The required value of a is 2 if the coefficient of x² is 1104 of the expansion (1 + ax)²⁴.
What is the Binomial Theorem?According to the binomial theorem, it is possible to expand any non-negative power of binomial (x + y) into a sum of the form,
(x+y)ⁿ = ⁿC₀xⁿy₀ + nC₁ xⁿ⁻¹y₁ + nC₂ xⁿ⁻² y2 + ... + nC x¹yⁿ⁻¹ + nCn x°yⁿ
where n ≥ 0 is an integer and each ⁿCₓ is a positive integer known as a binomial coefficient.
We have been given that the expansion as
(1 + ax)²⁴
As per the binomial theorem expansion of the term 3,
T₃ = ⁿC₂ a² x²
Since the coefficient of x² = 1104
⇒ n!/2!(n-2)a² x² = 1104
Here n = 24
⇒ 24!/2!(24-2)a² = 1104
⇒ 276a² = 1104
⇒ a² = 1104/276
⇒ a² = 4
⇒ a = 2
Therefore, the required value of a is 2 if the coefficient of x² is 1104 of the expansion (1 + ax)²⁴.
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Prove that for all integers a, b, n, if n = a + b, then a ≤ n/2 or b ≤ n/2 using proof by contradiction.
From the example that if a = 3 and b = 3 so the value of n = 6. It means that a ≤ n/2 and b ≤ n/2.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given that all integers a, b, and n, if n = a + b, then a ≤ n/2 or b ≤ n/2. Let the value of a = 3 and b = 3 now the value of n will be:-
n = a + b
n = 3 + 3 = 6
a = 3, n = 6 then a ≤ n/2.
b = 3, n = 6 then b ≤ n/2.
Therefore, the example that if a = 3 and b = 3 so the value of n = 6. It means that a ≤ n/2 and b ≤ n/2.
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Use the domain {1/2, 1, 2, 4, 8, 16} and plot the points on the graph that would best satisfy the equation y = log2x.
Given equation y = log2x
domain {1/2, 1, 2, 4, 8, 16}.
The graph of six points that would satisfy the equation.
In equation put the value of
x =1/2
y= -1
for x= 1
y=0
for x= 2
y=1
for x= 4
y=2
for x =8
y= 3
for x= 16
y=4
Plot the points {1/2, 1, 2, 4, 8, 16} on a coordinate plane
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Solve the system of equations.
x + y = 8
y=x²- 4
The solution for the given system of equations is (3,5) and (-4,12).
Given two systems of equations i.e. x+y=8 and y=[tex]x^{2}[/tex]-4 and asked to solve them.
⇒x+y=8; let's assume this equation as A
⇒ y=[tex]x^{2}[/tex]-4; let's assume this equation as B
From equation A
⇒y=8-x
From equation B
⇒y=[tex]x^{2}[/tex]-4
Equating both the values of y
⇒8-x=[tex]x^{2}[/tex]-4
⇒[tex]x^{2}[/tex]-8-4+x=0
⇒[tex]x^{2}[/tex]-12+x=0
{solving quadratic equation}
⇒[tex]x^{2}[/tex]-12+4x-3x=0 { factorizing the quadratic equation}
⇒[tex]x^{2}[/tex]+4x-3x-12=0
⇒x(x+4)-3(x+4)=0
⇒(x-3)(x+4)=0
Therefore, the value's of x=3,-4
⇒if x=3
From equation A
⇒y=8-3=5
For x=3 ; y=5
⇒if x=-4
From equation A
⇒y=8-(-4)=12
For x=-4 ; y=12
Therefore,The solution for the given system of equations is (3,5) and (-4,12).
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An amusement park charges $70 for admission before 6 P.M.
and $25 for admission after 6 P.M. On Saturday, the park took in a total of $28,000.
a. Write an equation that represents the number of admissions that may have been
sold. Let x represent the admissions sold before 6 P.M., and let y represent the
admissions sold after 6 P.M.
b. Graph the equation.
c. Find the x- and y-intercepts of the graph. What does each intercept represent? Please help the due date is tomorrow
The x-intercept is 0.4 and the y-intercept is 1.2.
Given that, an amusement park charges $70 for admission before 6 P.M. and $25 for admission after 6 P.M. On Saturday, the park took in a total of $28,000.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let x represent the admissions sold before 6 P.M., and let y represent the admissions sold after 6 P.M.
According to the question, we get the equation as 70x+25y=28,000
The graph of the obtained equation is given below.
The x-intercept is where a line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis.
From the graph, the x-intercept is 0.4 and the y-intercept is 1.2.
Therefore, the x-intercept is 0.4 and the y-intercept is 1.2.
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Which value c makes the expression x2 + 2x + c a perfect square trinomial?
The value of the c is 1 which makes the perfect square trinomial.
According to the statement
We have to find that the value of the c.
So, For this purpose, we know that the
An expression obtained from the square of the binomial equation is a perfect square trinomial.
From the given information:
The Given statement is:
x² - 2x + c
is a perfect square of the form
(x - a)² = x² - 2ax + a²
Now,compare with x² - 2x + c, then
- 2a = - 2 ⇒ a = 1,
thus
a² = 1² = 1 = c
(x - 1)² = x² - 2x + 1 ← perfect square trinomial
It means the value of c is 1.
So, The value of the c is 1 which makes the perfect square trinomial.
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A washer and a dryer cost $813
combined. The washer costs $87
less than the dryer. What is the cost of the dryer?
The cost of the dryer will be $450
In the given sum the combined cost of the washer and dryer is $813
let the cost of the dyer be x
the cost of the washer will be (87 - x) as it is mentioned in the question washer costs $87 less than the dryer
According to the problem :
∴ x + (x-87) = 813
=> x+x-87 = 813
=> 2x - 87 = 813
=> 2x = 813 +87
=> 2x = 900
=> x = 900/2
=> x = 450
So the cost of the dryer is $450
The cost of the washer is = x - 87 = 450 - 87 = $363
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Evaluate − 7 w + 2 p for w = − 2 and p = − 6
The simplification of the given expression − 7 w + 2 p is 2.
What is the multiplication rule for negative integers?Negative integers have been real integers less than zero. For instance, 147 and 4 are negative integers, but 0.4181554... and 10 are not; the former is a negative number yet not an integer, whereas the latter is a positive integer.
There are two simple points to remember: When a negative number is multiplied by a positive number, the product has always been negative. When two negative numbers as well as two positive numbers are multiplied, the product has always been positive.The given expression is;
= - 7 w + 2 p
The for the variables is given;
w = − 2 and p = − 6
put the values in the expression;
= -7(-2) + 2(-6)
Th multiplication of 2 negative will be positive while one positive one negative will give negative number only.
Thus,
= 14 - 12
Simply subtract;
= 2
Therefore, the result of the given expression is 2.
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Which of the following is equivalent to l x - 1 l < 5
In the above question the |x| represents the absolute value. |x - 1| < 5 is equivalent to -5 < x - 1 < 5.
What do you mean by absolute value?Algebra usually requires us to be careful about not just size of a value but also its sign. -10 is different than the 10. 3+7 yields a different result than the 3+(-7) . But there are circumstances in which sign doesn’t matter, in mathematics and in real life. Have you ever stumbled stepping on or off the moving walkway? It doesn’t really matter if you’re moving faster or slower than ground surface—it’s the magnitude of difference that makes you lose your balance. Or think of taking long hike—your feet will get just as the sore whether you go to north or south. Direction doesn’t matter, only the distance.
In mathematics, there’s a concept for dealing with the situations where size matters more than sign. It’s called the absolute value. Absolute value of a number is it's value regardless of its sign.
Given,
|x - 1| < 5
|x| this represents absolute value. It is the distance of x from 0, so value of x can be both positive and negative.
⇒ |x - 1| < 5 can be (x - 1) < 5 and -(x - 1) < 5
⇒ -(x - 1) < 5
⇒ (x - 1) < -5
So equivalent of |x - 1| < 5 is -5 < x - 1 < 5
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Answer:
Its C
which is –5 < x – 1 < 5
A bakery is making whole-wheat bread and apple bran muffins. For each batch of break they make $35 profit. For each batch of muffins, they make $10 profit. The break takes 4 hours to prepare and 1 hour to back. The muffins take 0.5 hours to prepare and 0.5 hours to bake. The maximum preparation time available is 16 hours. The maximum bake time available is 10 hours. Let x = # of the batches of bread and y = # of batches of muffins. How many batches of bread and muffins should be made to maximize profits?
4 batches of bread and 0 batches of muffins
4 batches of bread and 0 batches of muffins
2 batches of bread and 16 batches of muffins
2 batches of bread and 16 batches of muffins
4 batches of bread and 10 batches of muffins
4 batches of bread and 10 batches of muffins
1 batch of bread and 12 batches of muffins
The batches of bread and muffins should be made to maximize profits are 0 batches of bread and 16 batches of muffins
How many batches of bread and muffins should be made to maximize profits?The given parameters can be represented on the following table
Bread (x) Muffins (y)
Prepare 4 1 16
Bake 0.5 0.5 10
Profit 35 10
The parameters from the above table are
Max P = 35x + 10y
Subject to
4x + y <= 16
0.5x + 0.5y <=10
x, y > 0
Solving the above constraints using a graphing calculator, we have the following points
(x, y) = (4, 0) and (0, 16)
Substitute these values in Max P = 35x + 10y
So, we have
P = 35 x 4 + 10 x 0 = 140
P = 35 x 0 + 10 x 16 = 160
160 is greater than 140
Hence, the batches of bread and muffins should be made to maximize profits are 0 batches of bread and 16 batches of muffins
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There are five questions listed below. Each question includes the quantity 43. Match the 43 in each question on
the left to which part of the problem it represents on the right -- the base, percent, or amount. Some answer
options on the right will be used more than once.
What number is 15% of 43?
43% of 300 is what number?
12% of what number is 43?
43 is what percent of 106?
What percent of 43 is 6?
percent
base
amount
Click and hold an item in one column, then drag it to the matching item in the other column. Be sure your
What number is 15% of 43?
43 here is the base43% of 300 is what number?
Here 43 is the percent12% of what number is 43?
43 is used here as amount43 is what percent of 106?
43 is used here as amountWhat percent of 43 is 6?
43 here is the baseWhat is base?The base as used in the question refers to the main number that is a=to say the number on which other calculation are focused on.
What is percent?Percent is a term used in mathematics to refer to a fraction with a denominator of one hundred. Numbers in percent is accompanied with the percent symbol which is %. Any number having that symbol means that the number is a fraction with a denominator of one hundred.
What is amount?The term amount as used refers to the result gotten when some mathematical operation is being done on the base.
The calculations to the questions asked are below:
What number is 15% of 43?
= 15/100 x 43
= 6.45
43% of 300 is what number?
= 43/100 x 300
= 129
12% of what number is 43?
= 12/100 x 43
= 5.16
43 is what percent of 106
= 43/106 * 100
= 40.56%
What percent of 43 is 6
= 6/43 x 100
= 13.95%
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3. m/U = 3x°, and m/V = 3(m/U). Find the value of x that makes ZU and
ZV supplementary angles.
The value of x that makes ∠U and ∠V to be supplementary angles are; x = 15°
What are supplementary angles?
When we are talking about angle theorem and congruency in mathematics, it is well know that supplementary angles are defined as angles whose sum is equal to 180 degrees.
Now, we are given;
∠U = 3x°
∠V = 3(∠U)
Thus;
∠V = 3(3x°) = 9x°
From definition of supplementary angles, we can say that;
3x° + 9x° = 180°
12x = 180°
x = 180/12
x = 15°
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n.
D
5. Simplify an expression for
the perimeter of the square.
5.9x-33
5.9-3.3
EE163
5.9x-3.3
23.6x-13.2=50
CA
I don’t understand how you get 50
The value of the perimeter of square become is 36x - 132.
According to the statement
We have to find that the perimeter of the square.
So, For this purpose, we know that the
The perimeter of the square is defined as the total length of the boundary of a square.
From the given information:
The side of the square is given which is:
9x - 33
Then
We know that the
Perimeter of square = 4a
And substitute the values in it then
here a = 9x-33
Then after put the values Then
Perimeter of square = 4(9x-33)
Perimeter of square = 36x - 132.
The value of the perimeter of square become is 36x - 132.
So, The value of the perimeter of square become is 36x - 132.
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The length of a rectangle is 5 in longer than its width.
If the perimeter of the rectangle is 58 in, find its length and width.
Answer:
Length = 17 in
Width = 12 in
Step-by-step explanation:
Formula we use,
→ P = 2(L + W)
Then the value of L and W is,
→ P = 2(L + W)
→ 58 = 2(x + 5 + x)
→ 2(2x + 5) = 58
→ 4x = 58 - 10
→ x = 48/4
→ [ x = 12 ]
Then the width will be,
→ W = x = 12 in
Hence, the width is 12 in.
Now the length will be,
→ L = x + 5 = 12 + 5 = 17 in
Therefore, the length is 17 in.
replace the stars with digits. how many solutions does each problem have. ***-**=1
Answer: We have two solutions:
1000-998=2
or
1001 - 999 = 2
An online store sells two types of speaker docks for smartphones. The higher-priced speaker dock sells for $170 and the lower-priced speaker dock sells for $90. Last week the store sold three times
as many lower-priced speaker docks as higher-priced speaker docks. Combined sales totaled $3,080. How many lower-priced speaker docks did it sell?
Answer:
21
Step-by-step explanation:
the price of the lower priced docs for that week would be 3x because the store sold 3 times as many low priced than the higher priced.
> so 90(3x) = 270x
170x + 270x = 440x
3080/440 = 7
7 high priced speakers were sold
to find out the cost of the lower ones you'd do
3x7 and get 21
Write an expression to represent: 9 more than the quotient of 2 and x
Expression for given numerical is: 9+ (2/x)
Given that we have an word equation that is 9 more than the quotient of 2 and x
A quotient is a quantity produced by the division of two numbers.
Quotient of 2 and x is [tex]\frac{2}{x}[/tex].
Nine(9) more than 2/x is = 9+ (2/x)
So we have an expression that is:
9+ (2/x)
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What is the measurement of this angle ?
The measurement of the given angle is a 90 degree.
According to the statement
We have to find that the measurement of this angle.
So, For this purpose, we know that the
An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.
From the given information:
In the given figure, the measurement of the angle we have to find.
A 90-degree angle is a right angle and it is exactly half of a straight angle. It always corresponds to a quarter turn.
And from the figure it is clearly visible that the line of the angle exactly matches with the 90 degree.
Then the angle is 90 degree.
So, The measurement of the given angle is a 90 degree.
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A student receives the following grades, with an A worth 4 points, a B worth 3 points, a C worth 2 points, and a D worth 1 point. What is the student's weighted mean grade point score? B in 2 two-credit classes D in 1 two-credit class A in 1 three-credit class C in 1 three-credit class
The student's GPA is of 2.33.
What is GPA?Grade Point Average (GPA) is the measure used to summaries your academic achievement at Griffith.
Given:
A worth 4 points,
B worth 3 points,
C worth 2 points,
D worth 1 point
The GPA is
= 3(3) + 1(3) + 2(4) + 2(2)/9+3+4+2
=9+3+8+4/18
=2.33
Hence, The student's GPA is of 2.33.
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PLEASE HELP I WILL GIVE BRAINLIEST AND 50 POINTS !!!!
A circle has equation x^2+y^2=100 Tangents meet the circle at R(-6,-8) and S(-8,6)
Find the equation of these tangents.
Find the coordinates of the point where these tangents meet.
Answer:use demos cauculator
Step-by-step explanation:
Points A, B, C, D, and E are collinear and in
that order. Find AC.if AE = x + 50 and
CE = x + 32.
Points A, B, C, D, and E are collinear and in that order. The value of Ac is 18.
According to the segment addition postulate, if two points on a line segment, A and C, are given, a third point, B, will only be found on line segment AC if and only if the distances between the points satisfy the conditions of the equation AB + BC = AC.
Keep in mind that a line segment is a portion of a line that has two distinct end points. There are many points between the two end points that make up the object.
The segment addition postulate can be stated more simply by saying that if point B lies on line segment AC, then AB + BC will equal AC.
by the segment addition postulate,
AC + CE = AE so AC = AE - CE
AC = (x+50) - (x+32)
AC = x+50-x-32
AC = 18
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which is greater -2.75 or -2.25
Answer: -2.25
Step-by-step explanation:-2.25 because it is closer to 0
TOOIS
Question 3
A pipe is leaking at a rate of 8 fluid ounces per minute. How many gallons per hour will leak from the pipe?
0.02 gal/hr
A
B
C
D
3.75 gal/hr
17.07 gal/hr
3,840 gal/hr
If a pipe is leaking at a rate of 8 US fluid ounces per minute, then 3.75 US liquid gallons of the fluid will leak from the pipe in an hour.
As per the question statement, a pipe is leaking at a rate of 8 US fluid ounces per minute and we are required to calculate the amount of leak that will occur at the same rate of leakage, in an hour, in the units of US liquid gallons.
To solve this question, we need to know to know about two basic mathematical conversions, i.e.,
1 US Liquid Ounce = 0.00781 US Liquid Gallons, and
1 hour = 60 minutes.
Therefore, amount of leak that will occur at the rate of 8 US fluid ounces per minute, in an hour = [tex](8 * 60)=480[/tex] US fluid ounces.
And 480 US fluid ounces = [tex](0.00781 * 480)=3.75[/tex] US Liquid Gallons.
Hence, 3.75 US Liquid Gallons of fluid will leak from the pipe in an hour.
Fluid Ounce: It is an unit of volume, used for measuring liquids. "The British Imperial" and the "United States customary" fluid ounce are the only two that are still in use. The US Fluid ounce is an unit of capacity equal to one-sixteenth of a US pint (approximately 0.03 liter), while the British Imperial fluid ounce a unit of capacity equal to one twentieth of a pint (approximately 0.028 liter).Liquid Gallons: In the United States, Liquid Gallon is an unit of liquid capacity equal to four quarts or 231 cubic inches or 3.785 liters, while in the Great Britain, also known as the "Imperial Gallon", it is an unit of liquid and dry capacity equal to four quarts or 277.42 cubic inches or 4.544 liters.To learn more about Fluid Ounces and Liquid gallons, click on the klink below.
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Is this a function or not. Then state domain and range. WILL GIVE BRAINLEIST
Answer:
Yes
Step-by-step explanation:
It is a function look at the numbers
Question 15 (1 point)
Given the following definitions:
U = {1, 2, 3, 4, 5, 6, 7}
A = {1, 2, 4, 5]
B = {1, 3, 5, 7}
How many elements are in AUB?
Answer:
6
Step-by-step explanation:
The union is defined as the set of all elements in at least one of the sets.
[tex]A \cup B=\{1,2,3,4,5,7\}[/tex]
So, there are 6 elements.
If √x = 9, then x is between
O 80 and 90
O 4 and 5
O 2 and 3
O 15 and 20
Answer:
80 and 90
Step-by-step explanation:
[tex]\sqrt{x}=9 \implies x=9^2=81 \implies 80<x<90[/tex]
Urgent Please!
• What expression would represent the area of a square with side length 10?
—-
•Part C: What expression would represent the area of a square with side length 20?
—-
•Part D: What expression would represent the increase in area caused by changing the side length from 10 to 20?
Answer: B. 100
C. 400
D. 300
Step-by-step explanation:
A=area of square. s=side length of square.
B. A=s^2
A=10^2
A=100
C. A=20^2
A=400
D. I=Increase in Area
I=20^2 -10^2
I=400-100
I=300
If I add 9 by pi will it be irrational or rational?
Answer: irrational
Step-by-step explanation:
because it still cant be turned into a fraction after adding 9 to pi
Please help me
The elevation of Kristianstad, Sweden, a city founded by King Christian IV of Denmark, is meters . Which of these describes the elevation of Kristianstad?
The best description for the elevation of Kristianstad is below sea level.
How to find what describes the elevation of Kristianstad?The elevation of Kristianstad, Sweden, a city founded by King Christian IV of Denmark, is -2 meters .
The best option that describes the elevation of Kristianstad is as follows:
Therefore,
At sea level the elevation will be at 0 meters.
Above sea level the elevation will be above 0 meters. That will make the elevation to be positive
Below sea level the elevation will be below 0 meters. That will make the elevation to be negative.
Therefore, the best description for the elevation of Kristianstad is below sea level.
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Translate the following verbal expression into an algebraic expression.
Ten times a number plus seven times the same number.
Answer:
10x + 7(10x)
Step-by-step explanation:
X is the unknown number
Translate to an equation please.
four less than thirteen times a number is equal to that number added to eight
Hi
let call "a number" X.
then we have: 4-13X = X + 8 ..
