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3 years ago

For the parallelogram, fond the value of the variables. Show your work.

Mathematics

2 answers:

motikmotik3 years ago

5 0

The opposite sides of a parallelogram are congruent.

So we have

3y - 6 = 21

3y = 27 so y = 9 (answer)

and 5x + 2 = 17

5x = 15 so x = 3 (answer)

lisabon 2012 [21]3 years ago

3 0

For this case, the first thing you should know is that the opposite sides of the parallelogram are the same.

Therefore, we have the following equations:

$3y-6 = 21\\5x + 2 = 17$

From equation 1 we have:

$3y = 21 + 6\\3y = 27$

$y = \frac{27}{3}\\y = 9$

From equation 2 we have:

$5x = 17 - 2\\5x = 15$

$x = \frac{15}{5}\\x = 3$

Answer:

the value of the variables are:

$y = 9\\x = 3$

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3 years ago

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kirill115 [55]

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4 0

2 years ago

The length of a 200 square foot rectangular vegetable garden is 4feet less than twice the width. Find the length and width of th

inna [77]

Answer:

Length = 18.099 ft

Width = 11.049 ft

Step-by-step explanation:

let the length of the field be x ft

and the width be y ft

as per the condition given in problem

x=2y-4 -----------(A)

Also the area is given as 200 sqft

Hence

xy=200

Hence from A we get

y(2y-4)=200

taking 2 as GCF out

2y(y-2)=200

Dividing both sides by 2 we get

$y(y-2)=100$

$y^2-2y=100$

subtracting 100 from both sides

$y^2-2y-100=0$

Now we solve the above equation with the help of Quadratic formula which is given in the image attached with this for any equation in form

$ax^2+bx+c=0$

Here in our case

a=1

b=-1

c=-100

Putting those values in the formula and solving them for y

$y=\frac{-(-2)+\sqrt{(-2)^2-4 \times (-1) \times 100}}{2 \time 1}$

$y=\frac{-(-2)-\sqrt{(-2)^2-4 \times (-1) \times 100}}{2 \time 1}$

Solving first

$y=\frac{2+\sqrt{4+400}{2}$

$y=\frac{2+\sqrt{404}{2}$

$y=\frac{2+20.099}{2}$

$y=\frac{22.099}{2}$

$y=11.049$

Solving second one

$y=\frac{-(-2)-\sqrt{(-2)^2-4 \times (-1) \times 100}}{2 \time 1}$

$y=\frac{2-\sqrt{4+400}{2}$

$y=\frac{2-\sqrt{404}{2}$

$y=\frac{2-20.099}{2}$

$y=\frac{-18.99}{2}$

$y=-9.045$

Which is wrong as the width can not be in negative

Our width of the field is

y=11.099

Hence the length will be

x=2y-4

x=2(11.049)-4

x=22.099-4

x=18.099

Hence our length x and width y :

Length = 18.099 ft

Width = 11.049 ft

4 0

3 years ago