Determine the most precise name for ABCD (parallelogram, rhombus, rectangle, or square). Explain how you determined your answer. You must support your answer using length or slope.
A(3, 5), B(7, 6), C(6, 2), D(2, 1)
Answers
======================================================
Reason:
Let's find the distance from A to B. This is equivalent to finding the length of segment AB. I'll use the distance formula.
[tex]A = (x_1,y_1) = (3,5) \text{ and } B = (x_2, y_2) = (7,6)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-7)^2 + (5-6)^2}\\\\d = \sqrt{(-4)^2 + (-1)^2}\\\\d = \sqrt{16 + 1}\\\\d = \sqrt{17}\\\\d \approx 4.1231\\\\[/tex]
Segment AB is exactly [tex]\sqrt{17}[/tex] units long, which is approximately 4.1231 units.
If you were to repeat similar steps for the other sides (BC, CD and AD) you should find that all four sides are the same length. Because of this fact, we have a rhombus.
-------------------------
Let's see if this rhombus is a square or not. We'll need to see if the adjacent sides are perpendicular. For that we'll need the slope.
Let's find the slope of AB.
[tex]A = (x_1,y_1) = (3,5) \text{ and } B = (x_2,y_2) = (7,6)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{6 - 5}{7 - 3}\\\\m = \frac{1}{4}\\\\[/tex]
Segment AB has a slope of 1/4.
Do the same for BC
[tex]B = (x_1,y_1) = (7,6) \text{ and } C = (x_2,y_2) = (6,2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{2 - 6}{6 - 7}\\\\m = \frac{-4}{-1}\\\\m = 4\\\\[/tex]
Unfortunately the two slopes of 1/4 and 4 are not negative reciprocals of one another. One slope has to be negative while the other is positive, if we wanted perpendicular lines. Also recall that perpendicular slopes must multiply to -1.
We don't have perpendicular lines, so the interior angles are not 90 degrees each.
Therefore, this figure is not a rectangle and by extension it's not a square either.
The best description for this figure is a rhombus.
Answer:
Rhombus
Step-by-step explanation:
The diagonals of a parallelogram bisect each other. That is, they have the same midpoint. If they are the same length, that parallelogram is a rectangle. If they cross at right angles, it is a rhombus. If it is a rectangle and rhombus, then it is a square.
Diagonal midpointsThe midpoints of AC and BD are ...
(A+C)/2 and (B+D)/2
To determine if the midpoints are the same, we can skip the division by 2 and simply look at the sums:
A +C = (3, 5) +(6, 2) = (9, 7)
B +D = (7, 6) +(2, 1) = (9, 7)
The midpoints of the diagonals are the same, so the figure is at least a parallelogram.
Diagonal vectorsThe diagonal vectors will be the same length if the figure is a rectangle. They will be perpendicular if the figure is a rhombus. The vectors are ...
AC = C -A = (6, 2) -(3, 5) = (3, -3)
BD = D -B = (2, 1) -(7, 6) = (-5, -5)
The length of each of these is the root of the sum of squares of its components. These are obviously different lengths (3√2 vs 5√2).
The dot-product of these will be zero if they are perpendicular:
AC·BD = x1·x2 +y1·y2 = (3)(-5) +(-3)(-5) = -15 +15 = 0
ConclusionThe diagonals are different length and mutual perpendicular bisectors, so the figure is a rhombus.
__
Additional comment
Looking at the dot-product is a simple way to check that the slopes are opposite reciprocals. The slope of a vector with components (x, y) is m = y/x.
The requirement that slopes be opposite reciprocals means ...
y1/x1 = -1/(y2/x2) . . . . . . . . slope relationship
(y1)(y2)/((x1)(x2)) = -1 . . . . . multiply by y2/x2
y1·y2 = -x1·x2 . . . . . . . . . . multiply by (x1·x2)
x1·x2 +y1·y2 = 0 . . . . . . . . add x1·x2
This shows the vector dot product being zero is equivalent to the slopes being opposite reciprocals. The vectors are perpendicular in this case.
Related Questions
HELP ME PLEASE PLEASE PLEASE
Answers
If the angles of a convex octagon are [tex]2x+6,x+13,2x-1,2x+12,2x-17,3x-4,3x-10,4x.[/tex] then the smallest angle is 21°.
Given The exterior angles of convex octagon are [tex]2x+6,x+13,2x-1,2x+12,2x-17,3x-4,3x-10,4x.[/tex]
and we have to find the value of smallest angle.
The sum of the angles of a convex octagon is 360°
so to calculate the smallest angle we need to find out the value of x first and which is calculated by summing up all the exterior angles and put them equal to 360.
(2x+6)+(x+13)+(2x-1)+(2x+12)+(2x-17)+(3x-4)+(3x-10)+4x=360
2x+6+x+13+2x-1+2x+12+2x-17+3x-4+3x-10+4x=360
2x+x+2x+2x+2x+3x+3x+4x+6+13-1+12-17-4-10=360
19x-1=360
19x=360+1
19x=361
x=361/19
x=19
Putting the value of x in all the angles and we will find the following:
2x+6=2*19+6=44
x+13=19+13=32
2x-1=2*19-1=37
2x+12=2*19+12=50
2x-17=2*19-17=21
3x-4=3*19-4=51
3x-10=3*19-10=47
4x=4*19=76
Hence among all the exterior angles the smallest angle is 21°.
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Please help!! If........
Answers
Answer:
26
Step-by-step explanation:
[tex]f(x)=3x^{2} -5x+4\\f(-2)=3(-2)^{2} -5(-2)+4\\=3(4)+10+4\\=12+10+4\\=26[/tex]
Answer:
26
Step-by-step explanation:
3(-2)^2 = 12
5(-2) = -10
So 12 - (-10) + 4 = 26
I need some help please
Answers
Answer:
[tex]2261.9cm^{2}[/tex]
Step-by-step explanation:
Total Surface Area of Cylinder = [tex]2\pi rh+2\pi r^{2}[/tex]
Note: Do not get tricked by the 24cm (taking 24cm as the radius), that is the diameter.
To find r, radius = [tex]\frac{1}{2} d[/tex]
=[tex]\frac{1}{2} (24)\\[/tex]
= 12cm
Now we know r = 12cm, h = 18cm
Now we substitute r and h into the formula to find the total surface area.
Total Surface Area of Cylinder = [tex]2\pi (12)(18)+2\pi (12)^{2} \\=432\pi +288\pi \\=720\pi cm^{2} \\=2261.9cm^{2}[/tex]
The express elevator in a skyscraper goes up 51 floors in 123/4 seconds. How many floors does the elevator go up in 1 second
Answers
The express elevator will go 4 floors per seconds.
How to find rate?We have to find the rate of the express elevator before we can find how many floors one can go in one seconds.
time = 12 3 / 4 = 51 / 4 seconds
number of floor = 51 floors
rate = 51 / 51 / 4
rate = 51 × 4 / 51
rate = 4 floors per seconds
Therefore, the elevator will go 4 floors per seconds.
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Find the HCF of x³y² and x^2
Answers
Answer:
[tex]x^2[/tex]
Step-by-step explanation:
Hello!
The HCF or the highest common factor (sometimes also known as the greatest common factor, GCF), is the greatest factor between terms.
First, let's expand both terms:
[tex]x^3y^2 = x*x*x*y*y[/tex][tex]x^2 = x*x[/tex]If we keep them on top of another, we can see that the overlapping variables are [tex]x*x[/tex], meaning that the greatest common factor between them is [tex]x^2[/tex].
Choose the most convenient method to graph the line x=−3.
Select the correct answer below:
Recognize the equation as that of a vertical line passing through the x-axis at −3
Recognize the equation as that of a horizontal line passing through the y-axis at −3
Identify the slope and y-intercept and then graph
Find the x- and y-intercepts and then graph
Answers
Answer: Recognize the equation as that of a vertical line passing through the x-axis at −3
i cannot log in edge
only me?
Answers
Maths Trigonometry Question
100 points up for grabs!
Will give brainliest to whoever answers
Answers
Answer:
14) 21.136505024965 m
15) 43.076759215619 km
Step-by-step explanation:
14)
let h be the height of the lighthouse:
tan(41.3) = 18.7/h
Then
h = 18.7÷tan(41.5)
= 21.136505024965 m
………………………………………
15)
90-71.4 =18.6
Let s be the distance that the plane flew
towards the south:
tan(90 - 71.4) = s/128
Then
tan(18.6) = s/128
Then
s = tan(18.6)×128
= 43.076759215619 km
14.)
See the diagram below.
Here use tan rule:
[tex]\sf tan(x) = \dfrac{opposite}{adjacent}[/tex]
[tex]\sf tan(41+ \frac{30}{60} ) = \dfrac{18.7}{adjacent}[/tex]
[tex]\sf adjacent = \dfrac{18.7}{tan(41.5)}[/tex]
[tex]\sf adjacent = 21.14[/tex]
The height of the lighthouse is 21.14 m.
15.)
See the diagram below.
Here use tan rule:
[tex]\sf tan(x) = \dfrac{opposite}{hypotenuse}[/tex]
[tex]\sf tan(18.6) = \dfrac{opposite}{128}[/tex]
[tex]\sf opposite = 128 tan(18.6)[/tex]
[tex]\sf opposite = 43.08[/tex]
The plane travelled 43.08 km far south.
find two consecutive even integers such that 8 times the first equals 7 times the second
Answers
Answer:
Step-by-step explanation:
let the consecutive even integers be 2x,2x+2
8×2x=7(2x+2)
16x=14x+14
16x-14x=14
2x=14
x=14/2=7
so numbers are 2×7,2×7+2
or
14,16
Which number sentence matches the question below?
For how many days did Curtis practice juggling, if he practiced for 87 hours in all and for 3 hours each day?
A.
n ÷ 87 = 3
B.
3 ÷ n = 87
C.
87 ÷ n = 3
D.
n ÷ 3 = 87
Answers
The equation which represent number of days is 87 ÷ n = 3
What is Division?It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken.
Here,
total hour practicing = 87 hours
Daily hours for practicing = 3 hours
total number of days = n days
Now, according to question;
n X 3 = 87
87 ÷ n = 3
Thus, the equation which represent number of days is 87 ÷ n = 3.
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Which equation can be used to solve the problem? 10 is 50 percent of what number? StartFraction 10 divided by 1 Over 50 divided by 1 EndFraction = StartFraction 10 Over 50 EndFraction StartFraction 100 times 2 Over 50 times 2 EndFraction = StartFraction 200 Over 100 EndFraction StartFraction 10 divided by 2 Over 50 divided by 2 EndFraction = StartFraction 5 Over 25 EndFraction StartFraction 50 divided by 5 Over 100 divided by 5 EndFraction = StartFraction 10 Over 20 EndFraction Mark this and return
Answers
The option fourth StartFraction 50 divided by 5 Over 100 divided by 5 EndFraction = StartFraction 10 Over 20 EndFraction is correct.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
Let x be the number.
According to the problem.
50% of x = 10
x = 10 ÷ 50%
= 10×(50/100)
= (50÷5)/(100÷5) = 10/20
Thus, the option fourth StartFraction 50 divided by 5 Over 100 divided by 5 EndFraction = StartFraction 10 Over 20 EndFraction is correct.
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Rewrite in simplest terms: -3(7n+5n+8)-8n
Answers
Answer:
28n+24
Step-by-step explanation:
3 ( 7 n + 5 n + 8 ) - 8 n
combine 7n and 5n to get 12n
3 ( 12n + 8 ) - 8
distribute 3 to 12n +8
36n+24-8n
combine like terms
28n+24
since ypu cant simply any more it stays like thats
*by the way there is an app that helps with equation and explains the process, its Microsoft Math Solver. hope it helped
An item is regularly priced at $60. Jane bought it at a discount of 30% off the regular price. How much did Jane pay?
$
X
5
Answers
Answer:
$72
Step-by-step explanation:
100%-$60
1%-$0.60
100%-30%=70%
70%-$0.60x70=$42
How much would we pay per barrel of crude oil if the price goes up to US$ 75 and the US$ exchange rate stays the same?
Answers
If the price of a barrel of crude oil went up to $75, the amount that would be paid per barrel is $75.
What currency is oil denominated in?The U.S. dollar is the main currency for trade around the world which includes the trade of crude oil.
This means barrels of crude oil are denominated in dollars. An increase of crude oil to $75 per barrel means that Americans would be $75 because they already use the currency that the oil is denominated in.
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What is the volume of a right circular cylinder with a radius of 6 m and a height of 9 m?
• 547 m²
. 108 m²
3247 m³
4867 m²
Help
Answers
The volume of the right circular cylinder with a radius of 6 m and a height of 9 m is 1018 m².
The volume of a substance is the total space occupied by a three-dimensional object.
The volume of a right circular cylinder with a radius of r units and a height of h units is given by the formula V = πr²h square units.
We are asked to find the volume of the right circular cylinder with a radius of 6 m and a height of 9 m.
Substituting these values in the formula, we get Volume,
V = π(6)²(9) m² = 324π m² = 1017.876 m² ≈ 1018 m².
Therefore, the volume of the right circular cylinder with a radius of 6 m and a height of 9 m is 1018 m².
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In the video, the water level was 15 milliliters before adding the chain, and 20 milliliters after adding the chain. When I weighed the chain, its mass was 67.2 grams.
I believe the chain is solid metal (not gold plated), but is probably a blend of gold and other metals. I looked up that gold has a density of 19.3 g/ml, while the other metals like silver and copper usually blended with gold have a combined density of about 9.7 g/ml.
Determine what percentage of the chain is gold, by mass, to at least 1 decimal place?
Answers
The percentage of gold will be equal to 39.7%
What are percentages?The Percentage is defined as representing any number with respect to 100. It is denoted by the sign %.
1. First find the density of your chain
Density = mass / volume
Volume = displaced water volume
= Volume of Final level of water - initial level of water
= 20 ml - 15 ml = 5 ml
Mass = 66.7 g
Density = 66.7g / 5 ml = 13.34 g/ml
2. Second, write the density of the chain as the weighted average of the densities of the other metals:
Mass of gold x density of gold + mass of other metals x density of other metals, all divided by the mass of the chain.
Calling x the amount of gold, then the amount of other metals is 66.7 - x:
[(19.3x+(9.7)(66.7-x)] / 66.7 = 13.34
19.3x + 635.66 - 9.7x = 889.778
9.6x = 254.118
x = 26.47
Then, there are 26.47 grams of gold in 66.7 grams of chain, which yields a percentage of:
(26.47 / 66.7) x 100 = 39.7%
Therefore the percentage of gold will be equal to 39.7%
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the sum of all even numbers in 3 digit
it will mark as topper
Answers
Answer
sum of all 3 digit even number = 247050
The series is 100 + 102 + 104 + .... + 998
which by using formula Sn = N/2 ( a + an)
where N = number of terms
a = first term = 100
an = last term = 998
Each answer choice below represents a relation by a set of ordered pairs. In which of the answer choices is the relation a
function?
Select all correct answers.
Select all that apply.
□ {(-1,6), (4,4), (7, 13), (4,8)}
{(3,6), (3, 5), (9, 12), (0, -3)}
{(-5,0), (6, 8), (3,-5), (-5,-3)}
{(7,9), (8,4), (-2,4),(-3, 14)}
{(8,3), (3, 7), (6,4), (5,4)}
C
Answers
Answer:
D, E
Step-by-step explanation:
A set of ordered pairs represents a function if no x-value is repeated in the set.
Examine choices{(-1,6), (4,4), (7, 13), (4,8)} . . . . . not a function
{(3,6), (3, 5), (9, 12), (0, -3)} . . . not a function
{(-5,0), (6, 8), (3,-5), (-5,-3)} . . . . not a function
{(7,9), (8,4), (-2,4),(-3, 14)} . . . . no repeated x-values; is a function
{(8,3), (3, 7), (6,4), (5,4)} . . . . . .no repeated x-values; is a function
How would you answer this?: z^3/z^9
Answers
Hello !
Answer:
[tex]z {}^{ - 6} [/tex]
Step-by-step explanation:
[tex] \frac{z {}^{3} }{z {}^{9} } = z {}^{3 - 9} = z {}^{ - 6} [/tex]
Type an integer or decimal rounded to the nearest tenth f(80)=1000(0.5)80/30
Answers
The value of the function is 157.5
How to evaluate the function?The function is given as:
f(80)=1000(0.5)^(80/30)
Evaluate the quotient
f(80)=1000(0.5)^(8/3)
Evaluate the exponent
f(80)=1000 * 0.15749013123
Evaluate the product
f(80) = 157.49013123
Approximate
f(80) = 157.5
Hence, the value of the function is 157.5
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According to the National Postsecondary Student Aid Study conducted by the U.S. Department of Education in 2008, 62% of graduates from public universities had student loans.
We randomly select 50 students at a time.
What is the mean of the distribution of sampling proportions? Do not round, and enter your answer as a proportion (decimal number) not a percentage.
Answers
The mean of the distribution sample is 0.62 and the standard error of the distribution sample is 0.069
What is Mean ?Mean is the study of central tendency of a data set. The average value of the data points is the mean.
It is given that
The probability that the students have the student loan is = 62% = 0.62
The probability that the students do not have student loan is
1 - p
= 1 - 0.62
= 0.38
Total number of students is
n = 50
1) [tex]\rm \mu \;\hat p[/tex] = p = 0.62
2) [tex]\rm \sigma\hat p[/tex] = [tex]\rm \sqrt {p ( 1 - p ) / n}[/tex]
= [tex]\rm \sqrt {(0.62 * 0.38) / 50}[/tex]
= 0.069
Therefore the mean of the distribution sample is 0.62 and the standard error of the distribution sample is 0.069.
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Z
1
t
= [?]√
X
= Z
16
Answers
Answer: [tex]8\sqrt{5}[/tex]
Step-by-step explanation:
By the geometric mean theorem,
[tex]\frac{y}{16}=\frac{4}{y}\\\\y^{2}=64\\\\y=8[/tex]
So, by the Pythagorean theorem,
[tex]8^2 + 16^2 = x^2\\\\320=x^2\\\\x=\boxed{8\sqrt{5}}[/tex]
How much should you put in an investment paying simple interest rate of 8% if you need 4000 in six months?
Answers
The amount you should put is 3846
How to determine the principal amount?The given parameters are:
Amount, A = 4000
Rate, r = 8%
Time = 0.5 year i.e. 6 months
The amount on simple interest is calculated as:
A = P(1 + RT)
This gives
4000 = P * (1 + 8% * 0.5)
Evaluate the product
4000 = P * (1 + 0.04)
Evaluate the sum
4000 = P * (1.04)
Divide both sides by 1.04
P= 3846
Hence, the amount you should put is 3846
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mrs.darby works at the local bakery as a cake decorator if it takes her 1 1/3 hours to decorate one cake how many cakes can she dcorate in a 30-hour week.
Answers
The number of cakes Mrs Darby can decorate in a 30-hour week is 22.5 cakes.
Number of cakes to decorateTime taken to decorate a cake = 1 1/3 hoursTotal time for decoration per week = 30 hoursTime conversion
1 hour = 60 minutes
1 1/3 hours = 60 × 1 1/3
= 60 × 4/3
= 240/3
= 80 minutes
30 hours = 30 × 60
= 1800 minutes
Number of cakes decorated = 1800 / 80
= 22.5 cakes
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Slope is -4/5 and passes through the point (2, -3).
5
Answers
Answer:
y = (-4/5)x - 7/5
Step-by-step explanation:
The general equation of the line is slope-intercept form is:
y = mx + b
In this form, "m" represents the slope and "b" represents the y-intercept. You have been given the value of the slope (m = -4/5). To find the y-intercept, use the slope and values from the Point (2,-3) to isolate "b".
y = mx + b <----- Slope-intercept form
y = (-4/5)x + b <------ Plug -4/5 in "m"
-3 = (-4/5)(2) + b <----- Plug in "x" and "y" values from Point
-3 = -8/5 + b <------ Multiply -4/5 and 2
-15/5 = -8/5 + b <----- Assign common denominator
-7/5 = b <----- Add 8/5 to both sides
Now that you have the slope and y-intercept, you can construct the equation.
y = (-4/5)x - 7/5
There are 520 bridges on the freight rail network in the province of Ostenborg. Of these, 200 are classified as “old” rail bridges (i.e., 50 years or more in age). Past records indicate that 50% of all rail bridges in the state exhibit visible signs of structural distress. Of the bridges 70% are old or exhibit structural distress.
Find the probability that a randomly selected rail bridge will exhibit structural distress given that it is old.
Answers
Answer:
The probability that a selected randomly rail bridge will exhibit structural distress given that it is old
= (200/520) * 0.5 * 0.7 * 100
= 0.1346154 * 100
= 13.46154 %
The values in the table represent an exponential function. What is the common ratio of the associated geometric sequence?
x y
1 9
2 36
3 144
4 576
5 2304
Answers
The common ratio of the associated geometric sequence is 4
How to determine the common ratio?The table of values is given as:
x y
1 9
2 36
3 144
4 576
5 2304
The common ratio is calculated as:
Ratio = y(2)/y(1)
This gives
Ratio = 36/9
Divide
Ratio - 4
Hence, the common ratio is 4
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8. What is 3x times (3x² - 5)?
a.3x² + 5x -5
b.9x³-5
c.9x³ - 15x
d.15x³ - 25x
Answers
Answer:
9x^3-15x
Step-by-step explanation:
What is the order of rotational symmetry for the figure?
•A. 2
B. 1
C. 4 or more
D. 3
Answers
C is the right answer.
Trust me char!!
Na bakla na yswa!
Inferential statistics
Answers
Answer:
Inferential statistics use measurements from the sample of subjects in the experiment to compare the treatment groups and make generalizations about the larger population of subjects. There are many types of inferential statistics and each is appropriate for a specific research design and sample characteristics
Step-by-step explanation:
hope this helps (﹡ˆ﹀ˆ﹡)♡