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3 years ago

#1 What is the explicit equation of the sequence 10125, 2025, 405, 81, ..? *

Mathematics

1 answer:

vazorg [7]3 years ago

7 0

405/81=5
10125/2025=5

It seems like it divided by 5 each time.

So, the nth term of the sequence is (50625)n^(-5)

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Part 1

svetlana [45]

Answer:

A: This polynomial has a degree of 2 , so the equation 12x2+5x−2=0 has two or fewer roots.

B: The quadratic equation 12x2+5x−2=0 has two real solutions, x=−2/3 or x=1/4 , and therefore has two real roots.

Step-by-step explanation:

f(x) = 12x^2 + 5x - 2.

Since this is a quadratic equation, or a polynomial of second degree, one can easily conclude that this equation will have at most 2 roots. At most 2 roots mean that the function can have either 2 roots at maximum or less than 2 roots. Therefore, in the A category, 2nd option is the correct answer (This polynomial has a degree of 2 , so the equation 12x^2 + 5x − 2 = 0 has two or fewer roots).

To find the roots of f(x), set f(x) = 0. Therefore:

12x^2 + 5x - 2 = 0. Solving the question using the mid term breaking method shows that 12*2=24. The factors of 24 whose difference is 5 are 8 and 3. Therefore:

12x^2 + 8x - 3x - 2 = 0.

4x(3x + 2) -1(3x+2) = 0.

(4x-1)(3x+2) = 0.

4x-1 = 0 or 3x+2 = 0.

x = 1/4 or x = -2/3.

It can be seen that f(x) has two distinct real roots. Therefore, in the B category, 1st Option is the correct answer (The quadratic equation 12x2+5x−2=0 has two real solutions, x=−2/3 or x=1/4 , and therefore has two real roots)!!!

8 0

3 years ago

Suppose that the functions r and s are defined for all real numbers x as follows.

mixas84 [53]

ANSWER

Given

$r(x) = x - 1$

and

$s(x) = 3 {x}^{2}$
ANSWER TO QUESTION 1

$(r + s)(x) = r(x) + s(x)$

$(r + s)(x) = x - 1 + 3 {x}^{2}$

$(r + s)(x) = 3 {x}^{2} + x - 1$

ANSWER TO QUESTION 2

$(r \times s)(x) = r(x) \times s(x)$

$(r \times s)(x) = (x - 1) \times 3 {x}^{2}$

$(r \times s)(x) = 3 {x}^{3} - 3 {x}^{2}$

ANSWER TO QUESTION 3

$( r - s)(x) = r(x) - s(x)$

$( r - s)(x) = x - 1 - 3 {x}^{2}$

$( r - s)( - 3) = (- 3) - 1 - 3 ({ - 3}^{2} )$

$( r - s)( - 3) = - 4 - 3 \times 9$

$( r - s)( - 3) = - 4 - 27 = - 31$

4 0

3 years ago

4|n+8| = 56 <br><br>please help

Alchen [17]

To solve the absolute value equation you first need to get everything not in the absolute value bars to the other side of the equation.

Step 1) Divide by 4
|n+8| = 14

*Remember: when solving absolute value equations, you make what the expression (n+8) is equal to negative and positive. Not the other way around.

Step 2) Make two equations

n+8 = 14
n+8 = -14

Solve and you'll see that n= 6 and -22

3 0

3 years ago

Miles is planning to spend 2/3 as many hrs bicycling this week as he did last week. Is Miles going to spend more hrs or fewer hr

vladimir2022 [97]

He would be spending less time because 2/3 is not a full number. Let's make an equation out of the: 2/3(m). Note: 3(2) means 3 times 2 and the m is the amount of miles biked last week. We could insert the number 3 to our equation. 2/3(3). Now if you do it the proper way, it is 2/3(3/1) and if you do the math it is 6/3 aka 2. And 2 is less than 3. So it is less time spent

5 0

3 years ago

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5.The sales tax rate 6.3%. a. find the tax paid for a pair of earrings with a list price of $77

Nookie1986 [14]

Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions.
The answer is $4.85;$81.85<span> which is B. </span>

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3 years ago

Read 2 more answers