The binomial theorem tells us how to expand an expression of the form (a + b)^2 like this:
[tex](a+b)^n=nC_0a^nb^0+nC_1a^{n-1}b^1+\cdots nC_na^0b^n[/tex]And nCr is given by the following formula:
[tex]nC_r=\frac{n!}{r!(n-r)!}[/tex]Then, for this polynomial, we can apply the binomial theorem with a = x, b = -3 and n = 5 to get:
[tex](x-3)^5=5C_0x^5(-3)^0+5C_1x^4(-3)^1+5C_2x^3(-3)^2+5C_3x^2(-3)^3+5C_4x^1(-3)^4+5C_5x^0(-3)^5[/tex][tex]\begin{gathered} 5C_0=1 \\ 5C_1=5 \\ 5C_2=10 \\ 5C_3=10 \\ 5C_4=5 \\ 5C_5=1 \end{gathered}[/tex]Simplifying, we get:
[tex]\begin{gathered} (x-3)^5=(1)x^5(-3)^0+(5)_{}x^4(-3)^1+(10)_{}x^3(-3)^2+(10)x^2(-3)^3+(5)x^1(-3)^4+(1)x^0(-3)^5 \\ (x-3)^5=x^5+(5)_{}x^4(-3)^{}+(10)_{}x^3(9)+(10)x^2(-27)+(5)x^1(81)^{}-243 \\ (x-3)^5=x^5-15_{}x^4^{}+90_{}x^3-270x^2+405x^{}^{}-243 \end{gathered}[/tex]Then, the expanded polynomial is:
x⁵ - 15x⁴ + 90x³ - 270x² + 405x - 243
2x=8 what is the answer
To solve x:
Divide both sides of the equation into 2:
[tex]\begin{gathered} \frac{2}{2}x=\frac{8}{2} \\ \\ x=4 \end{gathered}[/tex]Then, the solution for the given equation is x=4Evaluate. 0⁵= equal
The most important concept to solve this questio
Answer:
0
Step-by-step explanation:
o^5 = 0 x 0 x 0 x 0 x 0 = 0
I need the answer right now please someone help.Use the figure below to complete the following problem.Given:R, S, T are midpoints of AC, AB, and CB. AB||RTRCTC
From the diagram provided, line AB is parallel to line RT
AB | | RT
When you add 12 to a number and then divide the sum by 13, you get the same result as when you subtract 13 from the number and then divide the difference by 12. What is the number?
What is the value of 1/2 x^2 -10 when x = 6?
If we have the expression:
[tex]\frac{1}{2}x^2-10[/tex]we can find its value when x=6 by replacing x with the value 6 and calculating the result:
[tex]\frac{1}{2}(6)^2-10=\frac{1}{2}\cdot36-10=18-10=8[/tex]Answer: the expression has a value of 8 when x=6.
3 1/4 x 2/3 = ??grade. 7th
Given the expression:
[tex]3\cdot\frac{1}{4}\cdot\frac{2}{3}[/tex]Fist step is to express the "whole" as a fraction, for this, divide it by 1
[tex]\frac{3}{1}\cdot\frac{1}{4}\cdot\frac{2}{3}[/tex]Second step, multiply the first two fractions:
[tex]\frac{3}{1}\cdot\frac{1}{4}=\frac{3\cdot1}{1\cdot4}=\frac{3}{4}[/tex]Third step, multiply the result of the first operation by the third fraction:
[tex]\frac{3}{4}\cdot\frac{2}{3}=\frac{3\cdot2}{4\cdot3}=\frac{6}{12}[/tex]Finally simplify the expression, both the numerator and denominator are divisible by 6 so:
[tex]\frac{6\div6}{12\div6}=\frac{1}{2}[/tex]Then the result for the given expression is 1/2
[tex]3\cdot\frac{1}{4}\cdot\frac{2}{3}=\frac{1}{2}[/tex]Solve the equation below.
3(x−9)−6=16x−72
3x-27-6=16x-72
3x-33=16x-72
3x-16x= -72+33
-13x=39
x= -3
help or I die,... HELP
Regarding the points on the given line, it is found that:
a) The midpoint is: (3,4.5).
b) The coordinates of C are: C(4,5).
c) The coordinates of the other end of the line are: (4,3).
MidpointThe midpoint between two points is given by the mean of the coordinates of these points.
In this problem, the coordinates of points A and B are given as follows:
A(0,3) and B(6,6).
Hence the coordinates of the midpoint are given as follows:
x-coordinate: (0 + 6)/2 = 3.y-coordinate: (3 + 6)/2 = 4.5.As for point C, we have that C is closer to B then A, hence:
The x-coordinate is greater than 3.The y-coordinate is greater than 4.5.The coordinates are integers, hence it is given as follows:
C(4,5).
As for line AB, it is found that:
The other line is parallel, hence the slope is also of 0.5. (change in y divided by change in x is of 0.5).For the x-coordinate, on line AB, they change by 6, hence in the new line they increase by 2/3 x 6 = 4.For the y-coordinate, on line AB, they change by 3, hence in the new line they increase by 2/3 x 3 = 3.Thus the other endpoint is:
(4,3).
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Tamera is using rice paper to make Japanese Lanterns. The expression 2s^2 + 40s represents the surface area of a lantern where the base edges are s inches long. What is the surface area of a lantern when is 9 in?
2s^2 = 2s to the power of two
The surface area of the Japanese Lanterns Tamera made when the sides are 9 inches long will be 522 sq inches.
What is surface area?The Surace area of any 2D or 3D figure is the outer area of the given figure.
Surface areas are of two types they are lateral surface area when we exclude the areas of top and bottom and total surface area is when we include all the sides.
Given that Tamera is using rice paper to make Japanese Lanterns.
The expression 2s² + 40s represents the surface area of a lantern where the base edges are 's' inches long.
Therefore to find The surface area of the Japanese Lanterns when the sides are 9 inches in length we have to substitute 9 into the variable s.
So, 2(9)² + 40(9).
= 2×81 + 360.
= 162 + 360.
= 522 sq inches.
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helpp pleasee List the domain of the following function.(0,1),(9,0), (2,7),(4,3)
Problem
Solution
For this case we want to determine the domain from the following relation:
(0,1), (9,0), (2,7), (4,3)
And if we see the first cooridnate for all the points we have the domain and then the answer we have:
0,2,4,9
A tortoise is walking in the desert it walks for 5.12 m at a speed of 4 m/min. how many minutes does it walk
1.3 minutes does the tortoise walk.
What is speed- distance formula?Speed, time, and distance relationships
Distance/Time x Speed This reveals how quickly or slowly an object is moving. It gives the amount of time it took to travel a certain distance divided by the distance travelled.Speed is inversely correlated with time and directly correlated with distance. Therefore, as the speed increases, the time required, because Time = Distance / Speed. Distance = Speed X Time.Each Speed, Distance and Time can be expressed in different units:
Time: seconds(s), minutes (min), hours (hr)Distance: (meters (m), kilometers (km), miles, feetSpeed: m/s, km/hrGiven:
distance= 5.2 m
speed= 4 m/ min
Now using
speed= Distance / time
4 = 5.2 / time
time= 5.2/4
time= 1.3 minutes.
Hence, 1.3 minutes does the tortoise walk.
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Show your work (no explanation just the answer and how you got it) DUE TODAY
The solutions to the absolute value equations are given as follows:
1. k = -8 or k = 8.
2. x = -7 or x = 7.
3. a = -10 or a = 6.
4. a = -2.5 or a = 2.5.
5. m = -4 or m = 22.
6. x = -4 or x = 6.8.
7. x = -16 or x = 9.
8. a = -2.4 or a = 1.2.
What is the absolute value function?The absolute value function is defined by the following piecewise rule, depending on the input of the function:
|x| = x, x ≥ 0.|x| = -x, x < 0.This means that there are two possible solutions for the equation |x| = a, which are:
x = a or x = -a.
Item 1The equation is:
|k| = 8.
Applying the definition of the absolute value function, we have that the possible solutions are:
k = -8 or k = 8.
Item 2The equation is:
|x| = 7.
Applying the definition of the absolute value function, we have that the possible solutions are:
x = -7 or x = 7.
Item 3The equation is:
|a + 2| = 8.
The possible solutions are that the inside term can be equals to either -8 or 8, hence:
a + 2 = -8 -> a = -10.a + 2 = 8 -> a = 6.Item 4The equation is:
|8a|/10 = 2
In standard format, the equation is:
|8a| = 20
Then the solutions are:
8a = -20 -> a = -20/8 = -2.5.8a = 20 -> a = 20/8 = 2.5.Item 5The possible solutions are:
-m + 9 = -13 -> m = 22.-m + 9 = 13 -> m = -4.Item 6The possible solutions are:
7 - 5x = -27 -> 5x = 34 -> x = 6.8.7 - 5x = 27 -> 5x = -20 -> x = -4.Item 7Applying cross multiplication, the expression is:
|2x + 7| = 25
The possible solutions are:
2x + 7 = -25 -> 2x = -32 -> x = -16.2x + 7 = 25 -> 2x = 18 -> x = 9.Item 8Applying cross multiplication, the expression is:
|-3 -5a| = 9.
The possible solutions are:
-3 - 5a = -9 -> 5a = 6 -> a = 1.2.-3 - 5a = 9 -> 5a = -12 -> a = -2.4.More can be learned about absolute value equations at https://brainly.com/question/5012769
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Mrs. Henry's sixth-grade class has 30 students, 18 of which are boys. Which of the following describes the ratio of boys to girls in Mrs. Henry's class?
(DUE TOMORROW)
Answer:
18:12
Step-by-step explanation:
Just subtract the 18 boys from the total 30, to get the girls total in the class.
Verizon Wireless charges you a one- time processing fee of $250 plus $75 every month for a cell phone. Sprint charges you a one-time processing fee of $50 plus $100 every month for a cell phone. Write an equation to represent the cost of each company. Then complete the table.
Answer:
8
Step-by-step explanation:
The number line is a graph of the
Rational number
Real numbers
Integers
The number line is a graph of the Real numbers.
Rational Number And Real Numbers Integers ?Rational and irrational numbers are the two basic categories for real numbers. All fractions and integers are considered rational numbers. The set of integers consists of all whole numbers and negative integers. All natural numbers and zero are considered whole numbers. The only positive and negative whole numbers and natural numbers that fall under the category of integers are real numbers. Due to rational and irrational numbers, real numbers can incorporate fractions; however, integers cannot. Since integers are a collection of all positive counting numbers, zero, and all negative counting numbers that count from negative infinity to positive infinity, they are all rational numbers. Decimals and fractions are not included in the set.
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A line passes through the point (-3, -9) and has a slope of -2.
Write an equation in slope-intercept form for this line.
6)26 A 4 R2 (B) 2 R4 © 4 DE
On red step we multiply 6 by 4 to obtan 24, and subtract with 26, the solution is 2
O green step we add a comma to 4 do add a zero on the last solution (2), now the number is 20 and multiply 6 by 3 to obtan 18 and the solution is 2
As we can see the number two will be repeated forever since 20 divided by 6 is not exact, then the 3 will repeat infinitely
Edgar has a credit card payment that is increasing each month. The records for his bank payment are shown below. What kind of function can be used to best represent this data? A) Linear B) exponential C) quadratic
Notice that:
[tex]\begin{gathered} 250=250\cdot1.1^0 \\ 275=250\cdot1.1^1 \\ 302.5=250\cdot1.1^2 \\ 332.75=250\cdot1.1^3 \end{gathered}[/tex]Therefore the function that best models the behavior is:
[tex]f(x)=250\cdot1.1^x[/tex]Which is an exponential function.
7^2 -(3 + 2)^2 + 3^3 *
We want to calculate the following expression
[tex]7^2-(3+2)^2+3^3[/tex]We have an order that we must do the operations. First, we need to solve what is inside of the parenthesis, then, solve the exponentials, and with their results, do the additions and subtractions.
[tex]\begin{gathered} 7^2-(3+2)^2+3^3 \\ =7^2-(5)^2+3^3 \\ =7^2-5^2+3^3 \\ =49-25+9 \\ =33 \end{gathered}[/tex]And this is the solution for our problem.
using the elimination method, find x and y: please explain to me, I want an explanation because I don't get this a 100% yet 4x - 3y = 25-3x + 8y = 10
Given the system of equations :
[tex]\begin{gathered} 4x-3y=25 \\ -3x+8y=10 \end{gathered}[/tex]To eliminate y :
multiply the first equation by 8 and the second equation by 3
[tex]\begin{gathered} 8\cdot4x-8\cdot3y=8\cdot25 \\ 3\cdot-3x+3\cdot8y=3\cdot10 \\ ================ \\ 32x-24y=200 \\ -9x+24y=30 \end{gathered}[/tex]Add the equation , we will find the sum of y = 0
[tex]\begin{gathered} (32x-24y)+(-9x+24y)=200+30 \\ 32x-24y-9x+24y=230 \\ (32x-9x)+(-24y+24y)=230 \\ (23x)+(0)=230 \end{gathered}[/tex]So, solve the the result for x
[tex]\begin{gathered} 32x-9x=200+30 \\ 23x=230 \\ \\ x=\frac{230}{23}=10 \end{gathered}[/tex]Then substitute with x at the first equation to find y
[tex]\begin{gathered} 4\cdot10-3y=25 \\ 40-3y=25 \\ -3y=25-40 \\ -3y=-15 \\ \\ y=\frac{-15}{-3}=5 \end{gathered}[/tex]So, the answer of the system of equations :
[tex]\begin{gathered} x=10 \\ y=5 \\ (x,y)=(10,5) \end{gathered}[/tex]
A hot air balloon descended 3240 feet in an hour. Find the change in altitude per minute?
Unit analysis is a tool that we can use to convert units. It involves multiplying the original number by a fraction to cancel out units.
Solving the QuestionWe're given:
[tex]\dfrac{3240\hspace{4}feet}{hour}[/tex]
We also know that:
[tex]\dfrac{hour}{60\hspace{4}minutes}[/tex]
Multiply the two to cancel out the hour:
[tex]\dfrac{3240\hspace{4}feet}{hour}\times\dfrac{hour}{60\hspace{4}minutes}\\\\=\dfrac{3240\hspace{4}feet}{60 minutes}[/tex]
Simplify:
[tex]=\dfrac{54\hspace{4}feet}{minute}[/tex]
Answer[tex]\dfrac{54\hspace{4}feet}{minute}[/tex]
help pleaseeeeee!!!!!!!!!!!!!!!!!!!
Answer:
1. No
2. Yes
3. No
4. No
Step-by-step explanation:
I keep getting the wrong answer for some reason, help please
In order to find the measure of angle A we have the next equation. Remember that the sum of the interior angles of a triangle is 180°
[tex](3x-6)+(8x+4)+(180-130)=180[/tex]Then we sum like terms
[tex]11x+48=180[/tex]Then we isolate the x
[tex]11x=180-48[/tex][tex]11x=132[/tex][tex]x=\frac{132}{11}[/tex][tex]x=12[/tex]For angle A
angle A= 3x-6=3(12)-6=30°
angle A=30°
Please help me solve the pictured problemFind the midline for f(x)=2cos(3x−5π6)−2.
Given the function:
[tex]f(x)=2cos(3x-\frac{5\pi}{6})-2[/tex]You need to remember that the General Equation of the Cosine Function is:
[tex]y=Acos(B(x+C))+D[/tex]Where:
- The Amplitude is:
[tex]|A|[/tex]- The Period is:
[tex]\frac{2\pi}{B}[/tex]- The horizontal shift is "C".
- The Vertical Shift is "D".
- The midlline is:
[tex]y=D[/tex]In this case, you can identify that:
[tex]D=-2[/tex]Therefore, the midline is:
6. Work The dollar amount d that Julia earns varies directly as the number of hours !that she works, and d=$116.25 when 1 = 15 h. Find t when d = $178.25.
Answer:
t = 23
Explanation:
If the dollar amount d varies directly as the number of hours, t, the equation that relates these variables is
d = kt
Where k is a constant.
We know that for d = $116.25, t = 15 h, so we can replace these values and solve for k as follows
116.25 = k(15)
116.25/15 = k(15)/15
7.75 = k
Then, the equation that relates d and t is
d = 7.75t
Now, we know that d = $178.25 and we want to calculate t, so replacing d and solving for t, we get
178.25 = 7.75t
178.25/7.75 = 7.75t/7.75
23 = t
Therefore t = 23
Find the equation of the line passing through the points (10,8) and (-10,30). Write your answer in the form
The equation of a line in slope-intercept form is given by:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
We know two points on the line: (10,8) and (-10,30).
The slope can be found by using the following formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Where (x1,y1) and (x2,y2) are the coordinates of two points on the line. By replacing the known coordinates we obtain:
[tex]m=\frac{30-8}{-10-10}=\frac{22}{-20}=-\frac{11}{10}[/tex]The y-intercept can be found by replacing the slope and one of the points in the slope-intercept formula, and solving for b:
[tex]\begin{gathered} 8=-\frac{11}{10}\cdot10+b \\ 8=-11+b \\ 8+11=b \\ b=19 \end{gathered}[/tex]Thus, the equation of the line is:
[tex]y=-\frac{11}{10}x+19[/tex]Miles per gallon of a vehicle is a random variable with a uniform distribution from 23 to 47. The probability that a random vehicle gets between 28 and 36 miles per gallon is?
The probability that a random vehicle gets between 28 and 36 miles per gallon is 0.3333.
What's probability?Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.
Given that,
a = 23
b = 47
P(c < x < d) = (d - c) / (b - a)
P(28 < x < 36) = (36 - 28) / (47 - 23) = 0.3333
Probability = 0.3333
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Each side of a square is lengthened by 5 inches. The area of this new, larger square is 49 square inches. Find the length of
a side of the original square.
Answer:
2 inches
Step-by-step explanation:
Since the area of the larger square is 49 inches, each side of this square is 7 inches, which is 5 inches longer than the original square. So each side of the original square is 2 inches.
Substitution method. show work.7.) y=x+2 10.) 2x+y=3 y=3x+4 3x-y=2elimination method. show work.11.) 5x+y=9 12.) -7x+y=-19 10x-7y=18 -2+3y=-19
Solution
7) y= x+2
replacing this in the second equation we got:
x +2 = 3x +4
-2 = 2x
x= -1
And solving for y we got:
y = -1 +2 = 1
10) 2x +y = 3
If we solve for y we got:
y = 3-2x
And replacing into the second equation we got:
3x - 3+2x = 2
5x = 5
x= 1
And solving for y we got:
y = 3 -2*1 = 3-2= 1
11) If we multiply the first equation by -2 and we add to the second one we got:
-10 x -2y = -18
10x -7y = 18
___________
-9y = 0
y=0
x= (9-0)/5 = 9/5
12) If we multiply the first equation by -3 we got:
21x -3y = 57
-2x +3y =-19
_______________
19x = 38
x= 2
y= (-19 + 4)/3= -5
Define a variable, using let statements, set up an equation, then solve. Mark flew from Boston to Baltimore, then Baltimore to Orlando. the number of people on his first flight was five more than four times the number of people on his second flight. if there were 365 people altogether on the two flights how many were on the flight from Baltimore to Orlando?
First flight = f
second flight = s
Equations
f + s = 365 Equation 1
f = 4s + 5 Equation 2
Solve by substitution
(4s + 5) + s = 365
4s + 5 + s = 365
5s = 365 - 5
5s = 360
s = 360 / 5
s = 72
Find f
f = 4(72) + 5
f = 288 + 5
f = 293
Result
In the flight from Baltimore to Orlando there were 72 people.
