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:
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.
Answer:
Im pretty sure its 32
Step-by-step explanation:
Related Questions
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]
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:
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]
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
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
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:
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
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.
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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.
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
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 ! :)
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)
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
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:
Hence, make a conjecture regarding the line joining the midpoints of two sides of any triangle:
Answers
Answer:
Plzzzz answer fast.....
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.
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
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
Need help will give brainliest!!!
Answers
Answer:
A
Step-by-step explanation:
they took the square root of both sides
What is the solution to the equation 4+5 -3- +5?
X=-1, x = 11
X=-1
0.x = 11
no solution
Answers
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
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]
which property is demonstrated?
Answers
Answer:
Associative Property
Explanation:
Associative property is when you add and group numbers in any combination.
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
here: https://brainly.com/question/1538726
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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
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
(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
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?