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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Omar will rent a car for the weekend. He can choose one of two plans. The first plan has no initial fee but costs $0.90 per mile driven. The second plan has an initial fee of $60 and costs an additional $0.80 per mile driven. How many miles would Omar need to drive for the two plans to cost the same?
Answer:For the two plans to cost the same Omar would need to drive 275 miles
Step-by-step explanation:Please give brainliest if right.
which function is not continuous? a. your altitude as a function of time while flying from reno to dallas. c. number of tennis balls that can fit completely inside a particular box as a function of the radius of the tennis balls. b. time of travel from miami to pensacola as a function of driving speed. d. area of a circle as a function of radius. please select the best answer from the choices provided a b c d
The function which is not continuous is C. number of tennis balls that can fit completely inside a particular box as a function of the radius of the tennis balls.
We know that a function that does not have discontinuities in the values that means any changes in value.
We have been given four statements.
a. your altitude as a function of time while flying from reno to Dallas.
c. number of tennis balls that can fit completely inside a particular box as a function of the radius of the tennis balls.
b. time of travel from Miami to Pensacola as a function of driving speed.
d. area of a circle as a function of radius.
We need to find a function which is not continuous.
The function which is not continuous is the statement C. number of tennis balls that can fit completely inside a particular box as a function of the radius of the tennis balls.
Because the number of these balls is discreet, not continuous (meaning that there cannot be 2.3 balls).
Therefore, The function which is not continuous is C. number of tennis balls that can fit completely inside a particular box as a function of the radius of the tennis balls.
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Max has a small pickup trunk that carries 3/4 cord of firewood. find the number of trips max would have to make in order to deliver 12 cords of wood?
The number of trips max would have to make in order to deliver 12 cords of wood is 16 trips.
We will use unitary method to solve this problem.
Pick up truck carry ( 3/4 ) cord of firewood in trip = 1
Pick up truck will carry 1 cord of firewood in the trips = ( 1/(3/4) ) trips
= ( 4/3 ) trips
Truck will carry 12 cords of firewood in the trips = 12 × ( 4/3 )
= 16 trips.
Therefore, the number of trips max would have to make in order to deliver 12 cords of wood is 16 trips.
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Solve the equation.
-8y-8=7y +22
Which of the following values are solutions to the inequality 3 − 4 x ≥ − 3 ? 3−4x≥−3?
The values in the solution set of the inequality are values that do not exceed 0
How to determine the values that are solutions to the inequality?The inequality expression is given as
3 − 4 x ≥ − 3
Rewrite the expression properly.
So, we have
3 − 4x ≥ −3
Add 3 to both sides of the inequality.
So, we have
3 + 3 − 4x ≥ −3 + 3
Evaluate the like terms
So, we have
− 4x ≥ 0
Divide both sides by -4
x ≤ 0
The above means that the values in the solution set of the inequality are values that do not exceed 0
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Put the following equation of a line into slope-intercept form, simplifying all fractions.
20x+4y=8
the answer for the given question is slope is -5 and y- intercept is 2.
The slope intercept form of a straight line is one of the most common ways to represent a line's equation. When given the slope of a straight line and the y-intercept, the slope intercept formula can be used to find the equation of a line (the y-coordinate of the point where the line intersects the y-axis).
The slope-intercept form is y = mx + b , where m is the slope and b is the y-intercept.
y = mx + b
Take 20x off both sides of the equation.
4y = 8 − 20x
Simplify each term by dividing it by 4y = 8 - 20x.
y = 2 − 5x
Reorder 2 and -5x.
y =−5x + 2
Therefore after simplification we get the slope as -5
and the y-intercept as 2
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A MATCHBOX HOLDS 48 MATCHES.HOW MANY MATCHBOXES ARE NEED TO HOLD 1104 MATCHES?
Answer:
23
Step-by-step explanation:
1104/48 = 23 boxes
The sun is about 93×10 to the fifth power miles from earth what is the distance when I am a whole Number
Answer:
93 x 10 = 930^5 = 695688369300000
Reflection across y = x
When we reflect a point across the line y = x, the x- and y-coordinates swap positions.
What do we mean by Reflection across y = x?When we reflect a point across the line y = x, the x- and y-coordinates swap places. When we reflect over the line y = -x, the x- and y-coordinates swap places and become negated (the signs are changed). The line y = x defines the point (y, x).The line y = -x is the point (-y, -x).Remember that each point of a reflected image is the same distance from the line of reflection as the corresponding point of the original figure. The line of reflection will be directly in the middle of the original figure and its image.Therefore, when we reflect a point across the line y = x, the x- and y-coordinates swap positions.
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An artist used 6 tubes of red paint, 2 tubes of yellow paint, 13 tubes of white paint, and 9 tubes of blue paint for a mural. what is the ratio of blue paint tubes to all the tubes of paint used?
The ratio of blue paint to all tubes of paint = 3:10
Number of tubes of red paint = 6 tubes
Number of tubes of yellow paint = 2 tubes
Number of tubes of white paint = 13 tubes
Number of tubes of blue paint = 9 tubes
Total no. of paint tubes = 6 red tubes + 2 yellow tubes+ 13 white tubes + 9 blue tubes = 30 tubes of paint
We use the following formula to find the required ratio:
The ratio of blue paint tubes to all tubes of paint = Number of blue paint tubes: Number of all tubes = 9:30 or 3:10
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Which formulas have been correctly rearranged to solve for radius? check all that apply. r = startfraction g times m subscript central baseline over v superscript 2 baseline endfraction. r = startfraction f subscript c baseline times m over v superscript 2 baseline endfraction. r = startfraction a subscript c baseline over v superscript 2 baseline endfraction r = startfraction v t over 2 pi endfraction r = startfraction a subscript c baseline times t over pi endfraction
r = \frac{GM}{v^{2} } formulas have been correctly rearranged to solve for radius.
What is circular motion ?
An object moving in a circular motion is defined as rotating while doing so. There are two types of circular motion: uniform and non-uniform. While the angular rate of rotation and speed are constant during uniform circular motion, they are not during non-uniform motion.The problem is asking to find the radius of the orbit of a satellite around a planet, given the orbital speed of the satellite.
For a satellite in orbit around a planet, the gravitational force provides the required centripetal force to keep it in circular motion, therefore we can write:
[tex]\frac{GMm}{r^{2} } = m\frac{v^{2} }{r}[/tex]
where
G is the gravitational constant
M is the mass of the planet
m is the mass of the satellite
r is the radius of the orbit
v is the speed of the satellite
Re-arranging the equation, we find
[tex]\frac{GM}{r} = v^{2}[/tex]
[tex]r = \frac{GM}{v^{2} }[/tex]
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Answer: a and d
Step-by-step explanation: edge 2022
Write this sentence as an inequality
Answer:
8b+2=3
Step-by-step explanation:
8b+2 have to addition
I don't know how to solve this.
The next three terms in the sequence are 116 , 159 and 209
We are supposed to find the next 3 terms in the sequence:
5, 6, 14, 29, 51, 80, ___, ___, ___.
Here we can are first supposed to find the pattern which is as follows:
[tex]6-5=1\\14-6=8\\29-14=15\\51-29=22\\80-51=29\\[/tex]
Therefore difference between the numbers is 7 more than the previous one i.e,
[tex]1+7=8\\8+7=15\\15+7=22\\22+7=29[/tex]
Let required three numbers be x, y and z
So [tex]x-80=29+7=36\\x=116[/tex]
[tex]y-116=36+7=43\\y = 159[/tex]
and [tex]z-159=43+7=50\\z=209[/tex]
Hence x = 116, y = 159 and z = 209
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tep 2 of 3: find the standard error of the sampling distribution to be used in constructing the confidence interval. round your answer to two decimal places.
Lower = 61.655811
Upper = 0.3441888
What is sampling distribution ?The probability distribution of a statistic acquired from a bigger sample size taken from a certain population is known as the sampling distribution. The frequency distribution of a variety of possible outcomes for a population statistic makes up the sampling distribution of a specific population. A population is the total group from which a statistical sample is taken in statistics. An complete collection of individuals, things, occasions, medical visits, or measures can all be referred to as a population. Thus, a population may be defined as an overall observation of persons that have been categorized according to a common characteristic.
=2.11(126)
=15(D28)
Lower = 61.655811
Upper = 0.3441888
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Which letter is at coordinate position (9, 5)?
OA. Y
OB. R
OC. F
OD. Q
The point R has an abscissa 9 and ordinate 5
a trapezoid was transformed on a coordinate grid using the rule (x, y) → (–x, y). which of the following describes this transformation?
reflect over x axis transformation represents this rule (x, y) → (–x, y).
How to find the type of transformation?Make a coordinate plot using squared paper.
An illustration.
take the coordinate points (2,3) and (-3,-2)
They are reflected in the x-axis.
The results that you should get are as follows.
(2,-3) and (-3,2)
The y-coordinate is the opposite of the original position, while the x-coordinate is unchanged.
This can be described generally as (x, y) → (–x, y).
When a point is reflected across the X-axis, its X-coordinate stays constant. On the other hand, the Y-coordinate is altered to the opposite sign.
The point (x,y) is therefore reflected across the X-axis as (x,-y).It is known as a reflect over x axis transformation.
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Find the area of ABCD with vertices A(-2, 6), B(4, 6), C(5, 4), and D(-1,-4).
The area of ABCD is
___ square units.
The area of the quadrilateral ABCD is equal to 12 square units.
How to determine the area of the parallelogram
In this question we find a parallelogram, of which a pair of parallel sides is parallel to the x-axis. The area of the parallelogram is equal to the product of its base and its height. The quadrillateral ABCD has a base of 6 units and the height is 2, and the area of the quadrillateral is equal to:
A = 6 · 2
A = 12
The area of the quadrilateral ABCD is equal to 12 square units.
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Find the distance between the two points in simplest radical form. (0,-1) and (-5, -5)
The distance between the given two points is 7 units.
What do we mean by distance?Distance is a numerical or qualitative measurement of the distance between two objects or points. The distance can refer to a physical length or an estimate based on other criteria in physics or everyday usage.Formula: [tex]\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
Put the values in the formula:
x₁ = 0 y₁ = -1x₂ = -5 y₂ = -5Then,
[tex]\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\\\sqrt{(-5-0)^{2}+(-5-(-1))^{2} } \\\sqrt{25+(25-1)} \\\sqrt{25+24} \\\sqrt{49} \\=7[/tex]
Therefore, the distance between the given two points is 7 units.
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Triangle ABC lies on the coordinate plane with the vertices A(7,6), B(-3,5) and C(-6,1).
The triangle is transformed using the rule (x, y) --> (x+4, 3y) to create triangle A'B'C'.
What are the coordinates of B'?
The transformation, the coordinates of point B' become (1, 15).
The transformation rule (x, y) → (x + 4, 3y) involves shifting the x-coordinate by 4 units to the right and stretching the y-coordinate by a factor of 3. To find the coordinates of B' after applying this rule, we take the coordinates of point B(-3, 5):
x-coordinate of B' = x-coordinate of B + 4 = -3 + 4 = 1.
y-coordinate of B' = y-coordinate of B * 3 = 5 * 3 = 15.
Therefore, after the transformation, the coordinates of point B' become (1, 15). This means that B' is located 4 units to the right of B along the x-axis and its y-coordinate is three times that of B. The transformation has shifted and stretched the original triangle, resulting in a new position for point B'.
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if there are ten marbles in a bag (those marbles being two yellow, three pink, and five blue) and two are randomly drawn, what is the probability of drawing two yellow marbles if the first one isn't put back before the second draw?
please help T^T
The probability of drawing two yellow marbles if the first one isn't put back before the second draw will be 1/45.
How to calculate the probability?Number of yellow marbles = 2
Number of pick marbles = 3
Number of blue marbles = 5
Total number = 10
The probability of drawing two yellow marbles if the first one isn't put back before the second draw will be:
= 2/10 × 1/9
= 2/90
= 1/45
The probability is 1/45.
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Scott types at a rate of 10 words per minute. How many words does he type in 5 minutes?
Answer: 50 words per minute
Step-by-step explanation: if he types 10 words per minute and if you multiply that by 5 the answer is 50 words per minute
pls help me i am not smart 4x + 2y = 12
Answer: (0,-6), (1,-4)
Step-by-step explanation:
Subtract 4x from both sides of the equation.
−
-2y=12−4x
Divide each term in -2y=12-4x by-2 and simplify
-
y=-6+2x
Rewrite in slope-int form.
y=2x-6
Next, you want to use the slope-int form to find the slope and y-int so you get (0,-6) and (1,-4)
solve the equation. (find only the real solutions. enter your answers as a comma-separated list.) 5x2 10x 4
Answer:
400
Step-by-step explanation:
5x2x10x4=
what is the product?
(3a²b^4)(-8ab³)
Answer:
-24a^3b^7
Step-by-step explanation:
Answer:
[tex]-24a^3b^7[/tex]
Step-by-step explanation:
Hello!
We can simplify by multiplying and expanding the expression. Then, multiply with the same variables.
Simplify[tex](3a^2b^4)(-8ab^3)[/tex][tex](3)(a^2)(b^4)(-8)(a)(b^3)[/tex][tex](3)(-8)(a^2)(a)(b^4)(b^3)[/tex][tex]-24a^3b^7[/tex]The simplified expression is [tex]-24a^3b^7[/tex].
The values of x and y vary directly
and one pair of values are given.
Write an equation that relates x
and y. Simplify completely.
x = -4, y = 6
[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{"y" varies directly with "x"}}{y=kx}\qquad \textit{we also know that} \begin{cases} x=-4\\ y=6 \end{cases} \\\\\\ 6=k(-4)\implies \cfrac{6}{-4}=k\implies -\cfrac{3}{2}=k~\hfill \boxed{y=-\cfrac{3}{2}x}[/tex]
Select the correct answer from each drop-down menu. what is the end behavior of function h? as x approaches negative infinity, approaches . as x approaches positive infinity, approaches .
Because the variable has an even power, we will see that:
As x approaches -∞, h(x) approaches -∞
As x approaches ∞, h(x) approaches -∞.
Here we have h(x) = -4x^2 + 11
Notice that the variable is squared, this means that the sign does not matter, the outcome of:
-4x^2 will always be negative. So in both ends (when x tends to infinity and negative infinity), we will have the same end behavior.
When we take that limit, -4x^2 will just tend to negative infinity, then in both cases, the function tends to negative infinity.
So we have:
As x approaches negative infinity, h(x) approaches negative infinity.
As x approaches positive infinity, h(x) approaches negative infinity.
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is c=3.75x proportional
Answer:
No
Step-by-step explanation:
If we put x=1 in equation y=x+3.75
y=(1)+3.75
y/x=4.75
If that is proportional then y/x will be the same in each scenario
and if we put x=2 then y=(2)+3.75
y=5.27
y/x=2.875
So, it is not equal, it means that equation is not proportional.
For a college chemistry experiment, students need to prepare a solution containing ethylene glycol. They are each given 20 fluid ounces of a solution containing 2% ethylene glycol, to which they will add another solution that contains 12% ethylene glycol. How much of the 12% solution should they add to obtain a 5% ethylene glycol solution?
Students should add 8.6 fluid ounces of 12% ethylene glycol.
Using the relation between concentration and volume of solution to find the required amount of 12% ethylene glycol to be used. Let the required amount of 12% ethylene glycol be x fluid ounces. Forming the relation as follows -
C₁ × V₁ + C₂ × V₂ = C₃ × V₃
C₁ and V₁ represents 2% ethylene glycol, C₂ and V₂ represents 12% ethylene glycol and C₃ and V₃ represents 5% ethylene glycol solution. As V₂ is x, so, V₃ will be (20 + x).
Keep the values in formula to find the value of x
2%×20 + 12%×x = 5%×(20 + x)
Solving the equation for the value of x
2/100×20 + 12/100×x = 5/100×20 + 5/100×x
0.4 + 0.12x = 1 + 0.05x
Rearrange the equation -
0.12x - 0.05x = 1 - 0.4
Performing subtraction on both sides -
0.07x = 0.6
Shifting 0.07 to Right Hand Side and performing division
x = 0.6 ÷ 0.07
x = 8.6 fluid ounces
Hence, 8.6 fluid ounces of the 12% ethylene glycol should be added.
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What does x equal in this problem ?
Answer:54
Step-by-step explanation:
Are they símilar? Yes or no
Answer:
yes
Step-by-step explanation: Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. If two or more figures have the same shape, but their sizes are different, then such objects are called similar figures.