How do I solve this using long division?

Find the lengths and slopes of the diagonals to name the parallelogram. Choose the most specific name. E (-2, -4), F(0, -1), G(-

Kay [80]

Answer:

1) d) Square

2) Proofs that PWRS is a rhombus are

Length of QS ≠ PR and

Slope of segment QR and PS is -1/2 and Slope of segment RS and QP is -2.

Step-by-step explanation:

The given points (x, y) of the parallelogram are;

E(-2, -4), F(0, -1), G(-3, 1), H(-5, -2)

The slope, m, of the segments are found as follows;

$Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$

By computation, the slope of segment EF = 1.5

The slope of segment FG = -0.67

The slope of segment GH = 1.5

The slope of segment HE = -0.67

Therefore, EF is parallel to GH and FG is parallel to HE

The length of the sides are;

$\sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}$

By computation, the length of segment EF = 3.61

The length of segment FG = 3.61

The length of segment GH = 3.61

The length of segment HE = 3.61

The diagonals are;

EG and FH

The length of segment EG = 5.099

The length of segment FH = 5.099

Therefore, the diagonals are equal and the parallelogram is a square

2) The given dimensions are;

P(-1, 3), Q(-2, 5), R(0, 4), S(1, 2)

A rhombus has all sides equal

The length of segment PQ = 2.24

The length of segment QR = 2.24

The length of segment RS = 2.24

The length of segment PS = 2.24

The diagonals are;

QS and PR

The length of segment QS = 4.24

The length of segment PR = 1.41

The slope of segment QR = -0.5

The slope of segment PS = -0.5

The slope of segment RS = -2

The slope of segment QP = -2

Therefore, QS≠QR the parallelogram is a rhombus

The correct option ;

Length of QS ≠ PR and

Slope of segment QR and PS is -1/2 and Slope of segment RS and QP is -2.

Where there are acute angles in parallelogram PQRS, then the correct option is d) Length of QR and PS is 2.2 and Length of RS and QP is 2.2

8 0

3 years ago

Enter and solve a polynomial equation for the situation described.

klasskru [66]

Height = x (This is given)

Length = 5x

Width = 6x

Volume = length × width × height

The equation will be: (5x)(6x)(x) = 1920

simplify:

30x² × (x) = 1920

30x³ = 1920

Divide both sides by 30

x³= 64

x = ∛64

x= 4

If x = height, then, the height is 4cm

5x = length

20cm = length

6x = width

24cm = width

7 0

3 years ago

1.

Alekssandra [29.7K]

Answer:

The number of visit so that both plan cost same is 10 .

Both the plan has equivalent choice of benefit

Step-by-step explanation:

Given as :

A gym has two membership plans.

For Gold plan

The charge per month = $50

The charge per visit = $3

For Platinum plan

The charge per month = $20

The charge per visit = $6

Let The number of visit for which each plan be same = n visits

Now, According to question

So,

The charge per month for gold plan+ The charge per visit × numbers of visit = The charge per month for platinum plan+ The charge per visit × numbers of visit

I.e $50 + $3 × n = $20 + $6 × n

Or, $50 - $20 = $6 × n - $3 × n

Or, $30 = ($6 - $3) × n

Or, $30 = $3 × n

∴ n = $\dfrac{30}{3}$

I.e n = 10

So, The number of visits = n = 10

Now, For Gold plan

The charge per month = $50

The charge per visit = $3 × 10 = $30

So, Total charge for gold plan = $50 + $30 = $80

Similarly For Platinum plan

The charge per month = $20

The charge per visit = $6×10 = $60

So, For Platinum plan ,total charge = $20 + $60 = $80

Hence, The number of visit so that both plan cost same is 10

and both the plan has equivalent benefit. Answer

4 0

3 years ago

Queston 132

Sever21 [200]

Answer:

68cm^2

Step-by-step explanation:

<h2>A trapezium is a type of quadrilateral with the two opposite sides parallel.</h2>

Area of a trapezium= 1/2(sum of parallel sides)×height

Area of the trapezium= 1/2(5+3)×17

Area of the trapezium= 1/2(8)×17

Area of the trapezium=4×17= 68cm^2

4 0

2 years ago

The points (-6, 5) and (r, 20) lie on a line with slope 5/4<br> Find the missing coordinate r.

mixas84 [53]

R = 6
(WORK SHOWN BELOW)

8 0

2 years ago