Answer:
If you are given 3 vertices of a parallelogram, as a Geometry student, you will be asked to find the exact coordinates of the 4th vertex. Just so that you can put your mind at ease, there can be different answers depending on how you decide to "draw" or "shape" your parallelogram. So if your answer is different than another student, it does not mean that you have done it incorrectly.
Suppose I am given 3 points as such, and I am looking for the coordinates of D:
A (2, 3)
B (8, 1)
C (11, 5)
D (x, y)
The line segments that make up our parallelogram is AD is parallel to BC, and CD is parallel to AB. Since the definition of a parallelogram is a quadrilateral with 2 pairs of parallel sides, we can use this fact to find the coordinate to the 4 vertex. A pair of parallel side also means that these 2 lines have the same slope. So if we do this on both pairs of parallel lines, we should have 2 equations with 2 variables, which should be simple to solve.
Slope of CD = Slope Slope of AB
(y - 5)/(x - 11) = (1 - 3)/(8 - 2)
(y - 5)/(x - 11) = -2/6
6(y - 5) = -2(x - 11)
6y - 30 = -2x + 22
equation #1: 6y + 2x = 52
Slope of AD = Slope of BC
(y - 3)/(x - 2) = (5 - 1)/(11 - 8)
(y - 3)/(x - 2) = 4/3
3(y - 3) = 4(x - 2)
3y -9 = 4x - 8
equation #2: 3y - 4x = 1
We now we have 2 equations with 2 variables, and we can use any method (substitution, linear combination, matrix) to solve for the x and y coordinates.
equation #1: 6y + 2x = 52
equation #2: 3y - 4x = 1
Multiply equation by -2
Equation 2: -2(3y - 4x = 1)
Equation 2: -6y + 8x = -2
Add equation 1 to equation 2
equation 1: 6y + 2x = 52
equation 2: -6y + 8x = -2
eq 1 + eq 2: 10x = 50
x = 5
Use any of the original equation to solve for y:
6y + 2x = 52
6y + 2(5) = 52
6y = 42
y = 7
So the 4th vertex for my first answer will be (5, 7)
If we draw the parallelogram in a different way using the given vertices, we will be looking for a different 4th vertex. So in our original question:
A (2, 3)
B (8, 1)
C (11, 5)
D (x, y)
Our line segments in this case will be draw as such:
AC is parallel to BD and CD is parallel to AB.
Slope of AC = slope of BD
(5 - 3)/(11 - 2) = (y - 1)/(x - 8)
2/9 = (y - 1)/(x - 8)
2(x - 8) = 9(y - 1)
2x - 16 = 9y - 9
equation 1: 2x - 9y = 7
Slope of CD = slope of AB
(5 - y)/(11 - x) = (3 - 1)/(2 - 8)
(5 - y)/(11 - x) = 2/-6
-6(5 - y) = 2(11 - x)
-30 + 6y = 22 - 2x
equation 2: 2x + 6y = 52
Solve the following linear system:
equation 1: 2x - 9y = 7
equation 2: 2x + 6y = 52
eq 1 - eq2: -15y = -45
-15y = -45
y = 3
Substitute y = 3 into any one of the original equation:
equation 1: 2x - 9y = 7
2x - 9(3) = 7
2x - 27 = 7
2x = 34
x = 17
So by drawing the parallelogram in a different way, the 4th vertex of this parallelogram is (17, 3).
Step-by-step explanation:
See Answer
The fourth coordinate for the given parallelogram will be (5, 7).
What is a parallelogram?A basic quadrilateral with two sets of parallel sides is known as a parallelogram.
A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.
There are 4 types of parallelograms, including 3 special types. The four types are parallelograms, squares, rectangles, and rhombuses.
Given the parallelogram ABCD are A(2, 0), B(4, 3), C(3, 1).
Now,
The slope of AB = Slope of CD
(y - 5)/(x - 11) = (1 - 3)/(8 - 2)
6(y - 5) = -2(x - 11)
⇒ 6y + 2x = 52 will be the first equation.
Now,
The slope of BC = Slope of AD
[(y - 3)/(x - 2)] = [(5 - 1)/(11 - 8)]
[(y - 3)/(x - 2)] = 4/3
3(y - 3) = 4(x - 2)
⇒ 3y - 4x = 1 will be the second equation.
Now, By substitution
x = 5 and y = 7
Hence "The fourth coordinate for the given parallelogram will be (5, 7)".
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The table and scatter plot show the number of hours worked, x , and the amount of money spent on entertainment, y, by each of 10 students. The equation of the line of best fit is y=0.3x+24.00 Use the equation of the line of best fit to fill in the blanks below. Give exact answers, not rounded approximations.
Answer:
number of hours worked equation
The observed amount are At x = 7.9, y = $33.50 and at x = 25.00, y = $25.00 predicted amount are At x = 7.9, y = $26.37 and At x = 12.1, y = $27.63 and residuals are $7.13 and -$2.63.
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
Observed amount:
At x = 7.9, y = $33.50
At x = 25.00, y = $25.00
We have a line of best fit:
y=0.3x+24.00
At x = 7.9
Predicated amount:
y = $26.37
At x = 12.1
Predicated amount:
y = $27.63
Residual (when x = 7.9) = $33.50 - $26.37 = $7.13
Residual (when x = 12.1) = $25.00 - $27.63 = -$2.63
Thus, the observed amount are At x = 7.9, y = $33.50 and at x = 25.00, y = $25.00 predicted amount are At x = 7.9, y = $26.37 and At x = 12.1, y = $27.63 and residuals are $7.13 and -$2.63.
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The surface area of a cube is 600 cubic centimeters. What is the volume? Answer Choices are on the Image.
Answer:
D. 1,000 cm^3
Step-by-step explanation:
Surface area of a cube is calculated by multiplying the square value of the edge by 6 which is shown as 6 × a^2
6 × a^2 = 600
a^2 = 100
a = 10
The volume of a cube is calculated by multiplying edge with itself three times which is shown as a^3
10^3 = 1000
Answer:
D
Step-by-step explanation:
10×10 on each side of the cube= 100. 6 sides = 600.
10×10×10= 1000
Estimate: 4.1 * 7.8 *2.3
Answer:
yea yeah
Step-by-step explanation:
singing challenge
The Bradenton Post polled 1,356 adults in the city to determine whether they wet their toothbrush before they put toothpaste on it. Of the respondents, 54% said they wet it first. Suppose 68% of all adults actually wet their toothbrush first. What are the mean and standard deviation of the sampling distribution?
Answer:
deviation = -95.50147493 mean = 61
Step-by-step explanation:
54% wet there brushes first
suppose 68% wet there brushes what is the mean
mean: a mean is where you add both numbers together to get a total then divide by how many numbers you added for now we wont need the amount of people we just need the percentages for this
54 + 68 = 122
we added to numbers so well divide by 2
122 divided by 2 or 122/2 is equal to 61
61 is our mean
standard deviation : this is were you take the known average 1356 adults and subtract the mean
1356- 61 = 1295 then divide by 1356 and times by 100
if the number is positive then the mean is higher than expected but luckily its a negative so its -95.50147493
Which expression is equivalent to (-4p+2) - (7p-5) A. 3p-3 B. 3p+7 C.-11-3 D.-11+7
Answer:
-11p + 7
Step-by-step explanation:
(-4p+2)-(7p-5)
-4p + 2 - 7p + 5
-11p +7
Answer:
-11p + 7
Step-by-step explanation:
Find an equation in standard form for a parabolic function that goes through the points (1,-12) (3,16) and has a stretch factor of 2
Answer:
Vertex form of a quadratic equation is y=a(x-h)2+k, where (h,k) is the vertex of the parabola.
The vertex of a parabola is the point at the top or bottom of the parabola.
'h' is -6, the first coordinate in the vertex.
'k' is -4, the second coordinate in the vertex.
'x' is -2, the first coordinate in the other point.
Step-by-step explanation:
Molten lava 50-feet thick cools at a rate of about 20 degrees Fahrenheit per month. What is the overall change in temperature of molten lava that is 50-feet think after four months?
HELLLLPPPP I WILL MARK BRAINLESTTTT
The equations of three lines are given below. Line 1: 6x-4y=6 Line 2: -2y=3x+5 Line 3: y=-2/3x+7 For each pair of lines, determine whether they are parallel, perpendicular, or neither.
Answer:
Line 1 and Line 2: Neither -- slopes are not same (one is negative one is positive)
Line 1 and Line 3: Perpendicular -- Line 3's slope is the negative reciprocal of Line 1's
Line 2 and Line 3: Neither -- different slopes
Step-by-step explanation:
Lines are parallel if they have the same slope but different y-intercept.
Lines are perpendicular if the slopes are negative reciprocals.
I need help arranging cards in a 4 x 4 grid with numbers 1-9 so that the sum of each row and each column is 20. This what the grid looks like:
Answer:
8, 2, 8, 2
7, 3, 7, 3
6, 4 6, 4
9, 1, 9, 1
Step-by-step explanation:
In the picture, it shows two of each number so I'm gonna base it off the picture but let me know if I should base it off the wording.
So we know that half of 20 is 10. This will be valuable information. So we need the sum of two numbers to equal 10. So for the rows we can just do 8+2+8+2, 7+3+7+3, 6+4+6+4, 9+1+9+1.
Since there are 18 numbers, I'm assuming we don't have to use all of them.
Answer:
9, 1, 9, 1
2, 8, 2, 8
3, 7, 3, 7
6, 4, 6, 4
Step-by-step explanation:
you would have to have the numbers repeat so it works, for instance, you could do 9,1,9,1 as the first row then 2,8,2,8 as the second row and for the third row you could do 3,7,3,7 and for the fourth row you could do 6,4,6,4 so both the columns and rows add to 20
Two third of a number is greater than one third of the number by 5. The number is ________
Let's assume the number as x
→ ⅔rd of x =( ⅔)x
Now ⅔ of x is greater than ⅓ of 5 .
[tex] \sf{ \implies \: \dfrac{1}{3} \times 5 = \dfrac{5}{3} } [/tex]
[tex]\sf{ \implies \: \dfrac{2}{3} \times x > \dfrac{5}{3} } [/tex]
[tex]\sf{ \implies \: x > \dfrac{5}{3} \times \dfrac{3}{2} }[/tex]
[tex]\sf{ \implies \: x > \dfrac{5}{2} }[/tex]
So number will be greater than 5/2 .
Answer:
the answer is 10
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i need more brainlees
plsss help me
Step-by-step explanation:
jack bought 4 bagels for 3.00. how many bagels can he buy for 4.50?
Answer:
The answer is
6 bagelsStep-by-step explanation:
In order to solve this problem we use ratio and proportion
From the question
He used 3.00 to buy 4 bagels
Then 4.50 will be
[tex] \frac{4.5 \times 4}{3} \\ = \frac{18}{3} [/tex]
We have the final answer as
6 bagelsHope this helps you
Which measurement represents the greatest length? 1 meter 27 inches 98 centimeters 6 feet?
Answer:
6 ft is the greatest length
Step-by-step explanation:
1 meter= 3.2 ft
1 meter= 100 centimeters
1 meter= 39.4 inches
6-3.2 = 2.8 which runs over
Hope this helps
Answer:
6 feet
Step-by-step explanation:
Alice earned $12 per hour. What equation shows the relationship between her weekly salary (w), hours per week (h), and rate per hour (r).
4/5 y = 8 , how do we solve pls help fast its urgent, I will mark u brainliest
Answer:
y = 10
Step-by-step explanation:
4/5 y = 8
4/5 y * 5/4 = 8 * 5/4 multiply by reciprocal
y = 10
Answer: y=10
Step-by-step explanation:
times each side by 5 so you're left with 4y=40
divide wach by 4 and then you got the answer
1.5d + 8.25 = 3 + 2.25d
pls help meee
Answer:
d=7
Step-by-step explanation:
1.5d-2.25d = 3-8.25
-0.75d= -8.25
d=7
Answer:
is it 11.25?
Step-by-step explanation:
PLEASE HELP!! PLEASE STEP BY STEP!
Answer:
answer is c
Step-by-step explanation:
Please help quickly! Thank you!
Larry is building a frame around a rectangular picture. He will need 40 inches of wood to do the entire frame. If the frame is 12 inches long, how wide is the frame?
Answer:
8
Step-by-step:
12+12=24
40-24= 16
there is 16 inches of wood left
16/2=8
8 inches of wood for each side of width.
The length of a rectangle is 3ft more than twice the width, and the area of the rectangle is 54ft^2. Find the dimensions of the rectangle.
Answer: Let length = 2x + 3
Let width = x
Area = 54 ft2
length × width = Area
x(2x + 3) = 54
2x2 + 3x = 54
2x2 + 3x - 54 = 0
(2x - 9)(x + 6) = 0
x = 9/2 and x = -6
x = 4.5 and x = -6
We accept x = 4.5 because length cannot be a negative value. Substituting this value into the dimensions:
width = 4.5 ft
length = 2(4.5) + 3 = 9 + 3 = 12 ft
Step-by-step explanation:
What is the rate of change of the function represented by the table?
A. –2.5
B .–1
C. 1
D. 2.5
NEEED HEEELP!!! WILL GIVE BRAINLIEST
Answer:
-2.5
Step-by-step explanation:
Subtract -8.5 from -6, and continue down the column.
Solve: (-4) - 16 ÷ (-4) × 10 + 20
Find the value of 3/4 of 2/5 of a century.
Answer:
a century = 100 years.
3/4 x 100 years = 75 years.
2/5 x 100 years = 40 years.
PLEASE ASAP Find the value of x
Answer: this is in a fraction: X = 16/5, decimal form: x = 3.2, and in a mix number: x = 3 1/5
Step-by-step explanation:
Answer:
The letter "x" is often used in algebra to mean a value that is not yet known. It is called a "variable" or sometimes an "unknown". In x + 2 = 7, x is a variable, but we can work out its value if we try! A variable doesn't have to be "x", it could be "y", "w" or any letter, name or symbol.
Step-by-step explanation:
Last month I had 8 guppies. This month I have 20 guppies. What is the percent of increase in guppies from last month to this month?
Answer: 150% increase
Step-by-step explanation:
percent of increase: new/old × 100%-100%
--------------
new/this month: 20 puppies
old/last month: 8 puppies
new/old×100%-100%
=20/8×100%-100%
=2.5×100%-100%
=250% -100%
=150% increase
Hope this helps!! :)
Please let me know if you have any question
Write the set of integers in order from least to greatest. 23, 14, -14, -5, 6, -2
Answer:
-14,-5,-2,6,14,23
Let me know if this helped :)
Sal deposited $5000 in a 60-month CD the paid 5% interest compounded annually. What was the total value of the CD after 5 years?
Plz fill the blanks in. 2 thousandths+ 9 ones 5 thousandths=_____thousandths=_______
Answer:
the thousandths equils 2
Step-by-step explanation:
yuh
Answer:
9007 thousandths = 9.007
Step-by-step explanation:
A unit is 1000 thousandths, so 9 ones is 9000 thousandths.
You have ...
0.002 + 9.005 = 9.007
2 thousandths + 9 ones 5 thousandths = 9007 thousandths = 9.007
Pls help i need the answer asap
Answer:
1) An triangle
2)Area is the same
3) Length times width then times 1/2
4)To find the polygon's area using the circle's measurement you us pi times radius squared(to find the circles area which is the same as the polygon's area)
HOPE THIS HELPS :)
Simplify 6(x + 4) 10x 6x + 4 6x + 24
Answer:
=360x4+1440x3+24x+24
Step-by-step explanation:
6(x+4)(10)xx(6)x+(4)(6)x+24
=360x4+1440x3+(4)(6)x+24
=360x4+1440x3+24x+24
Hope it helps!!