(2-a)³+(2-b)³+(2-c)³-3(2-a)(2-b)(2-c)
Pls step by step
Answers
The evaluation of (2-a)³+(2-b)³+(2-c)³-3(2-a)(2-b)(2-c) is mathematically given as
a^3+3 a b c-b^3-c^3+6 a^2-6 a b-6 a c+6 b^2-6 b c+6 c^2
This is further explained below.
What is the evaluation of (2-a)³+(2-b)³+(2-c)³-3(2-a)(2-b)(2-c)?(2-a)^3+(2-b)^3+(2-c)^3-3(2-a)(2-b)(2-c)
Use the Binomial Theorem.
2^3+3 * 2^2(-a)+3*2(-a)^2+(-a)^3 +(2-b)^3+(2-c)^3 -3(2-a)(2-b)(2-c)
8-12 a+6 a^2-a^3+(2-b)^3+(2-c)^3 -3(2-a)(2-b)(2-c)
Use the Binomial Theorem.
8-12 a+6 a^2-a^3+2^3+3 * 2^2(-b)+3 * 2(-b)^2+(-b)^3+(2-c)^3-3(2-a)(2-b)(2-c)
8-12 a+6 a^2-a^3+8-12 b+6 b^2-b^3 +(2-c)^3-3(2-a)(2-b)(2-c)
Use the Binomial Theorem.
8-12 a+6 a^2-a^3+8-12 b+6 b^2-b^3+2^3+3 \cdot 2^2(-c)+3 \cdot 2(-c)^2+(-c)^3-3(2-a)(2-b)(2-c)
8-12 a+6 a^2-a^3+8-12 b+6 b^2-b^3 +8-12 c+6 c^2-c^3-3(2-a)(2-b)(2-c)
Apply the distributive property.
8-12 a+6 a^2-a^3+8-12 b+6 b^2-b^3+8-12 c+6 c^2-c^3+(-3 * 2-3(-a))(2-b)(2-c)
Multiply -3 by 2 .
&8-12 a+6 a^2-a^3+8-12 b+6 b^2-b^3+8-12 c+6 c^2-c^3 +(-6-3(-a))(2-b)(2-c)
Multiply -1 by -3.
8-12 a+6 a^2-a^3+8-12 b+6 b^2-b^3 +8-12 c+6 c^2-c^3 +(-6+3 a)(2-b)(2-c)
Expand (-6+3 a)(2-b) using the FOIL Method.
Combine the opposite terms in
8-12 a+6 a^2-a^3+8-12 b+6 b^2-b^3+8-12 c+6 c^2-c^3-24+12 c+12 b-6 b c+12 a-6 a c-6 a b+3 abc
8+6 a^2-a^3+8+6 b^2-b^3+8+6 c^2-c^3-24-6 b c-6 a c-6 a b+3 abc
Simplify by adding numbers.
6 a^2-a^3+6 b^2-b^3+24+6 c^2-c^3-24-6 b c-6 a c-6 a b+3 abc
Combine the opposite terms in
6 a^2-a^3+6 b^2-b^3+24+6 c^2-c^3-24-6 b c-6 a c-6 a b+3 a b c
6 a^2-a^3+6 b^2-b^3+6 c^2-c^3-6 b c -6 ac-6 ab+3 abc
Re odrder
a^3+3 a b c-b^3-c^3+6 a^2-6 a b-6 a c+6 b^2-6 b c+6 c^2
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Related Questions
Select the better deal in the pair. Then give the unit rate for the better deal.
$56/25 gal
or
$32.05/15 gal
Answers
Answer:
The better deal is $32.05/15 gal
Step-by-step explanation:
Divide:
56/25
=2.24
32.05/15
=2.13666667
=2.14
Help please! Do not answer if you are not going to help me
Answers
9514 1404 393
Answer:
12. (x, D, E, F) = (8, 38°, 75°, 67°)
13. (x, P, Q, R) = (13, 126°, 30°, 24°)
Step-by-step explanation:
The sum of angles in a triangle is 180°. We choose to write the equations assuming all measures are degrees.
12. (5x -2) +(9x +3) +(11x -21) = 180
25x = 200 . . . . . . . add 20, simplify
x = 8 . . . . . . . . . divide by 25
Then the angle measures are ...
∠D = 5(8) -2 = 38°
∠E = 9(8) +3 = 75°
∠F = 11(8) -21 = 67°
__
13. (10x -4) +(4x -22) +(x +11) = 180
15x = 195 . . . . . . . . . . add 15, simplify
x = 13 . . . . . . . . . divide by 15
Then the angle measures are ...
∠P = 10(13) -4 = 126°
∠Q = 4(13) -22 = 30°
∠R = 13 +11 = 24°
The diagram shows an open rectangular box ABCDEFGH.
A straight stick AGM rests against A and G and extends outside the box to M.
a. Calculate the angle between the stick and the base of the box.
b. AM= 30 cm.
Show that GM= 4.8 cm, correct
to 1 decimal place.
Answers
The angle between the stick and the base of the box is 77. 9 degrees
How to determine the angleTo determine the angle between the stick and the base, we have to know the trigonometric identities.
These identities are;
sinecosinecotangenttangentsecantcosecantFrom the information given, we have;
sin A = FB/AB
Given that;
GB = 14.5cm
AB = 18. 6cm
substitute for the length of the sides, we have;
sin A = 14.5/18. 6
Divide the values, we have;
sin A = 0. 7796
Find the inverse sine
A = 77. 9 degrees
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What is the discriminant of the following equation: x2 − 2x + 2 = 0 Options: -8 -4 -12 12
Answers
Answer:
The answer is -4
Step-by-step explanation:
Write the problem as a mathematical expression.
What is the discriminant of the following equation :
x2 − 2x + 2 = 0
The discriminant of a quadratic is the expression inside the radical of the quadratic formula.
b2 - 4 (ac)
Substitute in the values of a, b, and c.
(-2)2 - 4 (1 * 2)
Evaluate the result to find the discriminant.
Then, simplify each term.
Raise -2 to the power of 2.
4 - 4 (1 * 2)
Multiply 2 by 1
4 - 4 * 2
Multiply -4 by 2.
4 - 8
Subtract 8 from 4.
-4
Rotate pentagon ABCDE 90 ° counterclockwise. Which point has the lowest x-coordinate?
Answers
Answer:
Just flip the points to the negative values in the 2nd quadrant
Which of the folloHow many solutions exist for the given equation?
12x + 1 = 3(4x + 1) – 2wing shows the graph of y = –(2)x – 1?
Answers
The equation 12x + 1 = 3(4x + 1) – 2 have infinite solutions
what is an equations?An equation is a mathematical statement that shows that two mathematical expressions are equal. In other terms we say that an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
To solve this problem, we can proceed to solve this equation by collecting like terms and then dividing through to know the coefficient of x.
⇒ 12x + 1 = 3(4x + 1) – 2
⇒ 12x + 1 = 12x + 3 – 2
⇒ 12x + 1 = 12x + 1
So that, The equation have infinite solutions.
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This problem have two question:
1) How many solutions exist for the given equation? 12x + 1 = 3(4x + 1) – 2
2) Which of the following shows the graph of y = –(2)x – 1?
we are giving the answer of question no.1
12. Which of these is an algebraic
expression?
A 3 - 1.4
B 1.4 - 3
C 1.4 - n
D 1.4 + 3
Answers
Answer:
C.
Step-by-step explanation:
Hi there!
for an expression to be algebraic, there needs to be a variable.
The only option with a variable is c, with a variable of n.
I hope this helped!
12
On the grid below shade the region that satisfies all these inequalities.
x21, y>-1, y<4-2x
T
4
2
-2-
पं
2
X
4
Answers
Evaluate the function f(x)= ∣x∣
x
at the the given values of the independent variable and simplify: (a) f(6) (b) f(−6) (c) f(r 2
),r
=0
Answers
To evaluate the function f(x) = |x| / x at the given values, we substitute the values into the function and simplify:
(a) f(6):
f(6) = |6| / 6
= 6 / 6
= 1
(b) f(-6):
f(-6) = |-6| / -6
= 6 / -6
= -1
(c) f(sqrt(2)), r ≠ 0:
f(sqrt(2)) = |sqrt(2)| / sqrt(2)
= sqrt(2) / sqrt(2)
= 1
Note: The function f(x) = |x| / x has a vertical asymptote at x = 0 since the denominator becomes 0 at x = 0. Therefore, the function is not defined for r = 0.
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You borrow $500 to goon a trip. The bank charges 11% interest for 2 years. Find the interest
Answers
The distance between the point (- 5 ,-2) and y-axis is
length unit.
(a) - 5
(b) – 2
(c) 2
(d) 5
Answers
Assuming that joe and matthew make their decisions independently, what is the probability that they will purchase no books on this visit to the bookstore?.
Answers
The likelihood that they won't buy any books during this trip to the bookstore is O.1250 or 12.5%.
How does probability work?
Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true. The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.
The suitable response is:
Let P(J) = John is unlikely to buy any books.
Let P(B) = Beth is unlikely to buy any books.
P( J n B ) will be;
There is a 0% chance that John and Beth will each buy 0 books, making a total of 0 books bought.
Since, the decisions to buy books are two independent actions,
P(J n B) = P(J) * P(B)
P(J) = 0.5
P(B) = 0.25
P(J n B) = 0.5 * 0.25
P(J n B) = 0.125 or 12.5%
Therefore, there is 12.5% chance that they will purchase no books on this visit to the bookstore.
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Evaluate the following expressions. Your answer must be an exact angle in radians and in the interval [0, π] (a) cos^-1 (√2 / 2) = _____
(b) cos^-1 (0) = _____
Answers
(a) The expression cos⁻¹(√2 / 2) evaluates to π/4 radians. (b) The expression cos⁻¹(0) evaluates to π/2 radians.
(a) To evaluate cos⁻¹(√2 / 2), we need to find the angle whose cosine is equal to √2 / 2. From the unit circle or trigonometric identities, we know that this corresponds to an angle of π/4 radians.
So, cos⁻¹(√2 / 2) = π/4
(b) To evaluate cos^⁻¹(0), we need to find the angle whose cosine is equal to 0. From the unit circle or trigonometric identities, we know that this corresponds to an angle of π/2 radians.
So, cos⁻¹(0) = π/2
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please help
thank you!!
Answers
Step-by-step explanation:
Hi joolin
Hyvwzzaetu =g m eet co de
Co me get free answers
Or give me the in sta id
Gabby is a makeup artist and carries a lot of makeup around with her. she has 20 cosmetics in her bag, including 4 eye shadows. what is the probability that a randomly selected makeup item from her bag will be an eye shadow? write your answer as a fraction or whole number.
Answers
The probability that a randomly selected makeup item from her bag will be an eye shadow is 1/5 or 20%.
The probability of selecting an eye shadow from Gabby's bag can be calculated by dividing the number of eye shadows in the bag by the total number of cosmetics in the bag.
There are 4 eye shadows in Gabby's bag, and a total of 20 cosmetics. Therefore, the probability of selecting an eye shadow is:
P(eye shadow) = 4/20 = 1/5
This means that there is a 1 in 5 chance, or a 20% chance, that a randomly selected makeup item from Gabby's bag will be an eye shadow.
The probability can be expressed as a fraction or a whole number, depending on the context of the problem. In this case, we can express the probability as the fraction 1/5, which means that out of 20 possible cosmetics, only 4 are eye shadows.
We can also express the probability as the whole number 0.2 or 20%, which represents the proportion of eye shadows in Gabby's bag.
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Please need help on this questions!
Answers
THis is the answer for ur question
Answer:
1) volume = 102.92 m²
2a) Perimeter = 28 inches
2b) Actual perimeter = 672 inches or 56 feet
2c) Exactly 24 times greater
Step-by-step explanation:
1)
4x5.5 = 22
full circle = (5.5²)(π) = 95
(30/360)(95) = 7.92
95+7.92 = 102.92 m²
2a)
Perimeter = (2)(6+8) = 28 inches
2b)
Actual perimeter = (2)(144+192) = 672 inches or 56 feet
2c)
(24)(28) = (2)(144+192)
672 = 672
Exactly 24 times greater
fastt
13. Calculate the compound interest of an annuity due of BD400 paid each 4 months for 6.2 years if the nominal rate is 3% thirdly? (3 Points)
Answers
Therefore, the compound interest of the annuity due of BD 400 paid each 4 months for 6.2 years at a nominal rate of 3% per annum is BD 40,652.17.
Compound interest of an annuity due can be calculated using the formula:A = R * [(1 + i)ⁿ - 1] / i * (1 + i)
whereA = future value of the annuity dueR = regular paymenti = interest raten = number of payments First, we need to calculate the effective rate of interest per period since the nominal rate is given per annum. The effective rate of interest per period is calculated as
:(1 + i/n)^n - 1 = 3/1003/100 = (1 + i/4)^4 - 1
(1 + i/4)^4 = 1.0075i/4 = (1.0075)^(1/4) - 1i = 0.0303So,
the effective rate of interest per 4 months is 3.03%.Next, we can substitute the given values in the formula:
A = BD 400 * [(1 + 0.0303)^(6.2 * 3) - 1] / 0.0303 * (1 + 0.0303)A = BD 400 * [4.227 - 1] / 0.0303 * 1.0303A = BD 400 * 101.63A = BD 40,652.17
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A school needs to buy new notebook and desktop computers for its computer lab. The notebook computers cost $275 each, and the desktop computers cost $150 each. How much would it cost to buy 14 notebooks and 16 desktop computers? How much would it cost to buy n n notebooks and d d desktop computers?
Answers
Answer
14 notebook computers: 3850$
16 desktop computers: 2400$
Step-by-step explanation:
275x14=3850
150x16=2400
Explain why a balance of less than - $10
represents a debt greater than $10.
Answers
Answer:
Answer down below.
Step-by-step explanation:
You can see that the 10 is negative. Now, imagine a number line. If you were to plot that on the number line, its less than 0. Anything in the positives is in the positive number range. If you were to do the same for negatives, it would represent a negative value, or in money standards, would be in debt.
Hope this helps!
9. Rich is a number of a gym. He pays a monthly fee plus a per-visit fee. The equation
below represents the monthly amount Rich pays for his membership to the gym per
month for x visits.
y = 3x + 10
What does the y-intercept of the graph of this equation represent?
Answers
Answer: it is the monthly fee
Step-by-step explanation: In y=3x+10 the y is the total amount he payed per month. The 3x is saying he payed $3 per visit (x) and slope, and the 10 is the monthly fee and y- int. He payed $10 at the start of each month.
The y-intercept of the graph is 10, which represents the monthly fee that Rich pays to the gym regardless of the number of visits.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
The given equation is, y = 3x + 10
This is in the form of a linear equation, where y represents the total cost per month and x represents the number of visits. The coefficient of x is 3, which represents the per-visit fee that Rich pays. The constant term is 10, which represents the monthly fee that Rich pays regardless of the number of visits.
The y-intercept of the graph of this equation is the value of y when x is equal to 0. Substituting x = 0 into the equation, we get,
y = 3(0) + 10
y = 10
Therefore, the y-intercept of the graph is 10, which represents the monthly fee that Rich pays to the gym regardless of the number of visits.
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Evaluate (-1)x(-2)x(-3)x(-4)x(-5).
Answers
Answer:
\((-1) \times (-2) \times (-3) \times (-4) \times (-5) = - 120\)
Step-by-step explanation:
By the rule of Integer multiplications,
\((-1) \times (-2) \times (-3) \times (-4) \times (-5) = [ (-1) \times (-2) ] \times [(-3) \times (-4)] \times (-5)\)
\(= [2] \times [12] \times (-5)\)
\(= -120\)
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which rule uses actual probability distributions to determine if hiring decisions have had adverse impact on minority groups? multiple choice question. the prima facie rule the standard deviation rule the four-fifths rule the bona fide occupational qualification rule
Answers
The prima facie rule uses actual probability distributions to determine if hiring decisions have had adverse impact on minority groups.
What do you mean by prima facie rule?The "prima facie" rule refers to a legal standard or a evidentiary standard used in the field of employment discrimination law. In the context of employment discrimination, a prima facie case refers to the minimum evidence required to establish a presumption of discrimination.
The term "prima facie" comes from Latin and means "at first sight" or "on its face." In other words, a prima facie case of discrimination is established if, at first sight, the evidence suggests that discrimination has taken place. Once a prima facie case has been established, the burden of proof shifts to the employer to provide a non-discriminatory explanation for the actions in question.
It is more commonly used in legal and ethical contexts to refer to a case or argument that is initially strong enough to establish a point, but may be challenged or overcome by further evidence or argument.
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5x + 5 (3) = 55
What is the answer to this equation. I'm on a account of my cousin's. I'm in 6th grade.
Answers
Answer:
x = 8 :)
Step-by-step explanation:
5x + 5(3) = 55
5x + 15 = 55
5x = 40
40/5 = 8x = 8
Answer:
8
Step-by-step explanation:
Step 1:
5x + 5 ( 3 ) = 55 Equation
Step 2:
5x + 15 = 55 Multiply
Step 3:
5x = 40 Subtract 15 on both sides
Step 4:
x = 40 ÷ 5 Divide
Answer:
x = 8
Hope This Helps :)
Is (3,4) a solution of y < 4x -2
Answers
Answer:
Yes
Step-by-step explanation:
Substitute:
Calculate the product or quotient:
Calculate the sum or difference:
Obtain a simplified relation:
Determine true or false: True
Answer: True
how do I tell if a fraction is bigger or smaller than another fraction?
Answers
Answer:
compare them
Step-by-step explanation:
first make the denominators the same, then compare the numerators
help with polynomails
Answers
step by step:
collect like terms and calculate
rewrite the expression in the best form
factorize the expression
d. -6.24, -4.03, -1.82, 0.39, ... Find the 20th term.
Answers
Answer:
the 20th term of the sequence is 35.75
PLEASE HELP I AM GROUNDED AND MY MOTHER IS SO MAD AT ME FOR MY GRADE
Answers
Answer:149
Step-by-step explanation:
180-31=149
solve this to get brainless
Answers
Yes. The expression 5 × (8 - 3) can be rewritten using the distributive property as (5 × 8) - (5 × 3).
What is the distributive propertyThe distributive property is a fundamental property of arithmetic and algebra that allows you to simplify expressions involving multiplication and addition or subtraction. The property states that for any numbers a, b, and c:
a × (b + c) = a × b + a × c and a × (b - c) = a × b - a × c
For the expression 5 × (8 - 3) can be rewritten as follows;
5 × (8 - 3) = (5 × 8) - (5 × 3).
Therefore, the expression 5 × (8 - 3) can be rewritten using the distributive property as (5 × 8) - (5 × 3).
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HELP ME PLEASEEE!
help
NO BOTS
Answers
The cubic root of 1000 is of 10, as 10³ = 1000.
What is the cubic root of 1000?We have that 1000 is equivalent to 10³, as:
10³ = 10 x 10 x 10 = 100 x 10 = 1000.
Then the cubic root is found as follows:
\(\sqrt[3]{1000} = \sqrt[3]{10^3} = 10\)
Hence, the cubic root of 1000 is of 10, as 10³ = 1000.
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Answer:
³√1000 = 10
Step-by-step explanation:
Now we have to,
→ Evaluate ³√1000
Let's solve the problem,
→ ³√1000
→ 10
Checking the answer,
→ x³ = 10³
→ 10 × 10 × 10 = 1000
Hence, the answer is 10.