What is a point on the line with equation y + 2 = 5 (x - 3) ? (- 3, 2) (- 2, 3) (2, - 3) (3, - 2) are my only choices

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).

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)".

Learn more about parallelograms ​here,

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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:

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!!

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:

Answer:

The answer is

Step-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

Hope this helps you

Answer:

Step-by-step explanation:

[tex]2x+7y+3x-4y\\\\\mathrm{Group\:like\:terms}\\=2x+3x+7y-4y\\\\\mathrm{Add\:similar\:elements:}\:2x+3x=5x\\=5x+7y-4y\\\\\mathrm{Add\:similar\:elements:}\:7y-4y=3y\\= 5x+3y[/tex]

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Hi my lil bunny!

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

             [tex]\boxed{5x + 3y}[/tex]

Let's simplify step-by-step.

[tex]2x+7y+3x-4y[/tex]

[tex]= 2x+7y+3x-4y[/tex]

Combine Like Terms:

[tex]2x+7y+3x-4y\\= ( 2x + 3x ) + ( 7y + -4y ) \\= 5x + 3y[/tex]

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Have a great day/night!

❀*May*❀

Answer:

36cm

Step-by-step explanation:

38 × 2 = 76

148 - 86 = 72

72/2 = 36

Answer:

a century = 100 years.

3/4 x 100 years = 75 years.

2/5 x 100 years = 40 years.

Answer:

-2.5

Step-by-step explanation:

Subtract -8.5 from -6, and continue down the column.

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:

Answer:

It is 0.56 Hope this helps!

Step-by-step explanation:

Answer:

0.5625

Step-by-step explanation:

divide and you get 0.5625. Simplified to the nearest tenth is .6

to the nearest hundreth if .56

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

Answer:

answer is c

Step-by-step explanation:

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.

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.

Learn more about the line of best fit here:

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Answer: The 4 in the number 5,401 is 10 times greater than the 4 in the number 3,642.

In the number 3,642 the number 4 is in the Tens Place.

In the number 5,401 the number 4 is in the Hundreds Place.

Tens < Hundreds

40 < 400

Q: How do we know it's 10 times greater?

A: Multiply!

You multiply 40×10 and get 400! To see if the answer is right divide 400÷40 and get 10. Or divide 400÷10 and get 40.

Basically, when you're multiplying something by 10 you just add a 0. When you divide by 10 you remove a 0.

That's how the number 4 in 5,401 is 10 times greater than the number 4 in 3,642.

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 :)

Answer:

[tex]x + \frac{2}{5} \times x = 70 \\ x + \frac{2}{5} x = 70[/tex]

Answer:

Let it be x the number.

We have to sum to x two fifths of him and we know the result is 70, so:

[tex]x + \frac{2}{5}x = 70[/tex]

We could also solve it:

[tex]\frac{5x}{5}+\frac{2x}{5}=\frac{350}{5}[/tex]

[tex]5x + 2x = 350[/tex]

[tex]7x = 350[/tex]

[tex]x=\frac{350}{7}=50[/tex]

Answer:

-14,-5,-2,6,14,23

Let me know if this helped :)

Answer:

-11p + 7

Step-by-step explanation:

(-4p+2)-(7p-5)

-4p + 2 - 7p + 5

-11p +7

Answer:

-11p + 7

Step-by-step explanation:

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

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

Answer:

4:3

Step-by-step explanation:

divide 8 by 2 and 6 by 2

8/2:6/2

4:3

Hi there!

Answer:

4:3

Step-by-step explanation:

Here is how we simplify a ratio:

1.Find the greatest common factor in both of the numbers

2.Divide both of the numbers by that factor.

3. And than your done solving the problem!

*******************************************************************

You have to divide both numbers by 2 because the GCF of 8 and 6 is 2

Remember; GCF means Greatest Common Factor...

8/2=4

6/2=3

Since we got 4 and 3...

The answer would be 4:3

So, 8:6 would equal to 4:3

Also if you want to simplify you have to divide and make it the smallest number you can!

If we simplify 8:6 it will be 4:3 but we can’t simplify 4:3 so that will be the answer.

(Note; Half of 8 is 4 and half of 6 is 3 so we know that’s correct, it’s also a way you can check your work)

~Have a great day!~

If you have any questions, feel free to ask! :)

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:

Answer:

The mean is 0.68 and the standard deviation is 0.0127. I hope this helps

Step-by-step explanation:

Answer:

Standard = 922Answer: Mean

Step-by-step explanation: vote

=Step-by-step explanation:If they say 54% wet their toothbrush first, then that means that there are about 732 people ...  More

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

Answer:

[tex]y=\frac{c-ax}{b}[/tex] is the answer

Step-by-step explanation:

ax+by=c

subtracting ax on both sides

ax-ax+by=c-ax

by=c-ax

dividing b on both sides

by/b=[tex]\frac{c-ax}{b}[/tex]

[tex]y=\frac{c-ax}{b}[/tex]

hope it will help ^_^

Answer:

y= (c-ax)/b

Step-by-step explanation:

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.