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mestny [16]
3 years ago
12

Which expression is equivalent to

Mathematics
1 answer:
Damm [24]3 years ago
4 0

Answer:

\frac{(2a+1)^{2} }{50a}

Step-by-step explanation:

\frac{2a+1}{10a-5} * \frac{4a^{2} - 1}{10a}\\ = \frac{2a+1}{5(2a-1)} * \frac{(2a+1)(2a-1)}{10a}\\=\frac{(2a+1)^{2} }{50a}

1.The expression given is in division so when changing to multiplication the fraction is reversed.

2.Using algebra identity a^{2}  - b^{2}  = (a+b)(a-b).

3. Taking the common factor 5 out.

4. Finally cancelling the like terms from the numerator and denominator.

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Lupe and her friends spend $20 on hot dogs and popcorn at a
vodomira [7]

Answer:

They buy 6 hotdogs and 5 popcorn

Step-by-step explanation:

Assume that they buy x hotdogs and y popcorn

∵ They buy a total of 11 hotdogs and popcorn

∵ The number of hotdogs is x and the number of popcorn is y

∴ x + y = 11 ⇒ (1)

∵ Hot dogs cost $2.50 each

∵ Popcorn costs $1.00 each

∵ They spend $20 on hot dogs and popcorn

→ Multiply x by 2.5 and y by 1, add the products and equate the sum by 20

∴ 2.5(x) + 1(y) = 20

∴ 2.5x + y = 20 ⇒ (2)

Now we have a system of equations to solve it

→ Subtract equation (1) from equation (2)

∵ (2.5x - x) + (y - y) = (20 - 11)

∴ 1.5x + 0 = 9

∴ 1.5x = 9

→ Divide both sides by 1.5 to find x

∴ x = 6

→ Substitute the value of x in equation (1) to find y

∵ 6 + y = 11

→ Subtract 6 from both sides

∴ 6 - 6 + y = 11 - 6

∴ y = 5

∴ They buy 6 hotdogs and 5 popcorn

8 0
2 years ago
Underneath the appropriate column of graphs from assignment 38.2, write an equation that solves for the variable in question (se
Gnesinka [82]
Newton Equations are such as Force = Mass * Acceleration, Potential Energy= mass * acceleration of gravity* height, Force of gravity= universal gravitational constant(Mass of the earth* Mass of Object)/( Distance in between)^2, Kinetic Energy= 1/2Mass (velocity) ^2, Momentum = speed * Mass and Voltage= current * resistance, Energy= Mass * (speed of light)^2 and etc, yet all of these are models for solving physics and mathematics problems.
8 0
3 years ago
The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges $3604 to rent
agasfer [191]

Answer: 14 tons

$3,860.50

Step-by-step explanation:

Let x = the amount of sugar transported.

First company:

The cost is $3157 truck rental plus $50.25 per ton of sugar.

Total cost = 3157 + 50.25x dollars

Second company:

There is no charge for truck rental, but it costs $275.75 per ton of sugar.

The total cost is

275.75x

When the two costs are the same, then

275.75x = 3157 +50.25x

225.5x = 3157

x = 14 tons

The total cost is 275.75*14 = $3,860.50

5 0
3 years ago
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What percent of 55 is 21.1
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11.6, if you need a decimal. it's in between 11 and 12

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