The expansion of g(x) = 8x - 1 in powers of (x - 1) is 7 + 8(x - 1).
To expand g(x) = 8x - 1 in powers of (x - 1), we use Taylor series expansion around the point x = 1. The Taylor series expansion is given by:
g(x) = g(1) + g'(1)(x - 1) + (1/2)g''(1)(x - 1)^2 + ...
First, find the derivatives of g(x) = 8x - 1:
g'(x) = 8
g''(x) = 0 (and all higher-order derivatives are also 0)
Now, evaluate these derivatives at x = 1:
g(1) = 8(1) - 1 = 7
g'(1) = 8
g''(1) = 0
Now substitute these values into the Taylor series expansion:
g(x) = 7 + 8(x - 1) + 0
Simplifying, we get:
g(x) = 7 + 8x - 8
So, the expansion of g(x) = 8x - 1 in powers of (x - 1) is:
g(x) = 8x - 1 = 7 + 8(x - 1).
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5.a.A tourist buys 5 pieces of Nepali cap at Rs 452 per piece including 13% VAT. How much will he recive while leaving Nepal?
Step-by-step explanation:
vat of a cap=13/100*452
=58.76
price after vat=58.76+452=510.76
price after vat of 5 cap = 510.76*5=2553.8
You have 35 coins. they are all quarters and nickels. if you have $3.15, how many nickels and how many quarters do you have?
Answer:
Step-by-step explanation:
You have 35 coins. they are all quarters and nickels. if you have $3.15, how many nickels and how many quarters do you have?
which is most likely to be the first step in solving a system of nonlinear equations by substitution
The correct option is C. Isolating a variable in one of the equations.
The first step in solving a system of nonlinear equations by substitution is to isolate a variable in one of the equations.
What is system of nonlinear equations?A set of two or more equations in two or more variables that includes at least one nonlinear equation is referred to as a system of nonlinear equations.
The method to solve a system of nonlinear equations by substitution is-
Figure out each equation's graph.One of the equations should be solved for either variable.Fill in the other equation using the expression from step 2.Put the resultant equation to use.The importance of systems of nonlinear equations are-
They aid in a lot of our everyday predictions. In addition, nonlinear equations need not involve numbers. Sometimes you have to deal with the numbers, but more often than not you are only dealing with the graph's shape, and in such case it pays to be aware of the characteristics of certain shapes.To know more about the system of equations, here
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The complete question is-
Which is most likely the first step in solving a system of nonlinear equations by substitution?
A. Substituting a number for one of the variables
B. Substituting one equation into the other equation
C. Isolating a variable in one of the equations
D. Taking the square root of both sides of one of the equations
Answer:
Isolating a variable in one of the equations.
Step-by-step explanation:
Abc co issues a zero coupon bond with 5 years to maturity. investor's required rate of return is 3.25%, what is the price of the zero coupon bond issued?
Based on the number of years till maturity and the required rate of return, the price of the zero-coupon bond is $852.22.
what price is the zero coupon bond selling at?When a bond's par value is not given, assume it is $1,000.
the price of a zero coupon bond is:
= par value / (1 + rate) ^ number of years till maturity
solving gives:
= 1,000 / (1 + 3.25%)⁵
= 1,000 / 1.17341139582939453125
= $852.22
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Determine whether the function f(x) = 3x is even or odd.
The function is even because f(-x) = f(x).
The function is odd because f(-x) = f(x).
The function is even because f(-x) = -f(x).
The function is odd because f(-x) = -f(x).
Answer:
A. f(-x) = f(x)
Step-by-step explanation:
When plugged into a graph, we can see that the y value of -x is equal to x.
This means, that if we compare the y value of x=3 and x=-3, they will be the same on the graph.
Can someone help me out on these geometry questions? ASAP!!!
Write formal proofs the HL Theorm.
Question 2
1) [tex]\overline{PR} \perp\overline{QS}, \overline{PQ} \cong \overline{PS}[/tex] (given)
2) [tex]\overline{PR} \cong \overline{PR}[/tex] (reflexive property)
3) [tex]\angle PRQ, \angle PRS[/tex] are right angles (perpendicular lines form right angles)
4) [tex]\triangle PRQ, \triangle PRS[/tex] are right triangles (a triangle with a right angle is a right triangle)
5) [tex]\triangle PRQ \cong \triangle PRS[/tex] (HL)
Question 3
1) [tex]\angle C[/tex] is a right angle, [tex]\overline{AC} \cong \overline{AE}, \overline{DE} \perp \overline{AB}[/tex] (given)
2) [tex]\angle DEA[/tex] is a right angle (perpendicular lines form right angles)
3) [tex]\triangle ACD, \triangle DAE[/tex] are right triangles (a triangle with a right triangle is a right angle)
4) [tex]\overline{AD} \cong \overline{AD}[/tex] (reflexive property)
5) [tex]\triangle ACD \cong \triangle AED[/tex] (HL)
6) [tex]\angle CAD \cong \angle DAE[/tex] (CPCTC)
7) [tex]\overline{AD}[/tex] bisects [tex]\angle BAC[/tex] (if a segment splits an angle into two congruent parts, it is an angle bisector)
As an oak tree grows taller, it also grows wider. In other
words, the diameter of its trunk increases. Imagine that a
tree's height is about 8 times its diameter. Assume this
relationship will not change, and that the tree trunk is a
rather cylindrical shape. Write a function for the volume of
wood in the tree's trunk as it grows
The volume of wood in the tree's trunk as it grows is [tex]16\pi r^3[/tex]
The capacity of a cylinder, which determines how much material it can carry, is determined by the cylinder's volume. There is a formula for the volume of a cylinder that is used in geometry to determine how much of any quantity, whether liquid or solid, may be immersed in it uniformly. A cylinder is a three-dimensional structure having two parallel, identical bases that are congruent.
Thus, the volume (V) of a right circular cylinder, using the above formula, is, [tex]V = \pi r^2h[/tex] , where
'r' is the radius of the base (circle) of the cylinder
'h' is the height of the cylinder
Given:
Height(h) = 8 x diameter = 16 x radius (r) (diameter = 2 x radius )
∴ h = 16r.
V= [tex]\pi r^2h[/tex]
Substituting h = 16r in the volume formula we get
V = [tex]\pi r^2(16r)[/tex] = [tex]16\pi r^3[/tex]
Thus the volume of wood in the tree's trunk as it grows is [tex]16\pi r^3[/tex].
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what is the potential energy of a rock that weighs 100 newtons that sits on a hill 300 meters high
Answer:
30000J or 30 KJ
Step-by-step explanation:
Formula for finding Gravitiational Potential Energy or GPE = mgh (or Wh since W = mg)
Given
W = 100N
h = 300m,
GPE = Wh = 100 x 300 = 30000J or 30 KJ
The cost of attending an amusement park is $10 for children and $20 for adults. On a particular day, the attendance at the amusement park is 30,000 attendees, and the total money earned by the park is $500,000. Use the matrix equation to determine how many children attended the park that day. Use the given matrix equation to solve for the number of children’s tickets sold. Explain the steps that you took to solve this problem.
Using a system of equations, it is found that 10,000 children attended the park that day.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable c: Number of children in the park.Variable a: Number of adults in the park.The attendance at the amusement park is 30,000 attendees, hence:
c + a = 30,000, which is the first equation in matrix form.
Then:
a = 30,000 - c
The cost of attending an amusement park is $10 for children and $20 for adults. The total money earned by the park is $500,000, hence:
10c + 20a = 500,000, which is the second equation in matrix form.
Since a = 30,000 - c, we replace:
10c + 20a = 500,000
10c + 20(30000 - c) = 500,000
10c = 100,000
c = 10,000.
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PLEASE HELP IM STUXK
Which graph represents a reflection across the x-axis of g(x) = Three-fourths(3)x?
On a coordinate plane, an exponential function approaches y = 0 in quadrant 4. The function comes up from quadrant 3 and increases into quadrant 4. It goes through (negative 2, negative 5), (0, negative 3), and (4, negative 1).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 3. It comes up from quadrant 4 and increases and curves into quadrant 3. It goes through (2, negative 6), (0, negative 1).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 1. It increases into quadrant 2 and goes through (negative 1, 2) and (negative 2, 6).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 2. It increases into quadrant 1 and goes through (1, 2) and (2, 6).
Using translation concepts, the graph that represents a reflection across the x-axis of [tex]g(x) = \frac{3}{4}(3)^x[/tex] is:
On a coordinate plane, an exponential function approaches y = 0 in quadrant 4. The function comes up from quadrant 3 and increases into quadrant 4. It goes through (negative 2, negative 5), (0, negative 3), and (4, negative 1).
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.
A reflection across the x-axis of g(x) means that:
f(x) = -g(x).
g(x) increases from the second quadrant into the first, hence for f(x) it will be from quadrant 3 into quadrant 4.
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Answer:
Option B
Step-by-step explanation:
Edge 2022
What is the domain of f(x)=
F(X). 4)*
?
A. x>0
B. All real numbers
C. y> 0
D. x<0
Answer: All real numbers
Step-by-step explanation:
The domain is the set of inputs.
Which equations are correct? select three options. n = 10 n = 7 cf = 59 fe = 42 cd = 30
Based on the calculations on this parallelogram, the correct equations are:
n = 10CF = 59FE = 42The properties of a parallelogram.Based on the image of the parallelogram shown in the image attached below, we can logically deduce that the opposite sides of this parallelogram are all equal. Thus, we have:
Side DE = Side CF
6n - 1 = 5n + 9
6n - 5n = 9 + 1
n = 10.
From Side CF, we have:
CF = 5n + 9
CF = 5(10) + 9
CF = 59.
For the measure of side FE, we have
FE = 4n + 2
FE = 4(10) + 2
FE = 42.
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Complete Question:
Figure CDEF is a parallelogram.
Parallelogram C D E F is shown. The length of F C is 6 n minus 1, the length of C D is 4 n + 2, and the length of D E is 5 n + 9.
Which equations are correct? Select three options.
n = 10
n = 7
CF = 59
FE = 42
CD = 30
Answer:
A,C,D
Step-by-step explanation:
Can someone help me with these problems having trouble and show work please !
Answer:
1.x=0, –10
2.x=3, 4
Step-by-step explanation:
1.
x(x+10)=0===> x=0, –10
2.
x²–3x–4x+12===> x²–7x+12=0
(x–3)(x‐4)=0====> x=3, 4
what is the solution to the equation 35-2x=23
Answer:
x = 6
Step-by-step explanation:
35 - 2x = 23
35 - 23 - 2x = 0
35 - 23 = 2x
12 = 2x
x = 6
35- 2x = 23
Subtract 35 from both sides.
-2x = 23 - 35Subtract 35 from 23 to get −12.
-2x = -12Divide both sides by −2.
x = -12 / - 2Divide −12 by −2 to get 6.
x = 6 ===> AnswerThe first three terms of a sequence are
given. Round to the nearest thousandth (if
necessary).
3, 6, 12, ...
Find the 9th term.
Answer: 768
Step-by-step explanation:
3, 6 ,12 ,24, 48, 96, 192, 384, 768
12 x 2 = 48
48 x 2 = 96
96 x 2 = 192
192 x 2 = 384
384 x 2 = 768
please help me im in a rush
Answer:
a. 25 seniors are randomly selected; 14 plan to go to a 4 year college
b. 420 students
Step-by-step explanation:
a. the less they have in common, the better
b. 14/25 is only between 25 students. make the denominator the same (750) and multiply the same to the numerator
750/25 = 30
14/25 x 30 = 420/750
I need help in this !! Thank you !!
(a) The median mark is 44
(b) The number of students who scored 54 marks or less is 120
(c) The number of students who scored 60 marks or more is 20
Cumulative frequency curve (OGIVE)From the question, we are to determine the median mark
The median mark for a cumulative frequency curve corresponds to the second quartile (Q₂)
Q₂ = 1/2(n+1)th mark
Where n is the total frequency
In the graph,
n = 160
∴ Q₂ = 1/2(160+1)th mark
Q₂ = 80.5th mark
The 80.5th mark is 44
∴ The median mark is 44
(b)
The number of students who scored 54 marks or less = 120 - 0
The number of students who scored 54 marks or less = 120
(c)
The number of students who scored 60 marks or more = 160 - 140
The number of students who scored 60 marks or more = 20
Hence, (a) The median mark is 44
(b) The number of students who scored 54 marks or less is 120
(c) The number of students who scored 60 marks or more is 20
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Solve the equation 3x^2-2x-10=0
Show all your working and give your answers correct to 2 decimal place
Answer:
Step-by-step explanation:
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 3
B = -2
C = -10
B2 - 4AC =
4 - (-120) =
= 124
Applying the quadratic formula :
2 ± √ 124
x = —————
6
√ 124 simplified
The prime factorization of 124 is
2•2•31
To be able to remove something from under the radical, there have to be 2 instances of it
√ 124 = √ 2•2•31 =
± 2 • √ 31
√ 31, rounded to 4 decimal digits, is 5.5678
So now we are looking at:
x = ( 2 ± 2 • 5.568 ) / 6
Two real solutions:
x =(2+√124)/6=(1+√ 31 )/3= 2.189
or:
x =(2-√124)/6=(1-√ 31 )/3= -1.523
Answer:
Step-by-step explanation:
3x^2-2x-10=0
This is a quadratic equation that can be solved using the quadratic formula where
a = 3, b = -2, and c = -10
x=−b±(b^2−4ac)^(1/2)/2a
x=−(−2)±((−2)2−4(3)(−10)^(1/2)/2(3))
x=2±(124)^(1/2)/6
Simplify the Radical:
x=((2/6) ±2(31)^(1/2))/6
x=26±231−−√6
Simplify fractions and/or signs:
x=1/3±√31/3
which becomes
x=2.18925
See the attached image for a more clear display of solving using the quadratic equation.
x=−1.52259
Determine whether the relationship is an inverse variation or not. Explain.
The relationship is not an inverse variation because the product xy is not a constant.
What is Inverse variation?Inverse variation is the relationship between two quantities whereby an increase in one quantity cause a decrease in the other quantity.
In this type of variation the product of the two quantities is constant.
Analysis:
if x is one quantity and y is the other,
Mathematically, x = [tex]\frac{k}{y}[/tex]
Where, k is a constant,
it means k = xy
from the table, when, x =2, y = 409, xy = 2 x 409 = 818
Also, x = 3, y = 240, xy = 3 x 240 = 720
Therefore, 720 not equal to 818.
In conclusion, The product xy is not a constant, so the relationship is not an inverse variation.
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On an exam you get two points for every question answered correctly, zero points for each question left blank and lose one-half point for each question answered incorrectly. what is your total score on the exam if you answered 13 questions correctly, leave 7 questions blank and answer 5 questions incorrectly?
Using multiplication, the total score on the exam if you answered 13 questions correctly, leave 7 questions blank and answer 5 questions incorrectly is 39 point.
According to the question,
For each correct question, you get 2 points, and there are 22 correct questions, so multiply 22 by 2
22 * 2 = 44 points.
For each question left blank, you get 0 points, and there are 7 questions left blank, so multiply 7 by 0
7 * 0 = 0 points
For each incorrect question, you get -1 point, and there are 5 incorrect questions, so multiply 5 by -1
5 * (-1) = -5 points.
The total number of score = 22*2 + 7*0 + 5*(-1) = 44 + 0 - 5 = 39 points.
Hence, using multiplication, the total score on the exam if you answered 13 questions correctly, leave 7 questions blank and answer 5 questions incorrectly is 39 point.
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ASAP GUYS PLEASE I NEED UR HELP THIS IS SO HARD
Solve: 5 − 7 ( z + 1 ) = 7 ( − 9 − 3 z )
Answer:
[tex]-\frac{61}{14}[/tex]
Step-by-step explanation:
Question: 5 - 7(z+1) = 7(-9-3z)
We multiply the number in front of the bracket first, since that is multiplication.
--> 5 -7z -7 = -63 - 21z
--> -7z -2 = -63 - 21z
Now, we move all the z and all the numbers to each side.
--> -7z +21z = -63 +2
--> 14z = -61
--> z = -61/14
This cannot be simplified further, so z is -61/14.
Could y’all help me
Answer:
16. C
17. C
Step-by-step explanation:
16.
this is just a multiplication of the 2 functions.
that means we multiply the functional expressions, and the result is the new functional expression of the multiplied functions.
2(3x - 5) × (-2x + 1) = (6x - 10) × (-2x + 1) =
= 6x×-2x + 6x×1 + -10×-2x + -10×1 =
= -12x² + 6x + 20x - 10 = -12x² + 26x - 10
17.
the domain of a function is the interval or set of all valid x values (or input values).
the range is the interval or set of all valid y or functional result values.
so, for the domain we need to see what values x may have for a 4th root.
for this we can imagine that a 4th root is the square root of the square root of x.
this is directly related to x⁴ being the square of the square of x.
the valid input values for a square root are all positive numbers (incl. 0). the result will be again a positive number (incl. 0), which is again a valid input number for the second square root.
therefore, the valid values of x for a 4th root are also the valid values for a square root. and vice versa.
and that is
0 <= x < infinity
FYI : we can never say x = infinity, because infinity is not a number, just a generation concept. so, infinity can never be included in any interval, it can only be listed as an excluded limit concept.
The range of a list of integers is 20, and the median is 17. What is the smallest possible number of integers in the list?
Answer:
4 is the smallest possible number of integers in the list.
PLEASE HELP ASAP
I think it’s supposed to be an arithmetic series or sequence.
Kaydence is saving for an RRSP. She saved $100 the first year, $200 the second year, $300 the third year, and so on. If she put $100 away on January 1, 2014, $200 away on January 1, 2015, and continued to put money away on the first of each year, how much money would Kaydence have saved by the end of the day on January 1, 2050?
Answer:
$70,300
Step-by-step explanation:
The amount Kaydence saved is the value of an arithmetic series with first term 100 and common difference 100. The number of terms in the sum is 37. The formula for the sum can be used.
Sum of an arithmetic seriesThe formula for the sum of n terms of an arithmetic series is ...
Sn = (2a1 +d(n -1))(n/2) . . . . . . first term a1, common difference d
ApplicationThe number of terms being added is ...
2050 -2014 +1 = 37 . . . . . . years Kaydence made deposits
The formula with a1=100, d=100, and n=37 is ...
[tex]S_{37}=(2\cdot100+100(37-1))\dfrac{37}{2}=\dfrac{(200+3600)\cdot37}{2}\\\\S_{37}=70,\!300[/tex]
Kaydence would have saved $70,300 by the end of Jan 1, 2050.
In a carnival drawing, a green ticket wins $1, a yellow ticket wins $5, and a blue ticket wins $10. There are 100 green tickets, 25 yellow tickets and 5 blue tickets. In simplest form, what are the odds in favor of winning $5 or more?
A. 1:4
B. 1:5
C. 1:25
D. 3:10
The odds in favor of winning $5 or more is 3 : 13
What are the odds in favor of winning $5 or more?The odds of winning $5 or more can be determined by finding the ratio of the total value of tickets that have a value of $5 or greater to the total value of tickets.
Total number of the tickets that have a value of $5 or more = 25 + 5 = 30
Total number of ticket = 25 + 5 + 100 = 130
Ratio : 30 : 130
3 ; 13
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what is the distance between the points (23,-33) and (4,9) if necessary round your answer to two decimal places
The distance between the points (23,-33) and (4,9) rounded to two decimal places is 46.10.
What is the distance between the points (23,-33) and (4,9)?The distance between two points on a graph can be determined using the equation;
D = √[ ( x₂ - x₁ )² + ( y₂ - y₁ )² ]
Given that;
x₁ = 23x₂ = 4y₁ = -33y₂ = 9We substitute our values into the equation above.
D = √[ ( x₂ - x₁ )² + ( y₂ - y₁ )² ]
D = √[ ( 4 - 23 )² + ( 9 - (-33) )² ]
D = √[ ( -19 )² + ( 42 )² ]
D = √[ 361 + 1764 ]
D = √[ 2125 ]
D = 46.10
Therefore, the distance between the points (23,-33) and (4,9) rounded to two decimal places is 46.10.
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[tex]\mathbb Question[/tex]
Attached above!!
Answer:
see explanation
Step-by-step explanation:
(a)
play ends at 9 : 55 pm
15 minutes to get to bus stop , then time is
9 : 55 + 15 min = 10 : 10 pm = 22 : 10
the earliest bus she can catch is 22 : 25
(b)
time to wait 22 : 10 → 22 : 25 = 15 minutes
Quick algebra 1 question for 50 points!
Only answer if you know the answer, quick shout-out to Yeony2022, tysm for the help!
I think it is 6. It may be because we can see the intersect of line is in (1,6) and (-1,-6). So I think that it is 6.
Jonathan bought a new computer for $1,716 using the electronic store's finance plan. he will pay $143 a month for 12 months. which equation can jonathan use to find out how much money he still owes after each month of the plan?
By this equation y = 1,716 - 112x he find that how much money he still owes after each month of the plan.
According to the statement
Jonathan bought a new computer for $1,716
He will pay $143 a month for 12 months.
Total amount he will for 12 months is 143(`12)
Now,
y = the money he still owes
x = the number of months (from x = 0 to x = 12)
y = 1,716 - 112x
So, By this equation y = 1,716 - 112x he find that how much money he still owes after each month of the plan.
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