{35 POINTS)What are the solutions of 2a^3-3a^2=8a-12 ?

Answers

Answer 1
Greetings!

[tex]2a^3-3a^2=8a-12[/tex]
Add -(8a-12) to both sides.
[tex](2a^3-3a^2)+-(8a-12)=8a-12-(8a-12)[/tex]
Simplify.
[tex]2a^3-3a^2-8a+12=0[/tex]
Rearrange.
[tex]2a^3-8a-3a^2+12=0[/tex]
Factor Out 2a.
[tex]2a(a^2-4)-3a^2+12=0[/tex]
Factor Out the difference of squares.
[tex]2a(a-2)(a+2)-3a^2+12=0[/tex]
Factor out -3.
[tex]2a(a-2)(a+2)-3(a^2-4)=0[/tex]
Factor Out the difference of squares.
[tex]2a(a-2)(a+2)-3(a-2)(a+2)=0[/tex]
Find Common Factor.
[tex](a+2)(a-2)(2a-3)=0[/tex]
Set Factors to Equal 0.
[tex](a+2)=0 \\ \\ (a-2)=0 \\ \\ (2a-3)=0[/tex]
[tex]a=-2 \\ \\ a=2 \\ \\ a=3/2[/tex]

Hope this helps.
-Benjamin

Related Questions

Carmelo puts $2,200.00 into savings bonds that pay a simple interest rate of 3.4%. How much money will the bonds be worth at the end of 5.5 years?

Answers

Hello there! So, the first thing we do when solving these types of problems is to find the interest rate. Because this is simple interest, the amount earned will be constant. The formula for this is I = prt. The principle is the $2,200. The rate earned per year is 3.4%. 2,200 * 3.4% (0.034) is 74.80. That's $74.80 worth of interest each year. The amount of time is 5.5 years. 74.8 * 5.5 is 411.4. Carmelo will earn $411.40 worth of interest in 5.5 years. However, that's not all. We are looking for the total amount of his bonds, which means add the interest and his initial amount in the bank. 2,200.00 + 411.40 is 2,611.4. Carmelo's saving bonds will be worth $2,611.40 at the end of 5.5 years.

The bonds will be $2611.40 at the end of 5.5 years.

What is simple interest rate?

Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.

Simple interest rate formula

F.V = [tex]P.V (1+rt)[/tex]

F.V = Final value

P.V = Principal value

Given

Principal value P.V = $2200.00

Rate r = 3.4%

Time t = 5.5 years

Simple interest rate formula

F.V = [tex]P.V (1+rt)[/tex]

F.V = [tex]2200(1+3.4 \% \times 5.5)[/tex]

F.V = [tex]2200(1+0.034 \times 5.5)[/tex]

F.V = 2200 × 1.187

F.V  = 2611.40

Hence,

The bonds will be $2611.40 at the end of 5.5 years.

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P = a + b + c

Solve for c


Answers

p-a-b=c
is the solution

P=a+b+c
we can rewrite this as a+b+c=P
a+b+c-a=P-a
b+c=P-a
b+c-b=P-a-b
c=P-a-b

here are 96 girls in a junior class of 176 students. Find the ratio of girls to boys.

Answers

176 - 96= 80

Meaning there's 80 boy in the class.

The unsimplified version of the ratio would be 80:96 or 80/96 in fraction form

But if your looking for it simplified it would be 5:6 or 5/6 in fraction form.

Hope this helps :)

plz help....Which relation describes a function?

A)
{(0, 0), (0, 2), (2, 0), (2, 2)}


B)
{(−2, −3), (−3, −2), (2, 3), (3, 2)}


C)
{(2, −1), (2, 1), (3, −1), (3, 1)}


D)
{(2, 2), (2, 3), (3, 2), (3, 3)}

Answers

the answer is B. {(-2,-3),(-3,-2),(2,3),(3,2)}
because the domain does not contain any repeated values.

The answer is B

a function is a set of ordered pairs such that for each domain element there is only one range element the set of ordered pairs{(-2,-3),(-3,-2),(2,3)(3,2) is the only set that does not pair a domain elemnt with two or more range elements.

find x on the triangle

Answers

This is an equilateral triangle, which means all the sides are the same length. So, the answer is 35. ☺♥

Hope this helps.
This is an isosceles triangle (two legs are of equal length).  Thus, x = 35.

A train leaves a station at 10:40 a.m. and arrives at its destination at 1:20 p.m. Find the distance between the stations if the average speed of the train was 60 mph.

Answers

The answer is 144 miles. I found that it took 2 hours and 40 minutes, then multiplied 2.4 times 60 and got 144 miles.

Answer:

160 miles.

Step-by-step explanation:

A train leaves a station at 10 : 40 a.m.

and arrives at its destination at 1 : 20 p.m.  = 13 : 20 p.m.

Now we will subtract the time of departure to calculate the total time taken by the train.

 13 : 20

- 10 : 40

  2 : 40       Train took 2 hours 40 minutes to reach its destination.

Now we will convert 2 hours 40 minutes to decimal form.

2 hours and (40/60) = 2.66 minutes

If the average speed of the train was 60 miles per hour.

Since in one hour train traveled 60 miles

Therefore, in 2.66 hours train traveled = 60 × 2.66

                                                                 = 159.6 ≈ 160 miles

The distance would be 160 miles.

Explain how you can use doubles when multiplying with 4 to find 4x8

Answers

you can figure out what four times eight is by adding eight and eight(16) and doubling it (32)

Corrine is organizing a bus trip to an amusement park. She has 245 people signed up to go on the trip. The coach buses can seat 55 people per bus. How many buses should Corrine hire?

Answers

Just divide 245 by 55 to find out how many buses are needed.

245/55 = 4.4545 buses

This means that Corrine needs 4.45 buses to haul everyone on the trip. However, it is ridiculous to think that it would be possible to hire only .45 of a bus, so to have our final answer, we would round up to the nearest whole number.

Corrine should hire 5 buses to shuttle everyone to the trip.

brianna choclotate chip cookies recipe will make about 3 dozen cholotate chip cookies . The recipe calls for 2 1/4 cups of flour and 3/8 cups o baking soda . If brianna was to adjust the recipe to include 1 cup of baking soda how many cups of flour would she need to use

Answers

so if she uses 2 1/4 for 3/8 thats 5/8 more which is 62.5% so 2 1/4+62.5 of 2 1/4 so 1 7/20+2 1/4 to get 3 3/5.

simplify
7x + 8 = 36

Answers

7x=36-8
7x=28
x=28/7
x=4

The correct simplification of [tex]7x + 8 =36[/tex]  for value of x is 4.

Given expression is:

[tex]7x+8 = 36[/tex]

To simplify the expression,

isolate  [tex]x[/tex] on one side of the expression or rearrange the expression rearranging like and unlike terms.

Subtract 8 from both side of the expression:

[tex]7x + 8 -8 = 36 -8[/tex]

[tex]7x = 36-8[/tex]

[tex]7x = 28[/tex]

To solve for [tex]x[/tex] , Divide both side of the equation by 7.

[tex]\dfrac{7x}{x} = \dfrac{28}{7}[/tex]

[tex]x = \dfrac{28}{7}[/tex]

Simplify further,

[tex]x = 4[/tex]

The solution for the  equation  [tex]7x + 8 =36[/tex] is 4.

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Maihua jogged for 1/2 hour a 6 km/h she jogged for another 1/4 hour at 8 km/h what distance did she jog altogether.

Answers

5 km (1/2 * 6 = 3, and 1/4 * 8 = 2, and 2+3=5).

What value of x makes the equation below true? 6x-9 39

Answers

6x-9=39
+9 +9
6x=48
x=48/6
x=8
And yes it is true

What is 2.75-23.68x=8.04+23.17x ?

Answers

First you need to subtract 23.17x on both sides to get 2.75-46.85x=8.04
Then you subtract 2.75 on both sides to get -46.85x=5.29
Finally you divide -46.85 on both sides to get x=-5.29/46.85 or-0.113

How do you write 6.7 in two other word forms for a 4th grade assignment

Answers

six and seven hundredths
Six and seven hundreds

Rebecca is planning to visit relatives in Omaha Nebraska. She will drive 610 miles from her home in Indianapolis. On her trip back home, will she be traveling –610 miles? Use mathematical vocabulary to justify your answer.

Answers

no she wouldn't be traveling -610 miles because distance is never negative
Final answer:

Rebecca will travel another 610 miles on her way back from Omaha to Indianapolis, not -610 miles, as distance is a scalar quantity and does not adopt a negative sign. The total round trip distance is therefore 1220 miles.

Explanation:

When Rebecca returns home from her trip to Omaha, Nebraska, she will indeed travel another 610 miles. However, the use of -610 miles might be misleading in this context. In mathematics, especially when discussing distance, the concept of negative numbers often represents direction rather than decrement. Therefore, saying Rebecca will travel -610 miles could imply direction, but since she is returning to her starting point, the actual distance traveled is 610 miles, the same as her outbound trip.

Distance, as a quantity, is scalar and therefore always non-negative. When keeping track of total distance travelled, irrespective of direction, the concept of positive and negative doesn’t apply—the distance simply adds up. So, the total distance Rebecca travels (going to Omaha and then back to Indianapolis) would be 1220 miles. This demonstrates the concept of absolute value in mathematics, where the focus is on the magnitude of a number without regard to its sign.

Mr. Winkle downloaded 34 more songs than Mrs. Winkle downloaded.
Together they downloaded 220 songs. How many songs did each download?
Please show how you got it...

Answers

220/2=110 each plus 34 for Mr Winkle.
Mr winkle had 134 and Mrs.Winkle had 76 which is the difference taken from her 110.

Mrs. Winkle downloaded 93 songs and Mr. Winkle downloaded 127 songs, which equals the total of 220 songs they downloaded together.

The total number of songs downloaded by Mr. and Mrs. Winkle is 220. If Mr. Winkle downloaded 34 more songs than Mrs. Winkle, we can set up a system of equations to solve for the number of songs each downloaded. Let x represent the number of songs Mrs. Winkle downloaded, so Mr. Winkle downloaded x + 34 songs.

The equation representing the total number of songs downloaded by both is:

x + (x + 34) = 220

Combining like terms gives us:

2x + 34 = 220

Subtracting 34 from both sides, we get:

2x = 186

Dividing both sides by 2, we find:

x = 93

So, Mrs. Winkle downloaded 93 songs and Mr. Winkle downloaded 93 + 34, which is:

Mr. Winkle downloaded 127 songs.

Jake earns $12.00 more per week on his paper route than three times the amount, s, that Steve does. Steve earns $15.00 per week. How much does Jake earn per week?

Answers

Let's say Jake = j
We already know that s = 15
j = 3s + 12
3(15) = 45, add 12 and you'd get 57.
So Jake earns $57.00 per week.

Name the place value to which each number was rounded.0.546 to 0.55

Answers

You've must've rounded to the nearest thousandths to get your answer.

The value of each digit in a number is known as the place value. The place value to which each number was rounded.0.546 to 0.55 is hundredths place value.

What is the place value of a digit in a number?

The value of each digit in a number is known as the place value. The 5 in 350, for example, represents 5 tens, or 50, whereas the 5 in 5,006 represents 5 thousand, or 5,000. It is critical that children that while a digit can be the same, its value is determined by its position in the number.

Identification of the place value of a digit in a number:

The place values on the left of the decimal point start as ones, tens, hundreds, and so on.The place value on the right of the decimal point starts from the point and goes to the right as tenths, hundredths and so onThe tens mean multiply by 10The tenth means the tenth part of that digit which is that digit divided by 10

Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.

Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits

Round 0.546 to the nearest hundredths place value.

We have, 0.546

Rounding to the nearest hundredths place value

4 is in hundredths place value

Since 6 is greater than 5 we can write 4 as 5.

0.55 is our answer.

Thus, if we round to the nearest hundredths place value we get 0.55.

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At a wedding reception, an equal number of guests were seated at 12 round tables. The 13 people in the wedding party were seated at a rectangular table. There were 121 people at the reception altogether. Which equation could you use to find the number of guests, n, seated at each round table?

Answers

12n + 13 = 121
-13 from both sides

12n = 108
÷12 from both sides

n=9

a story problem for 7 ×6=42

Answers

Bob goes to the store 7 times a week and buys 6 watermelons each time he goes. How many watermelons does Bob buy in one week?

What is the simplified form of the following expression? 4sg/-5g

Answers

the first thing i would do is eliminate 'g' becasue it is on the top and bottom and get   4s/-5, I do not see anything else ypu can do to simplify so I would leave it like that

Miss Lawrence buys 8 ounces of smoked salmon at $17.98 per pound. How much money does Miss Lawrence spend on the smoked salmon?

16 ounces= 1 pound

Answers

So if 16 ounces is one pound, 8 ounces is half a pound, If you buy a half pound at $17.98 per pound you multiply 17.98 by .5

So your answer is $8.99

Which sets of values can be the measures of the exterior angles of a triangle?
120°, 110°, 130°

35°, 103°, 122°

123°, 87°, 220°

120°, 120°, 120°

123°, 157°, 90°

can be more than one answer

Answers

The 3 angles must add up to 360 degrees

Only 1 and 4  fit the bill.

solve each equation x-6=8

Answers

Equation is
x-6=8
x=8+6
x=14
X equal to 14

The solution to the equation  x - 6 = 8 is x equal to 14.

What is a numerical expression?

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, An expression x - 6 = 8.

Now, Separating the variable and constants by moving them to other sides

we have, x = 8 + 6.

x = 14.

Also moving terms to the other sides changes its sign.

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What does it mean to say that a number is a perfect square? Give on example of number that is a perfect square and of one that is not. Explain your examples.

Answers

A number that is a perfect square is a number that can be square rooted kind of in a perfect match. Example would be 9 because it can be square rooted by 3 for 3 * 3. An example that would not be a perfect square would be 30 because it can divided by 6 * 5 but neither one of those numbers are perfect squares. 

Answer:

A number called a perfect square means that the number has an exact squared root. In other words, the number has an squared power, which is exact.

Other way to see this, it's taking natural number 1, 2, 3, 4... then, applying the squared power to each one, the results of each squared power is what we call a perfect square. For example, 1, 4, 9, 16, 25, 36,..., are all perfect square, because they are the result of a squared power:

[tex]1^{2}=1\\2^{2}=4\\3^{2}=9\\4^{2}=16\\5^{2}=25\\6^{2}=36[/tex]

Kai is making a chess board using pieces of wood that measure 1 in.². When he finishes, the chessboard will have an area of 64 in.². How many pieces of wood should he put along each side.

Answers

You have to find the square root of 64, since he is putting the same amount to both sides. The square root of 64 is 8, so Kai will be putting 8 pieces along each side. YOU'RE WELCOME :)

Answer:

8

Step-by-step explanation:

Please Help.
5, 6 and 7 have to equal to 37 what multiplication, division, sum and subtraction (I have to use all these) can i do?

Answers

5 x 6 + 7? Is that what the answer is, I didn't get the question towards the end. :)
37-7=30
30/6=5 
(37-7)/6=5
or.....
6*5+7=37

the quotient of five times a number and 7 is no more than 10

Answers

the sentence in numerical form is 5x/7≤10
to solve, multiply by 7
5x≤70
lastly, divide by 5
x≤14
14 is the answer okkkkkkkkkkkkkkkkkkkk

What polyhedron can be assembled from this net??

Answers

This would be a triangular prism

at a summer camp there are 40 boys out of 70 campers what is this ratio written as a fraction in simplist form

Answers

4/7 should be correct. Hope this helps! :)
40:70

4:7 is your answer

divide 10 from both sides

hope this helps
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