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3 years ago

Explain how to find the quotient of: (8a3+31a2-20a-5)/(8a-1)

Mathematics

1 answer:

pashok25 [27]3 years ago

4 0

Answer:

Quotient = a²+ 4a- 2

Step-by-step explanation:

(8a3+31a2-20a-5)/(8a-1)

a² +4a-2 ⇒ quotient

(8a-1)√(8a3+31a2-20a-5)

8a²- a² ⇒ Multiplying (8a-1) by a²

- + ⇒ Changing signs

32a²- 20a- 5

32a²- 4a ⇒ Multiplying (8a-1) by 4a

- + ⇒Changing signs

-16a -5

- 16a +2 ⇒ Multiplying (8a-1) by -2

+ - ⇒ Changing signs

-7 ⇒ Remainder

We follow the steps of simple division to get the quotient which is a²+ 4a- 2

We multiply (8a-1) by factors such as a², +4a and -2 to get the same terms as given in the dividend.

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Nine of 15 students completed their homework. What is the ratio of students who completed their homework to students who did not

Talja [164]

Answer:

The ratio of student that completed their homework to the students who didn't complete their homework is 9:6 = 9 /6

Step-by-step explanation:

9 of 15 students completed their homework .The ratio of students who completed their homework to the ratio that didn't complete their's can be calculated below

The total number of student that was given the homework is 15 . Out of this 15 students only 9 of the students completed their homework. The remaining student out of the 15 didn't complete their's.

The remaining number of student that didn't complete their homework is 15 - 9 = 6 .

Therefore,

The ratio of student that completed their homework to the students who didn't complete their homework is 9:6 = 9 /6

The ratio can be further reduced to 3/2

8 0

3 years ago

To avoid detection at customs, a traveler has placed 6 narcotic tablets in an Urn containing 9 vitamin pills that are similar in

Alexus [3.1K]

Answer:

$\frac{4}{91}$

Step-by-step explanation:

We are told that to avoid detection at customs, a traveler has placed 6 narcotic tablets in an Urn containing 9 vitamin pills that are similar in appearance.

To find the probability that the traveler will be arrested for illegal possession of narcotics we will use theoretical probability formula.

$\text{Probability}=\frac{\text{Number of favorable outcomes}}{\text{Number of possible outcomes}}$

Favorable outcomes will be $_{3}^{6}\textrm{C}$ .

$\text{Favorable outcomes}=_{3}^{6}\textrm{C}=\frac{6!}{(6-3)!3!}$

$\text{Favorable outcomes}=\frac{6!}{3!3!}$

$\text{Favorable outcomes}=\frac{6\cdot 5\cdot 4\cdot3!}{3\cdot 2\cdot 1\cdot3!}$

$\text{Favorable outcomes}=\frac{6\cdot 5\cdot 4}{3\cdot 2}$

$\text{Favorable outcomes}=5\cdot 4=20$

Now let us find number of possible outcomes.

$\text{Number of possible outcomes}=_{3}^{15}\textrm{C}=\frac{15!}{(15-3)!3!}$

$\text{Number of possible outcomes}=\frac{15!}{12!3!}$

$\text{Number of possible outcomes}=\frac{15\cdot 14\cdot 13\cdot 12!}{12!\cdot 3\cdot 2\cdot 1}$

$\text{Number of possible outcomes}=\frac{15\cdot 14\cdot 13}{ 3\cdot 2\cdot 1}$

$\text{Number of possible outcomes}=5\cdot 7\cdot 13=455$

Upon substituting our values in probability formula we will get,

$\text{Probability that the traveler will be arrested for illegal possession of narcotics}=\frac{20}{455}$

Upon dividing numerator and denominator by 5 we will get,

$\text{Probability that the traveler will be arrested for illegal possession of narcotics}=\frac{4}{91}$

Therefore, the probability that the traveler will be arrested for illegal possession of narcotics is $\frac{4}{91}$ .

6 0

3 years ago

E line plot below shows the amount of water Rickayla drinks in 10 days. Part a: how many cups of water did Rickayla drink in 10

Levart [38]

Answer:

$Total = 23\frac{1}{4}$ cups

Step-by-step explanation:

Incomplete question.

See attachment for line plot

Required

Total cups drank in 10 days

The number of x at the top of each dataset represent the frequency (i.e. number of cups) drank on that day.

To get the total, we simply multiply this frequency by the accompanying dataset.

So, we have:

$Total = 2 * 1\frac{1}{2} + 1 * 1\frac{3}{4} + 2 * 2 + 2 * 2\frac{3}{4} + 3 * 3$

Express fractions as improper fraction

$Total = 2 * \frac{3}{2} + 1 * \frac{7}{4} + 2 * 2 + 2 * \frac{11}{4} + 3 * 3$

Evaluate each product

$Total = 3 + \frac{7}{4} + 4 + \frac{11}{2} + 9$

Take LCM

$Total = \frac{12+ 7+16+22+36}{4}$

$Total = \frac{93}{4}$

$Total = 23\frac{1}{4}$

6 0

3 years ago

A scatter plot was constructed and a line of best fit was drawn, 25x 80. What is the equation of this best line of fit?

Tcecarenko [31]

Answer:

y = 5x + 25

Explaination:

To get the equation of a line, first get the slope of the line.

Slope = (change in y)/(change in x)

= (60-30)/(7-1)

= 30/6

= 5

Now use one point in the line (4,45) and a general point (x,y).

Slope = (change in y)/(change in x)

5 = (y - 45)/(x - 4)

5(x - 4) = (y - 45)

5x - 20 = y - 45

y = 5x -20 + 45

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4 years ago

What is the value of x in the following equation? 4(x-1) = 2(x +1)

Alla [95]

Start by multiplying to get rid of parentheses. Then use addition/subtraction to isolate x on one side of the equation. Finally, use division to determine the value of x.

3 0

3 years ago