Sod=1*1
to cover =30*14
to cover=420
to cover divided by one piece
=420/1
=420 pieces
The lengths (in centimeters) of the opposite side pairs are 59 cm , 38 cm. Option C) is the correct answer.
<u>Step-by-step explanation</u>:
<u>step 1</u> :
Given that,
Quadrilateral ABCD is a parallelogram if both pairs of opposite sides are congruent.
<u>step 2</u> :
The opposite sides are AB and CD respectively.
The another opposite sides are BC and AD respectively.
<u>step 3</u> :
If both pairs of opposite sides are congruent, then
AB = CD
44+3x = 64-x
3x+x = 64-44
4x = 20
x = 5
<u>step 4</u> :
BC = AD
33+y = 48-2y
y+2y = 48-33
3y = 15
y = 5
<u>step 5</u> :
Subsitute x=5 and y=5 in any of the given sides,
CD = 64-x = 64-5 = 59
∴ CD = 59 cm
BC = 33+y = 33+5 = 38
∴ BC = 38 cm
The lengths of the opposite side pairs are 59 cm , 38 cm.
Christopher purchased 2.8 pounds of almonds and 3.5 pounds to roasted pistachios.
Step-by-step explanation:
Cost of almonds per pound = $10
Cost of roasted pistachios = $12
Total amount spent = $70
Weight of nuts = 6.3
Let,
Weight of almonds = x
Weight of roasted pistachios = y
According to given statement;
x+y=6.3 Eqn 1
10x+12y=70 Eqn 2
Multiplying Eqn 1 by 10

Subtracting Eqn 3 from Eqn 2;

Dividing both sides by 2

Putting y=3.5 in Eqn 1

Christopher purchased 2.8 pounds of almonds and 3.5 pounds to roasted pistachios.
Keywords: linear equations, elimination method
Learn more about elimination method at:
#LearnwithBrainly
Let the amount of the first brand be x, and let the amount of the second brand be y.
0.09x + 0.14y = 240 * 0.13 .................(1)
x + y = 240 ..............(2)
y = 240 - x .......................(3)
Plugging the value for y from equation (3) into equation (1), we get:

...............(4)
Equation (4) simplifies to:
-0.05x = -2.4
giving the value for the required amount of 9% vinegar as 48 ml and the required amount of 14% vinegar as 240 - 48 = 192 ml.