Use the definitions and theorems of this section to evaluate and simplify the following expression. Be sure to express answers with positive exponents.
Answers
Answer:
x^5(1+x)(1-x+x^2)
Step-by-step explanation:
b^5 +b^8 =
You can easily solve this equation by doing factoring (a fancy word for dividing)
so, factor out the Greatest Common Factor (GCF)
which is
B^5
so in parenthesis write (1+b^3) next to it, think of subtracting the two exponents, and then since theres only 1 thing left after factoring out b^5, you leave a 1 behind.
b^5(1+b^3)
from here, in the parenthesis, you have 2 perfect cubes, 1 and b^3
take the cube root of that which is (1+b)
then use (a+b) which is already done
AND (a^2-ab+b^2) where a is equal to 1, and b is equal to variable b.
so, that would be
x^5(1+x)(1-1x+x^2) ( this is what you should get once you do multiply the square root out to just get constants and coefficients.
That gives us our final answer of x^5(1+x)(1-1x+x^2) because it is in the simplest form possible.
Related Questions
Find the amount and compound interest on Rs.3000 for 2 years at 15% per annum compounded annually .
Answers
Step-by-step explanation:
formula =P×(1+r/100)^2
3000×1.15^2=3967.50rs
the number of the x is 5 and the number of the Y
Answers
Answer:
Y is also 5 bro that is very easy question
find the exact coordinates of X on segment JK that is 1/3 the distance from j to k. J (-1,4) K(5,-3)
Answers
Answer:
Step-by-step explanation:
J (-1,4) ⇒ x₁ = -1 & y₁ = 4
K(5,-3) ⇒ x₂ = 5 ; y₂ = -3
m : n = 1/3 : 2/3 = 1 :2
[tex]X \left(\dfrac{mx_{2}+nx_{1}}{m+n},\dfrac{my_{2}+ny_{1}}{m+n} \right)\\\\\\X \left(\dfrac{1*5+2*(-1)}{1+2},\dfrac{1*(-3)+2*4}{1+2} \right) \\\\\\X \left(\dfrac{5-2}{3},\dfrac{-3+8}{3} \right)\\\\\\X \left(\dfrac{3}{3},\dfrac{5}{3} \right)\\\\\\X \left( 1 , \dfrac{5}{3} \right)[/tex]
Max makes three piles of cards, each consisting of only a Queen and a Jack. Lisa draws one card from each pile. What is the probability that Lisa draws two Queen and a Jack in any order? Make a tree diagram of all the choices
Answers
Answer:
3/8
Step-by-step explanation:
The probability of picking either a Queen or a Jack from each pile is always 1/2 (as there are only 2 cards).
There are only 3 ways in which Lisa can draw two Queens and a Jack:
Queen, Queen, Jack
Queen, Jack, Queen
Jack, Queen, Queen
The probability of each one happening is 1/8
This is because there is a 1/2 chance of picking a Queen or a Jack from each pile and to calculate the probability that Lisa will pick a Queen AND a Queen AND then a Jack (for example) you multiply the probabilities together:
1/2 x 1/2 x 1/2 = 1/8
This is the same for other examples and since there are only 3 ways that Lisa can draw two Queens and a Jack you multiply 1/8 by 3 (you add 1/8 together 3 times) to get 3/8
It can be represented on a tree diagram however I am not sure how I can show images/drawings on this
Find the number that makes the ratio equivalent to 10:6.
Answers
Answer:
9*10=90 so 6*9=54 then answer is 90:54
Step-by-step explanation:
Jordan has to solve this division problem: 42 divided by 7 = ?
Which of the following equations can he use?
42 + 7 = ?
7 x 42 = ?
? x 7 = 42
7 divided by 42 = ?
Answers
The correct equation that Jordan can use to solve the division problem 42 divided by 7 is:
? x 7 = 42
So, the correct equation is option 3) ? x 7 = 42.
Given that, Jordan has to solve this division problem: 42 divided by 7 = ?
In this case, Jordan needs to find the value of the missing factor, which represents how many times 7 can be multiplied to get 42.
Therefore, he can use the equation:
? x 7 = 42
This equation represents the inverse operation of division, which is multiplication.
When we know one factor (7) and the product (42), we can use multiplication to find the missing factor (the quotient).
By solving for the missing factor, he will find the correct answer to the division problem:
The missing factor = 42 / 7 = 6
So, the correct equation is option 3) ? x 7 = 42.
To learn more on division click:
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Josh keeps his socks and shirts in different drawers. He has twelve white, five blue, and seven black socks. He also has three white, five black, and two grey shirts. He pulled out a sock and a shirt in the dark.
What are the chances that he will get a black sock and a grey shirt?
Answers
Answer:
P(blk sk AND gy shr)=P(blk sk)*P(gy shr)=7 /578
P(gy shr)=2/34
P(blk sk)=7/34
blk=Black
sk=Sock
gy=Grey
shr=Shirt
Help meeee pleaseeee mehhhh
Answers
PLEASE HELP!!!!!!!!!! GIVING BRAINLIEST, THANKS AND FIVE STARS!!!!!!
Find the greatest common factor of each pair of numbers.
1. 24 and 36
2. 39 and 54
3. 42 and 98
4. 48 and 72
5. 65 and 91
6. 7 and 20
Answers
1. 12
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36
Then the greatest common factor is 12.
2. 3
The factors of 39 are: 1, 3, 13, 39
The factors of 54 are: 1, 2, 3, 6, 9, 18, 27, 54
Then the greatest common factor is 3.
3. 14
The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42
The factors of 98 are: 1, 2, 7, 14, 49, 98
Then the greatest common factor is 14.
4. 24
The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Then the greatest common factor is 24.
5. 13
The factors of 65 are: 1, 5, 13, 65
The factors of 91 are: 1, 7, 13, 91
Then the greatest common factor is 13.
6. 1
The factors of 7 are: 1, 7
The factors of 20 are: 1, 2, 4, 5, 10, 20
Then the greatest common factor is 1.
Hope this helps you *smiles*
2. 3
3.14
4.24
5.13
6.1
help me please
6(9 + 5x) = 54 +
Answers
Hi
to progress in math, you must : know by heart the rules and formulas then train.
rule : a ( b+c ) = a*b + a*c.
this propertie is call distributivity .
so we have : 6 ( 9+5X)
here : a = 6
b = 9
c = 5X
so 6 ( 9+5X) = ?
I let you have a shot. Ask in comments section if you are stuck. But try first !
Answer:
1) rearrange terms:
6(9 + 5x) = 54
6(5x + 9) = 54
2) Distribution :
6(5x + 9) = 54
30x + 54= 54
3) subtract 54 from both side:
30x + 54 = 54
30x + 54 - 54 = 54 - 54
4) Simplify: subtract the numbers
30x = 0
5) Divide both side of the equation by the same term:
30x = 0
30x√30 = 0√30
6) Simplify: cancel term that are in the both numerator and denominator
x = O√30
solution :
x = 0]
Max makes three piles of cards, each consisting of only a Queen and a Jack. Lisa draws one card from each pile. What is the probability that Lisa draws two Queens and a Jack in any order? Make a tree diagram of all the choices
id at least like how you would set up the whole tree diagram
Answers
In complete sentences, describe how Spain established territorial claims in the Caribbean and South America. Include these terms in your answer: Christopher Columbus, conquistadors, Hernán Cortés, Francisco Pizarro.
PLEASE help me
Answers
If you drew the image of this figure under a 90\circ∘ clockwise rotation using center P, (0,0), what would be the coordinates of the vertices?
Answers
Answer:
(-1,1) (-2,3) (1,3) (1,1)
Step-by-step explanation:
Which of the following equations is equivalent to
Answers
Answer:
Step-by-step explanation:
[tex]\frac{x+3}{3} =5- \frac{x-3}{6} \\(\frac{x+3}{3}) *6 =5 - (x-3)[/tex]
[tex]2x+6 = 5 - x+3[/tex]
Answer:
none
Step-by-step explanation:
We can start by multiplying both side of the equation by 6 in order to remove the fractions.
[tex]6*\frac{x+3}{3} = 6(5 - \frac{x-3}{6})[/tex]
[tex]2(x + 3) = 30 - 6*\frac{x-3}{6}[/tex]
[tex]2x + 6 = 30 -(x - 3)[/tex]
[tex]2x + 6 = 30 - x + 3[/tex]
Now, we can try to see if this equation is equivalent to the other options.
Every option has the left side as 2x - 6. In order to get that, we need to subtract 12 on both sides:
[tex]2x - 6 = 30 - x + 3 - 12[/tex]
This simplifies to
[tex]2x-6 = 18 - x + 3[/tex]
This is not the same as any of the options shown.
We can check this by solving the equations.
2x - 6 = 18 - x + 3
3x = 6 + 18 + 3
3x = 27
x = 9
Now, the first option:
2x - 6 = 10 - x - 3
3x = 6 + 10 - 3
3x = 13
x = 13/3
The second option is the exact same as the third, so they would have the same solution:
2x - 6 = 30 - x- 3
3x = 6 + 30 - 3
3x= 33
x = 11
Since none of the options have the answer 9, they are not equivalent to the equation shown.
Simplify the expression by combining like terms put each expression in its simplest form. 1. 5x^2-2xy+3y^2-4yx+3x-4y^2-5xy+2x-y
Answers
the trail mix uses 3 cups of almonds, 2 cups of cranberries, and 6 cups of peanuts. complete the following sentences.
there are cups ____ of peanuts for every cup of almonds.
there are ___ cups of peanuts for every cup of cranberries
Answers
Answer:
There are 2 cups of peanuts for every cup of almonds. There are 3 cups of peanuts for every cup of cranberries.
Step-by-step explanation:
First question - 6(peanuts) / 3(almonds) = 2 cups of peanuts for every cup of almonds
Second question- 6(peanuts) / 2(cranberries) = 3 cups of peanuts for every cup of cranberries
Answer:
2 cups
Step-by-step explanation:
6 divided by 3 is 2 and secondly 6 divided by 2 is 3
Hope this helps you
A triangle has the side lenths of 3, 4, and 5. Classify this triangle.
A. Scalene right triangle
B. Isosceles acute triangle
C. Equilateral triangle
D. Scalene acute triangle
E. Isosceles obtuse triangle
Answers
WILL MARK BRAINLIEST! Solve for X and Y
Answers
Answer:
1a) x = -41
1b) x = -1
1c) x = 29/3, or x = 9.66 in decimal form
1d) x = -4
----------------
2a) y = -3
2b) y = -60
2c) y = -83
2d) y = -50
Step-by-step explanation:
1a) y = x + 11
-30 = x + 11
-11 -11
------------------
-41 = x
1b) y = -2x - 32
-30 = -2x - 32
+32 +32
----------------------
2 = -2x
/-2 /-2
----------------------
-1 = x
1c) y = -3x - 1
-30 = -3x - 1
+1 +1
-----------------
-29 = -3x
/-3 /-3
------------------
29/3 = x
9.66 = x
1d) y = 5x - 10
-30 = 5x - 10
+10 +10
----------------------
-20 = 5x
/5 /5
----------------------
-4 = x
------------------------
2a) y = x + 3
y = -6 + 3
y = -3
2b) y = -2x - 72
y = -2(-6) - 72
y = 12 - 72
y = -60
2c) y = 3x - 65
y = 3(-6) - 65
y = -18 - 65
y = -83
2d) y = 4x - 26
y = 4(-6) - 26
y = -24 - 26
y = -50
Find the number that makes the ratio equivalent to 1:5.
6:
Answers
1:5 is the same as 1/5.
So, the question really is 1/5 = 6/what?
6/30 is the same as 1/5
So the missing number is 30.
Answer:
box = 30
Step-by-step explanation:
You could set this up very formally as a proportion. It would look like this.
1/5 = 6/x
Now all you have to do is cross multiiply.
1*x = 5 * 6
x = 30
So the answer that goes in the box is 30
Or you could just say to yourself. "The 1 was multiplied by 6. What do I have to multiply the 5 by to keep the ratio the same?"
The answer is 6
6 * 5 = 30
In higher math you are going to want to use the first method.
Needing help on tjis one
Answers
Answer:
she used about 2 gallons for her dining room
Step-by-step explanation:
she used a combined amount of 3 gallons in the other areas of the house so that left 2 gallons for the dining room
Answer:
B. 2 gallons
Step-by-step explanation:
[tex]5\frac{1}{4} -1\frac{1}{4}\\=4-1\frac{1}{8}\\=2\frac{7}{8}\\2\frac{7}{8}-\frac{3}{4}=2\frac{1}{8}\sim2[/tex]
Fill in the blanks
Blank- blank = blank
4.5* 10^9
4.443*10^9
5.7*10^7
1.2*10^2
Btw * means multiply and ^ means exponent
Answers
4.443* 10^9 = 4443000000
5.7* 10^7 = 57000000
1.2* 10^2 = 120
I hoped it will help.
Please help im giving 25 points
Answers
Answer:
4/15
Step-by-step explanation:
[tex]6\frac{3}{5} -6\frac{1}{3} \\\\\frac{33}{5} -\frac{19}{3} \\\\\frac{99-95}{15} =\frac{4}{15}[/tex]
4/15
(Decimal: 0.266667)
Step by step: =33/5 - 6 1/3
=33/5 - 19/3
=33/5 + -19/3
=4/15
=4/15
Identify square root of 3 as either rational or irrational, and approximate to the tenths place.
Answers
Answer:
It is an irrational number, [tex]\sqrt{3}[/tex] as a decimal rounded to the tenth place is 1.7
Step-by-step explanation:
All square roots are irrational numbers
Can somebody help me with questions 11 and 12 I’ll appreciate it!
Answers
Evaluate the expressions when x=1.8 and y=4
1.) 3xy
2.) 7.5xy
3.) 1.4y + 5.9x
Answers
Answer:
1. 21.6
2. 54
3.16.22
Step-by-step explanation:
1. 3(1.8)(4)
2. 7.5(1.8)(4)
3. (1.4)(4) + (5.9)(1.8)
2. 7.5(1.8)(4) = 54
3. 1.4(4) + 5.9(1.8)
5.6 + 10.62 = 16.22
Select all ratios equivalent to 2:3.
Answers
Answer:
12:18 and 10:12 (i think)
Step-by-step explanation:
After converting the given ratios in their simplest form, the equivalent form of 2:3 we get 12:18.
To find the simplest form of a fraction, you have to simplify the numerator and denominator to their lowest terms and keep dividing until you can no longer simplify the fraction any further.
The given ratios are,
12:18,
3:21,
10:12
For the ratio 12:18,
Simplify it by finding the greatest common divisor (GCD) of 12 and 18.
The GCD of 12 and 18 is 6.
By dividing both numbers by 6, we get the smallest ratio of 2:3.
Moving to the ratio of 3:21,
Find the GCD of 3 and 21, which is 3.
Dividing both numbers by 3 results in the smallest ratio of 1:7.
Find the smallest ratio for 10:12.
The GCD of 10 and 12 is 2.
Dividing both numbers by 2 gives us the smallest ratio of 5:6.
Hence, the simplest form of ratios for the given ratios are:
12:18 = 2:3,
3:21 = 1:7,
10:12 = 5:6.
Hence,
The ratio equivalent to 2:3 is 12:18.
Learn more about the ratio visit:
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Help me Guess just help please
Answers
Identify the side length in Figure 1 that corresponds to the side length MQ in figure 2.
YOU CAN ONLY SELECT ONE
Answers
Answer:
the side length corresponding to mq is AE
Select all ratios equivalent to 20:5.
Answers
The answer is : 40:10
*multiply by 2
If helpful, brainliest please !
Answer:
40:10 & 8:2
Step-by-step explanation:
20 * 2 = 40
5 * 2 = 10
8 * 2.5 = 20
2 * 2.5 = 5
2:1 does not work because only 2 * 10 = 20, but 1 *10 = 10 and there is no 10. There is only 5.
Can someone help me please
Answers
Answer:
[tex]◻ \: 827 \div 1120 \\ \\ ◻ \: \frac{827}{1120} \\ \\ ◻ \: 1120 | \bar {1120}[/tex]
And the second one wich is 1120/827
And the last one wich is 1120 on 827
Because Division means spreading a number into something so it’s not possible to spread 827 on 1120 because for example if you have 827 apples and you want to give it to 1120 students you won’t be able to do it so ya