An asymptote function is called such because it is a line that a curve approaches but never touches, or "asymptotically" approaches.
An asymptote is a line that a curve approaches but never actually touches. It is called an asymptote because the word comes from the Greek asymptōtos, which means "not falling together." Asymptotes are used in mathematics to describe curves that approach a particular line without ever intersecting it. For example, in a graph of a function, an asymptote is a line that the graph of the function approaches, but never intersects with, as it approaches infinity. Asymptotes are also used to describe straight lines in a plane that approach each other at a certain angle, but never meet. In both cases, the idea is that the line or curve approaches the asymptote, but never actually touches it, thus the name asymptaote.
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Which is a factor of x³ 7x 6?
The factor of [tex]x^3 -7x + 6[/tex] is (x - 1) (x +3) (x -2).
Now, According to the question:
The given expression to be factorized is :
[tex]x^3 -7x + 6[/tex]
This can be written in the form:
[tex]x^3 -7x + 6[/tex] = [tex]x^3[/tex] - (1 + 6)x + 6
[tex]x^3 -7x + 6[/tex] = [tex]x^3[/tex] -x - 6x + 6
Take common 'x' from the first two terms and -6 from the last two terms. Then we have,
[tex]x^3 -7x + 6[/tex] = x([tex]x^2 -1[/tex]) -6 (x -1)
= x{ [tex](x)^2 - (1)^2[/tex] } - 6(x -1)
= x(x +1) (x -1) - 6(x -1)
Finally, Take common (x -1) from the above expression:
[tex]x^3 -7x + 6[/tex] = (x -1) {x(x +1) - 6}
= (x -1) [tex](x^{2} +x-6)[/tex]
= (x -1)([tex]x^{2}[/tex]+3x -2x -6)
= (x - 1) (x (x +3) -2 (x +3))
= (x - 1) (x +3) (x -2)
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The complete question is this:
Which is the factor of [tex]x^3 -7x + 6[/tex]
1. x(x -6) (x -1)
2. [tex](x^{2} -6)[/tex] (x -1)
3. (x + 1) (x + 2) (x +3)
4. (x - 1) (x +3) (x -2)
Is 3x 1 a quadratic equation?
3x - 1 = 0 is not a quadratic equation.
What is a quadratic equation?A variable with the largest power of two in a quadratic equation is called a variable. Quad, which signifies square, is the root of the term quadratic. The phrase must be two times its own strength, neither higher nor lower.
Given that they are the x values for which f(x) = 0, the roots of the function f(x) = ax² + bx + c correspond to the solutions of the quadratic equation ax² + bx + c = 0.
The term ax² is known as the quadratic term (hence the function's name), the word bx is known as the linear term, and the value c is known as the constant term.
In the given equation: 3x - 1 = 0 , no ax² term is given, so it is not a quadratic equation.
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The complete question is as follows:
Is 3x - 1 = 0 a quadratic equation?
Which 3 transformations can be described as rigid transformations because they keep shapes congruent?
The size and shape of things are preserved by stiff transformations (reflections, translations, and rotations). As a result, archetypes and visuals are always compatible.
What is rigid transformations?The separation between each pair of the geometric object's points is preserved during a rigorous change of the object. In other words, a rigid transformation maintains the object's size and shape. For instance, the rigid transformation of a triangle retains the angles and lengths of the triangle. Imagine a stiff shape distortion, similar to a cardboard shape. The form remains the same after being pushed left and right, rotated, and flipped. When the mold was created using putty, the opposite was true. The thing can then be twisted and stretched. These conversions, nevertheless, are not exact. Stretching a form alters the distances between each pair of its points.
c + 18 + 10 = 42//
[tex]c = 42 -(18 + 10) cm = 14 cm\\s = 21 cm//[/tex]
Area = [tex]\sqrt{s(s - a)(s - b)(s - c) }[/tex]
and, here s = half the perimeter,
[tex](a + b + c)/2.[/tex]
A = [tex]21\sqrt{11}[/tex]
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A small company manufactures two products: A and B. Each product requires three operations: assembly, finishing and testing. Product A requires 1 hour of assembly, 3 hours of finishing, and 1 hour of testing. Product B requires 3 hours of assembly, 1 hour of finishing, and 1 hour of testing. The total work-hours available per week in the assembly division is 60, in finishing is 60, and in testing is 24. Each item of product A has a profit of $50, and each item of Product B has a profit of $75. How many of each should be made to maximize profit?
Hence,the company should produce 12 pieces of Model A and 6 pieces of Model B to get the maximum profit i.e. 168000.
How many of each should be made to maximize profit?Let x be the number of pieces of model A and y be the number of pieces of model B.
Let total profit be Z
Then, Total profit =8000x+12000y
Z=8000x+12000y .............. (i)
Now we have the following mathematical model for the given problem
Max Z=8000x+12000y
Subject to constraints
9x+12y≤180 .......... (Fabricating constraints)
3x+4y≤60 .......... (ii)
x+3y≤30 (Finishing constraints)........ (iii)
Let us evaluate the objective function Z at each point as shown below
At C(0,10), Z=8000×0+12000×10=120000
Maximum value of Z is 168000 at B(12,6)
Hence, the company should produce 12 pieces of Model A and 6 pieces of Model B to get the maximum profit i.e. 168000.
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A bakery records whether the customer is a loyalty program member or not on each receipt.
Total purchase price for both members and non-members is skewed toward the higher
prices.
The bakery takes separate random samples of 45 receipts from members and non-members.
They look at the difference in the mean total price from each group
(member - non-member).
What do we know about the shape of the sampling distribution of TM - IN, and why?
The sample size is more than 30 and according to the central limit theorem, with a sample size of more than 30, approximately normal distribution.
What is the central limit theorem?
The central limit theorem establishes that, in many situations, when independent random variables are summed up, their properly normalized sum tends toward a normal distribution even if the original variables themselves are not normally distributed.
We have,
the shape of the sampling distribution of the (mean of members - mean of non-members):
A. It's exactly normal because both populations are normally distributed.
B. It's approximately normal because both sample sizes are at least 30.
C. It's skewed, because the populations are skewed, and both sample sizes are at least 30.
D. The shape cannot be determined since we don't know the shape of either population distribution.
Option (B) is true, as the sample size is more than 30 and according to the central limit theorem, with a sample size of more than 30, approximately normal distribution.
Hence, the sample size is more than 30 and according to the central limit theorem, with a sample size of more than 30, approximately normal distribution.
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How do you solve inverse questions?
In order to solve a inverse function question we switch the coordinates of x with that of y and the perform the required calculations.
The result which we get as is considered as a relation and not as a function.
We an calculate inverse for functions which are one to one .
A function is known as a one to one function only when every second element matches the first value.
The inverse question is a type of function , when we solve this function we get another function which is represented as , ‘g’ and is known as the inverse of function .
y = f(x) then,
x = g(y)
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What is the space between contour lines called?
The space among contour lines are known as Sharp slopes which is closely spaced contour lines. Gently sloping or comparatively flat regions are shown by widely spaced contour lines.
Contour lines link places with the same elevation; if they are close together (they never intersect), the terrain is steep and the elevation changes quickly over a short distance. The elevation changes gently where the contour lines are far apart, indicating a moderate slope.
The areas between the contour lines are filled with colors when using the layer tinting technique. A particular height is indicated by each color. Contours are shown as lines. A hilltop is indicated by a contour line that creates a closed loop with no other contour lines inside. Sharp slopes are indicated by closely spaced contour lines. Gently sloping or comparatively flat regions are shown by widely spaced contour lines.
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A(n) _____ s a numerical summary of a sample. A(n) _____ is a numerical summary of a population.
Answer:
1. statistic 2. parameter
Step-by-step explanation:
A boat heading out to sea starts out at Point A, at a horizontal distance of 1032 feet
from a lighthouse/the shore. From that point, the boat's crew measures the angle of
elevation to the lighthouse's beacon-light from that point to be 15°. At some later
time, the crew measures the angle of elevation from point B to be 6°. Find the
distance from point A to point B. Round your answer to the nearest tenth of a foot if
necessary.
Answer:
1598.9 ft
Step-by-step explanation:
You want the distance between points A and B when observers at each point find the angle of elevation to a lighthouse beacon to be 15° and 6°, respectively. Point A is 1032 ft horizontal distance from the lighthouse.
TangentThe tangent relation for sides in a right triangle is ...
Tan = Opposite/Adjacent
This can be rearranged to ...
Opposite = Tan × Adjacent
SetupIf d is the distance in feet from A to B, two expressions for the same lighthouse height can be written:
height = tan(15°)(1032)
height = tan(6°)(1032 +d)
SolutionEquating these values of height, we have ...
tan(6°)(1032 +d) = tan(15°)(1032)
d = 1032(tan(15°) -tan(6°))/tan(6°) = 1032(tan(15°)/tan(6°) -1)
d ≈ 1598.946 . . . . feet
The distance from A to B is about 1598.9 feet.
To diplay the ditribution of the length in inche of a ample of brook trout, you could ue
To display the distribution of the lengths in inches of a sample of brook trout, the graph you should use is histogram. (Option A)
A histogram refers to a graphical representation of data points organized into user-specified ranges. It is an approximate representation of the distribution of numerical data. It is similar in appearance to a bar graph; however, the histogram condenses a data series into an easily interpreted visual by taking many data points and grouping them into logical ranges or bins. It is used to summarize discrete or continuous data that are measured on an interval scale. The histogram is represented by a set of rectangles, adjacent to each other, where each bar represents a type of data. Hence, in order to display the distribution of the lengths in inches of a sample of brook trout, the appropriate graph to use is histogram.
Note: The question is incomplete. The complete question is probably is: To display the distribution of the lengths in inches of a sample of brook trout, what graph should you use? A) histogram B) bar chart C) scatterplot D) pie chart E) line graph.
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Please give a step by step explanation
From the concepts and properties of triangles, m∠BDC is 26°.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know the sum of all the interior angles in a triangle is equal to 180°.
In the given ΔABD, line segment AD and BD are equal and hence it is an isosceles triangle.
Therefore,
x° + x° + 70° = 180°.
2x° = 110°.
x = 55°.
So, m∠DAB = m∠DBA = 55°.
We know the sum of linear pair of angles is 180°.
Therefore, m∠ABD + m∠DBC = 180°.
55° + m∠DBC = 180°.
m∠DBC = 125°.
Now,
m∠BDC + m∠DCB + m∠CBD = 180.
m∠BDC + 29° + 125° = 180°.
m∠BDC = 26°.
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What is the mean of the following numbers 23 45 87 40 50?
The mean of the set of numbers 23, 45, 87, 40, and 50 is 49. This is the average value of the set, and it is affected by all the values in the set.
The mean, also known as the arithmetic mean, of a set of numbers is found by adding up all the numbers in the set and dividing by the total number of numbers in the set. In this case, the set of numbers is 23, 45, 87, 40, 50. When we add up all the numbers in the set, we get a total of 245. There are 5 numbers in the set, so the mean is 245 / 5 = 49.
To find the mean, we first need to add up all the numbers in the set. Then, we divide that sum by the total number of numbers in the set. This gives us the average value of the set.
In summary, the mean of the set of numbers 23, 45, 87, 40, 50 is 49. This is the average value of the set, and it is affected by all the values in the set.
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Wanda is a cake designer with a specialty in rectangular silk screen photo cakes. For every cake that she makes, the width of the cake is 4 inches more than the width of the photo in the center of the cake, and the length of every cake is two times its width. The area of the cake wanda is currently working on is at least 254 square inches.
The inequality x² + 8x - 238 <= 0 represents the situation in which the area of the cake is at least 254 square inches.
The width of the cake is 4 inches more than the width of the photo, so the width of the cake can be represented by the expression x+4.
The length of the cake is two times its width, so the length of the cake can be represented by the expression 2(x+4).
The area of the cake is the product of its length and width, so it can be represented by the expression (x+4)(2(x+4)).
To represent the situation in which the area of the cake is at least 254 square inches, we can set the expression for the area equal to 254 and solve for x:
(x+4)(2(x+4)) >= 254
2x² + 16x + 16 >= 254
x² + 8x - 238 <= 0
The inequality x² + 8x - 238 <= 0 represents the situation in which the area of the cake is at least 254 square inches.
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Determine if the table shows a proportional relationship.
x 7.2 9.2 13.6
y 1.8 2.3 3.4
Yes, it is proportional because all y over x ratios are equivalent to one half.
Yes, it is proportional because all y over x ratios are equivalent to one fourth.
No, it is not proportional because 9.2 over 2.3 does not equal 1.8 over 7.2.
No, it is not proportional because 2.3 over 9.2 does not equal 13.6 over 3.4.
Answer:
the answer it's No, it is not proportional because 2.3 over 9.2 does not equal 13.6 over 3.4.
Answer: The answer is C!
Step-by-step explanation:
Sarah pays a flat rate plus a rate per minute for her phone plan as shown in the graph above. The cost of Sarah's phone plan, C(t), can be represented by which of the following functions? Responses C(t)=−0.10t+25 C t = - 0 . 10 t + 25 C(t)=0.10t+25 C t = 0 . 10 t + 25 C(t)=25(0.10)t C t = 25 0 . 10 t C(t)=25(1+0.10)t
With the help of Algebra the correct function is C(t) = 0.10t+25.
What is Algebra?
Algebra is a branch of mathematics that deals with the study of symbols and the rules for manipulating them. It is used to solve a variety of equations and problems by using formulae, equations and graphs. Algebra is primarily used to find unknown values, such as the unknown side of a triangle or the value of a variable in an equation. It can also be used to solve problems that involve more than one variable, such as those involving linear equations and systems of equations. Algebra is a powerful tool for problem-solving and can be used in various scientific fields, such as physics, chemistry and engineering. It is essential for developing a good understanding of mathematics and is an important part of any mathematics curriculum.
Assuming that : y = kx + b
plug in : ( 0, 25 ) and ( 50, 30)
25 = b
30 = 50k + 25
so, k = 0.10 after solving this equation
y = 0.10t+25
Hence the function is C(t)= 0.10t+25
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What equation can be formed that would relate the width length and the area of the room?
The equation that makes relationship between width, length and area of a room is Area of room = length of room × width of room and perimeter of room = 2× (length of room + width of room)
How to calculate the size of a room?The size of a room is either square or rectangle in shape. Whenever a room is rectangle shaped, we need to measure all the side lengths and finally area is found by product of two unequal side length. Besides, we can determine the perimeter of room by adding the two unequal side length and finally 2 is multiplied with it.
What is the formula for rectangle or square?We stated earlier that the size of a room is either rectangle or square.
area of square shaped room = (side length× side length)
area of rectangle shaped room = (bigger side length × smaller side length)
perimeter of square shaped room = 4 × side length = 4√(area of room)
perimeter of rectangle shaped room = 2(bigger side length + smaller side length)
hence, the above equations make relationship among the width, length, area and perimeter of a room.
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What are the solutions to the quadratic equation 2x² 4x 7?
x=-2+3√2/2 and x=-2-3√2/2 are solutions of the quadratic equation 2x²+4x=7.
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
The given quadratic equation is 2x²+4x=7
Subtract 7 from both sides of the equation.
2x²+4x-7=0
Use the quadratic formula to find the solutions.
x=-b±√b²-4ac/2a
x=-4±√16-4(2)(-7)/2(2)
x=-4±√16+56/4
x=-4±√16+56/4
x=-2±3√2/2
x=-2+3√2/2 and x=-2-3√2/2
Hence, x=-2+3√2/2 and x=-2-3√2/2 are solutions of the quadratic equation 2x²+4x=7.
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Is triangle LMN a right triangle?
It is demonstrated in the following figure itself that △LMN is a right triangle.
What is a right triangle?
A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangle triangle, is a triangle with one right angle, or two perpendicular sides.
The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.
A right triangle's hypotenuse is its longest side, its "opposite" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question.
To describe the sides of right triangles, we utilize specific terminology.
The side opposite the right angle is always the hypotenuse of a right triangle.
So, in the given figure, it is shown that △LMN is a right triangle.
Therefore, it is demonstrated in the following figure itself that △LMN is a right triangle.
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Look at this system of equations.
-4x + 3y = 8
2x + 5y = -3
What value of b will make this system have the same solution?
by = 2
2x + 5y = -3
b =
In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
What is the best math equation?Euler's identity is considered to be "the finest of equations" in maths classes because it describes an unlikely combination of five mathematical constants. Euler's equation (published by Leonhard Euler in 1755) applies in the case of a perfect fluid.The basic operations involved in arithmetic are addition, subtraction, multiplication, and division. Arithmetic mean (average) = Sum of values/Number of values.In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.The forms commonly encountered are empirical, molecular, structural, and projection formulas. An empirical formula consists of symbols representing elements in a compound, such as Na for sodium and Cl for chlorine, and subscripts indicating the relative number of atoms of each constituent element.A General Rule for Solving Equations
Simplify each side of the equation by removing parentheses and combining like terms.Use addition or subtraction to isolate the variable term on one side of the equation.Use multiplication or division to solve for the variable.x= 9, y= 15
-4x +3y= 8 -----(1)
2x +5y=-3-----(2)
(1) ×2:
-8x +6y= 16 -----(3)
(3) -(2):
-4x +6y -(-8x +6y)= 16 -1
-4x +6y +4x -5y= 15
y= 15
Substitute y= 15 into (1):
-4x +3(15)= 8
-4x+45=8
4x+45-8
4x=37
x=37÷4
x=9
b = 2(9) + 5(15) + 3
b = 13 + 75 + 3 = 91
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How do you find the height of an isosceles triangle without the base?
The height of the isosceles triangle is h = [tex]\sqrt{a^{2}-\frac{c^{2} }{4} }[/tex]
Given,
Isosceles triangle;
An isosceles triangle has two equal sides as well as two equal angles. The Greek words iso (same) and skelos are the source of the name (leg). An equilateral triangle is one in which all of its sides are equal, whereas a scalene triangle is one in which none of its sides are equal.
Follow these procedures to determine an isosceles triangle's height:
The lengths of the two equal sides are squared.Step 1 is then reduced by the square of the unequal side length, its result being divided by four.The outcome from Step 2's square root.The height of an isosceles triangle is the outcome.That is,
Height, h = [tex]\sqrt{a^{2}-\frac{c^{2} }{4} }[/tex]
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Rearrange w = 3(2a + b) - 4 to make a the subject.
Answer:
The answer is a = w + 4 - 3b/2
Step-by-step explanation:
w = 3(2a + b) - 4
add 4 both sides we get,
w + 4 = 3(2a + b) - 4 + 4
w + 4 = 3(2a + b)
w + 4 = 6a + 3b
Subtract 3b from both sides we get,
w + 4 - 3b = 6a + 3b - 3b
w + 4 - 3b = 2a
Now, Divide both sides by 2 we get,
w + 4 - 3b/2 = 2a/2
a = w + 4 - 3b/2
Thus, The answer is a = w + 4 - 3b/2
Need help!!
Maria is making t shirts to sell to earn money for a field trip. She only has enough money to make 25 t-shirts or less. If t represents the number of t shirts, write an equality that represents the situation
Answer: 25 smaller than or equal to t
Step-by-step explanation:
Because we know that she only has enough money to make 25 t-shirts or less, our number 25 will be smaller than or equal to t.
Miyo can make 5 origami figures in 3 minutes. How many origami figures can Miyo make in 18 minutes?
Answer:
Miyo can make 30 origami figures in 18 minutes
Step-by-step explanation:
tbh, i just counted up by 5's until i reached 18
Answer: 3
Step-by-step explanation: Because we know Miyo can make 5 origami figures in 3 minutes. and we want to know How many origami figures can Miyo make in 18 minutes? so, we know 5*3 is 15. right? well, then we take 18-15 and get 3 so, Miyo can make 3 origami figures in 18 mins.
What is a graph Grade 4?
Sets of points connected by typical lines or curves form graphs.
What is a graph?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.The relationships between two or more items are frequently represented by the points on a graph.The five main types are:Blank graph is a null graph, also known as an empty graph, is a graph with no connections connecting any of its vertices.A connected graph is one in which every pair of its vertices is connected by an edge path.A disconnected graph is one in which not every vertex is always connected by the path of the edges.A graph that can be divided into two sets of vertices, with edges passing solely between the two sets and not among them, is said to be bipartite.Weighted graph has assigned weights, or numerical values, to each of its edges is referred to as a weighted graph.To learn more about graphs, refer:
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help again asap pls!!!!!!!!!
Answer:
9
Step-by-step explanation:
vertical angles are congruent
110=13x-7
110+7=13x
117=13x
divide
9=x
x=9
What does ∆ mean in calculus?
Therefore, the Uppercase delta (Δ) in calculus denotes the change of variable.
What is calculus?Calculus is a discipline of mathematics that, in its most basic form, deals with rate of change. As an illustration, suppose you wanted to figure out how fast an automobile would slow down as it approached a stop sign. You may determine that change using calculus. Yes, calculus incorporates movement into math.
Here,
Given: Uppercase delta (Δ)
In math, the uppercase letter delta () typically denotes "change" or "the change."
Consider a scenario where the variable x represents an object's motion.
Consequently, "Δx" denotes "the change in movement." This mathematical interpretation of delta is used by scientists in a variety of scientific fields.
Therefore, the Uppercase delta (Δ) in calculus denotes the change of variable.
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Yin opened a savings account with $3500. The account
earns 8.75% simple interest annually. After how many years will the
balance of the account be $6000? Round to the nearest tenth, if
necessary.
The time required for the balance of the account to be $6000 is 19.5 years.
What is Simple interest?The simple interest method, which adds interest to the starting principal amount at the same rate every day, is a quick and easy technique to calculate the interest on that money.
Simple interest is a way to calculate the amount of interest that will be charged on a certain amount of money at a certain rate and for a certain period of time.
As per the information in the question,
Principal amount, p = $3500
Rate, r = 8.75%
End amount = $6000
SI = (p × r × t)/t
6000 = 3500 × 8.75% × t
t = (6000 × 100)/(3500 × 8.75)
t = (600000)/(3500 × 8.75)
t = 19.5 years.
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How do I solve for X?
Step-by-step explanation:
remember some of the angle theorems inside a circle.
first of all, arc angles are the angles of the corresponding circle segments at the center of the circle (the angle between the lines from the points on the arc to the center).
and, of course, all the arc angles together around a circle are therefore 360°.
so,
(8x + 20) + 104 + arc angle KJP = 360
and then :
the opposite angle is half of the arc angle for the same points on the circle arc.
angle L = 5x + 1 is the opposite angle of K and P, and that is therefore half of the arc angle KJP.
5x + 1 = (arc angle KJP)/2
arc angle KJP = 2×(5x + 1)
and by using this in the first equation we get
(8x + 20) + 104 + 2×(5x + 1) = 360
8x + 124 + 10x + 2 = 360
18x + 126 = 360
18x = 234
x = 234/18 = 13
Is purple math free?
Yes, Purple math is a completely free online math resource for students and teachers.
What is purple math?
Purple math is an online resource that provides comprehensive math lessons and problem-solving tools for students of all ages.
It offers step-by-step instructions for solving math problems, interactive tutorials, and helpful study guides.
The website also features practice tests, quizzes, and a variety of other learning resources to help students improve their math skills.
Purple math makes learning math fun and accessible to everyone, no matter their age or learning level.
According to the given question:
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what property is this? i’m so confused. like is it right?