Is the figure shown in the xy- plane a parallelogram? Why or why not. use the coordinates to history your answer.
Please help!!! Due in 15 mins !!
Answers
Answer:
Step-by-step explanation:
It is a parrallelogram, the two lines are Parallel to each other meaning they will never cross each other
The given xy- plane is a parallelogram.
When a plane figure is called a parallelogram?
A plane figure is called a parallelogram when it have four sides, in which opposite sides are parallel to each other and each side is equal in length to its opposite side.
How to find the distance between two points?If [tex](x_{1},y_{1} })[/tex] and [tex](x_{2},y_{2})[/tex] are the two points then the distance between these points is given by
[tex]d=\sqrt{(x_{2}-x_{1}) ^{2} +(y_{2}-y_{1} ) ^{2} }[/tex]
Where, d is the distance between two points.
According to the given question
We have a plane figure PSTO
And the coordinates of points P, S, T, and O are (a, b), (a + c, b), (c, 0) and (0,0) respectively.
Now, the length of the sides by distance formula
PS = [tex]\sqrt{(a-a-c)^{2}+(b-b)^{2} }[/tex]
PS = [tex]\sqrt{c^{2}+0 }[/tex]
PS = c
Similarly,
ST =[tex]\sqrt{(a+c-c)^{2}+(b-0)^{2} }[/tex]
ST = [tex]\sqrt{a^{2} +b^{2} }[/tex]
TO = [tex]\sqrt{(c-0)^{2}+(0-0)^{2} }[/tex]
TO = [tex]\sqrt{c^{2} }[/tex]
TO = c
And, PO = [tex]\sqrt{(a-0)^{2}+(b-0)^{2} }[/tex]
PO = [tex]\sqrt{a^{2} +b^{2} }[/tex]
From the above calculation we found that
PS = TO
PO = ST
⇒ Length of the opposite sides of the plane figure are equals.
And from the given figure we can see that the opposite sides are also parallel to each other.
Therefore, the given xy- plane is a parallelogram.
Learn more about parallelogram here:
https://brainly.com/question/11220936
#SPJ2
Related Questions
Help for 100 points if correct
Answers
Saved:-
[tex]\\ \sf\Rrightarrow 2\dfrac{1}{4}-\dfrac{3}{8}[/tex]
[tex]\\ \sf\Rrightarrow \dfrac{9}{4}-\dfrac{3}{8}[/tex]
[tex]\\ \sf\Rrightarrow \dfrac{18-3}{8}[/tex]
[tex]\\ \sf\Rrightarrow \dfrac{15}{8}[/tex]
[tex]\\ \sf\Rrightarrow 1\dfrac{7}{8}[/tex]
Answer:
[tex]\textsf{D)} \quad 1 \dfrac{7}{8}[/tex]
Step-by-step explanation:
Subtract the used volume of punch from the starting volume of punch.
Convert the mixed number to an improper fraction:
[tex]\begin{aligned} \implies 2\frac{1}{4}-\frac{3}{8} & = \dfrac{2 \times 4+1}{4}-\dfrac{3}{8}\\\\ & = \dfrac{9}{4}-\dfrac{3}{8}\end{aligned}[/tex]
Make the denominators of both fractions the same by multiplying the numerator and the denominator of 9/4 by 2:
[tex]\implies \dfrac{9 \times 2}{4 \times 2}-\dfrac{3}{8} = \dfrac{18}{8}-\dfrac{3}{8}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}-\dfrac{b}{c}=\dfrac{a-b}{c}:[/tex]
[tex]\begin{aligned} \implies \dfrac{18}{8}-\dfrac{3}{8} & = \dfrac{18-3}{8}\\\\ & = \dfrac{15}{8}\end{aligned}[/tex]
Convert back into a mixed number:
[tex]\begin{aligned}\implies \dfrac{15}{8} & = \dfrac{8+7}{8}\\\\ & = \dfrac{8}{8}+\dfrac{7}{8}\\\\ & = 1\dfrac{7}{8}\end{aligned}[/tex]
what is equivalent to the following expression:
2(- a + 5) – 3 (a + 5b-2)+b (6-a)
Answers
From the information given, it can be inferred that the expansion of the equation will be 5a - 9b + 16 - ab.
= 2(- a + 5) – 3 (a + 5b-2)+b (6-a)
We've to expand the functions and this will be:
= -2a + 10 - 3a - 15b + 6 + 6b - ab
Collect like terms
= - 2a - 3a - 15b + 6b + 10 + 6 - ab
= -5a - 9b + 16 - ab
Therefore, the expression is equivalent to 5a - 9b + 16 - ab.
Learn more about equations on:
https://brainly.com/question/13763238
Express the following equation in slope intercept form: 8x-2y=10
PLEESSSSSSSSSSSSSE
Answers
Answer:
[tex]y2 - y1 \div x2 - x1[/tex]
How do i Multiply and divide integers? please answer quick if possible ♀️
Answers
Answer
To multiply integers, simply multiply the unsigned numbers and place the sign on the product by repeating the above rules.
To divide unsigned integers, we divide the unsigned numeric values and put a minus sign on the result.
PLEASE HELPPPPP!!!
Find the slope and y-intercept of the graph of each question:
1. y=6x+11
(pretty sure 6 is the slope and 11 is the y-intercept... pls correct me if me wrong)
2. y=x+6
(1 is the slope and 6 is the y-intercept??)
Answers
Answer:
1. slope = 6, y-intercept = 11
2. slope = 1, y-intercept = 6
Answer:
you are correct
Step-by-step explanation:
6 is the slope and 11 is the y-intercept
1 is the slope and 6 is the y-intercept
Simplify w4z8 ÷ w2y2z4.
Answers
Answer:
w^2z^4/y^2
Step-by-step explanation:
the points (2,4) and (6,7) lie on a line. what is the slope of the line?
Answers
m = 3/4
Sorry if it’s not right
Please, Please help ASAP
Answers
Answer:
5 is the answer
please mark as brainlist
thank you
what is the least common denominator of 10 and 14
Answers
Answer:
70
Step-by-step explanation:
Given -
the least common denominator of 10 and 14 is - *70*
Prime factor of 14 are 2 and 7
14 = 2 * 7
Prime factor of 10 are 2 * 5
10 = 2 * 5
Now Multiplying the highest exponent prime factor to calculate the LCM of 14 and 10
LCM (10,14) = 2 * 5 * 7
LCM (10,14) = 70
The terminal side of an angle θ in standard position passes through the point (3, 1). Calculate the exact values of the six trig functions for angle θ.
Answers
Answer:
sin α = [tex]\frac{y}{r}[/tex] = [tex]\frac{1}{\sqrt{10} }[/tex]
cos α = [tex]\frac{x}{r}[/tex] = [tex]\frac{3}{\sqrt{10} }[/tex]
tan α = [tex]\frac{y}{x}[/tex] = [tex]\frac{1}{3}[/tex]
cot α = [tex]\frac{x}{y}[/tex] = [tex]\frac{3}{1}[/tex]
sec α = [tex]\frac{r}{x}[/tex] = [tex]\frac{\sqrt{10} }{3}[/tex]
csc α = [tex]\frac{r}{y}[/tex] = [tex]\frac{\sqrt{10} }{1}[/tex]
Step-by-step explanation:
If the point is given on the terminal side of an angle, then:
Calculate the distance between the point given and the origin:
r = [tex]\sqrt{x^2+y^2}[/tex]
Here it is: [tex]\sqrt{3^2+1^2}[/tex] = [tex]\sqrt{9+1}[/tex] = [tex]\sqrt{10}[/tex]
So we have:
x = 3
y = 1
r = [tex]\sqrt{10}[/tex]
Now we can calculate all 6 trig, functions:
sin α = [tex]\frac{y}{r}[/tex] = [tex]\frac{1}{\sqrt{10} }[/tex]
cos α = [tex]\frac{x}{r}[/tex] = [tex]\frac{3}{\sqrt{10} }[/tex]
tan α = [tex]\frac{y}{x}[/tex] = [tex]\frac{1}{3}[/tex]
cot α = [tex]\frac{x}{y}[/tex] = [tex]\frac{3}{1}[/tex]
sec α = [tex]\frac{r}{x}[/tex] = [tex]\frac{\sqrt{10} }{3}[/tex]
csc α = [tex]\frac{r}{y}[/tex] = [tex]\frac{\sqrt{10} }{1}[/tex]
I have two bags of marbles, each of which contains some red marbles and some blue marbles (and no marbles of any other color). The ratio of red marbles to blue marbles in the first bag is $3:5.$ The ratio of red marbles to blue marbles in the second bag is $3:2.$ When the two bags of marbles are mixed together, the ratio of red marbles to blue marbles is $11:9.$ What is the ratio of the number of marbles in the first bag to the number of marbles in the second bag?
Answers
========================================================
Explanation:
Let x and y be two positive whole numbers. They may or may not be equal.
The first bag has the ratio of red to blue as 3:5, which scales up to 3x:5x after multiplying both parts by x. We have 3x red and 5x blue.
The second bag has the ratio 3:2 which scales up to 3y:2y. This bag has 3y red and 2y blue.
We can make a handy table to keep track of all the expressions
[tex]\begin{array}{|c|c|c|}\cline{1-3}\text{ } & \text{Red} & \text{Blue}\\ \cline{1-3}\text{bag 1} & 3x & 5x\\ \cline{1-3}\text{bag 2} & 3y & 2y\\ \cline{1-3}\end{array}[/tex]
Based on that, we can then say:
The two red quantities add to R = 3x+3yThe two blue quantities add to B = 5x+2yEffectively, I added down along each column of that table.
Divide the two expressions for R and B to lead to the fraction 11/9, which is directly from the ratio 11:9
So,
(total red)/(total blue) = 11/9
R/B = 11/9
(3x+3y)/(5x+2y) = 11/9
---------------------
Let's cross multiply and then solve for y
(3x+3y)/(5x+2y) = 11/9
9(3x+3y) = 11(5x+2y)
27x+27y = 55x+22y
27y-22y = 55x-27x
5y = 28x
y = 28x/5
y = (28/5)x
y = 5.6x
We'll keep this in mind for later.
---------------------
Now let:
F = amount of marbles in the first bagS = amount of marbles in the second bagRecall that we had 3x red and 5x blue for the first bag. That means we have 3x+5x = 8x marbles in the first bag. Therefore, F = 8x.
Also, we had 3y red and 2y blue for the second bag.
So we have S = 3y+2y = 5y
Then we can apply further substitution to say
S = 5y
S = 5(5.6x) .... plug in y = 5.6x
S = 28x
---------------------
In short,
F = 8xS = 28xfor some positive whole number x. We don't have enough info to pin down what x is exactly; however, it doesn't really matter. This is because the x variable will cancel when dividing F over S
F/S = (8x)/(28x) = 8/28 = 2/7
The fraction 2/7 leads directly to the final answer of the ratio 2:7
In other words, the ratio 8x:28x simplifies fully to 2:7 after dividing both parts by 4x.
The ratio between the total marbles of the first bag and the second bag is 2:7.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 9 is an equation.
We have,
x marbles in the first bag.
red marbles = 3x
blue marbles = 5x
y marbles in the second bag.
red marbles = 3y
blue marbles = 2y
Now,
Total red marbles in both bags.
3x + 3y = 11 _____(1)
3x = 11 - 3y
x = (11 - 3y) / 3
Total blue marbles in both bags.
5x + 2y = 9 ______(2)
From (1) and (2) we get,
Multiply 2 in (1).
6x + 6y = 22
6y = 22 - 6x _____(3)
Multiply 3 in (2)
15x + 6y = 27 ______(4)
Putting (3) in (4)
15x + 22 - 6x = 27
9x = 27 - 22
9x = 5
x = 5/9
Now,
x = 5/9 in (3)
6y = 22 - 6(5/9)
6y = 22 - 10/3
6y = (66 - 10)/3
y = 56/18
y = 28/9
Now,
First bag.
Red marbles = 3x = 3 x 5/9 = 5/3
Blue marbles = 5x = 5 x 5/9 = 25/9
Total marbles = 5/3 + 25/9 = (15 + 25)/9 = 40/9
Second bag.
Red marbles = 3y = 3 x 28/9 = 28/3
Blue marbles = 2y = 2 x 28/9 = 56/9
Total marbles = 28/3 + 56/9 = (84 + 56)/9 = 140/9
Now,
The ratio between the total marbles of the first bag and the second bag.
= 40 :140
= 4:14
= 2:7
Thus,
The ratio is 2:7.
Learn more about equations here:
https://brainly.com/question/17194269
#SPJ2
20-5+15(25)=b+3+65(23)
Answers
Answer:
-1108
Step-by-step explanation:
Answer:
-b=-1108
Step-by-step explanation:
20-5+375=b+3+1495
-375 -375
20-5=b+3+1420
15=b+1423
-b -b
-b+15=1423
-15 -15
-b=1108
20-5+375=-1108+3+1495
390=390
2. Name 3 points that are collinear*
2
s
S
R
O points T, Q, and R
O points T, Q, and S
O points S, Q, and R
Answers
Answer:
T, Q, and R
Step-by-step explanation:
These points are all on the same line, making them collinear.
I hope this helps!!
Quick easy question
Answers
Answer:16
Step-by-step explanation:
144^0.5 = 12
400^0.5 = 20
a^2=b^2+c^2
20^2 = 12^2 +x^2
x^2 = 400-144= 256
x =16
Answer:
16
Step-by-step explanation:
Which function has only one x-intercept at (−6, 0)?
f(x) = x(x − 6)
f(x) = (x − 6)(x − 6)
f(x) = (x + 6)(x − 6)
f(x) = (x + 6)(x + 6)
Answers
Answer:
D: f(x) = (x+6)(x+6)
Step-by-step explanation:
The function has a multiplicity of 2, meaning the factor appears twice. So, x=-6 will be the only x-intercept.
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
The answer should be A......
PLEASE HELPPPP! ANYTHING U CAN ANSWER WOULD BE SOOO GREAT :) (AND NO ITS NOT A VIRUS)
Answers
Answer:
but what if it is a virus?
Step-by-step explanation:
Answer:
isnt oit iron pick
Step-by-step explanation:
Solve: 4|x| = 32
–8 or 8
8
24
no solution
Answers
Answer:
-8 or 8
Step-by-step explanation:
We are given the absolute equation:
[tex]\displaystyle \large{4|x|=32}[/tex]
First, divide both sides by 4 which leaves [tex]\displaystyle \large{|x|=8}[/tex]
Absolute Value Definition
[tex]\displaystyle \large{|x|=\begin{cases} x \ \ \ (x\geq 0)\\ -x \ \ \ (x<0) \end{cases}}[/tex]
So from |x| = 8, break into two intervals/conditions.
(1) when x ≥ 0
x = 8
(2) when x < 0
-x = 8
x = -8
From (1) and (2), the solution to 4|x| = 32 is 8 or -8
A board isThree boards are placed end to end to make a walkway. The first board is 2 feet 8 inches long, the second board is 6 feet 10 inches long, and the third board is 4 feet 9 inches long. How long is the walkway?
93 inches long. How long is it in feet and inches?
Answers
Answer:
wowo
Step-by-step explanation:
HELP. RIGHT NOW PLEASE :>
Simplify
Answers
Answer:
√
4
x
5
√
(
x
−
1
)
2
−
3
2
+
3
y
−
3
Step-by-step explanation:
√
4
x
5
√
(
x
−
1
)
2
−
3
2
+
3
y
−
3
express the radical using the imaginary unit i
Answers
Answer:
[tex]i[/tex][tex]\sqrt{30}[/tex]
Step-by-step explanation:
[tex]\sqrt{-30}[/tex]
= [tex]\sqrt{30 * -1}[/tex]
= [tex]\sqrt{30} * \sqrt{-1}[/tex] Separate the two numbers into 2 radicals.
= [tex]i\sqrt{30}[/tex] Simplify, knowing that [tex]i = \sqrt{-1}[/tex].
Which variable is most important to the following problem?
A tentmaker has 60,000 tents in stock. The Army decides to order 350 tents
for each of its 200 brigades. Will the tentmaker have enough tents in stock?
O A. the price of one tent
O B. the number of tents the Army orders
C. the size of each tent
Answers
Answer:
B.) the number of tents the army orders
Step-by-step explanation:
The word problem does not speak of any prices or tent sizes so it cant be A or C
Answer:
its B
Step-by-step explanation:
Please help me on this math problem
Answers
solve for x 12+6x/3= 5-9/2
Answers
Answer: I hope this helps! :)
x = -3
rearrange terms: 6x+12/3 = 5-9/2subtract the numbers: 6x+12/3 = -4/2eliinate fractions denominators: 3 times 6x+12/3 = 3(-2)simplify fractions: 6x+12/3 = -2eliinate fractions denominators: 3 times 6x+12/3 = 3(-2)multiplt the numbers: 6x + 12 = -6subtract 12 from both sides of the equation: 6x + 12-12 = -6-12simplify: 6x = -18divide both sides of the equation by the same factor: 6x/6 = -18/6x = -3Answer: x=-3
Answer:
[tex]x = -3[/tex]Step-by-step explanation:
[tex]\frac{12 + 6x}{3} = \frac{5 - 9}{2}[/tex]=> [tex]2(12 + 6x) = 3(5 - 9)[/tex]=> [tex]24 + 12x = 15 - 27[/tex]=> [tex]24 + 12x = -12[/tex]=> [tex]24 + 12 = -12x[/tex]=> [tex]36 = -12x[/tex]=> [tex]x = -3[/tex]Conclusion:
Therefore, x = -3
Hoped this helped.
[tex]GeniusUser[/tex]
9. 25 students each paid $6.50 to go to the museum. How much did they all pay together?
Answers
Answer:
They paid 247 dollar.
Step-by-step explanation:
They paid 247 dollar
Answer:
Step-by-step explanation:
1 student paid 6.50
25 students paid x
1/25 = 6.50 / x Cross multiply
x = 25 * 6.50
x = 162.50
The total for all 25 came to 162.50 dollars.
jonathan sells clothes and makes a 4% commission. On sunday, jonathan sold $768 worth of clothes. How much was his commission on his sunday?
Answers
Answer:
768x4%= 30.72
His commission was $30.72
Step-by-step explanation:
How i can answer this question, NO LINKS, if you answer correctly i will give u brainliest!
Answers
Answer:
1, 2, 10 i think this is correct
Answer:
1210Step-by-step explanation:
You answer the question by understanding what the problem statement is telling you.
The double number line shows that 2 1/2 bananas make 1 loaf of bread.
The first blank is filled with 1.
__
You notice the number of bananas on the second line of the table is double the number on the first line: 5 = 2 × (2 1/2). That means the number of loaves that can be made is 2 × 1 = 2.
The second blank is filled with 2.
__
You notice the number of loaves on the third line of the table is double the number of loaves you just filled in on the second line. That means the number of bananas required is double the number listed on the second line.
2 × 5 = 10
The third blank is filled with 10.
is it a. b. c. or d.
Answers
I may be wrong, but im pretty sure its C
Answer:
I might be wrong but I think it is B. or A.
Step-by-step explanation:
Determine the slope of the line that passes through pair of points: (-4, 11) and (1,-9)
Answers
Answer:
rise/run= -20/5= -4/1=-4 slope
or you sound use the slope formula (y2-y1)/(x2-x1)
(-9-11)/(1+4)
-20/5
-4
Hope this helps
An education website has 434,206 daily unique visitors. An e-commerce website gets double the number of visitors. How many visitors does the e-commerce website get? Thank you in advance:))
Answers
Answer:
868,412 visitors
Explanation:
434,206 x 2 (double)