Parallelogram ABCD has the following vertices: A(3,6), B(6,8), C(9,6), and D(6,4). In two ut more complete sentences, explain how you can use the coordinates of the vertices to prove that parallelogram ABCD is a rhombus.
Answers
Explanation:
A rhombus is a parallelogram in which the diagonals are mutual perpendicular bisectors. The coordinates of the vertices can be used to show ...
the diagonals bisect each otherthe diagonals are perpendicularWhen both these conditions are met, the quadrilateral is a rhombus.
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Mutual BisectorsThe diagonals will have the same midpoint (bisect each other) if the sum of the coordinates at the ends of one diagonal is the same as the sum of the end point coordinates of the other diagonal:
A +C = B +D
(3, 6) +(9, 6) = (6, 8) +(6, 4)
(3+9, 6 +6) = (6 +6, 8 +4)
(12, 12) = (12, 12) . . . . . . midpoints are the same; ABCD is a parallelogram
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PerpendicularThe diagonals will be perpendicular if the sum of the products of the coordinate differences of their end points is zero.
AC⋅BD = (C -A)⋅(D -B) = (9 -3, 6 -6)⋅(6 -6, 4 -8)
= (6, 0)⋅(0, -4) . . . . . end point differences; we want their dot-product
= (6)(0) +(0)(-4) = 0 +0 = 0 . . . . diagonals are perpendicular
_____
Additional comment
The midpoints are computed as (A+C)/2 and (B+D)/2. We have multiplied each of them by 2 to simplify the arithmetic. Our resulting sums of (12, 12) must be divided by 2 to get the actual midpoint of the rhombus: (6, 6).
The notion of "dot product" is a vector notion. Two vectors are perpendicular when their dot product is zero. The dot product is the scalar sum of the products of corresponding coordinates.
Related Questions
Consider the equation 4 plus v equals 8 minus startfraction 5 over 3 endfraction v.v 4 startfraction 5 over 3 endfraction v plus 4 equals 8 minus startfraction 1 over 3 endfraction v. v = 8. what is the resulting equation after the first step in the solution? v 4 = 8 – v startfraction 4 over 3 endfraction v plus 4 equals 8.v 4 = 8 4 v = 8 – 4 plus v equals 8 minus startfraction 5 over 3 endfraction v.v 2v 4 = 8
Answers
The resulting equation which is obtained after the first step in the solution of the provided equation is 2v +4=8.
What is an algebraic expression?Algebraic expression are the expression which consist the variables, coefficients of variables and constants. The algebraic expression is used to represent the general problem in the mathematical way to solve them.
Consider the following equation,
[tex]\dfrac{5}{3}v +4+\dfrac{1}{3}v=8[/tex]
To solve this equation, first we have to arrange the similar terms one side of the equation as,
[tex]\dfrac{5}{3}v+\dfrac{1}{3}v +4=8[/tex]
Solve it further by taking LCM,
[tex]\dfrac{5+1}{3}v +4=8\\\dfrac{6}{3}v+4=8\\2v +4=8\\[/tex]
Hence, the resulting equation which is obtained after the first step in the solution of the provided equation is 2v +4=8.
Learn more about the algebraic expression here;
https://brainly.com/question/2164351
Answer:
c on edge
Step-by-step explanation:
Is 3x^2-5x+205x^7 a perfect square?
Answers
Please help and match the following. Pt2
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Answer:
the first one will be B) x^2-4x+4
the sencond one will be A) x^2-16
the third one will be C) x^2+x-2
the fourth one will be D) -2x^3+4x^2+16x
Step-by-step explanation:
hope this helps now i gotta really go :)
Need help, see photo below.
Answers
Answer:
The correct answer would be option 2; Regular Hexagon
Hope this helps!
PLease help i will give brainliest
Answers
Answer:
I don't have a good knowledge of means but I know it isn't B or D.
Step-by-step explanation:
WILL GIVE BRAINIEST
in this equation 3x=n, John claims that for any value for x, the value of n will always be greater than or equal to the base of 3
Answers
A.2
3^2 = 9
(any number greater than one because 3^1 = 3, this is not greater than 3)
B. 0
3^0 = 1
(any number less than 1, so it can't be one, but can be a negative number or zero - any number to the power of zero is one)
Hope this helps!
Find the surface area of the prism formed by each net.
Answers
Answer:
378 in^2
Step-by-step explanation:
This is the sum of the area of the 6 rectangles
That is:
8*15 + 3*15 + 3*8 + 8*15 + 3*8 + 3*15
= 378 in^2
do you know the answer to this question 4x16+3-1
Answers
Answer:
66
Step-by-step explanation:
use
P- parenthesis
E- Exponents
M-multiplication
D-Division
A- addition
S- subtraction
NOTE THAT MULTIPLICATION IS NOT MORE IMPORTANT THAN DIVISION AND SAME GOES FOR ADDITION AND SUBTRACTION.
This means that that we do it from left yo right
4×16+3-1 --> 64+3-1 --> 67-1 = 66
The circumference of a circle is 71 in. Find its radius, in inches.
Answers
Answer: r = 11.3
Step-by-step explanation:
In order to find the radius given circumfrence we use the following formula
[tex]r=\frac{C}{2*\pi }[/tex]
[tex]r=\frac{71}{2*3.14 }[/tex]
r = 11.3
A store is selling a green rug for $54.50 and a white rug for $31.85. the green rug is marked down by 12%, and the white rug is marked up by 16%. after the markup and markdown, which rug is more expensive, and how much more expensive is it? round all dollar values to the nearest cent. a. the white rug is $1.09 more expensive than the green rug. b. the white rug is $5.35 more expensive than the green rug. c. the green rug is $1.44 more expensive than the white rug. d. the green rug is $11.01 more expensive than the white rug.
Answers
The a seer to the more expensive rug is; D: the green rug is $11.01 more expensive than the white rug.
How to calculate mark up and mark down?We are told that;
Current cost of Green rug = $54.50
Current cost of White rug = $31.85
Now the store wants to mark down the green rug by 12%. Thus;
New price of green rug = (100% - 12%) × 54.5
New price of green rug = $47.96
Now the store wants to mark up the white rug by 16%. Thus;
New price of white rug = (100% + 16%) × 31.85
New price of green rug = $36.95
Difference in New prices = $47.96 - $36.95
Difference in New prices = $11.01
Read more about Mark up at; https://brainly.com/question/1153322
How does the volume of a cylinder with a radius of 3 units and a height of 12 units compare to the volume of a rectangular prism with dimensions 16 units x 16 units x 9 units?
a. The volume of the cylinder is greater than the the volume of the prism
b. The volume of the cylinder is smaller than the volume of the prism.
C. The volume of the cylinder is the same as the volume of the prism
d.You cannot compare the volumes of different shapes
Answers
Answer:
The volume of the cylinder is greater than the volume of the prism.
Step-by-step explanation:
The Volume of a cylinder is given as:
= πr²h
Therefore, the volume of a cylinder with a radius of 3 units and a height of 12 units will be:
= πr²h
=3.14 × 3² × 12
=339.12
The volume of a rectangular prism with dimensions 3 units x 3 units x 12 units will be:
= Length × Width × Height
Based on the calculation, the volume of the cylinder is greater than the volume of the prism.
Answer:
B: The volume of the cylinder is smaller than the volume of the prism.
Step-by-step explanation:
In order to find the volume of the cylinder, we would use to formula [tex]\pi r^{2} h[/tex]. Substitute the given measures of the cylinder to get [tex]\pi[/tex]·3²·12. The simplified and calculated form would be 108 units cubed.
Now, we find the volume of the rectangular prism, which is [tex]l[/tex]·[tex]w[/tex]·[tex]h[/tex], or 16*16*9. This means the volume is 2304 units cubed.
Therefore, since 2304 un³>108 un³, answer choice b would be correct.
What key features do the functions f(x) = 12x and g of x equals the square root of x minus 12 end root have in common?
1-Both f(x) and g(x) include domain values of [-12, ∞) and range values of (-∞, ∞), and both functions have an x-intercept in common.
2- Both f(x) and g(x) include domain values of [12, ∞) and range values of [0, ∞), and both functions have a y-intercept in common.
3-Both f(x) and g(x) include domain values of [-12, ∞) and range values of (-∞, ∞), and both functions increase over the interval (-6, 0).
4-Both f(x) and g(x) include domain values of [12, ∞), and both functions increase over the interval (12, ∞).
Answers
Using the domain and the range of the function, it is found that the correct option is given by:
4- Both f(x) and g(x) include domain values of [12, ∞), and both functions increase over the interval (12, ∞).
What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input.The range of a function is the set that contains all the values of the output.Function f(x) is defined by: f(x) = 12x.
Line with positive slope, hence it is increasing all over it's domain.Range is all real values.No restriction, hence the domain is also all real values.Function g(x) is defined by: [tex]g(x) = \sqrt{x - 12}[/tex]
The square root function increases over all it's domain.The range is [tex](0, \infty)[/tex].The term inside the root cannot be negative, hence the domain is [12, ∞), which is contained into the domain of f(x).This means that option 4 is correct.
More can be learned about domain and range of a function at https://brainly.com/question/27274752
Write 1/20 as a percent
help
Answers
Answer:
5%
Step-by-step explanation:
1/20 of 100% is 5%. So that means 5%
The circumference of a circle is 6π cm. What is the area, in square centimeters?
Answers
Answer:
9Pi square units
Step-by-step explanation:
Area = Pi x Radius^2
Diameter = Circumference / Pi
= 6Pi / Pi
= 6
Radius = Diameter / 2
= 6 / 2
= 3
Area = Pi x 3^2
Hope this helps!!
Tamara's backyard pool needs a cover for the winter. The pool is
rectangular with a length of 12 feet and an area of 196.8 square feet.
What is the width of the pool cover Tamara's pool will need?
Answers
Answer:
16.4 feet
Step-by-step explanation:
Area of a rectangle: length * width = area
12*w=196.8
w=196.8/12
w=16.4 feet
PLS HELP MEEE I REALLY NEED HELP
Answers
a) 24.92
b) 65.616
c) 66.43
d) 6.13
e) 25.0862
f) 4.95
You went shopping and bought a total of 31 items, some of them pants and some of them shirts. The shirts cost $7 and the pants cost $22 and you spend $517 in total. How many shirts and how many pants did you buy?
Shirts________
Pants________
Answers
Brahmagupta’s solution to a quadratic equation of the form ax2 bx = c involved only one solution. which solution would he have found for the equation 3x2 4x = 6?
Answers
The value of the quadratic equation x has a value of 0.8968 and a negative value of 2.23.
What is a factorization, and how does it work?It is a method for dividing a polynomial into parts, each of which will be multiplied. At this time, the polynomial's value will be zero.
The equation for the expression is given below.
3x² + 4x = 6
3x² + 4x - 6 = 0
we know that the formula
[tex]\rm x = \dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Then we have
[tex]x = \dfrac{-4 \pm \sqrt{4^2-4*4*(-6)}}{2*3}\\\\x = \dfrac{-4 \pm \sqrt{112}}{6}\\\\x = 0.8968, \ -2.23[/tex]
More about the factorization link is given below.
https://brainly.com/question/6810544
what's the answer for 2/3+x=4
Answers
Step-by-step explanation:
what is the problem for you ?
to solve an equation ?
or to deal with fractions and how to relate them to whole numbers (e.g. how to convert whole numbers into fractions) ?
if you need any additional information, please let me know.
I am just solving the equation now :
2/3 + x = 4
x = 4 - 2/3 = 12/3 - 2/3 = 10/3 = 3 1/3
Answer:
Step-by-step explanation:
x = 4 - 2/3
x = 3 3/3 - 2/3
x = 3 1/3
Which terms complete the factorization of x2 27x 162 represented by the model? 27, 9x, 18x 9, 9x, 18x 27, 9x, 27x 9, 9x, 27x
Answers
Answer: 9, 9x, 18x
Step-by-step explanation:
Hope it helps :D
Need help with this question please and thank you
Answers
Answer:
The answer is C. [tex]y = \frac{1}{12}(x+2)^{2}+2[/tex]
If mBE=119 and mBKE=93, find mUH.
Answers
Answer:
arc UH = 67°
Step-by-step explanation:
the measure of a chord- chord angle is half the sum of the measures of the arcs intercepted by the angle and its vertical angle , then
[tex]\frac{1}{2}[/tex] ( BE + UH ) = ∠ BKE , that is
[tex]\frac{1}{2}[/tex] (119 + UH ) = 93° ( multiply both sides by 2 to clear the fraction )
119° + UH = 186° ( subtract 119° from both sides )
UH = 67°
Answer:
Step-by-step explanation:
∠HKU = ∠BKE {Vertically opposite angles}
∠HKU = 93°
Angles fromed by insecting chords equals half the sum of intercepting arcs.
[tex]\sf \angle HKU =\dfrac{1}{2}(arc \ HU + arc \ BE) \\\\ 93^ \circ = \dfrac{1}{2}(arc \ HU + 119)[/tex]
93 *2 = arc HU + 119
186 = arc HU + 119
186 - 119 = arc HU
arc HU = 67°
30 POINTS!!
LOOK AT PHOTOS!! (THERES 2!!)
Which graph displays points that correspond to the x and y values in the table?
Answers
Have a good day,
Answer:
A
Step-by-step explanation:
A is the only one with (4,0) (1,-1) (0,0) and (-2,5)
Of the 4 people attending a lecture, 2 have hazel eyes.
What is the probability that a randomly selected person will have hazel eyes?
Write your answer as a fraction or whole number.
Answers
Answer: 50%
Step-by-step explanation:
Because 2 of four is half, that that the probability is a 50% chance.
Answer:
1/2
Step-by-step explanation:
Think of this like a pizza or pie:
If there are four slices and two represent hazel eyes, how many slices are "hazel eyes?" It would be 2 of 4, or 2/4.
Because this is a fraction and it can be simplified, it would be 1/2.
So there is a 50% chance that the randomly selected person of the four people will have hazel eyes.
This sphere has a radius of 9 m. What is the surface area of the sphere? Enter your answer, in exact form, in the box
Answers
[tex]\textit{surface area of a sphere}\\\\ SA=4\pi r^2~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=9 \end{cases}\implies SA=4\pi (9)^2\implies SA=324\pi[/tex]
4) What is 15% of 22?
A) 3
B) 3.3
C) 30
D) 33
Answers
Answer: 3.3
Step-by-step explanation: Find the calculation in the picture
Please help I am very confused!
Answers
Answer:
m = -1
the line goes down in a straight line from the starting point
Answer: -1
Step-by-step explanation:
Slope formula y2-y1/x2-x1. -9-(-4)/3-(-2). -5/5= -1
The radius of a circle is 19m. Find its area to the nearest whole number.
Answers
1134.11m²
______----------________
Answer:
1134.11
Step-by-step explanation:
The problem with this equation is pi is an angle in radians. It has a never ending number of digits.
The area of a circle is basically a square r x r rotated through 180 degrees around the squares centre.
So the area can be written as 180 x 19 x 19 = 64980 degrees meters square.
This is a finite number. The area of a circle does not change. Pi r squared has an ever increasing result.
pi is a conversion factor between the finite areas of circles and the area in square units which can never have a result that is finite as squares cannot fill a circle, no matter how small.
To convert the round finite area to m squared you divide the area by 180/pi = 57.295779513 degrees per radian.
Area in degrees meters Squared 64980/ 57.295779513.
= 1134.1149479 radian meters squared.
This table gives the value of an investment for the first 14 years after the initial investment was made. The data can be modeled using an exponential function.
Years 2 4 6 8 10 12 14
Investment value $692 $952 $1,304 $1,813 $2,316 $3,256 $4,718
Based on the data, which amount is closest to the value of the investment 18 years after the initial investment? PLS HURRY I NEED THIS ANSWERED NOW, WILL GIVE 95 POINTS
Answers
Answer:
General form of an exponential equation: [tex]y=ab^x[/tex]
where:
a is the initial valueb is the growth factorx is the independent variabley is the dependent variableLet x = years
Let y = investment value
Use (2, 692) and (4, 952) to find a and b of the exponential equation:
[tex]ab^2=692[/tex]
[tex]ab^4=952[/tex]
[tex]\implies \dfrac{ab^4}{ab^2}=\dfrac{952}{692}[/tex]
[tex]\implies b^2=\dfrac{238}{173}[/tex]
[tex]\implies b=\sqrt{\dfrac{238}{173}}=1.17\:\textsf{(nearest hundredth)}[/tex]
[tex]\implies ab^2=a\left(\dfrac{238}{173}\right)=692[/tex]
[tex]\implies a=\left(\dfrac{59858}{119}\right)=503.01\:\textsf{(nearest hundredth)}[/tex]
Therefore, the exponential equation is:
[tex]y=503.01(1.17)^x[/tex]
18 years after the initial investment is when [tex]x=18[/tex]:
[tex]\implies 503.01(1.17)^{18}=8490[/tex]
Therefore, the amount closest to the value of the investment 18 years after the initial investment is $8490
(If you use the exact values for a and b rather than the rounded values, the amount is $8879)
Write each expression using exponents:
4*4*4*4*4
Answers
Answer:4^6
Step-by-step explanation:
The number of times a term is multiplied is the exponent you use.
In this problem
4 is multiplied 6 times.
Therefore: 4*4*4*4*4*4=4^6