Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. (9 - 2x)⁵ is expanded as 59049 − 65610x + 29160x² − 6480x³ + 720x⁴ − 32x⁵.
What is meant by binomial expansion theorem?The Binomial theorem tells us how to expand expressions of the form (a + b)ⁿ, for example, (x + y)⁷. The larger the power is, the harder it is to expand expressions like this directly.
The total number of terms in the expansion of (x+y)ⁿ are (n+1).
The sum of exponents of x and y is always n.
nC₀, nC₁, nC₂, … .., nCₙ are called binomial coefficients and also represented by C₀, C₁, C₂, ….., Cₙ
The binomial coefficients which are equidistant from the beginning and from the ending are equal.
i.e. nC₀ = nCₙ, nC₁ = nCₙ₋₁ , nC₂ = nCₙ₋₂ ,….. etc.
Let the function be (9 - 2x)⁵
By using binomial expansion theorem, we get
(9 - 2x)⁵ = 59049 − 65610x + 29160x² − 6480x³ + 720x⁴ − 32x⁵.
(9 - 2x)⁵ is expanded as 59049 − 65610x + 29160x² − 6480x³ + 720x⁴ − 32x⁵.
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Michael is a collage tutor. he charges a $50 to fee, and then makes $15 per hour that he tutors. if he made a total of $250 last month how many hours did he work?
Twelve cubes are stacked and if we removed 2 of them how would the surface area change
If Twelve cubes are stacked its surface area is: 36a² and how would the surface area change if the top two cubes are removed is 6a².
Surface areaa. Surface area
If the length of one side is a the area of one surface is a²
Hence,
Area=a²
a²(6+6+6+6+6+6)
=36a²
b. Change in surface area change if the top two cubes are removed:
a²(6×2+5×2+4×2)
a²(12 + 10 + 8)
=30a²
Hence,
36a²-30a²
=6a²
Therefore If Twelve cubes are stacked its surface area is: 36a² and how would the surface area change if the top two cubes are removed is 6a².
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For ΔABC, m∠A = 32.1° and m∠B = 101.7°. Determine m∠C. 133.8° 69.6° 46.2° 43.8°
The unknow angle of the triangle is as follows:
m∠C = 46.2°
How to find the angle of a triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
In simpler term, a triangle is a kind of polygon that 3 sides and 3 angles.
Therefore, the sum of angles in a triangle is equals to 180 degrees.
Hence, the sum of angles in ΔABC is 180 degrees.
Therefore,
m∠A + m∠B + m∠C = 180°
m∠A = 32.1°
m∠B = 101.7°
m∠C = x
32.1 + 101.7 + x = 180
x + 133.8 = 180
x = 180 - 133.8
x = 46.2 degrees.
Therefore, the unknow angle of the triangle is as follows:
m∠C = 46.2°
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Answer: 46.2
Step-by-step explanation:
540 was rounded to the nearest ten.
What is the lower bound?
Why is math soooo hard?
Answer: because it's is involved in everyday life, without math we would never have a fraction of the technology we have today
Step-by-step explanation:
Answer: we have to use our brain- =w=
Step-by-step explanation:
so basically right we should only need to know how to count money and maybe multiply bc thats what u do in life why do we need to do algebra for real life ocasions- smh
Find the inverse of each function. Determine whether each inverse is a function. f(x)=√x+6
The inverse of the function f(x)=√x+6 will be x²-12x+36.
Inverse function-A function that can reverse into another function is known as an inverse function or anti-function.
The given function is,
f(x)=√x+6
As we know inverse of the function is shown as,
y = f(x)
y=√x+6
For inverse function, we have to replace the variable's place value,
x=√y+6
√y=x-6
Squaring both sides,
(√y)²=(x-6)²
y=x²+36-12x
Hence,the inverse of the function f(x)=√x+6 will be x²-12x+36.
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Can someone help me express this as a single fraction, i’m not sure of my answer
Answer:
3x-6/2[tex]\sqrt{x-1[/tex]
Step-by-step explanation:
1. first we have to get the denominator the same, so we multiply by [tex]\sqrt{x-1[/tex] to the first fraction top and bottom which leaves as with
3(x-1)/2[tex]\sqrt{x-1[/tex] - 3/2[tex]\sqrt{x-1[/tex]
- we can expand the numerator of the first fraction which becomes
3x-3/ 2[tex]\sqrt{x-1[/tex] - 3/2[tex]\sqrt{x-1[/tex]
2. we can now subtract te fraction as we have the same denominator this gives us
3x-6/2[tex]\sqrt{x-1[/tex]
3. your final answer would be
3x-6/2[tex]\sqrt{x-1[/tex]
{If the question asked to simplify your answer you would rationalize your answer by multiplying top and bottom by [tex]\sqrt{x-1[/tex] to give you the answer of
(3x-6)[tex]\sqrt{x-1[/tex]/2x-2}
Please help with problem 11
Answer:
option a is the right answer
Answer:
Step-by-step explanation:
Ok so vertical means straight up and down if you have forgotten so
First lets look at 2x=y no that is not correct because it is not going striagt up and down
The answer is C so I dont have to go through them all it is C
Please help me please help me
Answer:
Step-by-step explanation:
Anytime something does a 180 rotation it just flips the sign
Example: (-4, -6) 180 rotation (4, 6)
So for yours, it would be (-1, -2) 180 rotation (1, 2)
If you are still confused don't hesitate to ask :)
Which is a true statement?
1. An object with more power does the same amount of work in less time.
2. Power is the amount of force exerted on an object over a unit of time.
3. An object with more power does the same amount of work in more time.
4. The work done on an object depends on how much time it takes to do the work.
A bakery sells apple pies for $9.15. If the pie has a diameter of 6 inches, what is the approximate cost per square inch of the apple pie? Round to the nearest hundredth.
a $1.30
b $0.64
c $0.32
d $0.08
Based on the diameter of the pie, and the cost of the apple pie, the approximate cost per square inch of the apple pie is $0.32
How to find the approximate cost?First, find the area of the apple pie sold by the bakery because this will be needed to find the approximate cost per square inch.
Area of the pie will be the area of a circle:
= π x radius x radius
Radius is:
= 6 / 2
= 3 inches
The area of the apple pie is:
= π x 3 x 3
= 28.29 inch²
The approximate cost per square inch is:
= 9.15 / 28.29
= $0.32
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Answer: the answer is C $0.32
Step-by-step explanation:
This answer is proving the other person's answer correct
I got the questions on this test correct so I know the answer
Here is photo proof that it is correct
You can trust me because I always try my best to provide the correct answers on these tests. Have a good day FLVS students :)
Suppose that x and y vary inversely. Write a function that models each inverse variation and find y when x=-5 . x=25 when y=2
Function models for inverse variation is y = 50.1/x and find y when x=-5 will be -10.
What is a function model?A function model or functional representation is an organized depiction of the functions (activities, actions, processes, and operations) inside the modeled system or subject area.
Inverse variation formula is y = k. 1/x
⇒ for x = 25 and y = 2,
The value of k will be -
k = y . x
k = 25 . 2
k = 50
⇒ y = 50 . 1/x is our function
⇒ for x = -5,
⇒ y = 50 / -5
⇒y = -10
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You play a game on your phone. For every correct move you make, you receive 50 points. For every second that it takes you to complete the game, you lose 3 points. You complete the game in 2 minutes 12 seconds using 30 correct moves. What is your score?
Answer:
1464
Step-by-step explanation:
Answer:
1104 points
Step-by-step explanation:
50 points for 30 correct moves is 1500 points
2 minutes and 12 seconds is equal to 132 seconds
at 132*-3 for each second is -396
1500-396 =1104 points
What is this? ба + 12 = 2(за - 8)
It's a simple linear (first degree) equation in ' a '.
It has no solution.
Can someone help me please I’ve been trying the last hour to figure this out
Answer:
It is the third one down.
Step-by-step explanation:
The two smaller angles would be the same measurement because the angle bisector cuts the big angle down the middle. So, if the big angle was 90°, the two smaller angels would be 45°.
Answer:
3
Step-by-step explanation:
its 3 because An angle bisector is a ray that divides an angle into two congruent angles if you multiply the measurement of GLH by two you will get the measurement of GLI. Which is the same as adding the measurement of GLH and HLI since they have the same measurement
Congruent: The same
the height of a triangle is twice its base the area is 144cm³ find the base
Answer:
Base = 12cm
Height = 24cm
Step-by-step explanation:
Hello glittersplanet,
The formula for the area of a triangle is A = 1/2 b * h where A equals the area, b equals the base, and h equals the height. You are given the area in this problem.
Let the following conditions apply:
Base = x
Height 2x <-------Problem states the height is twice its base, correct?
Therefore:
A = 1/2 b*h
144 = 1/2 (x)(2x)
Simplify by removing the fraction by multiplying through by 1/2 and you are left with x^2 correct? Therefore:
144 = x^2
x = √144
x = 12
Therefore, base = x = 12 while height = 2x = 2(12) = 24
x = √144
Footing-x=12
Height-x2=24
You want to purchase a new bike that costs 134.98. To save for the bike, you mow your neighbor’s yard for 45$ each week. How much money will you have left over if you buy the bike after saving for 4 weeks
Answer: $44.02
Step-by-step explanation: 180 - 135.98 =
44.02
Write the expression that represents the total length of each segment shown.
The expressions for the total length of each segment are x + 1, d + 4, and y + 3.
The total length of the segments will be the sum of the part so the segments.
Let's say a line segment AB is divided into two parts x and y then the expression for the length of the segment will be x + y.
Now,
For the first segment,
The two parts are x and 1.
The expression of the total length of the segment is:
x + 1
For the second segment,
The two parts are d and 4.
Then the expression for the total length of the segment is:
d + 4
For the third segment,
The two parts are y and 3.
Then the expression for the total length of the segment is:
y + 3
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The complete question is mentioned below:
Write the expression that represents the total length of each segment shown.
Solve the system of equations using a matrix
3 a+5 b=0
a+b=0
The solutions of a and b are 0 and 0 respectively using matrix.
Solving a system of linear equations using the inversion method involves two new matrices.Matrix A: representing variables Matrix B: represents a constant The system of equations can be solved by matrix multiplication which is given by [tex]X=A^{-1}B[/tex] ...(1)
We have given two equations 3a + 5b = 0 and a+b = 0
This can be written as AX=B
Where [tex]A=\left[\begin{array}{ccc}3&5\\1&1\\\end{array}\right][/tex] and [tex]X=\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex] , [tex]B=\left[\begin{array}{ccc}0\\0\\\end{array}\right][/tex]
A is the coefficient matrix, X the variable matrix and B the constant matrix.
[tex]|A|=3(1)-5(1)\\|A|=3-5=-2[/tex]
Since [tex]|A|\neq 0[/tex]
Hence, the system of equations is consistent and has a unique solution given
A inverse is given by [tex]A^{-1}=\frac{adjA}{|A|}[/tex] ....(2) and adj(A) is given by [tex]adjA=C^T[/tex]
[tex]M_{11}=1\\M_{12}=1\\M_{21}=5\\M_{22}=3[/tex]
Then Co -factors will be
[tex]C_{11}=1\\C_{12}=-1\\C_{21}=-5\\C_{22}=3[/tex]
Matrix C is represented by
[tex]C=\left[\begin{array}{ccc}1&-1\\-5&3\\\end{array}\right] \\\\C^T=\left[\begin{array}{ccc}1&-5\\-1&3\\\end{array}\right][/tex]
Putting |A| = -2 and transpose of C in equation (2) , we get
[tex]A^{-1}=\frac{1}{-2} \left[\begin{array}{ccc}1&-5\\-1&3\\\end{array}\right][/tex]
Putting the value of A inverse in equation (1) , we get
[tex]X=\frac{1}{-2} \left[\begin{array}{ccc}1&-5\\-1&3\\\end{array}\right]\left[\begin{array}{ccc}0\\0\\\end{array}\right]\\\\\left[\begin{array}{ccc}a\\b\\\end{array}\right]=\left[\begin{array}{ccc}0\\0\\\end{array}\right][/tex]
On comparing , we get a =0 , b= 0
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Write a function for each situation. Then find the value of each function after five years. Round to the nearest dollar. A baseball card bought for $ 50 increases 3 % in value each year.
$57.96 is the value of each function after five years.
How does exponential growth utilise e?
e is the constant growth rate that all processes that are growing continuously share. With e, you may compare a simple growth rate—where all change occurs at the end of the year—with a compound, continuous growth rate, where growth occurs once per nanosecond or quicker.Let the principle sum be P
Let the number of years be n
Thus the total sum for n years is
P( 1 + 3/100)ⁿ → P( 103/100)ⁿ
= $50 ( 103/100)⁵
= $57.96
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What type of number is √/2?
Which expression is equivalent to 9x + 4y + 2x - y²?
Answer:
11x + 4y - y^2
Step-by-step explanation:
You plus the same variables, in this time you got 9x and 2x so it's 11x!
Answer:
11x + 4y - y²
Step-by-step explanation:
9x + 4y + 2x - y²
combine like terms
11x + 4y - y²
NEED IT ASAP!!!! The length of the string of a pendulum, L, can be determined using the function L(p)=9.8(p/2pie)^2 , where p is the period of the pendulum. The velocity at the bottom of the pendulum can be modeled by the function v(L)=\sqrt{19.6L} .
Which function can be used to find the velocity at the bottom of the pendulum released from the same angle for any period, p?
A function which can be used to determine the velocity V(L(p)) at the bottom of the pendulum released from the same angle for any period, p is V(L(p)) = p/2π√192.08.
What is a function?A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable to an output variable.
Given the following data:
L(p) = 9.8(p/2π)².
V(L) = √19.6L
A function which can be used to determine the velocity V(L(p)) at the bottom of the pendulum released from the same angle for any period, p is given by:
V(L(p)) = √[19.6 × 9.8(p/2π)²]
V(L(p)) = √(19.6 × 9.8) × √(p/2π)²)
V(L(p)) = 192.08 × (p/2π)
V(L(p)) = p/2π√192.08
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Answer:
its B V(L(p)) = p/2π√192.08
Step-by-step explanation:
Honers Algebra 1 Math Questions (Please show all work) Day 2: Functions part 2
For numbers 1 & 2, find the domain of the function in interval notation:
1.g(x)=13x-15/x+4
2.y=x2-10x+2
For numbers 3 & 4, solve the word problems:
3.The temperature in degrees Fahrenheit that is equivalent to a temperature in degrees Celsius is given by the function F(C)=95C+32. Find the temperature in degrees Fahrenheit that corresponds to a temperature of 15 degrees Celsius.
4.A ball is thrown in the air and its height after t seconds is given by the following function: h(t)=-16t2+32tHow high is the ball after 2 seconds?
1. The domain of the function in interval g(x) = 13x-15/x+4
Domain: (−∞,0)∪(0,∞),{x|x≠0
Range: (−∞,∞),{y|y∈R}
2. The domain of the function in interval y=x2-10x+2
Domain: (−∞,∞) {x|x∈R}
Range: (−23,∞),{y|y≥-23}
3. By rearranging the equation so that C is in terms of F, you may determine the inverse:
F= 5/9C+32
32 is deducted from both sides.
F−32= 5/9C
Add five to both sides:
5(F−32)=9C
multiply both sides by 9.
C= 5/9(F−32)
C=− 25/9
−2.78C o 2.dp
The inverse is, in fact, a one-to-one function.
4. We are looking for the height at t=0 in order to determine the beginning height. To do this, replace t with 0 and find h.
h(t)= -16t2 + 32t + 24
h(0) = -16(0)2 + 32(0) + 24
h(0) = 24
24 feet is the initial height
The constant in the equation often represents height. 24 in this instance.
The coefficient of x, in this case 32, represents the beginning velocity.
32 feet per second is the beginning velocity.
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1. Which of the following does NOT show an identity property?
4x1=4
5+1=5
3-0=3
2+1=3
Answer: The Answer is 5+1=5 or B
Step-by-step explanation:
This is because 5+1 does not = 5
Sean is exploring a coral reef 91 feet below sea level and liz is hiking 91 feet above sea level. Who is hiking farther away from sea level
They are about same distance from sea level.
Sean is exploring a coral reel below level= 91 feet
Liz is hiking above sea level= 91 feet
When, we compare both distance from sea level, both have the sane distance. Although, the distance between both Sean and Liz is 91+91= 182 feet.
When compare the level of both , both are at 91 feet one is below the sea level and another is above the sea level. Hence, both are at the same distance from the sea level.
Hence, the correct answer is both at 91 feet from seal level.
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Hank's pickup can travel 90 miles on 5 gallons of gas. How many gallons will Hank's pickup need to travel 36 miles?
Hank's pickup will need
gallons of gas to travel 36 miles.
make d the subject of the formular h=d/3+2
Answer:
3h - 6
Step-by-step explanation:
→ Minus 2 from both sides
h - 2 = d / 3
→ Multiply both sides by 3
3h - 6 = d
Step-by-step explanation:
h=d/3+2
h=d/5
d=5h
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The ODDS IN FAVOR of a randomly selected person in a certain classroom is left handed are 4:21. What is the PROBABILITY that a randomly selected person from the room is left handed (as a percent!
P(Left)=
Moya is moving to a new house and packing up. She has 70 kilograms of books and 127 kg kilograms of clothing to send through the postal service. How much more do her clothes weigh than her books? How much is her shipping cost of she has to pay $80 per kg of books and $200 per kg of clothing?
The difference in her clothes and her books will be 57kg.
The difference in shipping cost if she has to pay $80 per kg of books and $200 per kg of clothing will be $19800.
How to calculate the value?From the information, Maya has 70 kilograms of books and 127 kg kilograms of clothing to send through the postal service, the difference in her clothes and her books will be:
= Weight of clothes - Weight of books
= 127 kg - 70 kg
= 57 kg
The difference in shipping cost if she has to pay $80 per kg of books and $200 per kg of clothing will be:
= 127(200) - 70(80)
= 25400 - 5600
= $19800
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