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leonid [27]
3 years ago
15

Given the sequence 7, 12, 17, 22, ...

Mathematics
1 answer:
abruzzese [7]3 years ago
7 0

Answer:

option D is true.

Step-by-step explanation:

Given the sequence

7, 12, 17, 22, ...

An arithmetic sequence has a constant difference 'd' and is defined by

a_n=a_1+\left(n-1\right)d

Computing the differences of all the adjacent terms

12-7=5,\:\quad \:17-12=5,\:\quad \:22-17=5

The difference between all the adjacent terms is the same

so

d=5

as

a_1=7

Thus, the nth term of the arithmetic sequence will be:

a_n=5\left(n-1\right)+7

a_n=5n+2

Therefore, option D is true.

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The curve for f(x) and g(x) have the same shape but only differs in their position relative to the y and x-axis. With respect to the y-axis, it shifted 5 units upward. With respect to the x-axis, it shifted 9 units to the right. Since the right hand side is equal to y, we add +5 to the right. Similarly, since the left hand side is equal to x, we add +9 to the left. If we transpose this to the right,it becomes -9. So the equation for g(x) is: <span>g(x)=(1/2)^x−9+5</span>

3 0
3 years ago
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Suppose that the cost (in dollars) for a company to produce x pairs of a new line of jeans is described by the formula below. C(
Ad libitum [116K]

Answer:

a) The marginal cost function is given by

C'(x) = 4 + 0.04x + 0.0003x² (in dollars)

b) C'(70) = $8.27

Step-by-step explanation:

C(x) = 1000 + 4x + 0.02x² + 0.0001x³

a) Marginal cost is usually defined as the cost of producing one extra unit of product. It expresses how much the total cost is changing with respect to number of units of product.

Mathematically,

MC = (dC/dx) = C'(x)

For this question,

C'(x) = 4 + 0.04x + 0.0003x²

b) C'(70) means the marginal cost at x = 70 units, that is, how much the total cost is changing after the production of 70 units; the cost of producing one extra unit of product after producing 70 units.

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8 0
3 years ago
Solve for this equation<br> z^2-12z=-13
ASHA 777 [7]

Answer:

z=\sqrt{-1}

Step-by-step explanation:

z^2-12z=-13\\z^2-\frac{-12}{+12} =-13+12\\z^2=-1\\\sqrt{z^{2} } =\sqrt{-1}\\ z=\sqrt{-1}

5 0
3 years ago
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irina [24]

Answer:

3x + 4

Step-by-step explanation:

We have a product of 3 and x. That's rewritten as 3x. We then have 4 more, so we add 4. That gives us the final answer of:  3x+4. (It is 1-4x for the third one). ( The fourth one) The sum of seven and the quotient of a number x and eight

Here, x be the number.

" quotient of a number x and eight" translated to x/8

Sum means '+'

"sum of seven and the quotient of a number x and eight" translated to 7+ x/8 +56+x/8

                               

then; the given statement is 56+x/8

⇒

Therefore, the given statement is 56+x/8

6 0
3 years ago
Please help answer these question​ I will give you brainliest
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Answer:

1) \frac{6+\sqrt{6} }{2}       2) -3 + \sqrt{12}

Step-by-step explanation:

Please ignore the squiggle in the middle of the page.

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8 0
3 years ago
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