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Sveta_85 [38]
3 years ago
13

An arithmetic sequence is shown below. You are not given many terms of this sequence, but you do have enough to fill in the miss

ing number. What number goes in the blank? 14, ,56,....
A.37
B.35
C.21
D.29
Mathematics
1 answer:
kicyunya [14]3 years ago
5 0

Answer:

B.35

Step-by-step explanation:

The sequence is

14, ,56,....

14 , x , 56

Think of it as 14 + d = x

x+ d = 56

d is the common difference

We now have 2 equations and 2 unknowns

Substitute the first equation in for x   into the second equation

x+d =56

(14+d) +d = 56

Combine like terms

14 + 2d = 56

Subtract 14 from each side

14-14 + 2d = 56-14

2d = 42

Divide by 2

2d/2 =42/2

d = 21

The common difference is 21

Now we can find x

14 + d = x

14+ 21 = x

35 =x

The unknown term is 35

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Contact [7]

Answer:

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3 0
2 years ago
mittens are marked down 25% the sale price is 3.15 a pair what was the original price of a pair of mittens
Sliva [168]
$12.6 -- 25% of 12.6 is exactly $3.15

I did this by taking 3.15 / 0.25
6 0
3 years ago
Read 2 more answers
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

\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

\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.

5 0
3 years ago
Twenty-seven less than twice a number is -1
11Alexandr11 [23.1K]

Answer: 13

Step-by-step explanation:

2x-27=-1

2x=26

X=13

5 0
3 years ago
give an example if an equation where any value if X will make the equation true. Infinite number of solutions. PLS HELP
defon

Answer:

x+3 = x+3

Step-by-step explanation:

No matter what you plug into x, both sides will be the same.

8 0
3 years ago
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