On a coordinate plane, parallelogram R S T U has points (negative 4, 4), (2, 6), (6, 2), and (0, 0). What is the area of parallelogram RSTU? 24 square units 26 square units 32 square units 38 square units

Answers

Answer 1

Answer:

The area of the parallelogram is;

32 square units

Step-by-step explanation:

The given parameters are;

The coordinates of the parallelogram RSTU = R(-4, 4), S(2, 6), T(6, 2), and U(0, 0)

We note that the area of a parallelogram = Base length × Height

From the drawing of the parallelogram RSTU, we have;

The base length = The length of [tex]\overline {TU}[/tex] = The length of [tex]\overline {SR}[/tex] = √((2 - (-4))² + (6 - 4)²) = 2·√10

The height of a parallelogram is perpendicular to its base length = The line [tex]\overline {VT}[/tex]

∴ Where, the slope of the base length = m, the slope of the height = -1/m

The slope, 'm' of [tex]\overline {SR}[/tex] = (6 - 4)/(2 - (-4)) = 1/3

Therefore, the slope of the height = -1/(1/3) = -3

We note that a point on the height is the point 'T', therefore, the equation of the line in point and slope form is therefore;

y - 0 = -3·(x - 0)

∴ y = -3·x

Therefore, the coordinates of the point 'V' is given by the simultaneous solution of the equations of [tex]\overline {SR}[/tex] and [tex]\overline {VT}[/tex]

The equation of the line [tex]\overline {SR}[/tex] in point and slope form from the point 'R' and the slope 'm = 1/3' is given as follows;

y - 4 = (1/3) × (x - (-4)) = (1/3) × (x + 4)

y = x/3 + 4/3 + 4 = x/3 + 16/3

y = x/3 + 16/3

We then have the coordinate at the point 'V' (x, y) is given as follows;

-3·x = x/3 + 16/3

-9·x = x + 16

-10·x = 16

x = -16/10 = -1.6

x = -1.6

∴ y = -3·x = -3 × -1.6 = -4.8

y = 4.8

The coordinate at the point, V = (-1.6, 4.8)

The length of the line [tex]\overline {VT}[/tex] = The height of the parallelogram = √((-1.6 - 0)² + (4.8 - 0)²) = 8/5·√10

The height of the parallelogram = 8/5·√10

The area of the parallelogram, A = Base length × Height

∴ A = 2·√(10) × 8/5·√(10) = (16/5) × 10 = 32

The area of the parallelogram, A =  32 square units.

On A Coordinate Plane, Parallelogram R S T U Has Points (negative 4, 4), (2, 6), (6, 2), And (0, 0).
Answer 2

Answer:

Im pretty sure its 32

Step-by-step explanation:


Related Questions

What is the solution to the equation 4+5 -3- +5?
X=-1, x = 11
X=-1
0.x = 11
no solution

Answers

The answer is 0.x=11

Answer:

Its C, trust me I'm an almost 20 year old still in high school. Failed Junior year twice. :)

Step-by-step explanation:

EDGE 2019

Find the Highest Common Factor of : 27, 36, and 54.​

Answers

Answer: 9

Step-by-step explanation:

The factors of 27 are: 1, 3, 9, 27

The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36

The factors of 54 are: 1, 2, 3, 6, 9, 18, 27, 54

Then the greatest common factor is 9.

Hope this helped ! :)

Im sped Help MEEEEE PLEASEEE

Answers

Answer:

2x^4

-x^3 + 3x^2 + 2x + 4

5x^2 + 5x + 5

-3x + 10

22

Step-by-step explanation:

find the highest exponent of each polynomials:

22=> 0 degree

-3x(equals to -3x^1) + 10=> 1st degree

5x^2 + 5x + 5=> 2nd degree

-x^3 + 3x^2 + 2x + 4=> 3rd degree

2x^4=> 4th degree

easy algebra question below first correct answer gets brainliest

Answers

Answer:

10

Step-by-step explanation:

We solve using Pythagoras Theorem. Pythagoras Theorem is used to solve for the missing side of a right angled triangle.

The formula for Pythagoras Theorem =

c² = a² + b²

c = √a² + b²

Where c is the longest side

From the above diagram, we are looking for c

c = ?

a = 6

b = 8

Hence,

c = √6² + 8²

c = √36 + 64

c = √100

c = 10

Therefore, side c = 10

8.5b−3.4*(13a−3.2b)+a
i need help ASAP

Answers

Answer:

19.38b - 43.2a

Step-by-step explanation:

Simplify :

8.5b−3.4*(13a−3.2b)+a

Open the bracket :

8.5b - 44.2a + 10.88b + a

Collect like terms :

8.5b + 10.88b - 44.2a + a

19.38b - 43.2a

Peter is driving from Pensacola to Jacksonville

Answers

Answer:   Peter had the fastest interval at D.

Step-by-step explanation:

Peter traveled roughly 180 miles in 3 hours for point D, thus making him the fastest.

Peter had the fastest interval at D.

What is speed ?

Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude.

From Point A to Point B Peter traveled roughly 30 miles in 30 minutes.

From Point B to Point C Peter traveled roughly 130 miles in 2 hours and 30 minutes.

From Point C he didn't move in distance but the hours moved so c is out.

From Point C to Point D, Peter traveled roughly 180 miles in 3 hours.

Therefore D Peter had the fastest interval at D.

To learn more about the speed here:

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Hence, make a conjecture regarding the line joining the midpoints of two sides of any triangle:​

Answers

Answer:

Plzzzz answer fast.....

Hey! Could someone explain to me how to find the perimeter of this figure? It would be greatly appreciated!

Answers

Answer:

3/2 pi + 12

Step-by-step explanation:

In this figure, we have 4 sides and one curve. The total length of the four sides is 3 x 4 = 12. To find out the length of the curve, we need to find the angle of the top figure. Since it is next to a square, that means the angle that is farthest from the curve is 90 degrees.

The formula for finding an angle of a curve is n/360 x 2 pi x radius, where n is the angle.

The radius of the arc is 3, because at the bottom we see the width of the figure is 3.

Substituting our known values, we have 1/4 x 2 x pi x 3 = 6 x 1/4 x pi = 3/2 x pi.

Therefore, our answer is 3/2 pi + 12

Help please I will give brainlist!

Answers

Answer:

2    4/6     8/12

3  2/4      5/10

4    8/10     40/50

Step-by-step explanation:

a bag contains 33 red blocks, 46 green blocks, 22 yellow blocks, and 24 purple blocks. You pick one block from the bag at random. Find the indicated theoretical probability. P(purple or yellow) WILL CHOOSE BRAINLIEST!!!

Answers

Answer:

purple bc there are more purple in the bag then yellow. I'm pretty sure this is right

Find the point-slope equation for
the line that passes through the
points (1, -9) and (-10, 101). Use
the first point in your equation.

Answers

Answer:

y - (-9) = -10 (x - 1)

Step-by-step explanation:

y = mx + b

m (slope) = (y'-y) / (x'-x) = (101 - (-9)) / (-10) - 1) = 110/(-11) = -10

pass (1 , -9)

m = (y - (-9)) / (x - 1) = -10

y - (-9) = -10 (x - 1)

Find the dimensions of the rectangle that has the given area. area=15 square meters (2x-1m) (x+3m)

Answers

Answer:

it is 90

Step-by-step explanation:

Answer:

x=2

Step-by-step explanation:

2*2-1m=3m

2+3m=5m

3m*5m=15m

Ignore the m it represents the meters

Photo shows how to get x=2

what is 5^2 simplified

Answers

Answer:

25

Step-by-step explanation:

which property is demonstrated?

Answers

Answer:

Associative Property

Explanation:

Associative property is when you add and group numbers in any combination.

Ms. Hill goes to a burger place in California and orders 5 hamburgers and 3 fries and 6 hamburgers and 2 fries. What could she do to make her order simpler?

Answers

she can order 11 burgers and 5 orders of fries

Expand. Your answer should be a polynomial in standard form. (x - 3)(x - 4) = Stuck? Watch a video or use a hint.​

Answers

Answer:

x^2 -7x + 12

Step-by-step explanation:

(x-3) (x-4)

Expand

x^2 -3x - 4x + 12

Simplify

x^2 -7x + 12

Hope that helps!

Answer:

x²-7x+12

Step-by-step explanation:

When doing these types of problems, you have to multiply each term with each other.

Lets take a look at this.

We have to multiply each term with each other, so x times x =x²

x times -3=-3x

x times -4=-4x

-3 times -4=12

now we add them all up to get

x²-7x+12

10 people take 8 days to build a wall.
How long will it take 4 people to do the same job?

Answers

Answer:

20 days

Step-by-step explanation:

10 to get to 4 needs to be divided by 2.5 so we do the opposite to the other side since with fewer people it would take longer. (2.5 times longer).

10/2.5 = 4

8x2.5 = 20 days

A maple tree is 16 yards tall and its shadow is 12 yards long. A nearby observation tower is 12 yards tall. How long is the observation tower's shadow? Write your answer as a whole number or a decimal. Do not round.

Answers

Answer: 9 yards

Step-by-step explanation:

Given

The maple tree is 16 yards tall and its shadow is 12 yards tall

Suppose the angle made by the maple tree is x

[tex]\Rightarrow \cos x=\dfrac{12}{16}[/tex]

For the tower also, the angle made by the tower and its shadow is x

Suppose the length of the shadow is y

[tex]\Rightarrow \cos x=\dfrac{y}{12}[/tex]

Substitute the value of [tex]\cos x[/tex]

[tex]\Rightarrow \dfrac{y}{12}=\dfrac{12}{16}\\\\\Rightarrow y=9\ \text{yards}[/tex]

Dos libras de carne de res y dos de chivo cuestan $334 pesos, si duplico la libra de carne de res y una libra de chivo cuestan $420 pesos. ¿Cuál es el precio por libra de cada producto?

Answers

Answer:

El precio por libra de la carne de res es $84.33 y el precio por libra de chivo es $82.67.

Step-by-step explanation:

Con la información proporcionada puedes escribir las siguientes ecuaciones:

2x+2y=334 (1)

4x+y=420 (2), donde:

x es el precio por libra de carne de res

y es el precio por libra de chivo

Primero, puedes despejar x en (1):

2x=334-2y

x=334/2-2y/2

x=167-y (3)

Ahora, debes reemplazar (3) en (2) y despejar y:

4(167-y)+y=420

668-4y+y=420

668-3y=420

668-420=3y

248=3y

y=248/3

y=82.67

Finalmente, puedes reemplazar el valor de y en (3) para encontrar el valor de x:

x=167-y

x=167-82.67

x=84.33

De acuerdo a esto, la respuesta es que el precio por libra de la carne de res es $84.33 y el precio por libra de chivo es $82.67.

Help me please!!!!!!!!!!!!!!!!

Answers

Answer:

x = 4

Step-by-step explanation:

By intersecting chords theorem:

[tex]8(4x + 2) = 9(4x) \\ \\ 32x + 16 = 36x \\ \\ 32x - 36x = - 16 \\ \\ - 4x = - 16 \\ \\ x = \frac{ - 16}{ - 4} \\ \\ x = 4[/tex]

Find the value of y that makes 120y a perfect square​

Answers

Step-by-step explanation:

y = 30

120y = 120×30 = 3600

√3600 = 60

The value of y is 60 which makes 120y a perfect square.

What is a perfect square?

A perfect square is a number that represents the square of a natural number.

For example 9,16,36,64,121 etc

Here given that we have to calculate the value of y for which 120y will be a perfect square.

so 120y = n² where n is the natural number

For calculating the value of y first factorize 120

120= 2*2*2*3*5

= 2² * 2*3*5

=4 *30

from the above, it is clear that 120 can be written as 4*30 where 4 is a perfect square but 30 is not a perfect square.

So if we multiply 30 by 120 then the product has 2²*30² which will be a perfect square.

Therefore the value of y is 30 for which 120*30=n² where n=60.

Learn more about perfect square

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how is 14 - (-2) = 16?

I just need someone to explain how this works lol ty

Answers

Answer:

because

Step-by-step explanation:

when you make 16-2 it equals= 14

The polygons are similar. Find the value of X.

Answers

Answer:

the polygon on the right side is doubled the size of the one on the left, therefore x=11

Can someone please help me with this question

Answers

Answer:

70° angle because it's not an obtuse angle so it wouldn't be C, D, or E and 25° is to small so the answer is B

Answer:

70 degrees

Step-by-step explanation:

90 degrees is a right angle, which is just straight up, and has a. square symbol. So, we can use that to compare the answers. Anything over 90 degrees would have its angle tilt to the left. So, anything over 90, like the ones at 100 degrees are wrong. 20 would be really close to the bottom. So, its 70

Thomas is buying football jerseys for his high school football team. The cost of each jersey is $80. The company also charges a processing fee of $100. Write a function that represents Thomas' total cost, P(x), for purchasing x number of jerseys. What is Thomas' total cost, if he buys 55 jerseys?

Answers

Answer:P(c) =80x+100

First of all why is thomas buying 55 jerseys and the total is $4500

Step-by-step explanation:

(2) Parv has a $50 gift card. He uses the gift card to buy a pack of games
for $9.99. He also wants to buy some movies (n). Each movie costs
$3.99. Which inequality describes how many movies Parv can buy?

Answers

Answer:

$50 - $9.99 = $40.01

$40.01 ÷ $3.99 = 10

so the answer is 10

Step-by-step explanation:

if thats not whats being asked sorry

Inequality shows a relationship between two numbers or two expressions.

The inequality describes the number of movies Parv can buy.

9.99 + 3.99x ≤ 50

Where x is the number of movies.

The number of movies Parv can buy is 10.

What is inequality?

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal= ≥

We have,

Gift card = $50

Cost of a pack of games = $9.99

Cost of each movie = $3.99

x = number of movies

The inequality describes the number of movies Parv can buy.

9.99 + 3.99x ≤ 50

Where x is the number of movies.

Solve for x.

9.99 + 3.99x ≤ 50

Subtract 9.99 on both sides.

3.99x ≤ 50 - 9.99

3.99x ≤ 40.01

Divide both sides by 3.99

x ≤ 40.01/3.99

x ≤ 10

This means the number of movies Parv can buy is 10.

We can cross-check.

9.99 + 3.99 x 10 ≤ 50

9.99 + 39.9 ≤ 50

49.89 ≤ 50

Thus,

The number of movies Parv can buy is 10.

Learn more about inequalities here:

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What is the simplified expression for 5 to the power of 4 multiplied by 5 to the power of 3 over 5 to the power of 5?

52
53
54
55

Answers

Answer:

C. 5^4

Step-by-step explanation:

(5^4 * 5^5) / 5^5

5^9 / 5^5

5^4

Need help will give brainliest!!!

Answers

Answer:

A

Step-by-step explanation:

they took the square root of both sides

Look at this graph :
Is this relation a function?

Answers

Answer:

Step-by-step explanation:

The solid, blue line is the graph of a function. The dotted, blue line is not a function.

Shazia sells 25x^2+5x+5 flowers in one day. If she sells the same number of flowers each day for rs 5x each , how much money will she have at the end of five days


Anyone help

Answers

Answer:

[tex]Total = 625x^3 + 125x^2 + 125x[/tex]

Step-by-step explanation:

Given

[tex]Flowers = 25x^2 + 5x + 5[/tex]

[tex]Unit\ price = 5x[/tex]

Required

The total price for 5 days

First, calculate the total for a day.

[tex]1\ day = Unit\ price * Flowers[/tex]

[tex]1\ day = 5x * (25x^2 + 5x + 5)[/tex]

Open bracket

[tex]1\ day = 125x^3 + 25x^2 + 25x[/tex]

For 5 days, the total will be.

Total = days * sales of a day

So, we have:

[tex]Total = 5 * [ 125x^3 + 25x^2 + 25x][/tex]

[tex]Total = 625x^3 + 125x^2 + 125x[/tex]

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