how would the expression x^3-3sqrt(3) be rewritten using difference of cubes?
Answers
x^3-y^3=(x-y)(x^2+xy+y^2)
In this case it would be
C)
Answer:
Correct option is:
C. [tex](x-\sqrt{3})(x^2+3+x\sqrt{3} )[/tex]
Step-by-step explanation:
x^3-3sqrt(3)
= [tex]x^3-3\sqrt{3} \\\\=x^3-\sqrt{3}^3[/tex]
= [tex](x-\sqrt{3})(x^2+3+x\sqrt{3} )[/tex]
(since, [tex]a^3-b^3=(a-b)(a^2+b^2+ab)[/tex])
Hence, the correct option is:
C. [tex](x-\sqrt{3})(x^2+3+x\sqrt{3} )[/tex]
Related Questions
What is the value of the underlined digit in the following number?
3.69
9 hundredths
90 hundredths
9 tenths
9 thousandths
Answers
A cone is placed inside a cylinder as shown. The radius of the cone is half the radius of the cylinder. The height of the cone is equal to the radius of the cylinder. What is the volume of the cone in terms of the radius, r?
Answers
her H = r and R = 0.5r so the volume of the cone is
1/3 * pi * (0.5r)^2 * r
= 1/3 * pi * 0.25 r^3
= (1/12) pi r^3 Answer
Answer:
Volume of the cone is [tex]\frac{1}{12}\pi r^{3}[/tex]
Step-by-step explanation:
Formula to find the volume of a cone is V = [tex]\frac{1}{3}\pi r^{2}h[/tex]
Here r is the radius of the cone and h is the height of the cone.
Since radius of cone = [tex]\frac{1}{2}(\text{Radius of cylinder})[/tex]
= [tex]\frac{r}{2}[/tex]
Height of the cone = radius of the cylinder = r
Now we put the values of radius and height of cone in the formula
Volume of cone = [tex]\frac{1}{3}\pi (\frac{r}{2})^{2}(r)[/tex]
= [tex]\frac{1}{3}\pi(\frac{r^{2}}{4})(r)[/tex]
= [tex]\frac{1}{12}\pi r^{3}[/tex]
Therefore, volume of the cone is [tex]\frac{1}{12}\pi r^{3}[/tex]
For a party, liam ordered 1 taco for each guest, for $2.50 each, and paid a $2.00 delivery fee. michelle ordered 1 burrito for each guest, for $1.80 each, and paid a $3.00 delivery fee. let g represent the number of guests that attended the party. which simplified expression represents the total cost of the two orders?
a. 4.3g + 5
b. 4.5g + 4.8g
c. 6.3g + 3
d. 9.3g
Answers
What is the equation of a line that passes through the point (5, −4) and is parallel to the line whose equation is 2x + 5y = 10?
Answers
Rewrite the given equation in slope intercept form:
5 y = 10 – 2 x
y = - 0.4 x + 2
Since the two lines are parallel, therefore they have similar slope which is – 0.4, so the equation is:
y = - 0.4 x + b
Given that x = 5, y = -4, find for b:
-4 = - 0.4 (5) + b
b = -2
So the answer is:
y = - 0.4 x – 2
or
2 x + 5 y = - 10
what is the perimeter of a square with a side length of 5/7 units.
Answers
Where x = 5/7
4* 5/7
p= 20/7
The answer will be a mixed fraction
p= 2 6/7 units
Hope that helps!
The perimeter is
[tex] \frac{20}{7} \: units[/tex]
or
[tex]2 \frac{6}{7} \: units[/tex]
EXPLANATION
The perimeter of a plane figure is the distance around the figure.
The perimeter of a square is given by the formula,
[tex]p = 4l[/tex]
Where
[tex]l = \frac{5}{7} [/tex]
is the length of one side of the square.
We therefore substitute this value into the equation to obtain,
[tex]p = 4 \times \frac{5}{7} [/tex]
This will simplify to
[tex] p = \frac{20}{7} units[/tex]
or
[tex]2 \frac{6}{7} \: units[/tex]
Which statement could describe the dog’s movement 5 seconds after the command was given
Answers
Answer:
The dog is rather running towards the trainer to receive a treat. So it is the second answer.
Katlin divided a fraction by 1/2 the result was a mixed number. was the fraction less than or greater than 1/2? EXPLAIN.
Answers
When you divide by a fraction, it is equal to multiplying by its reciprocal. The reciprocal of 1/2 is 2/1, or just 2. Therefore, dividing by 1/2 equals the same thing as when you multiply by 2.
A mixed number has a whole number and a fraction added together. So, the mixed number must be greater than 1.
1/2 is equal to 0.5, and 0.5 multiplied by 2 equals 1. A fraction less than 1/2 multiplied by 2 would equal a number less than 1, while a fraction greater than 1/2 would equal a number greater than 1.
Because a mixed number must be greater than 1, and a fraction greater than 1/2 multiplied by 2 would be greater than 1, the fraction that resulted in a mixed number after being multiplied by 2 must have been greater than 1/2.
Trevor is holding 5 red balloons and 4 blue balloons. He randomly selects a balloon to give his sister, and then he randomly selects a balloon to give his brother. Are two events dependent or independent? Explain.
A) Dependent. The two siblings will want the same color balloon.
B) Independent. Girls always want red and boys always want blue.
C) Independent. There are a set number of red balloons and blue balloons.
D) Dependent. When the first balloon is taken, it affects the ratio of red to blue balloons.
Answers
Answer:
Dependent. When the first balloon is taken, it affects the ratio of red to blue balloons.
Step-by-step explanation:
Whatever color the sister choses is irrelevant, eliminating answers A and B, but it does change the odds. If there are 5 red balloons and 4 blue balloons, if the sister is given a blue balloon, the odds of the brother receiving a red balloon increases (vis versa).
a jeweler bought some necklaces and bracelets for $1,100. the cost of the necklaces was 20% more than the cost of the bracelets. how much did the jeweler pay for
A) the necklaces?
B) the bracelets?
Answers
x + y = 1100
x = 1.2y
1.2y + y = 1100
2.2y = 1100
y = 500
x =600
plz tell me what 3ab-9ab+7ab
Answers
The value of the equation 3ab - 9ab + 7ab is [tex]\boxed{ab}[/tex].
Further explanation:
There are two properties.
1. The property of addition or property of sum.
2. The property of subtraction.
3. The property of division.
4. The property of multiplication.
Given:
The equation is 3ab - 9ab + 7ab.
Explanation:
Consider the equation S = 3ab - 9ab + 7ab.
The equation contains the two variables that are “a” and “b”.
In the equation we have two operations one is addition and another is subtraction.
Solve the above equation to obtain the value of the equation.
First add 3ab and 7ab.
[tex]\begin{aligned}X&=3ab+7ab\\&=10ab\\\end{aligned}[/tex]
Now subtract 9ab from 10ab.
[tex]\begin{aligned}S&=10ab-9ab\\&=1ab\\&=ab\\\end{aligned}[/tex]
The value of S is ab.
Hence, the value of the equation 3ab - 9ab + 7ab is [tex]\boxed{ab}[/tex].
Learn more:
1. Learn more about inverse of the function https://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Number System
Keywords: property, zero, eight, sum, addition, identity, shows, subtraction, number sentence, division, multiplication, variables.
Which graph represents the function y – 3 = (x – 4)?
Answers
The graph represents the function y = (x - 1), as per linear equation.
What is a linear equation?A linear equation represents an equation that has one or multiple variables with the highest power of the variable is 1.
The given equation is:
y - 3 = x - 4
⇒ y = x - 1
Therefore, for x = 0, y = - 1
for x = 1, y = 0
for x = - 1, y = - 2
Therefore, the graph will pass through points (0, - 1), (1, 0), (- 1, - 2).
Learn more about linear equation here: https://brainly.com/question/12710278
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Answer:
its A
Step-by-step explanation:
Express 112 as a product of prime numbers in index form?
Answers
/ \
2 56
/ \
2 28
/ \
2 14
/ \
2 7
So, the answer is 2 x 2 x 2 x 7 or 2^3 x 7
Final answer:
To express 112 as a product of prime numbers in index form, we perform prime factorization to get 2⁴ x 7.
Explanation:
To express 112 as a product of prime numbers in index form, we start by performing prime factorization, which is breaking down a composite number into the prime numbers that, when multiplied together, give the original number.
Let's find the prime factors of 112:
112 is divisible by 2 (the smallest prime number).112 ÷ 2 = 5656 is also divisible by 2, so 56 ÷ 2 = 28Continuing this process, 28 ÷ 2 = 14, and then 14 ÷ 2 = 7The number 7 is a prime number and cannot be divided further.So, we can express 112 as a product of prime factors as 2⁴ × 7¹ or simply 2⁴ × 7, since any number to the power of 1 is the number itself.
James buys a shirt and a pair of socks on sale for 25% off. if the price of the shirt before the sale was $24 and he spent a total of $24, what was the original price of the socks?
Answers
Answer:
The original price of socks was $8.
Step-by-step explanation:
James buys a shirt and a pair of socks on sale for 25% off.
The price of the shirt before the sale was $24 that means after discount the price was:
[tex]24-(0.25\times24)[/tex] = $18
And James paid a total of $24.
That means the price of socks after discount is = [tex]24-18[/tex] = $6
Let the original price of socks be x. And after 25% discount, it was for $6.
So, [tex]x-0.25x=6[/tex]
=> [tex]0.75x=6[/tex]
x = 8.
Hence, the original price of socks was $8.
A grocery store gives away a $10 gift card to every 25th customer and a $20 gift card to every 60th customer. a. Which customer will be the first to receive both gift cards?After this customer receives both gift cards, what is the total amount in gift cards that the store has given away?
Answers
25,50,75,100,125,150,175,200,225,250,275,300
60,120,180,240,300
The 300th customer will receive both cards, and a total of $220 and 17 gift cards were given away.
What is the missing polynomial? ? – (20 – 4x – 5x2) = 20 – 7x2 A. 4x-12x^2 B. 4x-2x^2 C. 40-4x-12x^2 D. 40-4x-2x^2
Answers
Irvan bought a drink for $1.90, a sandwich for $ 2.25, and an apple for $.75. What is the total amount of money he spent
Answers
1.90+.75++2.25=4.90
Factor the expression. X^4+6x^2-7 completely. Show work!
Answers
Let's let y = x^2
Substitute y into the equation
y^2 + 6y - 7
Now, we need two factors of -7 that add up to 6
-1 and 7 should work
Now, factor
(y - 1)(y + 7)
Substitute y=x^2 back into the equation
(x^2 - 1)(x^2 + 7)
Edit: Garydesir1 made an important note. (x^2 - 1) can be factorized into (x+1)(x-1)
Your full factorization is (x-1)(x+1)(x^2 + 7)
Have an awesome day! :)
The answer is: (x + 1)(x -1)(x² + 7)
----------------------------------------------------
Well, I am not sure how to explain this. But what you need to realize is that you have x^4. It means that you gonna need two x in the left and one x^2 on the right side.
I hope this help!
What is the value of e^Ln7x ?
A. 1
B. 7e
C. 7x
D. 7
Answers
Answer:
the answer is 7x on edg... i just took the pretest
Step-by-step explanation:
Carrie made a square tablecloth with an area of 169 square inches. What was the length of each side of the tablecloth?
Plz hurry
Answers
The length of each side of the tablecloth is 13 inches.
Explanation:To find the length of each side of the tablecloth, we need to take the square root of the area. Since the area is given as 169 square inches, we can take the square root of 169. The square root of 169 is 13, so each side of the tablecloth is 13 inches long.
can 0.525252 be written as a fraction why or why not
Answers
.525252/1 is a fraction
Or you can find the exact numbers/ratio that will yield that exact repeating number.
99 subtracted from m is 299. What is the equation for the sentence shown?
Answers
The expression of the word problem can be written as M-99=299 where M is 398.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that 99 subtracted from m is 299. The expression for the word problem can be written as:-
M-99=299
M = 299 + 99
M = 398
Therefore, the expression of the word problem can be written as M-99=299 where M is 398.
To know more about an expression follow
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Veronica gave 20% of her money to Bill. She used 50% of the remaining money to buy books.
If Veronica gave $35 to Bill, she spent $ to buy books and she has $ left.
Answers
Answer:
If Veronica gave $35 to Bill, she spent $70 to buy books and she has $70 left.
Step-by-step explanation:
A projectile is thrown upward so that its distance above the ground after t seconds is given by the function h(t) = -16t² + 704t. After how many seconds does the projectile take to reach its maximum height? Show your work for full credit.
Answers
Putting in vertex form: -16(t^2 -44t +484) + 704
h(t) = -16(t-22)^2 + 704
It takes 22 seconds to reach the maximum height, which is the vertex of the parabola at (22,704)
Answer:
22 secs.
Step-by-step explanation:
h(t) = -16t^2 + 704t
The maximum will happen where the first derivative is equal to 0.
h’(t) = -32t + 704
-32t + 704 = 0 => -32t = -704 After subtracting 704 from both sides of the equation
Now divide both sides of the equation by -32
t = 22 secs.
Double Check: recalculated/reasonable ✅ ✅
Answer: 22 secs.
Just an interesting aside. After 22 secs, the projectile will be -16(22)^2 + 704(22) = -7744 + 15,488 = 7744 units up as its maximum height.
6L127ml=__________ mL
Answers
Decide if the following is a properly formed syllogism.
If you drink tea, you always add sugar.
If sugar is added, then the tea is sweeter.
Therefore, if it is sweet, then you’re drinking tea.
a. This is not a syllogism.
b. This is a syllogism.
Answers
Hope this helps!
Have a Nice Night!
-Nana
The following is not a properly formed syllogism.
Option A is the answer.
What is a syllogism?A syllogism is a form of argument where the conclusion follows from the truth of two or more given statements.
We have,
Statements:
If you drink tea, you always add sugar.
If sugar is added, then the tea is sweeter.
Conclusion:
If it is sweet, then you’re drinking tea.
This is not a conclusion from the truth of the given statements.
There is nowhere mention of tea in the statements.
Thus,
It is not a properly formed syllogism.
Learn more about syllogism here:
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If it costs a restaurant $11.90 to produce 2 white chocolate tortes and each torte is cut into 8 slices, how much does each slice cost to make?
Answers
so 1 torte has 8 slices, but you have to do 8 + 8 = 16
11.90 is how much you have to pay for 2 tortes with a total of 16 slices.
All you have to do now is divide: 11.90 / 16
It costs $0.74 to produce just one slice.
Hope I helped :D
Final answer:
To find the cost of each slice of white chocolate torte, divide the total cost to produce two tortes ($11.90) by the total number of slices (16), resulting in approximately 74 cents per slice.
Explanation:
Cost of Each Slice of White Chocolate Torte
To calculate the cost of each slice of white chocolate torte, we start by determining the total cost of producing the tortes. The restaurant's cost is $11.90 for 2 tortes, and each torte is cut into 8 slices. This means there's a total of 2 tortes × 8 slices/torte = 16 slices. Dividing the total cost by the number of slices gives us the cost per slice:
Total cost for 2 tortes: $11.90
Number of slices per torte: 8
Total number of slices: 2 tortes × 8 slices/torte = 16 slices
Cost per slice: $11.90 / 16 slices = $0.74375 per slice
Therefore, each slice costs approximately 74 cents to make.
.The population in the Northeast was 53,594,378 people in 2000 and 55,317,240 people in 2010. By about what percent did the population change? Did the population grow or shrink? Answer:
Answers
C = 100*(55,317,240 - 53,594,378) / 53,594,378 = 3.2%. This is positive, so the population grew
Figure ABCD is a parallelogram
Answers
Answer:
x = 7
Step-by-step explanation:
Figure ABCD is a parallelogram
So sides AD and BC will be parallel and their length will be same.
[Since opposite sides of parallelogram are equal in length]
So mAD = mBC
(5x + 3) = 38
5x = 38 - 3 = 35
x = [tex]\frac{35}{5}[/tex]
x = 7
Therefore, x = 7 will be the answer.
–2x + 3y = 21
3x – 2y = 21
–2x – 3y = 21
–2x + 3y = 7
Answers
Answer:
D.
Step-by-step explanation:
-2x+3y=7.I just took the test.
Which expression is equal to (3x−5)(2x−7)?
6x2−31x+35
5x2−21x+12
6x2+31x−35
6x2−31x−12
Answers
6x^2 - 21 x -10x +35
6x^2 -31x +35
The first one
Answer:
[tex]6x^2-31x+35[/tex]
Step-by-step explanation:
Given expression,
[tex](3x-5)(2x-7)[/tex]
By using distributive property,
[tex](3x-5)(2x) - (3x - 5)(7)[/tex]
Again by distributive property,
[tex]3x(2x) - 5(2x) - 3x(7) + 5(7)[/tex]
[tex]6x^2 - 10x - 21x + 35[/tex]
[tex]6x^2-31x+35[/tex]
Hence, FIRST option is correct.