ABCD is a parallelogram. Find the value of x, y, w, and z.

Summary:

Step-by-step explanation:

Given

We know opposite sides of a parallelogram are equal.

Therefore,

now subtitute AD = x-28 and BC = 3x in AD = BC

AD = BC

x-28 = 3x

switch sides

3x = x-28

subracting x from both sides

3x-x = x-28+x

2x = -28

divide both sides by 2

2x/2 = -28/2

x = -14

Therefore,

The value of x = -14

Now subtitute AB = 12 and CD = 2/3y in AB = CD

AB = CD

12 = 2/3y

switching sides

2/3y = 12

y = 3/2 × 12

y = 18

Therefore,

The value of y = 18

We also know that the opposite angles of a parallelogram are equal.

Therefore,

5w = 70°

divide both sides by 5

5w/5 = 70°/5

w = 14

Therefore,

The value of w = 14

We know that the sum of the measures of the adjacent angles of a parallelogram is 180°.

Here,

m∠B = 70°.

m∠A = (3w+2z)°

As m∠B is adjacent to m∠A.

so

m∠A + m∠B = 180°

so substituting m∠B = 70° and m∠A = (3w+2z)° in the equation

70° + (3w+2z)° =  180°

now substituting w = 14 in the equation

70° +  (3(14) + 2z)° = 180°

70° + (42+2z)° =  180°

70° + 42 + 2z = 180°

112 + 2z = 180°

2z = 180° - 112

2z = 68

divide both sides by 2

2z/z = 68/2

z = 34

Therefore,

The value of z = 14

Summary:

step-by-step explanation:

∆abc has the points a(1, 7), b(-2, 2), and c(4, 2) as its vertices. formed with the point d(1, 2) as its third vertex, then ∆abd is triangle.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1