Mathematics High School

Factor the trinomial below.

6x2 – 9x – 6

A. 3(2x + 1)(x – 6)
B. 3(2x + 2)(x – 1)
C. 3(2x + 1)(x – 2)
D. 3(2x + 6)(x – 1)

Answers

Answer 1
For this case we have the following trinomial:
 6x2 - 9x - 6
 Rewriting we have:
 3 (2x2 - 3x - 2)
 Factoring we have:
 3 (2x + 1) (x-2)
 Answer:
 The factored expression for this case is given by:
 C. 3 (2x + 1) (x - 2)
Answer 2

Answer:

C.  3(2x+1)(x-2)

Step-by-step explanation:

To factor the trinomial 6x² - 9x -6, we will follow the steps below;

First, 3 is common among the three numbers, so we will start by factoring out 3, so that the expression becomes;

3(2x² -  3x - 2)

We will now proceed to factorize; 2x² -  3x - 2  

Find two numbers such that its product gives -4 and its sum gives -3.

Such number is -4 and 1

-4 × 1 = -4

-4 + 1 = -3

We will replace -3x by -4x + x in the above expression

2x² -  4x + x - 2

(2x² -  4x) (+x - 2)

In the first parenthesis, 2x is common, so we will factor out 2x while in the second parenthesis 1 is common, so we will factor out 1. Hence;

2x(x - 2)  + 1(x-2)

(2x+1)(x-2)

3(2x² -  3x - 2)  = 3(2x+1)(x-2)

6x² – 9x – 6 = 3(2x+1)(x-2)

Therefore the factorized form of 6x² – 9x – 6  is   3(2x+1)(x-2)

Related Questions

Eric plans to rent a car for a day from Easy Car Rental. He has a coupon for 25% off the daily base rate of $40. He will also have to pay an additional $0.15 for each mile he drives. Which expression represents the situation?

Answers

Let x represent the number of miles he drives

Base rate: 40 - (40 · 0.25)  plus  mileage: 0.15 · x
Total cost = 30 + 0.15x

If i = sqrt -1 what is the value of i3

A. -1
B. i
C. 1
D. -i

Answers

i^3  = i * i * i  = i^2 * i  = -1 * i = -i Answer

Its D

Answer:

The value of i3 is equal to D. -i

Step-by-step explanation:

We can find the answer by taking the definition of i :

i = sqrt(-1)        (1)

i ^2 = (sqrt(-1)) ^2 = -1             (2) because square root and squaring are inverse operations

so from (2)

i ^3= i ^2* i = -1*i = -i

So -i is the final answer or  – (sqrt(-1))         which is the same

x/3+6=9
what does x equal
x=___?

Answers

9514 1404 393

Answer:

  9

Step-by-step explanation:

  x/3 +6 = 9 . . . . . given

  x/3 = 3 . . . . . . . subtract 6 from both sides

  x = 9 . . . . . . . multiply both sides by 3

Now we have to,

find the required value of x.

→ x/3 + 6 = 9

→ x/3 = 9 - 6

→ x/3 = 3

→ x = 3 × 3

→ [x = 9]

Hence, 9 is the value of x.

A test has multiple choice questions with 5 choices for each answer; only one answer is correct for each question. Suppose a student guesses the answer to each question. Assuming the guesses are independent, find the probability that the student will not guess correctly on any one question.

a. 0
b. 1/5
c. 4/5

Answers

Number of choices per question = 5
Number of wrong answers = 4
P(wrong answer) = 4/5

Answer: 4/5

The value of the probability that the student will not guess correctly on any one question is,

⇒ 4 / 5

What is mean by Probability?

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Given that;

A test has multiple choice questions with 5 choices for each answer; only one answer is correct for each question.

Now, Suppose a student guesses the answer to each question.

Hence, we get;

The value of the probability that the student will not guess correctly on any one question is,

⇒ 4 / 5

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Find the surface area of the following triangular prism

Answers

The surface area of the triangular prism is 144 ft³

How to find the surface area

The surface area of the prism is solved using the formula

= 2 * area of the base + Lateral surface area

Area of the base

= 2 * 1/2 * 6 * 8

= 48

Lateral surface area

= (10 + 6 + 8) * 4

= 24 *  4

= 96

Total surface area

= 48 + 96

= 144 ft³

In the year 2000, there were 200,000 cell phone subscribers in a city in New York. The number of subscribers increased by 60 percent per year after 2000. Which equation can be used to model the number of subscribers, y, in the city t years after 2000?
A) y=200,000(1+60)t
B) y=200,000(1+0.6)t
C) y=200,000(1-60)t
D) y=200,000(1-0.6)t

Answers

The first step is to calculate the percentage increase for each year.
If the subscribers increase by 60%, it means that the subscribers will be (100+60)% of the previous year. 

(100+60)% = (100/100 + 60/100)
                     (1 + 0.6)

After 2,000, the subscribers will be 200,000×(1+0.6).
For the following years the 200,000×(1+0.6)t

So, the value of y will be given by,

Y=200,000(1+0.6)t

Answer: The answer is B

Step-by-step explanation:

A five question multiple choice quiz has five choices for each answer. Use the random number table provided, with 0’s representing incorrect answers, and 1’s representing correct answers to answer the following question: What is the experimental probability of correctly guessing at random exactly two correct answers?

Answers

Found a similar question online. Is the attached picture the same one as yours? Are these the choices also?
a. 5%
b. 65%
c. 45%
d. 25%

The answer is Letter D - 25%. Use the table and count the number of guesses that has two correct answers represented by 1. 01010, 10001, 11000, 01001, 00011 = a total of 5 numbers having 2 correct guesses out of 20 questions. Which means that there's twenty-five percent possibility of correctly guessing the answer out of 20 questions. 5/20 = 25%

Probability of correctly guessing at random exactly two correct answers is; 25%

How to find the experimental probability?

The table is missing but from the table shared by the first answer, we can  count the number of guesses that has two correct answers.

Now, the ones that have two number of 1's are referred to as correct answers. Thus, counting them in the question, they are;01010, 10001, 11000, 01001, 00011.

Thus, there are 5 posssible correct answers out of 20. Thus;

Probability of correctly guessing at random exactly two correct answers is; 5/20 = 25%

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An empty box weighs 200g the box is filled with birthday party goozy bags and now weighs 6.2kg Each goody bag weighs 150Work out how many goody bags are inside the box

Answers

For this case, the first thing we are going to do is define variables.
 We have then:
 x: number of birthday party goozy bags
 y: total weight
 We then have the following equation:
 y = 150x + 200
 For y = 6200 we have:
 6200 = 150x + 200
 Clearing x:
 x = (6200-200) / (150)
 x = 40
 Answer:
 there are 40 goody bags inside the box

Answer:

40

Step-by-step explanation:

A map is drawn using a scale of 80 mi to 1 cm. On the map , the two cities are 7.5 cm apart. What is the actual distance between the two cities ??

Answers

we know that
scale =measure in the map/measure in the actual
measure in the actual=measure in the map/scale
scale=1 cm/ 80 mi
for
measure in the map=7.5 cm
measure in the actual=?
measure in the actual=7.5 /(1/80)-----> 7.5*80-----> 600 mi

the answer is
the actual distance between the two cities is 600 miles

The sum of the square of a positive number and the square of 44 more than the number is 250250. what is the​ number?

Answers

let p positive number:

p²+44²>250250

p²>250250-44²

p²>248314

take the square root of both sides:

√p²>+√248314

p> 498.3 or 500 is the number

ANOTHER FILL IN THE BLANKS QUESTION, MARKING BRAINLIEST FOR CORRECT ANSWER

Answers

Hi, again!
First blank: multiplication property of equality
Both sides of the equation were multiplied by (1/2). 

Second blank: m<E
Angle E is an inscribed angle intercepting arc FGD, so by the inscribed angle theorem, its measure is half the measure of the arc.

Third blank: m<G
Same explanation as the prior blank

Fourth blank: substitution property of equality
Since angle E is equal to half the measure of arc FGD, we can replace that term. Likewise with angle G.

46 points for yall, i need math help.

Answers

Your answer would be the fourth choice, 6/13.
(4x-8)=(-9x-2)

4x= -9x+6

-5x= 6

x= -(6/5)



What’s the quadratic expression for this one

Answers

We have the following expression:
 (2x + 5) * (7-4x)
 Rewriting we have:
 14x - 8x ^ 2 + 35 - 20x
 Grouping terms with the same exponent:
 -8x ^ 2 + x (14-20) + 35
 Rewriting:
 -8x ^ 2 - 6x + 35
 Answer:
 the quadratic expression for this is:
 -8x ^ 2 - 6x + 35

20 POINTS AND A FOLLOW plus BRAINIEST IF RIGHT 1. What is the area of sector GHJ, given that 0=pi/4 radians ? Express your answer in terms of pi and as a decimal rounded to the nearest tenth. Show your work.

2. Construct the circle that circumscribes triangle DEF . Use a straightedge and a compass.
(show work by step)

Answers

1. To solve this we are going to use the formula for the area of a sector of a circle: [tex]A= \frac{1}{2} r^2 \alpha [/tex]
where
[tex]A[/tex] is the area of the sector 
[tex]r[/tex] is the radius of the circle 
[tex] \alpha [/tex] is the angle in radians

We know from our problem that the radius of the circle is 5 cm and the angle of the sector is [tex] \frac{ \pi }{4} [/tex], so [tex]r=[/tex] and [tex] \alpha = \frac{ \pi }{4} [/tex]. Lets replace those values in our formula:
[tex]A= \frac{1}{2} r^2 \alpha [/tex]
[tex]A= \frac{1}{2} (5)^2( \frac{ \pi }{4} )[/tex]
[tex]A= \frac{25 \pi }{8} [/tex]
[tex]A=9.8[/tex]

We can conclude that the area of sector GHJ in terms of pi is [tex] \frac{25 \pi }{8}[/tex] [tex]cm^2[/tex], and as a decimal rounded to the nearest tenth is 9.8 [tex]cm^2[/tex].

2. To construct the circle that circumscribes triangle DEF, we are going to draw the perpendicular bisectors of triangle DEF, and then we are going to draw the circle with radius at the interception point of the bisectors. Remember that the perpendicular bisector are the lines that passes trough the midpoint of the segment and are perpendicular to the segment.

What is the equation, in slope-intercept form, of the line that passes through (0, 3) and has a slope of −6?
y = 3x + 6
y = 3x − 6
y = −6x − 3
y = −6x + 3

Answers

Y = 3x - 6, slope is the last number in the equation.

Answer:

y=-6x+3

Step-by-step explanation:

Using the formula,

[tex](y-y_{1})=m(x-x_{1})\\(y-3)=(-6)(x-0)\\y-3=-6x\\y=-6x+3[/tex]

A vegetable store sold 3 tons of vegetables less on the first day than on the second, and on the third day it sold 5/9 of the amount sold in the first two days. How many vegetables was the store selling every day if it sold altogether 98 tons of vegetables for the three days?

Answers

let
x---------> quantity (ton) of vegetables sold the first day
y---------> quantity (ton)  of vegetables sold the second day
z---------> quantity (ton) of vegetables sold the third day

we know that
x=y-3---------> equation 1
z=(5/9)*(x+y)------> equation 2
x+y+z=98-----> equation 3
substitute equation 2 in equation 3
x+y+[(5/9)*(x+y)]=98----> multiply by 9----> 9x+9y+5x+5y=882
14x+14y=882-----> equation 4

to resolve the equations system formed by
x=y-3
14x+14y=882

using a graph tool
see the attached figure
the solution is
x=30
y=33
x+y+z=98----> z=98-(x+y)----> z=98-63---> 35

the answer is
vegetables sold the first day----> 30 ton
vegetables sold the second day----> 33 ton
vegetables sold the third day------> 35 ton

Answer:
amount sold on first day = 30 tons
amount sold on second day = 33 tons
amount sold in third day = 35 tons

Explanation:
Assume that the amount of vegetables sold on the second day is x.
We are given that:
Amount of vegetables sold on the first day is 3 tons less that sold on the second day.
This means that:
amount sold on first day = x - 3 
Amount of vegetables sold on the third day is 5/9 the amount sold on the first two days.
This means that:
amount sold on third day = (5/9) (x + x - 3)
amount sold on third day = [tex] \frac{10}{9} x - \frac{5}{3} [/tex]

Now, we know that:
Total amount sold is 98 tons.
This means that:
98 = x - 3 + x + [tex] \frac{10}{9} x - \frac{5}{3} [/tex]

Now, we will solve for x as follows:
98 = [tex] \frac{28}{9} x - \frac{14}{3} [/tex]

882 = 28x - 42
882 + 42 = 28x
924 = 28x
x = 924/28
x = 33 tons

This means that:
amount sold on first day = x - 3 = 33 - 3 = 30 tons
amount sold on second day = x = 33 tons
amount sold on third day = [tex] \frac{10}{9} x - \frac{5}{3} [/tex] = [tex] \frac{10}{9} (33) - \frac{5}{3} [/tex] = 35 tons

Hope this helps :)

Assuming that one-pint is equal to 473 ml., how many pints can be found in one liter?

Answers

we know that
 1 pint is equal to --------> 473 ml
1 liter is equal to--------> 1000 ml
so
1 pint is equal to --------> 473 ml
x pints------------------> 1000 ml
x=1000/473-----> 2.11 pints

the answer is
2.11 pints can be found in one liter
For this case we can make the following rule of three:
 1 pint -------> 473 ml
 x -------------> 1000 ml
 Clearing x we have:
 x = (1000/473) * (1)
 x = 2.114164905
 Rounding off we have:
 x = 2
 Answer:
 can be found 2 pints in one liter

Find area of trapezoid using the Pythagorean theorem

Answers

You should either divide or add
This is a multistep problem. So, let's split it up.

Finding the height:
We need to look at the equation for find the diagonal of a triangle.
a²+b²=c²
We don't have leg one, but we have leg two. If we subtract the longer base by the shorter base, we have leg two.
11-7=4
a²+4²=5²
a²+16=25; let's subtract 16 from both sides.
a²=9
a=3

So, the height is 3.

Finding the area of the trapzoid:
Let's look at the formula for finding the area.
(b1+b2)(h÷2)=A; let's fill the variables in.
(7+11)(3÷2)=A
(18)(1.5)=A
27=A

So, the area of the trapezoid is 27 in²

Jacob is cutting a tile in the shape of a parallelogram. Two opposite angles have measures of (6n − 70)° and (2n + 10)°. What are the two different angle measures of the parallelogram-shaped tile? 20° and 160° 50° and 130° 30° and 150° 70° and 110°
URGENT

Answers

Answer:

Step-by-step explanation:Jacob is cutting a tile in the shape of a parallelogram. Two opposite angles have measures of (6n − 70)° and (2n + 10)°.

Answer : 50° and 130°

Final answer:

To find the angle measures of the parallelogram, we set the expressions for opposite angles equal to each other, solve for 'n', and then determine the angle measures, which are 50° and 130° respectively.

Explanation:

The students wants to find the two different angle measures of a parallelogram-shaped tile where two opposite angles are given by the equations (6n − 70)° and (2n + 10)°. Since opposite angles in a parallelogram are equal, we can set these two expressions equal to each other to find the value of 'n':

6n − 70 = 2n + 10

Solving for 'n', we get:

4n = 80

n = 20

Now, we'll plug the value of 'n' back into the expressions to get the angle measures:

6n − 70 = 6(20) − 70 = 120 − 70 = 50°

2n + 10 = 2(20) + 10 = 40 + 10 = 50°

Since opposite angles are equal in a parallelogram, the other two angles must also add up to 180°. Therefore, the other two angles are 180° - 50° = 130°. The angles of the parallelogram are 50° and 130°.

Please give an explanation with you answer, thank you :)

Answers

[tex]f(x)=2( \sqrt[3]{27})^{2x} [/tex]

Here 2 on left most side is the coefficient, 2x is the exponent and the of the function is cube root of 27.

So,

[tex]Base= \sqrt[3]{27} \\ \\ Base= \sqrt[3]{3^{3} } \\ \\ Base=3 [/tex]

Thus, the simplified base for the function is 3. So correct answer is option  B

Karen makes $5 per hour baby-sitting and $12 per hour giving music lessons. one weekend, she worked a total of 18 hours and made $139. how many hours did she spend baby-sitting?

Answers

Let the number of hours she spent in baby- sitting is x

and the number of hours she spent in music lessons is y.

Now, we have been given that she worked a total of 18 hours. Hence, we have

[tex]x+y=18\\ y=18-x...............................(1)[/tex]

And she made $139. Thus, we have

[tex]5x+12y=139..............................(2)[/tex]

Substituting the value of y from equation 1 in 2, we get

[tex]5x+12(18-x)=139\\ 5x+216-12x=139\\ -7x=-77\\ x=11[/tex]

Therefore, she spent 11 hours in baby-sitting.

Final answer:

Karen spent 11 hours baby-sitting and 7 hours giving music lessons.

Explanation:

Let x be the number of hours spent baby-sitting, and let y be the number of hours spent giving music lessons.

We are given the following information:


 Karen makes $5 per hour baby-sitting, so she earned 5x dollars from baby-sitting.
 Karen makes $12 per hour giving music lessons, so she earned 12y dollars from giving music lessons.
 She worked a total of 18 hours, so x + y = 18.
 She made a total of $139, so 5x + 12y = 139.



We can now set up a system of equations:


 x + y = 18
 5x + 12y = 139


To solve this system, we can use substitution or elimination method. Let's use the elimination method:


 Multiply the first equation by 5 to make the coefficients of x the same: 5x + 5y = 90.
 Subtract this new equation from the second equation: (5x + 12y) - (5x + 5y) = 139 - 90.
 Simplify both sides of the equation: 7y = 49.
 Divide both sides of the equation by 7: y = 7.
 Substitute y = 7 into the first equation: x + 7 = 18.
 Solve for x: x = 11.

Therefore, Karen spent 11 hours baby-sitting and 7 hours giving music lessons.

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Solve 4x - 2= 86
thanks

Answers

4x-2=86
   +2  +2            (-2 and +2 cancel each other out)
_______
4x=88               ( divide 4 on both sides)

x=22
x = 22

4x-2=86
    +2  +2
_______
4x=88
4x/4=x
88/4=22

If an egg is thrown up and off the roof of a 100 foot building with an initial upward velocity of 10 feet per second, how long until it hits the ground?

Answers

The equation of the height as a function of time for this case is given by:
 h (t) = - 16t ^ 2 + 10t + 100
 By the time the egg hits the ground we have:
 -16t ^ 2 + 10t + 100 = 0
 We look for the roots of the polynomial:
 t1 = -2.2069555463432966
 t2 = 2.8319555463432966
 As it is about time, we use the positive root:
 t = 2.83 s
 Answer:
 it hits the ground at:
 t = 2.83 s

A painter places an 8.5 ft ladder against a wall. the bottom of the ladder is 4 ft from the base of the wall. how high up the wall does the ladder reach?

Answers

Use the Pythagorean Theorem:
a² + b² = c²
4² + b² = 8.5²
16 + b² = 72.25
        b² = 56.25
        b = 7.5

 The ladder reaches a height of 7.5 ft on the wall

Simplify the expression 9xy + 6xy − 2xy. What is the coefficient of the simplified expression?

Answers

Hi there!

To find our answer we need to collect the terms of the expression.

[tex]9xy + 6xy - 2xy = \\ 15xy - 2xy = \\ 13xy[/tex]

The coefficient (which is the number just before the variable) of the simplified expression is 13.
9xy + 6xy - 2xy
13xy is the answer. THey are all like terms so just add then subtract.

Kym spends an average of $78 per week on groceries. She can save 10% of her total grocery bill by joining the store's free shopper's club.About how much money will Kym save in a year (52 weeks) if she joins the shopper's club

Answers

Total amount Kym can save in 52 weeks will be given by:
(amount saved per week)×(number of weeks)
amount saved per week:
10/100×78
=$7.8
The total amount saved for 52 weeks will be:
52×7.8
=405.6

Paula caught a tarpon with a weight that was 11 times as great as the weight of a permit fish she caught. The total weight of the two fish was 180 pounds. How much did each fish weigh?

Answers


[tex]11 + 1 = 12 \\ 180 \div 12 = 15 \\ 15 \times 1 = 15 \\ 15 \times 11 = 165[/tex]
Tarpon=165
Permit=15

The weight of the permit fish will be 15 pounds and the weight of tarpon will be 165 pounds

What is Equation Modelling?

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Assume that the weight of the permit fish is x pounds.

Then the weight of the tarpon would be 11x pounds.

According to the question, we can write equation as -

x + 11x = 180

12x = 180

x = 15

Weight of permit fish = 15 pounds

Weight of tarpon = 11 x 15 = 165 pounds

Therefore, the weight of the permit fish will be 15 pounds and the weight of tarpon will be 165 pounds.

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a speed camera takes two photographs of a car

Answers

Hello!

First you have to count how many tallies the car went 9 tallies

Multiply the amount of tallies by how far they represent

9 * 0.8 = 7.2 meters

The car when 7.2 meters in half a second so we double this to get how fast it was going a second

7.2 * 2 = 14.4

The answer is 14.4 m/s

Hope this helps!

Answer:The answer is 14.4 m/s

Step-by-step explanation:

A bag contains 12 red marbles and 6 blue marbles. two marbles are drawn with replacement. find the probability.

Answers

248376203488451-5814-0395681-03581-403951-0958904680968590147514095714095714-5714578140587109p54

Use the given information to match the answers.

ABC is a right triangle.

1. 2√13
2. √5
3. 3√3

1. If b = 2 and c = 3, then a =
2. If a = 3 and c = 6, then b =
3. If a = 4 and b = 6, then c =

Answers

using formula
[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]
1)
[tex] {3}^{2} = {a}^{2} + {2}^{2} \\ a = \sqrt{ {3}^{2} - {2}^{2} } \\ a = \sqrt{5} [/tex]
2)
[tex] {6}^{2} = {3}^{2} + {b}^{2} \\ b = \sqrt{ {6}^{2} - {3}^{2} } \\ b = \sqrt{27} \\ b = \sqrt{9} \sqrt{3} \\ b = 3 \sqrt{3} [/tex]
3)
[tex] {c}^{2} = {4}^{2} + {6}^{2} \\ c = \sqrt{ {4}^{2} + {6}^{2} } \\ c = \sqrt{52} \\ c = \sqrt{4} \sqrt{13} \\ c = 2 \sqrt{13} [/tex]
Hey there!

Solve them by using
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]


1.
[tex] {a}^{2} + {2}^{2} = {3}^{2} \\ {a}^{2} + 4 = 9 \\ {a}^{2} = 9 - 4 \\ {a}^{2} = 5 \\ a = \sqrt{5} [/tex]

2.
[tex] {3}^{2} + {b}^{2} = {6}^{2} \\ 9 + {b}^{2} = 36 \\ {b}^{2} = 36 - 9 \\ {b}^{2} = 27 \\ b = \sqrt{9 \times 3} \\ b = 3 \sqrt{3} [/tex]

3.
[tex] {4}^{2} + {6}^{2} = {c}^{2} \\ 16 + 36 = {c}^{2} \\ {c}^{2} = 52 \\ c = \sqrt{13 \times 4} \\ c = 2 \sqrt{13} [/tex]

Hope this helps. - M
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Cicero and Seneca introduced ideas of a successful government, including popular sovereignty, which means: Find the new concentration of a solution if 25.0 mL of water is added to 125.0 mL of 0.150 M NaCl solution. What is the final volume? mL The _____ proposes that the emotion we experience is influenced by feedback from facial muscles or skin. facial network proposal feedback principle physiological-feedback initiative facial feedback hypothesis Seventeen years after this vote and this article, Japan attacked the united states at pearl harbor. is there a possible connection between the immigration quota act of 1924 and pearl harbor? What are three reasons children may experience speech difficulties? Which box plot represents the data? 30, 35, 25, 5, 5, 25, 40, 45, 50, 10, 15, 40 The endpoints of a line segments are at the coordinates (-6,3,4) and (4,-1,2) what is the midpoint of the segment Measuring the Orbital Speeds of PlanetsIntroductionA Boeing 747 can fly 624 miles per hour. Thats pretty fast! Right now, Earth and other objects in thesolar system are orbiting the Sun, but how fast are these objects moving? In this assignment, you willcalculate the orbital speeds of objects in our solar system.Part A: Planetary PeriodsIn the 1600s, Johannes Kepler discovered three laws that govern the motion of objects around the sun.Keplers first law explains that objects travel in an elliptical, or oval-shaped, path around the sun.Keplers second law explains that an object travels faster in its orbit when it is closer to the Sun andslower in its orbit when it is farther away. In this activity, you will investigate Keplers third law: therelationship between an objects distance from the sun and the time it takes the object to complete anorbit around the sun.Access the Gizmo from within today's lesson. The exploration guide found within this simulation willhelp you work through the Gizmo. Click on the Lesson Materials link, which appears on the top leftcorner of the screen once you enter the simulation, to access the student exploration sheet. Use it asyou work through Activity C and answer all parts.Part B: Calculating Orbital SpeedEvery object moves at a different average speed in its orbit around the Sun. In this activity, you will usedata collected from Part A to calculate the average orbital speeds of each planet and of Pluto.1. Recall that the path an object takes around the Sun is an ellipse, and not a circle. However, toapproximate the circumference, or length, of each orbit, you will treat the orbits as circles. Goback to your notes in your student exploration sheet from Part A. Using the mean orbital radius(R) that you recorded, calculate the circumference of each planets orbit and record it in thetable below. Use the following formula to calculate the circumference:Circumference 2 = r2. Using the periods you recorded in your student exploration sheet and the circumference of orbitthat you just calculated, calculate the average orbital speed of each planet and record it in thetable below. Use the following formula to calculate speed:Distance Circumference Average Orbital Speed Time Period = =The units of your answer will be in AU/year.3. To give you a better perspective of how fast these orbital speeds really are, convert the orbitalspeeds you just calculated from AU/year to miles/hour. 1 AU/year = 10,604 miles/hour. Recordyour answers in the table below.TableObjectMeanorbitalradius (AU)(copy from#6 in part A)Circumference ofOrbit (AU)Period(EarthYears)(copyfrom #6in partA)Orbital Speed(AU/year)Orbital Speed(miles/hour)MercuryVenusEarthMarsJupiterSaturnUranusNeptunePlutoDrawing Conclusions4. Which planet takes the longest amount of time to travel once around its orbit? Which planettakes the shortest amount of time?5. How does an increase in orbital radius affect average orbital speed?ExtensionperihelionIn astronomy, the term refers to the point in the orbit of an asteroid, comet, or planet atwhich it is closest to the sun. Aphelion refers to the point at which the object is furthest away from thesun. Research facts about the dwarf planet Ceres. Calculate the average orbital speed of Ceres inmiles/hour when it is closest to the sun and when it is farthest away. The equilibrium constant for the reaction sr(s) + mg2+(aq) sr2+(aq) + mg(s) is 3.69 1017 at 25c. calculate e o for a cell made up of sr / sr2+ and mg / mg2+ half-cells. How did a move toward mercantilism strengthen royal power?a. by increasing the amount of a nations importsb. by allowing nobles to control taxationc. by creating colonies that supported the kingd. by ensuring more economic prosperity for the merchant and middle classes According to abraham maslow, people are motivated by: question 3 options:a.optimal arousal.b.drive reduction.c.a hierarchy of needs. and) instincts. Without the skeletal system, the body could not fight off infection. Please select the best answer from the choices provided. T F During the 1950's, the typical suburban male was all of the following except white, young, blue-collar, or married with children? What layer of the rainforest do gliding leaf frogs live in? Francesca is in junior high, and her parents have decided to divorce, due to a high-conflict marriage. despite the difficulty of adjusting, francesca may be better off because children in high-conflict intact families ____________ than children in divorced families. ) a pair of fair dice is rolled. what is the probability that the sum of the top faces is a number 10 or greater? Explain how the difference of a fraction or a rational number and its additive inverse is equal to zero. Encryption and decryption algorithms are known as ________________. How does the chef justify the theft of the professors briefcase and identity? which visual aid is best for showing comparative data? A. photograph B. video clip C. chart D. diagram