Need help with this please

Given:

The three vertices of parallelogram are (0,6),(5,-4),(-1,-5).

To find:

The fourth vertex of the parallelogram.

Solution:

Consider the given vertices of parallelogram are A(0,6), B(5,-4), C(-1,-5).

Let the fourth vertex be D(a,b).

Midpoint formula:

[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]

We know that the diagonal of parallelogram bisect each other. It means their midpoints are same.

Midpoint of AC = Midpoint of BD

[tex]\left(\dfrac{0+(-1)}{2},\dfrac{6+(-5)}{2}\right)=\left(\dfrac{5+a}{2},\dfrac{-4+b}{2}\right)[/tex]

[tex]\left(\dfrac{-1}{2},\dfrac{1}{2}\right)=\left(\dfrac{5+a}{2},\dfrac{-4+b}{2}\right)[/tex]

On comparing both sides, we get

[tex]\dfrac{5+a}{2}=-\dfrac{1}{2}[/tex]

[tex]5+a=-1[/tex]

[tex]a=-1-5[/tex]

[tex]a=-6[/tex]

And,

[tex]\dfrac{-4+b}{2}=\dfrac{1}{2}[/tex]

[tex]-4+b=1[/tex]

[tex]b=1+4[/tex]

[tex]b=5[/tex]

Therefore, the coordinates of fourth vertex are (-6,5).

Answer:

0 votes

Answer:27000Step-by-step explanation:interest= principal×rate×time÷ 100=270000×5×2÷100=27000

Answer:

0.95

Step-by-step explanation:

A depreciation of 5% from the original 100% is

100% - 5% = 95% = [tex]\frac{95}{100}[/tex] = 0.95

Answer:

wish that will help u

Answer:

16

Step-by-step explanation:

From the diagram;

AC = 2CE

Given that AC = 32

32 = 2CE

Swap

2CE = 32

CE = 32/2

CE =16

Hence the length of CE is 16

Rs 121428.5714 is Answer:

let quantity be x

17% of x=Rs 8500

x=8500×100/7=Rs 121428.5714

Answer:The first one

Step-by-step explanation:

Cheap data's distribution is more symmetrical

Answer:

the answer for both of them is x=4/5y-4

Step-by-step explanation:

Step 1: Add 8y to both sides.

10x−8y+8y=−40+8y

10x=8y−40

Step 2: Divide both sides by 10.

10x/10=8y−40/10

x=4/5y−4

Answer:

x=4/5y−4

hope this helped :)

Answer:

74 feet

Step-by-step explanation:

24^2 + 70^2 = 74^2

Pythagorean Theorem

Answer:

Exact Form:

265/3

Decimal Form:

88.3 (with a line over the 3)

Mixed Number Form:

88 1/3

Answer: 7

Step-by-step explanation:

-x^2 -6y+13x+7

The constant is the term with no variable attached to it

7 is the constant

Answer:

7

Step-by-step explanation:

Answer:

RT = 86

Step-by-step explanation:

Here, we want to find the value of RT

looking at the given triangle, we can deduce that the smaller triangle SPQ is half the measure of the bigger triangle SRT

what this mean is that we have to multiply the dimensions on SPQ by 2 to get the equivalent dimensions of similar sides in SRT

Thus, we have it that;

2(15x -17) = 23x -6

30x - 34 = 23x -6

30x -23x = -6 + 34

7x = 28

x = 28/7

x = 4

So, we make a substitution

for RT;

23x-6

= 23(4) - 6 = 92-6 = 86

Answer:

[tex]\triangle LKJ \sim \triangle LHG[/tex]

Step-by-step explanation:

Let suppose that JK and GH are parallel to each other and the length of JK is a multiple of the length of GH ([tex]JK = m\cdot GH[/tex]), then we know that [tex]\angle H \cong \angle J[/tex] and [tex]\angle G \cong \angle K[/tex] by alternate internal angles and [tex]\angle L_{1} \cong \angle L_{2}[/tex] by opposite angles, then [tex]KL = m\cdot GL[/tex] and [tex]HL = m\cdot JL[/tex]. Lastly, we conclude that [tex]\triangle LKJ \sim \triangle LHG[/tex]

Answer:

Gobi Desert and karakum desert

Step-by-step explanation:

Answer: (-5,0)  will be your answer hope this helps

Step-by-step explanation:

Answer:

ummm 3rd answer. i did this i forgot. sorry if i got it wrong for you. at least i tried

Step-by-step explanation:

Answer:

multiply the distance by 0.7

Answer:

Divide it by 10, multiply it by 7

Example:

Find 7/10ths of 20

20/10 = 2

2x7=14

Answer:

D The set represents y as a function of x because each y-value corresponds to exactly one x-value​

Step-by-step explanation:

Answer:

y=-4 or y=-6

Step-by-step explanation:

y^2-14y+49=2y^2-4y+73

y^2+10y+24=0

(y+4)(y+6)=0

y=-4 or y=-6

Answer:

B

Step-by-step explanation:

0.075 l+

0.200 l

=0.275 l

Answer:

B.)

Step-by-step explanation:

I took the test

Answer:

15u + 141 = 420

Step-by-step explanation:

So basically we are modelling how much the coach is spending. Each player is given a uniform and a basketball

We can use 'u' as the cost of a single uniform

We can use 'b' as the cost of a single basketball

Since there is 15 players we must give a ball and uniform to each so

15u + 15b = 420

The problem gives us the cost of each basketball: 9.40

so now 15u + 15(9.4) = 420

15u + 141 = 420

Answer:

4

Step-by-step explanation:

Given:

4 - 0.25g + 0.5h

When,

g = 10; and h = 5

4 - 0.25g + 0.5h

= 4 - 0.25(10) + 0.5(5)

= 4 - 2.5 + 2.5

= 4

Therefore,

4 - 0.25g + 0.5h = 4 when g = 10 and h = 5

Answer:

m=-2

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

-4x + 7 = 2y - 3

7 = 2y - 3 + 4x

0 = 2y - 3 + 4x - 7

-2y = -3 + 4x - 7

-2y = 4x - 10

y = -2x + 5

As the slope of the line is equal to the value of x, the slope of this line is -2

Answer:

14.9cm

Step-by-step explanation:

hope it helps you good day.

Answer:

[tex]\theta = 53.13 degrees[/tex]

Step-by-step explanation:

From the question we are told that:

intercept co_ordinate (x,y)

(3/5,4,5)  

Generally the value for [tex]\theta[/tex] is mathematically given by

[tex]cos \theta = 3/5\\sin \theta = 4/5\\\theta = cos^-1 (3/5 )[/tex]  

[tex]\theta = 53.13 degrees[/tex]

Answer:

2(x - 7) = 2x - 14

Step-by-step explanation:

→ Expand out equation

2x - 14 = 2x - 14

→ Minus 2x from both sides

-14 = -14