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3 years ago

10 Points! Please help thanks!

Mathematics

1 answer:

cestrela7 [59]3 years ago

5 0

Answer:

Area = 200x - x², Max area is 10000m² with dimensions 100m × 100m

Step-by-step explanation:

Total fencing = perimeter

Let length of the sides be x and y,

2(x + y) = 400

x + y = 200

y = 200 - x

Area = x × y

= x(200 - x)

Area = 200x - x²

For max area, convert area into the completed square form

-(x² - 200x)

-(x² -2(x)(100) + 100² - 100²)

-[(x - 100)² - 10000]

-(x - 100)² + 10000

Max area is 10000 m²

Because the least value of (x - 100)² is 0.

That too when x = 100

When x = 100,

y = 200 - x = 200 - 100 = 100

Dimensions are 100m × 100m

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1. Dorothy bought a teddy bear and sold it at a 20% profit to Kim. Kim bought a suit costing $100 and dressed the teddy bear up

makkiz [27]

1. Dorothy paid $200 for the teddy bear

2. y is more than x by $33\frac{1}{3}$ %

Step-by-step explanation:

1. The given is:

Dorothy bought a teddy bear and sold it at a 20% profit to Kim
Kim bought a suit costing $100 and dressed the teddy bear up in the suit
Kim then sold the teddy bear in the suit to Karen for $442
Kim made a profit of 30%

We need to find how much Dorothy paid for the teddy bear

Assume that Dorothy bought a teddy bear for $x

∵ Dorothy bought a teddy bear for $x

∵ She sold it at a profit 20% to Kim

By using the ratio method

→ Buying price : Profit : Selling price

→ 100% : 20% : 120% ⇒ (100% + 20%)

→ x : : ?

By using cross multiplication

∴ 100% × Selling price = x × 120%

- Divide both sides by 100%

∴ Selling price = 1.2x

∴ Dorothy sold the teddy bear for $1.2x to Kim

∵ Kim bought a suit costing $100 and dressed the teddy bear

up in the suit

∴ The cost of the teddy bear = 1.2x + 100

∵ Kim sold the teddy bear in the suit to Karen for $442

∵ Kim made a profit of 30%

By using the ratio method

→ Cost price : Profit : Selling price

→ 100% : 30% : 130% ⇒ (100% + 30%)

→ 1.2x + 100 : : 442

By using cross multiplication

∴ (1.2x + 100) × 130% = 100% × 422

- Divide both sides by 130%

∴ 1.2x + 100 = 340

- Subtract 100 from both sides

∴ 1.2x = 240

- Divide both sides by 1.2

∴ x = 200

∴ Dorothy bought the teddy bear for $200

Dorothy paid $200 for the teddy bear

2. The given is:

x is less than y by 25%
Then y is more than x by how many percent

Assume that y is 100%

∵ y = 100%

∵ x is less than y by 25%

∴ x = 100% - 25%

∴ x = 75%

- The percentage of increasing of y = $\frac{y-x}{x}$ × 100%

∵ The percentage of increasing of y = $\frac{100-75}{75}$ × 100%

∴ The percentage of increasing of y = $\frac{25}{75}$ × 100%

∴ The percentage of increasing of y = $\frac{1}{3}$ × 100%

∴ The percentage of increasing of y = $33\frac{1}{3}$ %

y is more than x by $33\frac{1}{3}$ %

Learn more:

You can learn more about the ratio in brainly.com/question/4713715

#LearnwithBrainly

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3 years ago

Solve the simultaneous equations 2x-y=7 3x+y=3

Debora [2.8K]

Answer:

Step-by-step explanation:

Using elimination method:

2x - y = 7

3x + y = 3

--------------

5x = 10

Divide both sides of the equation by 5

$\frac{5x}{5} = \frac{10}{5}$

Calculate

$x = 2$

Now, substitute the given value of X in the equation

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$3 \times 2 + y = 3$

Multiply the numbers

$6 + y = 3$

Move constant to R.H.S and change it's sign

$y = 3 - 6$

Calculate

$y = - 3$

The possible solution of this system is the ordered pair ( x , y )

---------------------------------------------------------------------

Check if the given ordered pair is the solution of the system of equation

$2 \times 2 - ( - 3) = 7$

$3 \times 2 - 3 = 3$

Simplify the equalities

$7 = 7$

$3 = 3$

Since all of the equalities are true, the ordered pair is the solution of the system

Hope this helps..

Best regards!!

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3 years ago

How can you find 75% of any number?

Aleks04 [339]

Answer:

Step-by-step explanation:

Multiply it by 0.75, or find 3/4 of that number. Whichever you prefer! The first one always works though the second one sometimes does but sometimes 3/4 of the number isn't that obvious.

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Answer:

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