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3 years ago

Solve the inequality k + 3<5

Mathematics

1 answer:

lina2011 [118]3 years ago

5 0

Answer:

3324333

Step-by-step explanation:

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A factory is to be built on a lot measuring 210 ft by 280 ft. A local building code specifies that a lawn of uniform width and e

Tresset [83]

Answer:

Width of lawn = 35 ft

Dimensions of factory = length: 210 ft, width: 140 ft

Step-by-step explanation:

The total area of the lot can be calculated as:

$A_{lot} = 210 * 280\\A_{lot} = 58800 ft^{2}$

Since, the area of factory should be equal to area of lawn:

$A_{lot} = A_{factory} + A_{lawn}\\58800 = 2 A_{factory or lawn}\\\\A_{factory or lawn} = \frac{58800}{2}\\A_{factory or lawn} = 29400 ft^{2}$

Now, let 'x' be the width of lawn, the dimensions of factory can be written as:

$(210-2x)\\(280-2x)\\$

Since, area is equal to length x width:

$(210-2x)*(280-2x) = 29400\\Simplifying:\\210*280 - 210*2x - 2x*280 + 4x^{2} = 29400\\58800 - 420x - 560x +4x^{2} = 29400\\4x^{2} - 980x +58800 = 29400\\4x^{2} - 980x + 29400 = 0\\$

Divide whole equation by 4,

$x^{2} - 245 + 7350 = 0\\$

Solving above quadratic equation, we get,

$x = 210\\x = 35\\$

x = 35 seems realistic width of the lawn.

Now, finding the dimension of factory:

$(210-2x) = 210 - 2(35) = 140 ft\\(280-2x) = 280 - 2(35) = 210ft$

We can also reconfirm the area of factory by multiplying the above two lengths:

140 * 210 = 29400 ft

8 0

3 years ago

A scientist need 10 liters of a 20% acid solution for an experiment, but she only has a 5% soliution and a 40% solution. To the

Stolb23 [73]

Answer:

5.7 liters of 5% solution and 4.3 liters of 40% solution is needed to be mixed to get 10 liters of a 20% acid solution

Step-by-step explanation:

Let

x = Amount of 5% solution needed

(10 - x) = Amount of 40% solution needed

Equation:

5% of x + 40% of (10-x) = 20% of 10

0.05x + 0.40(10-x) = 0.20 * 10

Open parenthesis

0.05x + 4.0 - 0.40x = 0.20 * 10

Collect like terms

4.0 - 0.35x = 2.0

Add 0.35x to both sides of the equation

4.0 = 2.0 + 0.35x

Subtract 2.0 from both sides of the equation

2.0 = 0.35x

Divide both sides by 0.35

2.0 / 0.35 =x

5.7 = x

5.7 liter of the 5% solution is needed

Next is to find the amount of 40% solution needed

(10 - x) = Amount of 40% solution used

Amount of 40% solution used = 10 - 5.7

= 4.3

4.3 liters of 40% solution is needed

6 0

3 years ago

Do number 5 please and don get the wrong answer :/

Law Incorporation [45]

Answer:

ok good job

Step-by-step explanation:

5 0

3 years ago

Three friends go grocery shopping together, and each guys the same kinds of strawberries. Akio buys 2 pounds and pays 1.50. Gord

Sav [38]

Answer: Graph B

Step-by-step explanation:

The unit price for the strawberries is:

= 1.5 / 2

= $0.75 per pound

Graph B is the right graph as it uses a unit price of $0.75 per pound for strawberry price. This is why it has points of the graph that mirror the friends purchases such as (2, 1.5) , (3, 2.5) and (4, 3).

4 0

3 years ago

Read 2 more answers

How to compare an order fraction into a decimal

Nitella [24]

You can convert the fraction to a decimal form.
7/9 is .778
.778 is greater than .6

6 0

3 years ago

Solve the inequality k + 3<5​

Solve the inequality k + 3<5