x+10

Find the measure of the angle indicated and show work please help I need this soon

Answers

The answer is 120 degrees I hope this helps
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