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3 years ago

Which condition is sufficient to show that quadrilateral DEFG is a parallelogram?

Mathematics

1 answer:

Whitepunk [10]3 years ago

4 0

Answer:

Option D

∠GDE is supplementary to ∠DEF and also supplementary to ∠FGD

Step-by-step explanation:

To use the supplementary property to identify a parallelogram. The condition must be that that the same-side interior angles (consecutive angles) are supplementary.

Thus for parallelogram DEFG

D --------------------E

/ /

G---------------------F

Thus, we have it that the condition that is most sufficient to show that quadrilateral DEFG is a parallelogram is

∠GDE is supplementary to both ∠DEF and ∠FGD

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Silas had 3 times as much money as Raja. Silas spent $84 of his money to buy a birthday gift for his grandma while Raja was awar

Tamiku [17]

Answer:

Total amount Silas and Raja has at first = $252

Step-by-step explanation:

Let,

Amount Silas had = x

Amount Raja had = y

According to given statement;

x = 3y Eqn 1

x-84 = y+42 Eqn 2

Putting value of x from Eqn 1 in Eqn 2

3y - 84 = y+42

3y-y = 42+84

2y = 126

Dividing both sides by 2

$\frac{2y}{2}=\frac{126}{2}\\y=63$

Putting y = 63 in Eqn 1

x = 63(3)

x = 189

Total amount they had = 189 + 63 = $252

Hence,

Total amount Silas and Raja has at first = $252

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2 years ago

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Answer:

Step-by-step explanation:

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3 years ago

Which one is proportional? Im a little confused lol

Kobotan [32]

Answer:

y = x + 4

——————-

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2 years ago

Maddy made $22.50 for babysitting for 5 hours for her aunt. Maddy was paid $21.00 for 3.5 hours of babysitting for her neighbor.

Greeley [361]

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Step-by-step explanation:

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3 years ago

Solve by substitution 3x+y=3 and 7x+2y=1

balu736 [363]

3x + y = 3

7x + 2y = 1

First isolate one of the variables (x or y) in one of the equations.

Isolate "y" in the first equation(because it is the easiest to isolate) and substitute it into the second equation.

3x + y = 3 Subtract 3x on both sides

3x - 3x + y = 3 - 3x

y = 3 - 3x

7x + 2y = 1

7x + 2(3 - 3x) = 1 [since y = 3 - 3x, you can substitute (3-3x) for "y"]

Multiply/distribute 2 into (3 - 3x)

7x + (3(2) - 3x(2)) = 1

7x + 6 - 6x = 1

x + 6 = 1 Subtract 6 on both sides

x = -5

Now that you know "x", substitute it into one of the equations (I will do both)

3x + y = 3

3(-5) + y = 3 [since x = -5, you can plug in -5 for "x"]

-15 + y = 3 Add 15 on both sides

y = 18

7x + 2y = 1

7(-5) + 2y = 1

-35 + 2y = 1 Add 35 on both sides

2y = 36 Divide 2 on both sides

y = 18

x = -5, y = 18 or (-5, 18)

5 0

3 years ago