All categories

3 years ago

Algebra Find the values for x and y in parallelogram ABCD. AE= 2x, EC=y+4, DE=x, EB=2y-1. AC and BD intersect at point E

Mathematics

1 answer:

erastova [34]3 years ago

6 0

Answer:

−

Step-by-step explanation:

You might be interested in

The circular mirror below has a frame with a circumference of 28.26 inches.

Karo-lina-s [1.5K]

Answer: it is 3

Step-by-step explanation:

6 0

3 years ago

The three lines given below form a triangle. Find the coordinates of the vertices of the triangle.

LenKa [72]

Answer:

(3, 5), (1, 2) and (5, 1)

Step-by-step explanation:

Make three systems with pairs of lines and solve them to work out the vertices.

1) Line 1 and line 2

-3x + 2y = 1
2x + y = 11

Double the second equation and subtract equations:

-3x + 2y - 2(2x + y) = 1 - 2(11)
-3x - 4x = 1 - 22
-7x = - 21
x = 3

Find y:

2*3 + y = 11
6 + y = 11
y = 11 - 6
y = 5

The point is (3, 5)

2) Line 1 and line 3

-3x + 2y = 1
x + 4y = 9

Triple the second equation and add up equations:

-3x + 2y + 3(x + 4y) = 1 + 3(9)
2y + 12y = 1 + 27
14y = 28
y = 2

Find x:

x + 4*2 = 9
x + 8 = 9
x = 1

The point is (1, 2)

3) Line 2 and line 3

2x + y = 11
x + 4y = 9

Double the second equation and subtract the equations:

2x + y - 2(x + 4y) = 11 - 2(9)
y - 8y = 11 - 18
- 7y = - 7
y = 1

Find x:

x + 4*1 = 9
x + 4 = 9
x = 5

The point is (5, 1)

8 0

2 years ago

Please someone help me to prove this.

morpeh [17]

Answer: see proof below

Step-by-step explanation:

Use the Double Angle Identity: sin 2Ф = 2sinФ · cosФ

Use the Sum/Difference Identities:

sin(α + β) = sinα · cosβ + cosα · sinβ

cos(α - β) = cosα · cosβ + sinα · sinβ

Use the Unit circle to evaluate: sin45 = cos45 = √2/2

Use the Double Angle Identities: sin2Ф = 2sinФ · cosФ

Use the Pythagorean Identity: cos²Ф + sin²Ф = 1

Proof LHS → RHS

LHS: 2sin(45 + 2A) · cos(45 - 2A)

Sum/Difference: 2 (sin45·cos2A + cos45·sin2A) (cos45·cos2A + sin45·sin2A)

Unit Circle: 2[(√2/2)cos2A + (√2/2)sin2A][(√2/2)cos2A +(√2/2)·sin2A)]

Expand: 2[(1/2)cos²2A + cos2A·sin2A + (1/2)sin²2A]

Distribute: cos²2A + 2cos2A·sin2A + sin²2A

Pythagorean Identity: 1 + 2cos2A·sin2A

Double Angle: 1 + sin4A

LHS = RHS: 1 + sin4A = 1 + sin4A $\checkmark$

6 0

3 years ago

Sophia Thompson is 12 years old. Her mother is 5 years less than four times as old as Sophia. How old is mrs. Thompson? Please e

Ugo [173]

Sophia is 12. Four times that is 48. If her mother is 5 years less than this, she is 43.

(12 x 4) - 5 = 43

7 0

3 years ago

What is 0.316 in expanded form

Inessa [10]

0.316 in expanded form is= 0.3 + 0.01 + 0.006.

5 0

3 years ago