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2 years ago

Which expressions are equivalent to 2(2x + 4y + x − 2y)?

Mathematics

2 answers:

Sholpan [36]2 years ago

6 0

Answer:

Step-by-step explanation:

2(x+2y)=2x+4y

2x+4y

So option B is the correct answer

Vesnalui [34]2 years ago

4 0

Answer:

$2(3x + 2y)$

ANSER is c

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In fig if x+y=w+z then prove that AOB is a line.

frez [133]

Answer:

As Given, x+y=w+z

To Prove: AOB is a line or x+y=180

∘

(linear pair.)

According to the question,

x+y+w+z=360

∘

∣ Angles around a point.

(x+y)+(w+z)=360

∘

(x+y)+(x+y)=360

∘

∣ Given x+y=w+z

2(x+y)=360

∘

(x+y)=180

∘

Hence, x+y makes a linear pair.

Therefore, AOB is a straight line

4 0

3 years ago

A certain number of sixes and nines is added to give a sum of 126; if the number of sixes and nines is interchanged, the new sum

galina1969 [7]

Answer:

Original number of sixes = 6

Original number of nines = 10

Step-by-step explanation:

We are told in the question that:

A certain number of sixes and nines is added to give a sum of 126

Let us represent originally

the number of sixes = a

the number of nines = b

Hence:

6 × a + 9 × b = 126

6a + 9b = 126.....Equation 1

If the number of sixes and nines is interchanged, the new sum is 114.

For this second part, because it is interchanged,

Let us represent

the number of sixes = b

the number of nines = a

6 × b + 9 × a = 114

6b + 9a = 114.......Equation 2

9a + 6b = 114 .......Equation 2

6a + 9b = 126.....Equation 1

9a + 6b = 114 .......Equation 2

We solve using Elimination method

Multiply Equation 1 by the coefficient of a in Equation 2

Multiply Equation 2 by the coefficient of a in Equation 1

6a + 9b = 126.....Equation 1 × 9

9a + 6b = 114 .......Equation 2 × 6

54a + 81b = 1134 ........ Equation 3

54a + 36b = 684.........Equation 4

Subtract Equation 4 from Equation 3

= 45b = 450

divide both sides by b

45b/45 = 450/45

b = 10

Therefore, since the original the number of nines = b,

Original number of nines = 10

Also, to find the original number of sixes = a

We substitute 10 for b in Equation 1

6a + 9b = 126.....Equation 1

6a + 9 × 10 = 126

6a + 90 = 126

6a = 126 - 90

6a = 36

a = 36/6

a = 6

Therefore, the original number of sixes is 6

7 0

3 years ago

In 2008 the price of gas was $4.02 in 1990 it was only $1.37 what was the increase percentage

Murrr4er [49]

Answer:

2.65

Step-by-step explanation:

8 0

3 years ago

What is the value of x in the triangle?

topjm [15]

Answer:

Step-by-step explanation:

Using the sine ratio in the right triangle and the exact value

sin30° = $\frac{1}{2}$ , then

sin30° = $\frac{opposite}{hypotenuse}$ = $\frac{x}{8}$ = $\frac{1}{2}$ ( cross- multiply )

2x = 8 ( divide both sides by 2 )

x = 4

7 0

3 years ago

car as the following utility function: U(X,Y)equals10Upper X squaredY where X is her consumption of Blu-ray disks with a pri

mr_godi [17]

Answer:

She consumes 30 blue ray disk and 60 DVD respectively.

Step-by-step explanation:

Consider the provided information.

$U(x,y)=10x^2y$

Calculate marginal utility of good

Differentiate with respect of x and y.

$MU_x=20xy$

$MU_y=10x^2$

Her consumption of Blu-ray disks (X) with a price of $40 and Y is her consumption of DVDs with a price of $10.

The ratio of marginal utility of good x to y is equal to the price ratio:

$\frac{MU_x}{MU_y}=\frac{P_x}{P_y}$

Substitute the respective values.

$\frac{20xy}{10x^2}=\frac{40}{10}$

$\frac{2y}{x}=4$

$2y=4x$

$y=2x$

She has $1800 with which to spend on the two goods.

Her consumption of Blu-ray disks (X) with a price of $40 and Y is her consumption of DVDs with a price of $10. She has $1800 with which to spend on the two goods.

Therefore, $40x+10y=1800$

$4x+y=180$

Substitute the value of y in above equation.

$4x+2x=180$

$6x=180$

$x=30$

Thus, $y=60$

She consumes 30 blue ray disk and 60 DVD respectively.

6 0

3 years ago