The constant term of the binomial expansion is 3.9344626e+22
How to determine the constant term of the binomial expansion?From the question, we have the following binomial expression that can be used in our computation:
(-3x⁷ + -2/x)⁴⁸
This expression can be rewritten
So, we have the following representation
(-3x⁷ + (-2/x))⁴⁸
The nth term of a binomial expression (a + b)ⁿ is represented as
(a + b)ⁿ ⇒ ⁿCₓaⁿ⁻ˣbˣ
This means that
a = -3x⁷
b = (-2/x)
n = a
So, we have the following representation:
ⁿCₐaⁿ⁻ᵃbˣ = ⁴⁸Cₐ(-3x⁷)ⁿ⁻ᵃ(-2/x)ᵃ
Expand
ⁿCₐaⁿ⁻ᵃbˣ = ⁴⁸Cₐ * (-3)ⁿ⁻ᵃ * (x⁷)ⁿ⁻ᵃ * (-2)ᵃ * (-1/x)ᵃ
By comparing both sides of the equation, we have the following equations"
Coefficient = ⁴⁸Cₐ * (-3)ⁿ⁻ᵃ * (-2)ᵃ * (-1)ᵃ
Like factors = (x⁷)ⁿ⁻ᵃ * (1/x)ᵃ
This gives
Like factors = (x⁷)ⁿ⁻ᵃ * (x⁻¹)ᵃ
Like factors = (x⁷)ⁿ⁻ᵃ * (x⁻ᵃ)
Apply the law of indices
Like factors = (x)⁷ⁿ ⁻ ⁷ᵃ ⁻ ᵃ
This gives
Like factors = (x)⁷ⁿ ⁻ ⁸ᵃ
So, we have
7n - 8a = 0
Where
n = 48 i.e. the number of terms
So, we have
7 * 48 - 8a = 0
This gives
8a = 7 * 48
Divide by 8
a = 42
Recall that:
Coefficient = ⁴⁸Cₐ * (-3)ⁿ⁻ᵃ * (-2)ᵃ * (-1)ᵃ
So, we have
Coefficient = ⁴⁸C₄₂ * (-3)⁴⁸⁻⁴² * (-2)⁴² * (-1)⁴²
This gives
Coefficient = 12271512 * (-3)⁶ * (-2)⁴²
Evaluate the products
Coefficient = 3.9344626e+22
So, the constant term is 3.9344626e+22
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A dairy farmer wants to mix a 45% protein supplement and a standard 15% protein ration to make 1200 pounds of a high-grade 40% protein ration. How many pounds of each should he use?
A dairy farmer needs to mix 450 pounds of protein supplement, 30 pounds of protein ration and 480 pounds of high-grade protein ration.
Given that, a dairy farmer wants to mix a 45% protein supplement.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Let x be number of pounds farmer wants to mix a 45% protein supplement.
Here,
0.45x + 0.15(1200-x) = 0.40(1200)
⇒ 0.45x +180-0.15x = 480
⇒ 0.30x=480-180
⇒ 0.30x=300
⇒ x=300/0.30
⇒ x=1000
Here, 45% of 1000
= 450 pounds
15% of (1200-100)
= 0.15×200
= 30 pounds
40% of 1200
= 480 pounds
Therefore, a dairy farmer needs to mix 450 pounds of protein supplement, 30 pounds of protein ration and 480 pounds of high-grade protein ration.
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Determine the value of x.
Answer:
14.5
Step-by-step explanation:
You would use cos for this. 12/cos 56 = 14.5...Therefore you would have 14.5
The value of x in the triangle using trigonometric identities is 14.5 units.
Option A is the correct answer.
We have,
Sin x = Perpendicular / Hypotenuse
Now,
From the triangle,
Sin 56 = 12/x
0.83 = 12/x
x = 12/0.83
x = 14.46
x = 14.5
Thus,
The value of x in the triangle is 14.5 units.
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Please answer the questions in the picture I will mark brainliest!!!
Answer:
AED=118
CED=118
Step-by-step explanation:
20+42=62
180-62=118
hence AED=118
hence CED=118
(VERTICALLY OPPOSITE ANGLE)
ASAP
Determine the value for x in the equation x over 6 and 4 tenths equals 3 and 6 tenths.
23.04
19.2
10.0
2.8
The value of variable x is 19.20.
How to solve equations ?Let's find the value of variable x in the equation.
A variable is a number represented with letters in an equation.
Therefore,
x / 6 + 4 / 10 = 3 + 6 / 10
Therefore, let's find the variable x.
10x + 24 / 60 = 30 + 6 / 10
10x + 24 / 60 = 36 / 10
60 × 36 = 10(10x + 24)
2160 = 100x + 240
2160 - 240 = 100x
1920 = 100x
divide both sides by 100
x = 1920 / 100
x = 19.20
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Help me please!!!! quick please :(
Answer:
One solution, One solution, Infinitely many solutions, One solution, No solutions
Step-by-step explanation:
There are no solutions if the equations represent parallel lines.
There is one solution if the equations represent intersecting lines.
There are infinitely many solutions if the equations can be manipulated to be exactly the same.
For each function, select whether it’s inverse is a function or not a function. refer to the attached picture.
Function
y=x⁴
y=x⁹
y=x⁸
y=x¹¹
The inverses of the functions y= x⁹ and y= x¹¹ are functions.
The inverses of the functions y = x⁴ and y= x⁸ are not functions.
How is the functionality of the given functions determined?(a )Consider ,the inverse of the function is a function
(2 ) y= x⁹
The inverse of the function is given by,
x = [tex]\sqrt[9]{y}[/tex]
Here y is an element of the real numbers.
i.e. y ∈R
So, this is a function.
(4) y= x¹¹
The inverse of the function is given by,
x = [tex]\sqrt[11]{y}[/tex]
Here y is an element of the real numbers.
i.e. y ∈R
Similarly , this is a function.
(b ) Consider ,the inverse of the function is a not a function
(1 )y = x⁴
The inverse of the function is given by,
x = [tex]\sqrt[4]{y}[/tex] (y ≥0)
It is of one- one correspondence,
when y = 4 ,
x = ±√2
Thus, it is not a function.
(3) y= x⁸
The inverse of the function is given by,
x = [tex]\sqrt[8]{y}[/tex]
Likewise , this is not a function.
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which function is positive for the entire interval 3 2
The graph is representing the function that is positive for the entire interval [-3 , -2] .
In the question ,
four graphs are given ,
we need to identify the graph of the function that is positive for the interval [-3 , -2] .
From the graphs given , we observed that
Graph1 :
the value of the function at -3 is 0 , and it is decreasing from [-3 , -2] . Thus the function is negative in the interval.
Grpaph2:
we can clearly see that the function has a positive value, through the interval [-3 , -2] .
In Graph3 :the value of the function is negative in the given interval . and in Graph4 : the value of the function is both positive and negative in the given interval .
Therefore , the function represented by Graph 2 is positive .
The given question is incomplete , the complete question is
Which function is positive for the entire interval [-3 , -2] from the given graphs ?
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The steps a student used to calculate 100 × (–3) × (–1.01) ÷ 3 are shown. What property did the student use in Step 2 and why?
Step 1. 100 × (–3) × (–1.01) ÷ 3 = 100 × (–3) × (–1.01) × 13
Step 2. = 100 × (–1.01) × (–3) × 13
Step 3. = (100 × (–1.01)) × (−3×13)
Step 4. = –101 × (–1)
Step 5. = 101
Answer:
Commutative Property
Switching (-1.01) with (-3) rearranges the problem so it's easier to calculate mentally.
Step-by-step explanation:
What is 6\9 reritten.
Answer:
Simplied:
2/3
Step-by-step explanation:
So basically so look at the factors and find that 6 and 9 both divided by 3 so 6/3=2 and 9/3=3
so 2/3
But if you are looking for equivalent:
8/12
6/9= 0.66 repeating which is 60/90 (I think)
HOPE THIS HELPS!!
Expand.
Your answer should be a polynomial in standard form.
−5qx^{2} ( − q − 5 ) =
The expansion of the polynomial expression is −5q²x² + 25qx²
How to expand the polynomial expression?The polynomial expression is given as
−5qx^{2} ( − q − 5 ) =
Rewrite the expression properly
So, we have the following representation
−5qx²(−q − 5)
Remove the bracket
So, the expression becomes
−5qx²(−q − 5) = −5qx² * −q −5qx² * − 5
Evaluate the products
−5qx²(−q − 5) = −5q²x² + 25qx²
Hence, the expanded expression is −5q²x² + 25qx²
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Leah has an action figure collection of 500 action figures. She keeps 430 of the action figures on her wall. What percentage of Leah’s action figure collection does she keep on her wall?
The percentage of Leah's action figure collection she kept in her wall is 86%.
What is percentage?Percentage is a number or ratio that can be expressed as a fraction of 100.
To calculate the percentage of Leah's action figure collection she kept in her wall, we use the formula below.
Formula:
W(%) = (W/T)×100Where:
W(%) = Percentage of Leah's action figure collection she kept in her wallW = Number of Leah's action figure collection she kept in her wallT = Total action figure collection of LeahFrom the question,
Given:
W = 430 action figure collectionT = 500 action figure collectionSubstitute these values into equation 1
W(%) = (430/500)×100 W(%) = 86%Hence, the percentage of Leah's action figure collection is 86%.
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Please answer and don't do it just for the points.
Answer:
15x, 5 * (x * 3)
Step-by-step explanation:
15x, 5 * (x * 3) >-<
Place value is important to know when you are talking about prices. What items have prices that are in the hundreds of dollars? thousands of dollars? tens of thousands of dollars? Think about the prices of items with place values in the hundreds, thousands and ten thousands. Give at least two examples of each.
In math, every digit in a number has a place value.
What is place value?Place value can be defined as the value represented by a digit in a number on the basis of its position in the number.
For example, the place value of 7 in 3,743 is 7 hundreds or 700. However, the place value of 7 in 7,432 is 7 thousands or 7,000. Here, we can see that even though the digits are same in both the numbers, it’s place value changes with the change in it’s position.
The place value of a digit increases by ten times as we move left on the place value chart and decreases by ten times as we move right.
From the question;
Prices for items in the value of hundreds
A smartphone - $100Nike Jordan's - $156Prices for items in the value of thousands
A smart TV - $1,500A MacBook Pro - $2,550Prices for items in the value of ten thousands
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What are 2 ways to solve a division problem?
Answer: Put it as a fraction then divide the numerator by the denominator but they have to be divided by the same number. Or just divide.
Step-by-step explanation:
How do you find the missing side of a congruent triangle?
Triangles that are exactly the same in size and shape are said to be congruent. Two triangles are said to be congruent when their corresponding sides and angles are also congruent.
What is Traingle?
A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.
Using the Triangle Sum Theorem, we can determine the third angle in a triangle when only two angles are known.
The two angles' combined angles are subtracted from 180 degrees.
The diagram needs a third angle. Try to match the angles and sides of two triangles with the provided information if the congruence statement is not provided in the problem.
List the corresponding vertices in the same order once the vertices of the two triangles have been matched. The congruence assertion reads as follows if vertex A relates to vertex D, vertex B to E, and vertex C to F:
△ABC≅△DEF
Congruent triangles are two triangles that are the same size and shape. Two congruent triangles are still congruent even if we flip, spin, or otherwise alter one of them.
Two triangles must have the same angles and, as a result, must be congruent if their sides are the same. If two triangles are congruent or not, we may determine this simply by looking at their sides.
These two triangles are also equivalent if we know that two sides of one triangle and the angle between them are congruent to two sides and the angle between them of another triangle.
Likely, these two triangles are congruent if we know that two angles and the side between them in one triangle are congruent with two angles and the side between them in another triangle.
When two angles and a non-included side in a triangle are congruent to one another, this is the final scenario that results in congruent triangles.
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(b) Circle the two pairs of numbers that have
Highest Common Factor (HCF) 4 \4 and
Least Common Multiple (LCM) 60
The pairs of numbers that have HCF 4 and LCM 60 are : 4 and 60 , 12 and 20.
What is LCM and HCF?In this case, we must use the following relationship between HCF and LCM:
Number 1 + Number 2 = HCF x LCM
In other words, multiplying both factors equals multiplying the given numbers that we are looking for. We don't know the numbers yet, but we can get an idea of what they could be by calculating the product of the factors:
4 x 60 = 240
We know that the products should be 240 and that if the HCF is 4 , then both numbers can be divided by 4 as the highest factor, so let's write the multiple of 7:
4-digit multiples:
4, 8, 12, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60
By using, we can get an idea: if 60 x 4 = 240, all we need to do is find the other two numbers that result in 240:
So the pairs of numbers are 4 and 60 , 12 and 20.
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A semimonthly salary of $985 is less money per year than a biweekly salary of $912.
Answer: A semimonthly payroll is paid twice a month, usually on the 15th and last days of the month. If one of these pay dates falls on a weekend, the payroll is instead paid out on the preceding Friday. A biweekly payroll is paid every other week, usually on a Friday.
Step-by-step explanation:
Evaluate 732,178 + 167 - 542,137 =
Answer: 190208
Step-by-step explanation:
what is the value of this expression when w 5 w2 3w 11 a 51 b 36 c 16 d 1
The value of this expression when w = -5 in w² + 3w - 11 is -1
Algebraic expressions comprises of at least one variable and one operation, it is an expression built up from integer constants, variables, and the algebraic operations
We need to find the value of this expression when w = -5 in w² + 3w - 11
After substituting the value of x as 5, we get the expression as
5² + 3(-5) - 11
25 - 15 - 11
25 - 26
= -1
Therefore, the value of this expression when w = -5 in w² + 3w - 11 is -1
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Help with my math please
Answer:
$27,000 at 8%$3,000 at 7%Step-by-step explanation:
You want the amounts invested in each of two accounts, one earning 7% and the other earning 8% simple interest, when the total investment of $30,000 earns total interest of $2370.
SetupLet x represent the amount invested at 8%. Then the amount invested at 7% is 30000-x. The total interest earned is ...
0.08(x) +0.07(30000-x) = 2370
Solution0.01x +2100 = 2370 . . . . simplify
0.01x = 270 . . . . . . . . subtract 2100
x = 27000 . . . . . . . multiply by 100
30000-x = 3000
Deshaun invested $27,000 at 8% and $3,000 at 7%.
equation for line using exact numbers
Answer:
y= -0.5x -3.5
Step-by-step explanation:
y= mx+b is the slope intercept form
m- slope
b- y intercept
we can find slope using slope formula
y2-y1/x2-1
Using (1,-4) and (3,-5)
-5-(-4)/3-1
-5+4/2
-1/2
-0.5
Now we can fill this is
y= -0.5x
And we can find the exact y intercept by inserting the coordinates to find b
-5=-0.5(3)+b
-5= -1.5=b
+1.5 +1.5
-3.5=b
Now we can write the equation as
y= -0.5x -3.5
Hopes this helps please mark brainliest
Suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model. A sample of 1100 bacteria selected from this population reached the size of 1257 bacteria in six hours. Find the hourly growth rate parameter
.Note: This is a continuous exponential growth model.
Write your answer as a percentage. Do not round any intermediate computations, and round your percentage to the nearest hundredth.
The hourly growth rate parameter is equal to 2.22%.
How to determine the hourly growth rate parameter?In Mathematics, an exponential function simply refers to a mathematical function whose values are generated by a constant that is raised to the power of the argument.
Mathematically, an exponential function can be modeled by using this equation:
A(t) = ae^{kt}
Where:
a represents the initial value.t represents time.k represents the rate of change or growth rate.Based on the information provided, we have the following:
A(t) = 1100e^{6k} .....equation 1.
A(6) = 1257 .....equation 2.
Equating the two equations, we have:
1100e^{6k} = 1257
e^{6k} = 1257/1100
e^{6k} = 1.1427
Taking the natural log (ln) of both sides of the equation, we have:
6k = ln(1.1427)
6k = 0.1334
Hourly growth rate, k = 0.1334/6
Hourly growth rate, k = 0.0222
As a percentage, we have:
Hourly growth rate, k = 0.0222 × 100
Hourly growth rate, k = 2.22%.
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Identify the recursive formula for the sequence 900, 850, 800, 750,...
C (3rd Answer)
1st term is 900 and as n increases (number of terms increase), each time it goes down by 50 if n is greater than 1.
what is the center of a circle whose equation is x2 y2 12x 2y 12 0
The center is (6, 1) of the given circle with the equation x²+y²-12x-2y+12=0.
What are circles?Simply put, a circle is a rounded shape without any edges or line segments. It has the geometric shape of a closed curve.
A circle is a closed shape that can be created by following a moving point in a plane while maintaining a constant distance from another point.
The Greek word kirks, which means hoop or ring, is whence the word circle gets its form.
So, we have the equation: x²+y²-12x-2y+12=0
Compared to the circle's basic equation:
2 + y² + 2gx + 2fy + c = 0
2g = -12, 2f = -2, c = 12
g = -6, f = -1
Centre = (-g, -f)= (6, 1)
Now, fill in the square:
x² - 12x + 36 + y² - 2y + 1 = -12 + 36 + 1
(x - 6)² + (y - 1)² = 25
(x - 6)² + (y -1)² = 52
When compared to the equation for a circle with the centers at (h, k) and radius "r," Centre = (h, k) = (6,1).
Therefore, the center is (6, 1) of the given circle with the equation x²+y²-12x-2y+12=0.
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Correct question:
What is the center of a circle whose equation is x²+y²-12x-2y+12=0?
Answer:
6,1
Step-by-step explanation:
trust me
The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 7 to 4. If there were
10,164 total votes, how many yes votes were there?
Answer:
There are 6468 yes votes
Step-by-step explanation:
10164÷(7+4)×7
=10164÷11×7
=924×7
=6468
What is linear inequality examples?
The linear inequality examples are as follows,
What is linear inequality?
Any two real numbers or two algebraic expressions associated with the symbol ‘<’, ‘>’, ‘≤’ or ‘≥’ form a linear inequality. For example, 9<11, 18>17 are examples of numerical inequalities and x+7>y, y<10-x, x ≥ y > 11 are examples of algebraic inequalities.
The examples of linear inequalities in two variables are:
3x < 2y + 5
8y – 9x > 10
9x ≥ 10/y
x + y ≤ 0
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What is root domain example?
The root domain in the DNS system of the Internet is a domain that is indicated by an empty name (i.e., containing no characters).
Each domain is split from the next when you enter a domain name, and there may also be a dot at the end of the name to demarcate the empty name for the root domain. If this dot is present and in its proper location, such as "www.example.com," the domain name is regarded as full (absolute). The name is regarded as relative if there isn't a dot at the end ("www.example" or "www.example.com").
Even if the phrase "root domain" was frequently used, the primary domain name of the website is the one that must be purchased or registered with a TLD extension.
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A box is 36 inches long,18 inches wide, and 6 inches deep. How many
cubic feet are in the box?
A 2.25 cubic feet
B) 4.5 cubic feet
C) 5 cubic feet
D) 3 cubic feet
Answer:
A
Step-by-step explanation:
The volume in cubic inches is [tex](36)(18)(6)=3888[/tex].
This is equal to [tex]3888/12^3=2.25[/tex] cubic feet.
A Fibonacci-type sequence that has been studied by mathematicians is the Lucas sequence, named after a French mathematician of the nineteenth century. The first ten terms of the Lucas sequence are 1, 3,
4,7, 11, 18, 29, 47, 76,123 what
is the
term of the Lucas
The eleventh term of the Lucas sequence is?
The eleventh term of the Lucas' sequence is 199
How to determine the eleventh term of the sequence?From the question, we have the following parameters that can be used in our computation:
1, 3, 4,7, 11, 18, 29, 47, 76,123
As a general rule of Fibonacci, the current term of a sequence is the sum of the two previous terms
This means that
11th term = 10th term + 9th term
Substitute the known values in the above equation, so, we have the following representation
11th term = 123 + 76
Evaluate the sum
11th term = 199
Hence, the 11th term is 199
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Function and function notation
Please help asap
The value of function f(1/2) = 9.
What is function?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between input variables in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x seems to be the input. A function is typically represented as y = f. (x). In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) as well as their outputs (also referred to as the codomain), where each input does have exactly one output and the output could be linked to its input.
Given function f(x) = (4+x)/x
put x = 1/2,
f(x) = (4+1/2)/1/2
f(x) = 9/2/1/2
f(1/2) = 9
Now f(3) = (4+3)/3
=7/3
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