using long division to divide 3x^4-2x^3+x-1 by x^2-x-2

The rock will hit the water after approximately 2 seconds.

The time it takes for the rock to hit the water, we need to set the height h equal to zero and solve for t . The equation representing the height of the rock is given by:

[tex]\[ h = -16t^2 + 12t + 40 \][/tex]

Setting h to zero:

[tex]\[ 0 = -16t^2 + 12t + 40 \][/tex]

Now, we have a quadratic equation.

To solve for t , we can use the quadratic formula:

[tex]\[ t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]

In this equation, [tex]\( a \), \( b \), and \( c \)[/tex] are the coefficients from the quadratic equation [tex]\( at^2 + bt + c = 0 \).[/tex]In our case:

[tex]\[ a = -16, \quad b = 12, \quad c = 40 \][/tex]

Substitute these values into the quadratic formula:

[tex]\[ t = \frac{-12 \pm \sqrt{12^2 - 4(-16)(40)}}{2(-16)} \]\\[/tex]

Now, calculate the values under the square root:

[tex]\[ t = \frac{-12 \pm \sqrt{144 + 2560}}{-32} \][/tex]

[tex]\[ t = \frac{-12 \pm \sqrt{2704}}{-32} \][/tex]

[tex]\[ t = \frac{-12 \pm 52}{-32} \][/tex]

Now, consider both the positive and negative roots:

1. For the positive root:

[tex]\[ t_1 = \frac{-12 + 52}{-32} = \frac{40}{-32} = -\frac{5}{4} \][/tex]

2. For the negative root:

[tex]\[ t_2 = \frac{-12 - 52}{-32} = \frac{-64}{-32} = 2 \][/tex]

Since time cannot be negative in this context, we discard the negative root.

Therefore, the rock will hit the water after approximately t = 2 seconds.

The gross pay for Alisson this week is $432.22. So option (d) is correct.

To calculate her gross pay, we first need to find the total number of hours worked during the week. We add up the hours worked each day:

1. Monday: 8:03 am to 5:13 pm = 9 hours and 10 minutes

2. Tuesday: 7:58 am to 4:49 pm = 8 hours and 51 minutes

3. Wednesday: 7:46 am to 4:41 pm = 8 hours and 55 minutes

4. Thursday: 8:32 am to 4:50 pm = 8 hours and 18 minutes

5. Friday: 7:31 am to 4:32 pm = 9 hours and 1 minute

Total hours worked = 43 hours and 15 minutes.

Since Alisson worked more than 40 hours this week, any hours beyond 40 are paid at time and a half. So, she worked 40 regular hours and 3 hours and 15 minutes of overtime.

Her regular pay = 40 hours * $9.32/hour = $372.80

Her overtime pay = 3.25 hours * ($9.32/hour * 1.5) = $59.42

Therefore, her total gross pay for the week is $372.80 + $59.42 = $432.22.

Complete Question;

If Alisson worked the times in the table and makes $9.32 an hour, how much was her gross pay this week?

8:03 am 5:13 pm

7:58 am 4:49 pm

7:46 am 4:41 pm

8:32 am 4:50 pm

7:31 am 4:32 pm

Remember that any time worked over 40 hours is paid at time and a half.

(a) $372.80

(b) $410.08

(c) $412.41

(d) $432.22

To round 26.99 to the nearest tenth, we increase the tenths place by 1 because the hundredths place is 9, resulting in 27.0.

When rounding 26.99 to the nearest tenth, we need to look at the hundredths place, which is 9. Since 9 is greater than 5, we round up the digit in the tenths place by 1. Therefore, the number rounded to the nearest tenth is 27.0.

This question pertains to the voting options and procedures during a homeowners association meeting, covered under the broader subject of Social Studies in the context of High School education. It involves understanding quorum requirements and voting rules as per bylaws for decision-making on motions.

The question revolves around a homeowners association meeting where a board member has three options to participate in a vote: vote yes, vote no, or abstain from a motion. There are three motions for which each board member must decide how to vote. In such meetings, the rules outlined typically require a quorum to conduct business, the ability to make amendments to bylaws, and procedures for electing members, as seen in various articles of an organization's bylaws and rules of procedure. These rules ensure that the organization conducts its affairs in an orderly and democratic manner, often requiring a majority or unanimous consent for certain actions.

Meetings like these are essential, as they also involve critical decisions such as annual meetings, bylaw amendments, or the dissolution of the organization, each depending on the vote of the board members or the members of the organization. Membership eligibility and voting rights are typically determined by the board of directors or outlined within the bylaws. Furthermore, certain organizational procedures such as elections, member qualifications, and the transparency measures such as keeping a journal of proceedings of each meeting are often mandated.

the rate of change is -2 for every set shown in the chart on the right

 so 6 to 7 would be -11 -2 = -13

7 to 8 would be -13-2 = -15

8 to 9 = -15-2 = -17

 B is the answer

she did (x+8)*5

2015 = (x+8)*5

divide both sides by 5

403=x+8

x = 403-8 = 395

using same number if she followed instructions it would be

395*8 =3160+5 = 3165

To calculate GPA we will find the total points of the student and the total credit hours of the student.

The grades point average (GPA) of the student is 3.47.

Given to us

Points of the students = earned grades x corresponding credit hours

Total points = 8 +24 + 3 + 24 = 59

Total Credit hours = 4 + 6 + 1 + 6 = 17 hours

[tex]\rm{Grade\ point\ average\ (GPA) = \dfrac{Total\ points\ of\ the\ students}{Total\ Credit\ hours}[/tex][tex]\rm{Grade\ point\ average\ (GPA) = \dfrac{59\ points}{17\ hours} = 3.47[/tex]

Hence, the grade point average (GPA) of the student is 3.47.

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To write this in scientific notation, we have to move the decimal place to the left. Moving the decimal place to the left indicate a positive movement, therefore the correct scientific notation in this case is:

8.28 x 10^8 micrometers

Answer:

[tex]4x^2[/tex]

Step-by-step explanation:

We are asked to find the GCF of [tex]28x^3[/tex] and [tex]16x^2y^2[/tex].

The greatest common factor of numerical part would be GCF of 28 and 16.

Factors of 28: 1, 2, 4, 7, 14, 28.

Factors of 16: 1, 2, 4, 8, 16.

The greatest common factor of 28 and 16 is 4.

The GCF of variable part:

[tex]x^3=x\cdot x\cdot x[/tex]

[tex]x^2y^2=x\cdot x\cdot y\cdot y[/tex]

The greatest common factor of [tex]x^3[/tex] and [tex]x^2y^2[/tex] is [tex]x^2[/tex].

Upon combining the GCF of numerical part and algebraic part, we will get:[tex]4x^2[/tex]

Therefore, the greatest common factor of both expressions is [tex]4x^2[/tex].

Answer:

1)[tex]10+10+1+1=22[/tex]

2)[tex]10+1+1+1+1+1+1+1+1+1+1+1+1=22[/tex]

Step-by-step explanation:

Mrs. Sims has to put 22 books.

She can either put them in stacks of 10 or arrange them as single book(single stack).

There could be two ways in which she could arrange the books.

First way:

She could arrange the books in two stacks of 10 books ([tex]2\times10=20[/tex] and the remaining two books can be arranged as single books.

So, the arrangement is [tex]10+10+1+1=22[/tex]

Second way:

She could arrange books in one stack of 10 books and and remaining twelve books can be arranged as single books.

So, the arrangement is [tex]10+1+1+1+1+1+1+1+1+1+1+1+1=22[/tex]

The ratio of bulls to cows does not remain the same after adding 4 more cows and 4 more bulls.

To determine if the ratio of bulls to cows remains the same after adding 4 more cows and 4 more bulls, we need to compare the new ratio to the original ratio.

Initial ratio of bulls to cows: 18/45 = 2/5

After adding 4 more cows and 4 more bulls, the new ratio becomes (18+4)/(45+4) = 22/49.

Since the new ratio is different from the original ratio, the ratio of bulls to cows does not remain the same after adding 4 more cows and 4 more bulls.

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Answer:

The pipe is leaking at the rate of 1.875 gallons of water per day.

Step-by-step explanation:

In this question we will find the leakage per day first, then convert it into gallons.

The janitor discovered a leak, leaking with a rate = 10 oz per hour

And we know that there are 24 hours in a day therefore, pipe leaking per day will be = 24×10 = 240 oz.

Since 1 oz  = 0.0078125 gallons

Therefore, 240 oz = 240×0.0078125

                               = 1.875 gallons

The pipe is leaking at the rate of 1.875 gallons of water per day.