On solving the provided question, we can say that - the function value will be [tex]g(x) = -3 + 12x + 15[/tex] and
what is function?The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.
Here,
[tex]y =a(x-x1)(x-x2),[/tex] y equals a(x-5)(x+1)
g(x) = -3(x-5)(x+1)
[tex]g(x) = -3(x-5)(x+1)[/tex]
g(x) = -3 + 12x + 15
y-intercept of g(x) is (0,15)
Therefore , the solution to the given problem of the equation comes out be y-intercept of g(x) is (0,15).
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A line with a slope of -3 passes through the point (-4, 3). if (-3, p) is another point on the line, what is the value of p
The y-coordinate of the point (-3, p) is p = 0.
A line can be represented by the equation y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis).
In this case, the slope of the line is given as -3, and the line passes through the point (-4, 3). We can use this information to write an equation for the line in the form y = mx + b:
y = (-3)x + b
We are told that the line passes through the point (-4, 3), so we can substitute these values into the equation to find the value of b:
3 = (-3)(-4) + b
3 = 12 + b
-9 = b
Therefore, the equation for the line is y = -3x - 9.
To find the value of p, we need to substitute the x-coordinate (-3) into the equation and solve for y:
y = (-3)(-3) - 9
y = 9 - 9
y = 0
Therefore, the y-coordinate of the point (-3, p) is p = 0.
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The y-coordinate of the point (-3, p) is p = 0.
Now, According to the question:
y = mx + b is the slope intercept form of writing the equation of a straight line. In the equation 'y = mx + b', 'b' is the point, where the line intersects the 'y axis' and 'm' denotes the slope of the line. The slope or gradient of a line describes how steep a line is. It can have either a positive or a negative value. When a standard form of a linear equation is of the form Ax + By = C, where 'x' and 'y' and 'C' are variables and 'A', 'B' are constants, the slope-intercept form is the most preferred way of expressing a straight line due to its simplicity, as it is very easy to find the slope and the 'y intercept' from the given equation.
In this case, the slope of the line is given as -3, and the line passes through the point (-4, 3). We can use this information to write an equation for the line in the form y = mx + b:
y = (-3)x + b
We are told that the line passes through the point (-4, 3), so we can substitute these values into the equation to find the value of b:
3 = (-3)(-4) + b
3 = 12 + b
-9 = b
Therefore, the equation for the line is y = -3x - 9.
To find the value of p, we need to substitute the x-coordinate (-3) into the equation and solve for y:
y = (-3)(-3) - 9
y = 9 - 9
y = 0
Therefore, the y-coordinate of the point (-3, p) is p = 0.
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Which of the following is not equivalent to the other three?
Answer:
The answer is D
Step-by-step explanation:
Trust me on this, its hard to explain but Im 100% sure.
find an equation of the tangent line to the curve at the given point. y = x4 + 6x2 − x, (1, 6)
The equation of the line tangent to the curve is -
(y - 6) = 17(x - 1).
What is the equation of tangent to a curve?The equation of the tangent to the curve y = f(x), passing through the point (a, b) can be written as -
(y - b) = (dy/dx) (x - a)
Given is the curve y = f(x) = x⁴ + 6x² − x.
The given curve is -
y = x⁴ + 6x² − x
f'(x) = dy/dx = d(x⁴ + 6x² − x)/dx
f'(x) = dy/dx = 4x³ + 12x + 1
Now -
f'(x){1, 6} = (dy/dx){1, 6} = 4 x 1 x 1 x 1 + 12 x 1 + 1
f'(x){1, 6} = 17
We can write the equation as -
(y - 6) = 17(x - 1)
Therefore, the equation of the line tangent to the curve is -
(y - 6) = 17(x - 1).
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Moolah has 24 coins that are all dimes and quarters. The value of the coins is $3.75. How many dimes and how many quarters does Moolah have?
By solving a system of equations we will see that she has 9 quarters and 15 dimes.
How many dimes and how many quarters does Moolah have?
Let's define the variables.
d = number of dimes.q = number of quarters.We know that Moolah has 24 coins, then:
d + q = 24
And the total value is $3.75, then:
q*0.25 + d*0.10 = 3.75
Then we can write the system of equations:
d + q = 24
q*0.25 + d*0.10 = 3.75
We can isolate d on the first equation to get:
d = 24 - q
Replacing that in the other equation we will get:
q*0.25 + (24 - q)*0.10 = 3.75
q*0.15 + 2.4 = 3.75
q*0.15 = 3.75 - 2.4
q*0.15 = 1.35
q = 1.35/0.15 = 9
So Moolah has 9 quarters and 15 dimes.
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After many studies, a researcher finds that the probability of a word recognition program correctly interpreting a hand-written word is 9/10 . How many words would the researcher expect the program to interpret correctly out of 40 words?
If a researcher finds that the probability of a word recognition program correctly interpreting a hand-written word is 9/10 . The number of words that the researcher expect the program to interpret correctly out of 40 words is 36 words.
How to find the number of words?Using this formula to find the number of words
Number of words = Probability of correctly interpreting a hand-written word × Expected words
Let plug in the formula
Number of words = 9/10 × 40
Number of words = 36 words
Therefore we can conclude that the number of words is 36 words.
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This is a regular polygon find the value of x
For the given regular polygon with the angle sum of 10x + 4, the value of x = 143.6
What is regular polygon?They are referred to as regular polygons if the interior angles and sides are all equal. Equilateral triangles, squares, and other shapes are examples of regular polygons. Along with the sides being congruent, regular polygons also have congruent angles. They are equiangular, according to that.
We know that sum of interior angles of a regular polygon is
( n − 2 ) × 180°, where n is sides
For the given question
( 10 − 2 ) × 180°
= 8 × 180°
= 1440°
Given that
10x + 4 = 1440°
10x = 1436
x = 1436/10
x = 143.6
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This image please help
Answer:
y ≤ -3/2x -2
Step-by-step explanation:
You want the inequality shown on the graph that has a solid line through points (0, -2) and (2, -5).
SlopeThe slope of the solid boundary line can be found from the slope equation:
m = (y2 -y1)/(x2 -x1)
m = (-5 -(-2))/(2 -0) = -3/2
InterceptThe y-intercept is the point marked on the y-axis: (0, -2).
Slope-intercept equationThe boundary line has the slope-intercept equation ...
y = mx +b . . . . . . . . where m is the slope and b is the y-intercept
y = -3/2x -2
ShadingThe shading is to the left and below the boundary line, so y-values in the shaded area are less than those on the line. The inequality reflects this:
y ≤ -3/2x -2
__
Additional comment
The solid boundary line is included in the solution set, so we use the ≤ symbol, instead of the < symbol that excludes the line. When the < symbol is used, the boundary line is dashed.
We use the term "y-intercept" to refer to both the ordered pair that describes the point on the y-axis, (0, -2), and the y-value in that ordered pair, -2. We understand the x-value of any point on the y-axis is 0.
What is the probability that three points chosen uniformly and independently on a circle fall on a semicircle
The probability that three points chosen uniformly and independently on a circle fall on a semicircle is 1/2 or 50%.
The probability of three points chosen randomly and independently on a circle falling on a semicircle is 1/2, or 50%. This is because the probability of a point landing on either side of the semicircle is equal. The points are chosen on a circle, so each point has an equal probability of being on either side of the semicircle. Therefore, the probability of three points randomly chosen on a circle landing on a semicircle is 1/2 or 50%.
Let A, B, and C be the three points chosen on a circle.
The probability that A, B, and C fall on the semicircle is:
P(A on semicircle) x P(B on semicircle) x P(C on semicircle)
= (1/2) x (1/2) x (1/2)
= (1/2)^3
= 1/8
Therefore, the probability that three points chosen randomly and independently on a circle fall on a semicircle is 1/8 or 12.5%.
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The probability that three points chosen uniformly and independently on a circle fall on a semicircle is written as 1/8.
The term probability in math is defined as the chances of something materializing based upon the ratio of its number of outcomes to the number of outcomes of the whole sample space the event relies upon.
While we looking into the given question, here let us consider that A, B, and C be the three points chosen on a circle.
Then the probability that A, B, and C fall on the semicircle is calculated as,
=> P(A on semicircle) x P(B on semicircle) x P(C on semicircle)
Now, we have to apply the value of each probability, then we get
=> (1/2) x (1/2) x (1/2)
Therefore, the resulting value is
=> (1/2)³ = 1/8
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There are 75 students in the eighth grade. Forty-five of those go to music class. The rest of the students have art. What percent have music?
The percentage of students in eighth grade who have music is 60%
How to find percentage?Total number of eighth grade students = 75
Number of students who goes to music class = 45
Number of students who have art = Total number of eighth grade students - Number of students who goes to music class
= 75 - 45
= 30
Percentage of students who have art = Number of students who have art / Total number of eighth grade students × 100
= 30/75 × 100
= 0.4 × 100
= 40%
Percentage of students who have music = Number of students who have music / Total number of eighth grade students × 100
= 45/75 × 100
= 0.6 × 100
= 60%
Hence, 60% of the eighth grade students have music.
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(b) Sketch the graph of f.
Identify two points for each line and connect to graph lines.
Consider that x = 1 is the critical point, which gives us one included point (1, 0) marked as closed circle and one excluded point (1, 3) marked as open circle.
The second point for the first line is selected at x = - 3, which is (-3, 4) and for the second line is selected at x = 3, which is (3, 7).
See the lines attached.
Find g(x), where g(x) is the reflection across the x-axis of f(x)=6(x–7)2+2.
The reflection of f(x)=6(x–7)2+2 is g(x) = -1 * (6(x–7)^2 + 2) = -6(x–7)^2 - 2.
What is the reflection of a function?
A reflection is a transformation of the graph of a function over the x-axis or the y-axis (or both). The function retains its basic shape; however, by including a negative sign in the appropriate place in the equation, the graph of the function will flip over one or the other of the axes.
To find the reflection of a function across the x-axis, we can simply multiply the function's y-coordinate by -1.
For f(x) = 6(x–7)^2 + 2,
the reflection across the x-axis is
g(x) = -1 * (6(x–7)^2 + 2) = -6(x–7)^2 - 2.
Hence, the reflection of f(x)=6(x–7)2+2 is g(x) = -1 * (6(x–7)^2 + 2) = -6(x–7)^2 - 2.
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To be eligible for the playoffs, a baseball team cannot lose more than 40% of its remaining games. The team has 18 games remaining in the regular season.
5. Write and solve an inequality to find the number of games g that the
team could lose and still be eligible for the playoffs.
6. If the baseball team loses 8 of its remaining games, will the team
advance to the playoffs? Explain your answer
Answer:
Below
Step-by-step explanation:
To find the number of games g that the team could lose and still be eligible for the playoffs, we can write the inequality:
g / 18 ≤ 40%
g / 18 ≤ 0.4
g ≤ 7.2
We can round down to 7 to get the maximum number of games the team could lose and still be eligible for the playoffs.
If the baseball team loses 8 of its remaining games, they will not advance to the playoffs. This is because 8 is greater than the maximum number of games they could lose and still be eligible for the playoffs, which is 7.
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Evaluate the given expression an 44P2 44P2=0
The given expression of an [tex]{ }^{44} P_2[/tex] is 1892.
The given expression is [tex]{ }^{44} P_2 & =[/tex]0
[tex]{ }^{n} P_r[/tex]:-
It serves to represent permutation.The grouping of the pieces into a certain sequence or order is known as a permutation.There are n ways to arrange each of the r things in a set of n objects.[tex]{ }^{n} P_r=[/tex][tex]\frac{n !}{(n-r) !} \\[/tex]
where
n = total number of thingsr = number of things that have to be selected and arranged.In the nPr formula, the letter "P" stands for "permutation," which is another word for "arrangement." The nPr formula calculates the number of possible combinations for choosing and arranging r items from the given n items.
Let's imagine that r various objects should be chosen and organised among n different objects. Let's explore some options for how to accomplish this.
Since there are n total objects, there are n methods to select the first one.
The number of options for selecting the second thing is limited because the first object has already been selected (n - 1).
Similar to how there are numerous ways to select the third item (n - 2).
While choosing the [tex]r^{th}[/tex] object, there are only (n - r + 1) objects are left and hence it can be chosen in (n - r + 1) ways.
[tex]{ }^{44} P_2 & =? \\\\P(n, r) & =\frac{n !}{(n-r) !} \\\\44 P_2 & =\frac{44 !}{(44-2) !} \\\\& =\frac{44 \times 43 \times 421}{421} \\[/tex]
=44×43
=1892
[tex]{ }^{44} P_2=[/tex]1892
Therefore, the value of [tex]{ }^{44} P_2[/tex]=1892.
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This shape is drawn on a centimetre square grid. What is the area of the shape?
Answer:
13 square centimeters.
Step-by-step explanation:
There are 13 squares making up the shape
What is the domain and range
Madison's free throw percentage is at 78%. Lara's free throw ratio is
24
Who is the better free throw shooter? How do you know?
Answer:
Madison
Step-by-step explanation:
Madison is the better free throw shooter. We can tell this because her free throw percentage of 78% is higher than Lara's free throw ratio of 24, which is the number of successful free throws out of 100 attempted shots. Hope this helps!
A group of 169 tourist will hire minibuses for a tour around tokyo. if each minibus can accommodate 26 passengers how many how many minibuses should be hired?...
number of minibuses required = 7
what is division?
Division is the process of dividing some object into a number of parts. It is opposite to the multiplication process. In mathematics, the number that is divided by other number is called dividend and the other number is called divisor.
How many minibuses should be hired?
given, number of tourists = 169
each minibus can accommodate 26 passengers.
number of minibuses required for the total 169 tourists.
will be 169/26 = 6.5 = 7
they need to hire total 7 minibuses for a tour around Tokyo.
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which is not a solution to the differential equation y" + 4y = 0? A y = 10 B y=4e-2X C. y=3 sin(2x) D. y-2 cos(2x) + 4
D. y-2 cos(2x) + 4 is not a solution to the differential equation y" + 4y = 0.
The homogeneous Linear DifferentialThe differential equation y" + 4y = 0 is a second-order, homogeneous linear differential equation with constant coefficients. The general solution to this type of differential equation is of the form y = e^(rt) where r is a root of the characteristic equation r² + 4 = 0. The roots of this equation are r = +/- √(4) = +/- 2i, which are both imaginary. Therefore, the general solution to the differential equation is y = c1cos(2x) + c2*sin(2x), where c1 and c2 are arbitrary constants.
Option D. y - 2 cos(2x) + 4 is not a solution to this differential equation because it doesn't have the same form as the general solution. It is a combination of a constant term, cosine and sine function but the general solution only contains sine and cosine function.
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Find the sum of 6x^2-3 and 8x^2–5x-1
By grouping like terms and taking common factors, we will see that the addition of the polynomials gives:
(6x^2 - 3) + (8x^2 - 5x - 1) = 14x^2 - 5x - 4
How to find the sum of the polynomials?Here we want to add two polynomials:
6x^2 - 3
And
8x^2 - 5x - 1
To make that addition, we just need to group like terms and take common factors.
We start with:
(6x^2 - 3) + (8x^2 - 5x - 1)
Grouping like terms we will get:
(6x^2 + 8x^2) + (-5x) + (-3 - 1)
Now we can simplify that, so we will get:
(6 + 8)*x^2 - 5x - 4
14x^2 - 5x - 4
That is the addition of the polynomials.
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5. rhombus
(6x + 32)º
(17x - 1)º for what value of x is the figure given the special parallelogram
The value of x from the given quadrilateral is 3.
What is rhombus?A rhombus is a closed two-dimensional plane figure. It is considered a special parallelogram, and because of its unique properties, it gets an individual identity as a quadrilateral. A rhombus is also called an equilateral quadrilateral since all of its sides are equal in length.
Given that, rhombus (6x + 32)º and (17x - 1)º for what value of x is the figure given the special parallelogram.
A rhombus has two diagonals that bisect each other at right angles and diagonal bisects angles.
Now, (6x + 32)º=(17x - 1)º
17x-6x=32+1
11x=33
x=3
Therefore, the value of x is 3.
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What is the completely factored form of the expression?
The given expression [tex]x^{2} +8x+15[/tex] , can be expressed in completely factored form as [tex](x+5)(x+3)[/tex] .
The expression that is to be written in factored form is [tex]x^{2} +8x+15[/tex] ;
we will use the split the middle term method to express it in factored form , in this method we split the middle term and then write down the common factors .
the middle term [tex]8x[/tex] can be written as [tex]3x+5x[/tex] ;
we get ; [tex]x^{2} +3x+5x+15[/tex] ;
taking "x" common from first 2 terms and "5" common from the next two terms ,
we get ;
⇒ [tex]x(x +3)+5(x+3)[/tex] ;
⇒ [tex](x +3)(x+5)[/tex] ;
So , we get that the expression [tex]x^{2} +8x+15[/tex] is equivalent to [tex](x +3)(x+5)[/tex] .
Therefore , the completely factored form is [tex](x +3)(x+5)[/tex] .
The given question is incomplete , the complete question is
What is the completely factored form of the expression [tex]x^{2} +8x+15[/tex] ?
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The larger of two numbers is 9 more than twice the smaller. The sum of the numbers is 3 less than five times the smaller. Find the numbers.
Answer:
6 & 21
Step-by-step explanation:
Let x be the smaller number. Let y be the larger number.
We have:
x + y = 5x - 3
However, we also know the larger number is 2x + 9 (nine more than twice the smaller). So, we can plug in 2x + 9 for y:
x + (2x + 9) = 5x - 3
x + 2x + 9 = 5x - 3
3x + 9 = 5x - 3
9 = 2x - 3
12 = 2x
x = 6
Now solver for the larger:
2x + 9 = 6*2 + 9 = 12 + 9 = 21
Therefore, the numbers are 6 and 21.
I hope this helps :D
6.
Suppose there are 8 runners competing in the 400-meter race. The fastest 3 runners win a ribbon. In how many
ways can the runners finish in first, second, and third place? (lpt)
Answer: 56
Step-by-step explanation:
There are 8 runners competing in the 400-meter race, and the fastest 3 runners win a ribbon. This means that there are 3 places that the runners can finish in: first, second, and third.
Since the order in which the runners finish matters, we need to use permutations to find the number of ways that the runners can finish in first, second, and third place.
The number of permutations of a set of n objects taken r at a time is given by the formula:
n! / (n - r)!
In this case, there are 8 runners, so n = 8, and we are selecting 3 runners at a time, so r = 3. Plugging these values into the formula gives us:
8! / (8 - 3)! = 8! / 5! = 8 * 7 * 6 / 5 * 4 * 3 = 56
Therefore, there are 56 ways that the runners can finish in first, second, and third place.
Hi! can you help me with this?
x²-x = 156
Answer:
x = - 12 , x = 13
Step-by-step explanation:
x² - x = 156 ( subtract 156 from both sides )
x² - x - 156 = 0 ← in standard form
(x - 13)(x + 12) = 0 ← in factored form
equate each factor to zero and solve for x
x + 12 = 0 ⇒ x = - 12
x - 13 = 0 ⇒ x = 13
What is datatype and its 4 types?
There are four main datatypes: String, Integer, Float, and Boolean.
String: A string data type is used to store textual data. Strings are usually enclosed in quotation marks, and are used to represent words or phrases.
Integer: An integer data type is used to store numeric values that are whole numbers. Integers are usually used to represent counts or quantities.
Float: A float data type is used to store numeric values that have decimal points. Floats are usually used to represent real numbers, such as money amounts, measurements, and scientific values.
Boolean: A boolean data type is used to store values that can only be either true or false. Booleans are usually used to represent logical values, such as whether a certain condition is met or not.
Datatype is a classification of data which tells the computer how the programmer wants to use the data. It is used to store different types of values such as strings, integers, floats, and booleans. Each data type has its own specific purpose and can be used to store different types of information.
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May I ask on how do I evaluate 3x-5/y? Thank you...
Answer:
excluded values
y=0
Simplify the expression
3xy−5/y
Step-by-step explanation:
The arithmetic sequence cn is defined below. Find the first five terms of the sequence ifc, is the first term and d is the common difference. Ci -6 -7 d Select the correct answer below.O -6.-13.-22. – 29.-38.... O -6,-14, -22, -30, -38,... O -7.-12, -21, -28.-33... O -6.-13, -20, -27,-34.... O -6, 13, -20, -13,6,...
Given an arithmetic sequence with the first term -6 and the common difference -7, the first five terms are: -6, -13, -20, -27, -34.
The formula for the n-th term of an arithmetic sequence is given by:
a(n) = a(1) + (n - 1) d
Where:
a(1): the first term
d = common difference
The consecutive terms of an arithmetic sequence can be obtained as:
a(n) = a(n - 1) + d
Information available in the problem:
first term = a(1) = -6
common difference = d = -7
Hence,
a(1) = -6
a(2) = -6 - 7 = -13
a(3) = -13 - 7 = -20
a(4) = -20 - 7 = -27
a(5) = -27 - 7 = -34
Therefore the first five terms are: -6, -13, -20, -27, -34
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A gardener already has 4 2/3 ft of fencing in his garage. he wants to fence in a square garden for his flowers. The length of one side of the garden is 3 1/4, how much more fencing will the gardener need to purchase? A. 8 1/3 B. 12 3/7 C. 13 1/4 D. 18 2/3
HELP FAST PLS
The quantity of fencing that the gardener would need to purchase would be = 1 5/12.
How to calculate extra fencing that is needed?The total quantity of fencing the gardener needs to fence the the square garden = 4⅔
The length of one side of the garden = 3¼
The quantity of fencing the gardener needs to purchase would be = x
4⅔ = 3¼ + X
14/3 = 13/4 + X
X = 14/3 -13/4
X =56-39 /12
X= 17/12
X = 1 5/12ft.
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The isosceles triangle EJF is one of an unknown number of isosceles triangles from the original arch.
Each isosceles triangle had the same vertex angle as triangle EJF. The sum of the vertex angles equals 180
Let x = the number of isosceles triangles.
Fill in the equation with your answer from Q12 and solve for x.
___ • x = 180
(USE PICTURE TO HELP ANSWER PROBLEM)
The value of the vertex(central) angle EJF formed by the given polygon is; 30°
How to find the central angle of a polygon?To find the central angle of a polygon, we will simply divide 360 degrees by the number of sides of the polygon.
Now, we are told that the sum of the central vertex angles sums up to 180 degrees. Now, by careful observation, we can tell that the number of isosceles triangles that will be formed in the semi circle are 6. Thus;
Number of polygon sides of the semi circle = 6 sides
Thus;
Central angle = 180/6
Central angle = 30°
Now, we know that the base of isosceles triangles are equal. Since we know that the sum of angles in all triangles is 180 degrees, then we can say that;
∠E = ∠F = [180 - 30]/2
∠E = ∠F = 75°
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Find the first four terms of the binomial series for the given function.
(1 + x/4) ^ - 2
OA. 1 - 1/2 * x + 3/16 * x ^ 2 - 3/16 * x ^ 3
OB. 1 - 1/2 * x + 1/4 * x ^ 2 - 3/32 * x ^ 3
Oc. 1 - 1/2 * x + 3/16 * x ^ 2 - 1/16 * x ^ 3
OD. 1 - 1/2 * x + 1/4 * x ^ 2 - 1/8 * x ^ 3
The first four terms of the binomial series are 1- 1/2 x+ 3/16 x^2- 1/16 x^3. (Option C)
In mathematics, the binomial series is a generalization of the polynomial that comes from a binomial formula expression like ^n for a nonnegative integer n. For a binomial series, the formula for the expansion of any terms is given by
(1+x)^m=1+mx+ m(m-1)/2! x^2+ m(m-1)(m-2)/3! x^3+⋯.
For the given function (1+ x/4)^(-2)
m = -2
x = x/4
Hence, using the above expansion formula
The first term = 1
The second term = mx = (-2)(x/4) = -x/2
The third term =m(m-1)/2! (x/4)^2= (-2(-2-1))/(2*1*16) x^2=3/16 x^2
The fourth term = m(m-1)(m-2)/3! (x/4)^3=(-2(-2-1)(-2-2))/(3*2*1*64) x^3=-1/16 x^3
Hence, the first four terms of the binomial series are 1- 1/2 x+ 3/16 x^2- 1/16 x^3.
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