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Which expressions are a sum or difference of cubes? Sort each expression into the correct category.
64x3 - 216
Sum or Difference of Cubes
Not a Sum or Difference of Cubes
8x9 +27
x3 + 125
36x3 - 121
x6 - 16
Answers
Answer:
The answer to your question is given below.
Step-by-step explanation:
To which of the above expression is a sum or difference of cube, or not a sum or difference of cube, we shall do the following simplification:
Note: The Cube root of a particular number is simply a multiplication of an identical number in three places.
64x³ – 216
64 has a cube root of 4 and 216 has a cube root of 6. Therefore, the above expression can be written as:
4³x³ – 6³
(4x)³ – 6³
64x³ – 216 = (4x)³ – 6³
Therefore, 64x³ – 216 can be expressed as a difference of cube.
8x^9 + 27
8 has a cube root of 2, x^9 has a cube root of x³ and 27 has a
cube root of 3. Therefore, the above expression can be written as:
2³(x³)³ + 3³
(2x³)³ + 3³
8x^9 + 27 = (2x³)³ + 3³
8x^9 + 27 can be expreessed as a sum of cube
x³ + 125
125 has a cube root of 5. Therefore, the above expression can be written as:
x³ + 5³
x³ + 125 = x³ + 5³
x³ + 125 can be expressed as a sum of cube
36x³ + 121
36 and 121 has no cube root. Therefore, the above expression is not a sum or difference of cube.
x^6 – 16
x^6 has a cube root of x² and 16 has no cube root. Therefore, the above expression is not a sum or difference of cube.
Summary:
Sum or Difference of cubes
64x³ – 216
8x^9 + 27
x³ + 125
Not a Sum or Difference of cubes
36x³ + 121
x^6 – 16
Answer:
look at attached picture
Related Questions
18x + 18 = 17 What is the variable x and how do you get that answer?
Answers
Answer:
x = - 1/18
Step-by-step explanation:
Move all terms not containing x to the right side of the equation
Divide each term by 18 and simplify
The result can be shown in multiple forms
x = -1/18
Decimal form= -0.05
Answer: x=-1/18
Step-by-step explanation:
18x+18=17
you subtract 18 from both sides
18x=-1
then you divide by 18 on both sides
x=-1/18
In a school, half of the 300 students saw Zootopia, 180 students saw Finding Dory, and 45 students did not see either movie. How many students saw both movies?
Answers
Answer:
150
Step-by-step explanation:
Answer:
150 = half of 300
± 180
230
soooo 230 students
Step-by-step explanation:
solve the equation 2p square + 11p=30
Answers
Answer:
[tex]p=- \frac{15}{2}[/tex]
[tex]p=2[/tex]
Step-by-step explanation:
[tex]2p^2+11p=30[/tex]
Subtract 30 on both sides.
[tex]2p^2+11p-30=30-30[/tex]
[tex]2p^2+11p-30=0[/tex]
Factor left side of the equation.
[tex](2p + 15)(p-2)=0[/tex]
Set factors equal to 0.
[tex]2p+15=0[/tex]
[tex]2p=-15[/tex]
[tex]p=\frac{-15}{2}[/tex]
[tex]p-2=0[/tex]
[tex]p=2[/tex]
Please answer it in two minutes
Answers
Answer:
2√3
Step-by-step explanation:
Since this is a 30-60-90 triangle, we can find s by finding the short leg (bottom), then the hypotenuse (s).
To find the short leg, we can divide the long leg (which is 3mm) by sqrt 3 (also √3, as any of them are fine), and we will have 3/√3. Since we don't want the square root on the bottom, we can multiply √3 on both sides, giving us 3√3/3, which is technically √3 because of simplifying.
Since you have the short leg now, you can find s. By finding s, you can multiply the short leg by 2, which will be √3 * 2 which is 2√3.
A builder wrote the measurements needed for a door.
height of door
2032 mm
width or door
Why did the builder write these measurements using millimetres instead of cm or m?
Answers
Answer:
Check the answer below.
Step-by-step explanation:
This is a very trivial but professional question. Note that all of millimetre, centimetre and metres are acceptable metric units but the millimetre is more preferable by builders and architects because:
1. It is easier to work with integer values on building and architectural plans, an advantage given by measuring and recording in millimetre.
2. working in millimetre allows for precision. The builder will record values that are very close to the true value
3. The measurement will be easily readable by anybody that sees it.
Rewrite the equation of the circle (x + 2)^2 + (y + 5)^2 = 9 in general form.
Answers
Answer:
x² + 4x + y² + 10y + 20 = 0
Step-by-step explanation:
Step 1: Expand (x + 2)²
x² + 2x + 2x + 4 + (y + 5)² = 9
Step 2: Combine like terms
x² + 4x + 4 + (y + 5)² = 9
Step 3: Expand (y + 5)²
x² + 4x + 4 + y² + 5y + 5y + 25 = 9
Step 4: Combine like terms
x² + 4x + 4 + y² + 10y + 25 = 9
Step 5: Move 9 over
x² + 4x + 4 + y² + 10y + 25 - 9 = 0
Step 6: Combine like terms
x² + 4x + y² + 10y + 20 = 0
Answer:
x^2+y^2+4x+10y+20=0
Step-by-step explanation:
(x+2)^2+(y+5)^2=9
x^2+4x+4+y^2+10y+25-9=0
general form: x^2+y^2+4x+10y+20=0
Pls help really need help
Answers
Answer:
12*3*2=72
10*3*2=60
12*10*2=240
240+72+60=312+60=372
hope this helps
Step-by-step explanation:
Answer:
Answer is c 480 in2
Step-by-step explanation:
What are the independent and dependent variables in the relationship?
Answers
w is the width and it is the independent variable. You can pick any positive whole number you want (within reason of course; you can't go to infinity or go beyond some set boundary). Whatever you picked for w, the expression 2w-5 will be dependent on it. So the length is dependent on the width.
For instance, if the width is w = 10 feet, then 2w-5 = 2*10-5 = 20-5 = 15 feet is the length. The choice of 10 feet for the width directly affects the length being 15 feet.
The marked price of a watch is 30% above the cost price. When it is sold allowing
20% discount on it, there is a gain of Rs 150. Find the marked price of watch.
Answers
Answer:
The marked price = Rs 4,475.
Step-by-step explanation:
Let the marked price of the watch = x
Let the cost price of the watch = y
The given information are;
The marked price of the watch = 30% above the cost price
The discount when it was sold = 20%
The gain when it was sold = Rs 150
Therefore, we have marked price = y + 30/100×y = y + 0.3·y = 1.3·y
The selling price with 20% discount is therefore, 1.3·y - 0.2×1.3·y
The selling price = 1.04·y
The gain = Selling price - cost price = 1.04·y - y = 0.04·y
Rs 150= 0.04·y
y = Rs 150/0.04 = Rs 3,750
Therefore, the marked price = 1.3×y = 1.3×3,750 = Rs 4,875
The marked price = Rs 4,475.
Find a12 of the sequence 1/4,7/12,11/12,5/4,
Answers
Answer:
Your ans is. a12 = 47/12
Step-by-step explanation:
First, you need to find if the series has a common ratio or a common difference between each term. Based from observation, there is a common difference of 1/3 so the series is an arithmetic series.
The solution for this problem goes like this
an=a1+(n-1)d
a12=1/n+(12-1)(1/3)
a12=47/12
Hope it helped you.. Please mark BRAINLIEST
Tysm
Use a calculator to find the values of the inverse trigonometric functions. Round to the nearest degree. sin–1 (two-thirds) = ° tan–1(4) = ° cos–1(0.1) = °
Answers
Answer:
sin-1(2/3)=42 tan-1(4)=76 cos-1(0.1)=84
Step-by-step explanation:
solve systems by substitution method x + y = 12 3x - y = 20
Answers
Step-by-step explanation:
x+y=12
3×+y=20
×=12-y
3 (12-y)+y=20
36-3y+y=20
36-4y=20
-4y=20-36
-4y= -16
y =16÷4
y=4
×+y=12
×+4=12
×=12-4
×=8
therefoer;y=4,x=8
What is f(x) = - 2x + 7 where x = - 5?
A) -3
B) 3
C) -7
D) 17
Answers
Answer:
answer is D
Step-by-step explanation:
f(x) = -2(-5) + 7
f(x) = 10 + 7 = 17
the solution is 17
Simplify: 34w-(-8w)
Answers
Answer: 42w
Step-by-step explanation:
Subtracting a negative is like adding.
Since two negatives equal a positive.
does the table represent a function why or why not?
Answers
Answer:
Yes, because each x-value corresponds to one y value.
Step-by-step explanation:
If you look at the table, you notice that there is one output (y) for every input (x). This means that it is a function. It would NOT be a function if you had two outputs for an input. For example, there are two x values that are 6. For one coordinate pair, the table says (6,9) and (6,8). Since there are two values for the same input- it wouldn't be a function. In this case, there is an input of 4 and 5 with the same output. That is okay! Even though they have the same y value, those inputs still only have ONE output.
Where is the function increasing?
A)1
B)3< X
C)-infinity < x < 1
D)-infinity
Answers
Answer:
A) [tex]1<x<\infty[/tex]
Step-by-step explanation:
Given:
A graph of a function.
When we analyze the given graph, it is of a parabola.
To find:
The interval of values of [tex]x[/tex] where the function is increasing.
Solution:
First of all, let us learn about the meaning of increasing and decreasing functions.
1. A function [tex]y=f(x)[/tex] is known as increasing in an interval [tex]a<x<b[/tex] when
Value of y keeps on increasing when we move from the value of x from a to b.
2. A function [tex]y=f(x)[/tex] is known as decreasing in an interval [tex]a<x<b[/tex] when
Value of y keeps on decreasing when we move from the value of x from a to b.
On analyzing the given graph , we can see that the graph is decreasing on the interval: [tex]-\infty<x<1[/tex]
and is increasing on the interval: [tex]1<x<\infty[/tex]
When we choose from the options,
The correct answer is option A) [tex]1<x<\infty[/tex]
im stuck on this question helm me out I will mark you as brainliest
Answers
Answer: it is =4176000000000000
Step-by-step explanation:
(2.9)(100000)(7.2)(10^2)
5(10^−8)
=
(290000)(7.2)(10^2)
5(10^−8)
=
2088000(10^2)
5(10^−8)
=
(2088000)(100)
5(10^−8)
=
208800000
5(10^−8)
=
208800000
5(1/100000000)=
208800000/1
20000000
=4176000000000000
hope i helped
-lvr
I don't understand this factorisation
a2+ 4a+3
Answers
Answer:
[tex] \boxed{\sf (a + 3)(a + 1)} [/tex]
Step-by-step explanation:
[tex] \sf Factor \: the \: following: \\ \sf \implies {a}^{2} + 4a + 3 \\ \\ \sf The \: factors \: of \: 3 \: that \: sum \: to \: 4 \\ \sf are \: 3 \: and \: 1. \\ \\ \sf So, \\ \sf \implies {a}^{2} + (3 + 1)a + 3 \\ \\ \sf \implies {a}^{2} + 3a + a + 3 \\ \\ \sf \implies a(a + 3) + 1(a + 3) \\ \\ \sf \implies (a + 3)(a + 1) [/tex]
Earl worked 18 hours last week. If he had earned $2.00 an hour more but had worked only 15 hours, he would have earned the same amount. How much per hour does Earl earn? * A) $5.00 B) $10.00 C) $12.00 D) $15.00
Answers
Answer:
B) $10.00
Step-by-step explanation:
10 × 18 = 180
10 + 2 = 12
12 × 15 = 180
Answer:
B) $10.00Step-by-step explanation:
x - Earl's earnings per hour
The equation:
18x = 15(x + 2) use the distributive property
18x = (15)(x) + (15)(2)
18x = 15x + 30 subtract 15x from both sides
18x - 15x = 15x - 15x + 30
3x = 30 divide both sides by 3
3x : 3 = 30 : 3
x = 10
Given f(x) = 3x - 1 and g(x) = 2x + 1, find (f +g)(3)
Answers
Answer:
(f + g)(3) = 15Step-by-step explanation:
f(x) = 3x - 1
g(x) = 2x + 1
To find (f +g)(3) , first find (f + g)(x)
To find (f + g)(x) add g(x) to f(x)
That's
(f + g)(x) = 3x - 1 + 2x + 1
= 3x + 2x + 1 - 1
(f + g)(x) = 5x
Now to find (f + g)(3) substitute 3 into
(f + g)(x)
That's
(f +g)(3) = 5(3)
(f + g)(3) = 15Hope this helps you
please answer this A bicycle store costs $2400 per month to operate. The store pays an average of $60 per bicycle that is sold in the shop. This is called a company’s overhead. The average selling price of each bicycle is $120. How many bicycles must the store sell each month to break even? A bicycle store costs $2400 per month to operate. The store pays an average of $60 per bicycle that is sold in the shop. This is called a company’s overhead. The average selling price of each bicycle is $120. How many bicycles must the store sell each month to break even?
Answers
Answer: The store must sell 40 bikes.
Step-by-step explanation:
y=60x+2400
y=120x
120x=60x+2400
-60x on both sides
60x=2400
divide 60 on both sides
2400/60=40
x=40
Please Help!!!!
Which statement is true about the end behavior of the graphed function?
A: As the x-values go to positive infinity, the function's values go to negative infinity.
B: As the x-values go to zero, the function's values go to positive infinity.
C: As the x-values go to negative infinity, the function's values are equal to zero.
D: As the x-values go to negative infinity, the function's values go to positive infinity.
Answers
Answer:
D: As the x-values go to negative infinity, the function's values go to positive infinity.
Step-by-step explanation:
Since we are dealing with end behavior, we look at the graph infinitely:
When x-values go to negative infinity, we see that f(x) values go to positive infinity.
When x-values go to positive infinity, we see that f(x) values also go to positive infinity.
Therefore. our only correct answer is D.
Select the correct answer.
What is the exact solution to the system of equations shown on the graph?
Answers
Answer:
Option (B)
Step-by-step explanation:
There are two lines on the graph representing the system of equations.
First line passes through two points (-3, 1) and (-2, 3).
Slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{3-1}{-2+3}[/tex]
m = 2
Equation of the line passing through (x', y') and slope = m is,
y - y' = m(x - x')
Equation of the line passing through (-3, 1) and slope = 2 will be,
y - 1 = 2(x + 3)
y = 2x + 7 ----------(1)
Second line passes through (0, 1) and (-1, 4) and y-intercept 'b' of the line is 1.
Let the equation of this line is,
y = mx + b
Slope 'm' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{4-1}{-1-0}[/tex]
= -3
Here 'b' = 1
Therefore, equation of the line will be,
y = -3x + 1 ---------(2)
From equation (1) and (2),
2x + 7 = -3x + 1
5x = -6
x = [tex]-\frac{6}{5}[/tex]
x = [tex]-1\frac{1}{5}[/tex]
From equation (1),
y = 2x + 7
y = [tex]-\frac{12}{5}+7[/tex]
= [tex]\frac{-12+35}{5}[/tex]
= [tex]\frac{23}{5}[/tex]
= [tex]4\frac{3}{5}[/tex]
Therefore, exact solution of the system of equations is [tex](-1\frac{1}{5},4\frac{3}{5})[/tex].
Option (B) will be the answer.
Answer:
B. (-1 1/5, 4 3/5)
Step-by-step explanation:
What is the domain and range of y=-5x2+3x+10
Answers
Answer:Domain is (-infiniti,infiniti) and Range is (-infiniti,10.45)
Step-by-step explanation:
can someone help me with this?
Answers
Answer:
-5z^3-z^4+4z^5
-2x(x+3)-(x+1)(x-2) please help me solve this
Answers
Answer:
u have to multiply these.
it's too easy .
see I will tell you the answer.
-2x²-6x-(x²-2x+x-2)
Now the signs of the underlined terms will change because negative sign is outside it.
-2x²-6x-x²+ 2x-x + 2
Now we have to solve it simply
-2x²-x²-6x+ 2x-x + 2
-3x²-5x+2
so here is ur answer.
for Indians it is soo simple question bro
I am Indian
if u need any help plz let me know.
What is the volume of a square pyramid with base side length of 22 cm and height of 8cm?
Answers
Answer:
Volume of a pyramid is
[tex] \frac{1}{3 } \times (area \: \: of \: base) \times height[/tex]
Since it's a square pyramid the base is a square
So we have
Area of a square = l²
where l is the length of one side
Area of square = 22²
= 484 cm²
So volume of the pyramid is
[tex] = \frac{1}{3} \times 484 \times 8 = 1290.7 {cm}^{3} [/tex]
Hope this helps you
A chef uses 12 cup of cheese for a small pizza. There are 6 grams of fat in 14 cup of cheese. Drag one expression next to each question. The correct expression for each row is a way to answer that question.
Answers
Answer:
I guess that we want to find how many grams of fat we have in a small pizza.
In a small pizza, we use 12 cups of cheese.
in 14 cups of cheese, we have 6 grams of fat.
Then, in 12 cups of cheese, we have x grams of fat.
We want to find the value of x.
We know that the ratio between the number of cups must be the same as the ratio between the grams of fat then:
12cups/14cups = x/6grams
x = (12/14)*6grams = 5.14 grams
Then in the 12 cups of cheese, we have 5.14 grams of fat.
The table shows the number of flowers in four bouquets and the total cost of each bouquet. A 2-column table with 4 rows. The first column is labeled number of flowers in the bouquet with entries 8, 12, 6, 20. The second column is labeled total cost (in dollars) with entries 12, 40, 15, 20. What is the correlation coefficient for the data in the table? –0.57 –0.28 0.28 0.57
Answers
Answer:
The correct option is;
0.28
Step-by-step explanation:
The given data values are;
x, f(x)
8, 12
12, 40
6, 15
20, 20
Where;
x = The number of flowers in the bouquet
f(x) = The total cost (in dollars)
The equation for linear regression is of the form, Y = a + bX
The formula for the intercept, a, and the slope, b, are;
[tex]b = \dfrac{N\sum XY - \left (\sum X \right )\left (\sum Y \right )}{N\sum X^{2} - \left (\sum X \right )^{2}}[/tex]
[tex]a = \dfrac{\sum Y - b\sum X}{N}[/tex]
Where:
N = 4
∑XY = 1066
∑X = 46
∑Y = 87
∑X² = 644
(∑X)² = 2116
b = (4*1066 - 46*87)/(4*644 - 2116) = 0.5696
a = (87 - 0.5696*46)/4 = 15.1996
The standard deviation of the x- values
[tex]S_X = \sqrt{\dfrac{\sum (x_i - \mu)^2}{N} }[/tex]
[tex]\sum (x_i - \mu)^2}[/tex] = 115
N = 4
Sx =√(115/4)
Sx = 5.36
[tex]S_Y = \sqrt{\dfrac{\sum (y_i - \mu_y)^2}{N} }[/tex]
[tex]\sum (y_i - \mu_y)^2}[/tex] = 476.75
N = 4
Sy =√(476.75/4)
Sy= 10.92
b = r × Sy/Sx
Where:
r = The correlation coefficient
r = b × Sx/Sy = 0.5696*5.36/10.92 = 0.2796 ≈ 0.28
The correct option is 0.28.
Answer:
C on edge
Step-by-step explanation:
Suppose a company needs temporary passwords for the trial of a new time management software. Each password will have one digit, followed by one letter, followed by two digits. The digit 7 will not be used. So, there are 26 letters and 9 digits that will be used. Assume that the digits can be repeated. How many passwords can be created using this format?
Answers
Answer: 18954
Step-by-step explanation:
The given format for password : Each password will have one digit, followed by one letter, followed by two digits. The digit 7 will not be used. So, there are 26 letters and 9 digits that will be used.
We assume that the digits can be repeated.
Then by using fundamental principle of counting,
Number of passwords can be created = (Number of digits) x (Number of letters) x (Number of digits)x(Number of digits)
= 9 x 26 x 9 x 9
= 18954
Hence, Number of passwords can be created= 18954