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3 years ago

2(5x - 3) - 4 = x + 4 solve for x and show work

2 answers:

6 0

1. distribute --> 10x-6-4=x+4
2. do -6-4 --> 10x-10=x+4
3. add 10 on both sides --> 10x=x+4+10
4. subtract x on both sides and simplify equation --> 9x=14
5. divide both sides by 9 --> x=14/9

Katen [24]3 years ago

4 0

Answer:

x= 14/9 = 1 5/9

Step-by-step explanation:

Use the distributive property to multiply 2 by 5x−3.

2(5x−3)−4=x+4

Subtract 4 from −6 to get −10.

10x−6−4=x+4

Subtract x from both sides

10x−10=x+4

Combine 10x and −x to get 9x.

10x−10−x=4

Add 10 to both sides.

9x−10=4

Divide both sides by 9.

x= 14/9

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A bakery works out a demand function for its chocolate chip cookies and finds it to be q = D (x) = 943 - 17 x, where q is the q

Alex73 [517]

Answer:

See expla below

Step-by-step explanation:

Given the demand function:

q = D (x) = 943 - 17 x

a) Find the elasticity:

Find the derivative of the demand function.

D'(x)= -17

Thus, elasticity expression is:

$\frac{x D'(x)}{D'(x)}$

$= \frac{x (-17)}{943 - 17x}$

$= \frac{17x}{943 - 17x}$

Elasticity expression = $E(x) = \frac{17x}{943 - 17x}$

b) At what price is the elasticity of demand equal to 1?

This means E(x) = 1

Substitute 1 for E(x) in the elasticity equation:

$E(x) = \frac{17x}{943 - 17x}$

$1 = \frac{17x}{943 - 17x}$

Cross multiply:

$943 - 17x = 17x$

Collect like terms

$17x + 17x = 943$

$34x = 943$

$x = \frac{943}{34}$

x = 27.74

Elasticity at the price of demand = 1 is 27.74

c) At what prices is the elasticity of demand elastic?

This means E(x) > 1

Therefore,

$\frac{17x}{943 - 17x} > 1$

Cross multiply:

$17x > 943 - 17x$

Collect like terms

$17x + 17x > 943$

$34x > 943$

$x > \frac{943}{34}$

x > 27.74

The elasticity of demand is elastic at x > 27.74

d) At what prices is the elasticity of demand inelastic?

This means E(x) < 1

Therefore,

$\frac{17x}{943 - 17x} < 1$

Cross multiply:

$17x < 943 - 17x$

Collect like terms

$17x + 17x < 943$

$34x < 943$

$x < \frac{943}{34}$

x < 27.74

The elasticity of demand is inelastic at x < 27.74

e) At what price is the revenue a maximum:

Total revenue will be:

R(x) = x D(x)

= x (943 - 17x)

= 943x - 17x²

R(x) = 934 - 17x(price that maximizes total revenue)

Take R(x) = 0

Thus,

0 = 943 - 17x

17x = 943x

$x = \frac{943}{17}$

$x = 27.74$

Total revenue is maximun at x= 27.74 per cookie

f) At x = 21 per cookie, find the price:

Thus,

R (21) = (943 * 21) - (17 * 21²)

= 19803 - 7497

= 12306

At x = 27.74, find the price:

R(27.74) = (943 * 27.74) - (17 - 27.74²)

= 26158.82 - 13081.63

= 13077.19

We can see the new price of cookie causes the total revenue to decrease.

Therefore, with a small increase in price the total revenue will decrease.

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3 years ago

Which of the following is the solution to the compound inequality below?

Minchanka [31]

Answer:

b. x ≥-2 or x ≤-6

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3 years ago

There are 800 desks at Washington Middle School. The custodial staff at the school plans to inspect 6.5% of the desks every week

Talja [164]

Answer:

208 desks

Step-by-step explanation:

To find out how many desks they will inspect each week, we multiply

800 * 6.5%

800 * .065

52 desks per week

Over a 4 week period, they will inspect

52 desk per week * 4 weeks =

208 desks

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3 years ago

Mr. Rives' rotating sprinkler waters his lawn up to a radius of 7 feet. What is the maximum number of square feet of lawn mr. Ri

zaharov [31]

Answer:

Step-by-step explanation:

Mr. Rives' rotating sprinkler waters his lawn up to a radius of 7 feet. The formula for determining the area of a circle is expressed as

Area = πr²

Where

π is a constant whose value is 3.14.

r represents the radius if the circle.

The area covered by one of Mr. Rives' rotating sprinkler would be

3.14 × 7² = 3.14 × 49 = 153.86ft²

Therefore, the maximum area of lawn that two sprinklers can cover would be

153.86 × 2 = 307.72 ft²

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3 years ago

47 of the 50 participants in a triathlon are men and the rest are women. What is the ratio of the number of men participating to

tatyana61 [14]

Answer:

Step-by-step explanation:

47/50

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3 years ago