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2 years ago

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Mathematics

1 answer:

spayn [35]2 years ago

3 0

Answer:

15th term of the sequence is 36

Step-by-step explanation:

Given in the question,

a₁ = First term = -20

d = common difference = 4

Expression for the nth term of an arithmetic sequence is,

$T_n=a_1+(n-1)d$

Here, n = number or term

We have to calculate 15th term of the sequence,

$T_{15}=-20+(15-1)(4)$

= -20 + 56

= 36

Therefore, 15th term of the sequence is 36.

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The constraints of a problem are listed below. What are the vertices of the feasible region?

Grace [21]

The vertices are the intersections between the lines.

1) line x + y = 5 and y = 3:

y = 3 => x + 3 = 5 => x = 5 - 3 => x = 2

=> vertix = (2,3)

2) line x + y = 5 and y = 0

=> y = 0 => x + 0 = 5 => x = 5

=> vertix = (5,0)

3) line x + y = 5 and x = 0

=> 0 + y = 5 => y = 5

=> (0,5) ------> this is not a vertix because it is above the line y = 3

4) line y = 3 and x-axis

=> vertix = (0,3)

5) x-axis and y-axis => origin => vertix = (0,0)

So, there are four vertices: (0,0), (5,0), (2,3) and (0,3)

Answer: That is the first option:(<span>0, 0), (0, 3), (2, 3), (5, 0)</span>

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3 years ago

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163, 159, 155, 151.... What will the 23rd term in this sequence be?

Bogdan [553]

The rule is n-4;
163 - 4 = 159
159 - 4 = 155
155 - 4 = 151
151 - 4 = 147

A quick way to solve this is to mutliply 4 by 23 and subtract the product from the 1st term.

23 x 4 = 92
163 - 92 = 71

The 23rd term is 71.

I hope this helps!

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3 years ago

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Which of the following expressions could represent the total amount withdrawn from Brandon’s checking account during the time pe

den301095 [7]

The Solution:

Given:

Each withdrawal by Brandon = $x

ATM charge per transaction = $2

Required:

To find an expression for Brandon's total withdrawal if he withdraws the same amount once a week for 7 weeks.

Step 1:

We shall find the total amount of each withdrawal, that is, the sum of the amount withdrawn and the ATM charge for the transaction.

$\text{ Each withdrawal=x+2=\$(x+2)}$

Step 2:

Finding the required total amount, we have:

$\text{ Total amount withdrawn=7(x+2)=\$7(x+2)}$ $\begin{gathered} 7(x+2) \\ or \\ 7x+14 \\ \text{ or} \\ 7\mleft(x\mright)+7\mleft(2\mright) \end{gathered}$

Therefore, the correct answers are: [options 2, 3, and 4]

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1 year ago

4. For f(x) = 1/x-5

ioda

Answer:

g(x) = x^2 +2
f(g(x)) = 1/(x^2 -3)

Step-by-step explanation:

A. g(x) is given:

g(x) = x^2 +2

B. f(g(x)) = f(x^2 +2) = 1/((x^2 +2) -5) . . . . substitute for g(x) and simplify

f(g(x)) = 1/(x^2 -3)

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2 years ago

1. Simplify: (6-√5)(5+√5)

aniked [119]

150 because 6 times 5 is 30 then you multiply whats inside the square root thing so you'd get 25, 25 is a perfect square which simplifies to 5 then 5 times 30 is 150.

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3 years ago

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