Answer:
a) [tex](3x)^{15} + 15(3x)^{14}(\frac{2}{x}) + 105(3x)^{13}(\frac{2}{x})^2 + ... + 15(3x)(\frac{2}{x})^{14} + (\frac{2}{x})^{15}[/tex]
b) [tex](2x)^{20} + 20(2x)^{19}(-\frac{3}{x}) + 190(2x)^{18}(-\frac{3}{x})^2 + ... + 20(2x)(-\frac{3}{x})^{19} + (-\frac{3}{x})^{20}[/tex]
Step-by-step explanation:
The binomial expansion formula is:
[tex](a + b)^n = a^n + \binom{n}{1}a^{n-1} b + \binom{n}{2}a^{n-2}b^2 + ... + \binom{n}{r}a^{n-r}b^{r} + ... + b^n[/tex]
The (n r) in front of each term is the binomial coefficient. This can be calculated on a calculator using the nCr button (in this case, you'd put 15C1 for (n 1), 15C2 for (n 2), etc). This can be calculated without a calculator using this formula:
[tex]\binom{n}{r} = \frac{{n!}}{{r!\left( {n - r} \right)!}}[/tex]
In a), a = 3x, b = 2/x and n = 15.
You can plug these into the formula above to get:
[tex](3x)^{15} + 15(3x)^{14}(\frac{2}{x}) + 105(3x)^{13}(\frac{2}{x})^2 + ... + 15(3x)(\frac{2}{x})^{14} + (\frac{2}{x})^{15}[/tex]
Here's how to do this without the formula:
Start with the a^nIn the second term, you subtract 1 from a's power (in this case, 15 to 14) and add 1 to b's power (0 to 1). Then you multiply it by nCr.This keeps going until you get to b^n. To check you've done it correctly, the powers of a and b in each term should add up to n. For example, in term 3 above, a's power is 13 and b's power is 2. These add to make 15.Remember, a's power goes down by 1 each time, and b's power goes up by 1 each time. There is no b in the first term because b^0 = 1.You could 'simplify' this by expanding the brackets, but this gives you massive numbers so it's probably best to leave it like this.
Applying this to b):
a = 2x, b = -3/x, n = 20
[tex](2x)^{20} + 20(2x)^{19}(-\frac{3}{x}) + 190(2x)^{18}(-\frac{3}{x})^2 + ... + 20(2x)(-\frac{3}{x})^{19} + (-\frac{3}{x})^{20}[/tex]
Maria orders t-shirts for her volleyball camp. Adult-sized T-Shirts cost $6.25 each and youth-sized T-Shirts cost $4.50. Maria has $550 to purchase both adult-sized and youth-sized T-Shirts. If she purchases 45 youth-sized T-Shirts, determine algebraically the maximum number of adult-sized T-Shirts she can purchase.
Answer:
55
Step-by-step explanation:
45 * 4.50 = 202.5
550 - 202.5 = 347.5
347.5/6.25 = 55.6 (55 full t shirts)
How does human behavior explain why the demand line slopes downward?
The decreasing of the prices and increasing of buying are correlated with the human behavior.
What is a Demand Graph ?Demand graph is the curve in the study of economics which tells us about the number of units purchased or the demand of the product with respect to the price.
The demand line slopes downward means the price is decreasing and more people are buying it.
The increase in the buying of the goods on decreasing prices is affected by human behavior as when the price decrease , the middle class people have a tendency to buy more quantity and
even there is need to satisfy unsatisfied wants , If a product was costlier before and the prices have decrease then to satisfy the wants , the people buy it ,
Hence decreasing of the prices and increasing of buying are correlated with the human behavior.
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Prove: ∠1 and ∠14 are supplementary angles.
Answer:
can you please send the images of figure of these angle
What is the value of x in the diagram
Answer:
51°
Step-by-step explanation:
the given angle of 102° is the arc angle between the 2 segment end points on the circle arc.
and this arc angle is always a seen from the center of the circle.
by moving the reference point back (to the other side of the circle) to the circle arc that angle is cut in half.
you could move that point to anywhere on the arc of the circle outside of the 2 endpoints, and the angle stays always the same.
FYI - now, if you move that point into the top half-circle between the 2 end points, the perspective flips around, and that angle becomes half of the 360-102 = 258° arc angle.
rearrange the equation 12n + 3px = 7px
From factoring, the given equation can be rearranged as [tex]x=\frac{3n}{p}[/tex].
Factoring
In math, factoring or factorization is used to write an algebraic expression in factors. There are some rules for factorization. One of them is a factor out a common term for example: x²-x= x(x-1), where x is a common term.
For solving this question, the given equation should be rewritten using the variables n and p in different sides. After that, you should factor out a common term.
[tex]12n + 3px = 7px\\ \\ 12n=7px-3px\\ \\ 12n=4px\\ \\ x=\frac{12n}{4p} =\frac{4*3n}{4p}=\frac{3n}{p}\\ \\ x=\frac{3n}{p}[/tex]
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Given the graph, which coordinate point is NOT a solution?
Answer: (1, 2) (The third option)
Step-by-step explanation: A solution has to be on the line. (1, 2) is the only point that isn't on the line.
Part 1 - Application
If the length of an arc of a circle of radius 7 is approximately 10.99 cm. What is the measure of the central
angle associated with the arc? Use 3.14 for It. Give your answer in degrees and radians (approximate to two
decimals and exact).
The measure of the central angle is 89.95 degree or 1.57 radians if the radius of the circle is 7 cm.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the centre of a circle)
We have a length of an arc of a circle of radius 7 is approximately 10.99 cm.
The radius r = 7 cm
The arc length l = 10.99 cm
We know,
l = rθ
θ is the central angle.
θ = l/r = 10.99/7 = 1.57 radians
To convert 1.57 radians into the degree multiply it by 180/π
θ = 89.95 degree
Thus, the measure of the central angle is 89.95 degree or 1.57 radians if the radius of the circle is 7 cm.
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What are the coordinates of the point where the line y = -x +5 intersects the x-axis?
O (0, -3)
O (0,3)
O (-3,0)
0 (3,0)
The answer is (3,0)
Sure hope this helps you
Which equation is represented by the graph below ?
The equation that represent the graph is y = (1/2)eˣ , Option B is the correct answer.
What is an Exponential Function ?An exponential function is what is denoted as y = eˣ
The graph has to be studied and the equation has to be determined.
To determine we will consider x = 0 for all the equation ,. which will give the y intercept , which is below 1 so Option C and D are stroked out.
Now we plot the graph for equation A and B
It can be easily understood from the graph that at x =0 , y = 0.5
Therefore , the equation that represent the graph is
y = (1/2)eˣ
Option B is the correct answer.
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Identify the type of function represented by f(x) = 2(1/2)^x
A. Exponential growth
B. Linear
C. Exponential decay
OD. Quadratic
Answer:
C) Exponential Decay
Step-by-step explanation:
Because the base inside of the parentheses is less than 1, the function will only get exponentially smaller over time.
A function and its inverse are shown on the same graph. Complete the sentences to compare the functions.
The y-intercept of f(x) has the same value as the ___
f(x)
The function(x) has a range including all values
greater than or equal to 0; therefore the, ____ does also.
The y-intercept of f(x) has the same value as the x-intercept. The function f⁻¹(x) has a range including all values greater than or equal to 0; function f(x) does also.
What is a function?Functions are found all across mathematics and are required for the creation of complex relationships.
A function and its inverse are shown on the same graph.
Complete the sentences to compare the functions.
The y-intercept of f(x) has the same value as the x-intercept.
The function f⁻¹(x) has a range including all values greater than or equal to 0; function f(x) does also.
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Use technology, what is the solution to this system? 4x+8y=30
Answer:
y=-1/2x+15/4
Step-by-step explanation:
transfer the equation into slope intercept form. subtract 4x from each side getting 8y=-4x+30 then divide by 8.
Kenji is using walnuts to bake muffins and granola for his restaurant. each batch of muffins
1
pound of walnuts. he needs 2 pounds of walnuts to make granola. kenji can use up
2
to 8 pounds of walnuts and still have enough for baking tomorrow.
uses
let b represent the number of batches of muffins kenji makes.
write an inequality that represents the situation.
Answer:
Step-by-step explanation:
1/2b + 2 ≤ 8
b ≤ 12
Answer:
Step-by-step explanation:
Stock for the jones corporation starts with a value of $39.63 and gains $0.30 in value per month. stock for the overton company starts with a value of $24.45 and gains $0.80 in value per month. when are the two stocks nearly equal in value?
Using linear functions, it is found that the two stocks will be nearly equal in 30 months.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Each of the stocks can be modeled by these following functions:
S1(t) = 39.63 + 0.3t.S2(t) = 24.45 + 0.8t.They will be equal when:
S1(t) = S2(t).
Hence:
39.63 + 0.3t = 24.45 + 0.8t
0.5t = 15.18
t = 15.18/0.5
t = 30.36.
Rounding, approximately 30 months.
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1. The area of a rectangular carpet is X² + X - 2. HINT: Area = length X breadth
a). if X is a whole number, use factorization to find the length and the breadth of the carpet in terms of X.
b). if X = 2 m, find the actual dimensions of the carpet.
c). it costs R50 per square metre to make such this carpet. how much will it cost to manufacture 5 carpets?
Answer:
look above
Step-by-step explanation:
hopeit hepls
Which polynomial is prime?
O x²+x+1
O x²-x-2
O x²-12x + 11
Ox²+2x-8
Answer:
The correct answer is x^2 + x + 1.
Step-by-step explanation:
A prime polynomial is one that cannot be factored. To solve this problem, we can use the process of elimination by eliminating all answer choices that can be factored.
x^2 - x - 2 = (x - 2)*(x + 1)
x^2 - 12x + 11 = (x - 11)*(x - 1)
x^2 + 2x - 8 = (x + 4)*(x - 2)
Since we cannot factor x^2 + x + 1, and we can factor all of the other answer choices, we know that x^2 + x + 1 is the answer.
Hope this helps!
What is the distance between the following points?
Answer:
B
10
Step-by-step explanation:
go up 7 then over 3, add them together and you got 10
Help pls i will give 10 points
Answer:
1/4 for blue and 3/8 for green
Step-by-step explanation:
2 blue sections out of 8
2/8 simplified is 1/4
3 green sections out of 8
3/8 is the simplest form
While traveling to europe, phelan exchanged 250 us dollars for euros. he spent 150 euros on his trip. after returning to the united states he converts his money back to us dollars. how much of the original 250 us dollars does phelan now have? round to the nearest cent.while traveling to europe, phelan exchanged 250 us dollars for euros. he spent 150 euros on his trip. after returning to the united states he converts his money back to us dollars. how much of the original 250 us dollars does phelan now have? round to the nearest cent. 1 european euro = 1.3687 us dollars
Answer:
$44.69
Step-by-step explanation:
150 x 1.3687 = $205.305 = $205.31
250 - 205.31 = $44.69
(Hope this helps ^-^)
Answer
44.70 US dollars
Step-by-step explanation: Edg right? If thats what youre reffering too then this is correct
what land is under muslim rule
Answer:
Under Islamic law, land ownership is classified into two main categories, frrstly, according to the mode of acquisition or how land came into the possession and ownership of the individual and secondly according to the type of taxation.
Answer:
Are you Muslim I think Pakistan or Saudi
If f(x)=8-10x and g(x) =5x +4, what is the value of (fog)(-2)?
Answer:
68
Step-by-step explanation:
Any function is evaluated by putting the argument value where the variable is, then doing the arithmetic. When the argument is another function value, that function value is evaluated first.
__
f∘gThe "o" in (fog) is a stand-in for the "ring operator" (∘) which is the operator used to signify a composition. A composition is evaluated right-to-left. That means (f∘g)(x) ≡ f(g(x)). The value of g(x) is found first, and is operated on by the function f.
Writing the composition in the form f(g(x)) lets you identify the layers of parentheses. As with any expression evaluation, the Order of Operations applies. It tells you to evaluate the expression in the innermost parentheses and work your way out.
g(-2)To evaluate (f∘g)(-2) = f(g(-2)), we must first evaluate g(-2). That is ...
g(x) = 5x +4
g(-2) = 5(-2) +4 = -10 +4 = -6 . . . . . put -2 where x is, do the math
f(g(-2))Now that we know g(-2) = -6, we know this expression is ...
f(-6) = 8 -10(-6) = 8 +60 = 68 . . . . . substitute for x in 8-10x
Then the value we're looking for is ...
(f∘g)(-2) = 68
Find the Area (Need help ASAP)
Answer:
32
It wont always be easy, but always try to do what ' s right!
In a world of worriers, be the warrior!
When nothing goes right, go left.
What is the formula for the nth term of the sequence 2,4,8,16,32
Answer:
Below in bold.
Step-by-step explanation:
4/2 = 2
8/4 = 2
Each term is obtained by multiplying the previous one by 2.
This is a geometric sequence with common ratio r = 2
the nth term
= a1r^(n-1) where a1 = the first term
= 2(2)^(n-1).
[tex] a_{n} = 2_{n}[/tex]
Step-by-step explanation:
[tex]a_{1} = 2[/tex]
[tex]d = a_{2} - a_{1}[/tex]
[tex] = 4 - 2 = > 2[/tex]
Getting the nth term
[tex]a_{n} = a_{1} + (n - 1)d[/tex]
[tex] a_{n} = 2 + (n - 1)2[/tex]
[tex] a_{n} = 2 + (2n - 2)[/tex]
[tex]a_{n} = 2 + 2n - 2[/tex]
[tex] a_{n} = 2n[/tex]
Find the interest and the amount repaid.
Principal 500.00
Rate 12%
Time 18 months
what is the amount
Answer:
3844.98
Step-by-step explanation:
Use this formula: P(1+b)^x
500(1.12)^18 (put in calculator).
Hope this helps!
If not I am sorry.
What values of c and d make the equation true? Assume x>0 and 20.
3
50x6y³ 5y √√2y
=
O c = 1, d = 3
O c = 1, d = 9
O c = 2, d = 8
O c = 2, d = 9
Answer:
c=1 and c=3
Step-by-step explanation:
If x>0 and y>0, then
\sqrt{\dfrac{50x^6y^3}{9x^8}}=\sqrt{\dfrac{25\cdot 2y^2\cdot y}{9x^2}}=\dfrac{5y\sqrt{2y}}{3x}.
9x
8
50x
6
y
3
=
9x
2
25⋅2y
2
⋅y
=
3x
5y
2y
.
If
\dfrac{5y\sqrt{2y}}{3x}
3x
5y
2y
is equal to
\dfrac{5y^c\sqrt{2y}}{dx},
dx
5y
c
2y
,
then
\begin{gathered}y=y^c\Rightarrow c=1,\\ \\3x=dx\Rightarrow d=3.\end{gathered}
y=y
c
⇒c=1,
3x=dx⇒d=3.
1 Pound brown sugar is equivalent to _____ cups.
Answer:
3 1/2 or 3.5 cups is equal to 1 pound
Step-by-step explanation:
1 Pound brown sugar is equivalent to ___3 1/2 or 3.5__ cups.
Hope This Helped
Answer:
3½ cups
Step-by-step explanation:
Question 4.
The angle of elevation of the top of a tree from a point on the ground 22 m away is 24⁰°.
Calculate the height of the tree (in metres) correct to 2 decimal places.
22 m
tree
Answer:
9.80 m
Step-by-step explanation:
The mnemonic SOH CAH TOA is intended to remind you of the relationship between sides of a right triangle and its angles.
__
setupThe geometry of this problem can be modeled by a right triangle, so these relations apply. We are given an angle and adjacent side, and asked for the opposite side, so the relation of interest is ...
Tan = Opposite/Adjacent
Using the given values, we have ...
tan(24°) = AC/AB = (tree height)/(distance from tree)
tan(24°) = AC/(22 m)
solutionMultiplying by 22 m gives ...
tree height = AC = (22 m)·tan(24°) ≈ 9.79503 m
The height of the tree is about 9.80 meters.
You have just invested 1,500 into a stock compounded yearly at a rate of 9%. How much money will be in your account in 60 days? (Please explain)
Answer:
1522.584
Step-by-step explanation:
1500(1+.09/12)^2=1522.584
In the figure below, which term best describes point X?
B
OA. Centroid
OB. Incenter
O C. Circumcenter
OD. Orthocenter
Answer:
Centroid
Step-by-step explanation:
It is a centroid because x is the center of the triangle
may I get brainliest?
Hope this helps :)
The term best describes point X is option A. Centroid.
What is the centroid of a triangle and its coordinates?The point of intersection of a triangle's medians is its centroid (the lines joining each vertex with the midpoint of the opposite side).
here, we have,
If the surface is plane triangle approximately and mass is uniformly distributed, then its center of mass will lie on the centroid of that triangle.
we have,
If the triangle has its vertices as (x1, y1) (x2,y2) (x3,y3)
then the coordinates of the centroid of that triangle is given by:
(x, y ) = (x1+x2+x3/3 , y1+y2+y3/3 )
Hence, The term best describes point X is option A. Centroid.
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If the triangle on the grid below is translated by using the rule (x, y) right-arrow (x + 5, y minus 2), what will be the coordinates of B prime?
On a coordinate plane, triangle A B C has points (negative 1, 0), (negative 5, 0), (negative 1, 2).
(–2, 0)
(0, –2)
(5, –7)
Using translation concepts, it is found that the coordinates of the image of point B is given by: (0, –2).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the rule is given by:
(x,y) -> (x + 5, y - 2).
Hence, the image of point B, given by B', is:
(-5,0) -> (-5 + 5, 0 - 2) -> (0,-2).
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