Answer:
(y + 7)^2 = 98
Step-by-step explanation:
To write the equation in standard form for the given circle, we need to complete the square for both the x and y variables.
Let's start by rearranging the equation:
y^2 = -x^2 - 14y
Next, we'll complete the square for the y variable. To do this, we need to add a constant term that will complete the square on the left side of the equation. We'll add (14/2)^2 = 49 to both sides:
y^2 + 14y + 49 = -x^2 - 14y + 49
Now, let's group the terms:
y^2 + 14y + x^2 = -14y - x^2 + 49
To simplify the equation further, we can combine the x^2 term and the -x^2 term:
x^2 - x^2 + y^2 + 14y = 49
The x^2 terms cancel each other out, and we are left with:
y^2 + 14y = 49
To complete the square for the y variable, we need to add (14/2)^2 = 49 to both sides:
y^2 + 14y + 49 = 49 + 49
Simplifying further:
(y + 7)^2 = 98
Now, we can write the equation in standard form:
(y + 7)^2 = 98
Therefore, the equation in standard form for the circle is (y + 7)^2 = 98.
Prove that the only automorphism of a well-ordered set is the identity?
The only automorphism of a well-ordered set is the identity.
To prove this statement, we need to show that any automorphism of a well-ordered set must be the identity function. An automorphism is a bijective function that preserves the order structure of the set.
Assume we have a well-ordered set (W, ≤), where W is the set and ≤ is the order relation.
Let f: W → W be an automorphism of the set.
We aim to prove that f is the identity function, i.e., f(x) = x for all x ∈ W.
Suppose, for contradiction, that there exists an element a ∈ W such that f(a) ≠ a.
Since f is a bijective function, there must exist some b ∈ W such that f(b) = a.
Since (W, ≤) is well-ordered, there is a least element c in the set {x ∈ W : f(x) ≠ x}.
Let d = f(c). Since f is an automorphism, f(c) ≠ c, and thus d ≠ c.
Since (W, ≤) is well-ordered, there is a least element e in the set {x ∈ W : f(x) = d}.
Consider the element f(e). Since f is a bijective function, there must exist some f^{-1}(f(e)) = e' ∈ W such that f(e') = f(e) = d.
By the definition of automorphism, f(f^{-1}(y)) = y for all y ∈ W. Applying this property to e', we have f(f^{-1}(f(e'))) = f(e') = d.
However, f^{-1}(f(e')) = e' ≠ c, and thus f(e') ≠ d. This contradicts the fact that e is the least element in the set {x ∈ W : f(x) = d}.
Therefore, our assumption that there exists an element a such that f(a) ≠ a is false.
Since we assumed f(a) ≠ a for arbitrary a ∈ W, it follows that f(x) = x for all x ∈ W.
Hence, the only automorphism of a well-ordered set is the identity function.
Therefore, we have proven that the only automorphism of a well-ordered set is the identity function.
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one card is drawn from a pack of 52cards each of the 52 cards being equally likely to be drawn. what is the probability that the card drawn is a king?
The probability of drawing a king from a standard deck of 52 cards is 1/13.
In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.
To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).
The total number of possible outcomes is 52 because there are 52 cards in the deck.
The favorable outcomes, in this case, are the four kings.
Therefore, the probability of drawing a king is given by:
Probability = (Number of favorable outcomes) / (Number of possible outcomes)
= 4 / 52
= 1 / 13
Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.
This means that out of every 13 cards drawn, on average, one of them will be a king.
It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.
Each draw is independent, and the probability of drawing a king is constant.
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Instructions: Create a table of values for the function graphed below using the
plotted points. Remember, table of values are written with the x-values in order
from least to greatest (read the graph from left to right). Then, state the domain
and range of the function.
-10
x
5
?
The graph is bounded and does not extend to infinity, the range is the subset of real numbers within that constraint.
To create a table of values for the given function graph, we will identify the x-values and their corresponding y-values.
Reading the graph from left to right, the x-values in order from least to greatest are: -10, -5, 0, 5.
By looking at the graph, we can determine the corresponding y-values for each x-value.
Let's say the y-values are y1, y2, y3, and y4 respectively.
Now, we can create the table of values:
x | y
-10 | y1
-5 | y2
0 | y3
5 | y4
To state the domain and range of the function, we need to consider the set of all possible x-values and the set of all possible y-values.
In this case, the domain of the function is the set of x-values, which is {-10, -5, 0, 5}.
The range of the function is the set of y-values, which corresponds to {y1, y2, y3, y4}.
It is important to note that without specific values for y1, y2, y3, and y4, we cannot provide the exact range of the function.
The domain of the function is {-10, -5, 0, 5}, which is the set of all possible x-values.
Regarding the scope of the function, since you said that the y values correspond to {y1, y2, y3, y4}, it i not possible to determine the exact scope of the function since there are no specific values. y4 function for y1, y2, y3.
However, based on the chart and the information given, we can say that the range will be a series of real numbers, depending on how the chart behaves.
If the graph extends infinitely in both the positive y-direction and the negative y-direction, the range consists entirely of real numbers.
However, we can say that the range will be a set of real numbers depending on the behavior of the graph.
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You stop at the grocery store on the way home to pick up a few items. Round to the place of the first digit the items valued at $3.72, $.41, $1.28, and $.65.
Answer: 3.7 + 0.41 + 1.3 + 0.7
Step-by-step explanation: for 3.7 you see the number after 7 is 2 and that tells u to round down
0.41 - the digit after the 4 is 1 so u round down
1.3 - the digit after the 2 is 8 so u round up
0.7 - the digit after the 6 is 5 so u round up
Which expression demonstrates the use of the commutative property of addition in the first step of simplifying the expression (–3 + i) + (18 + 5i)?
Answer: [tex](-3+18)+(i+5i)[/tex]
Step-by-step explanation:
The commutative property of addition states that the order in which numbers are added does not change the sum. In the context of complex numbers, this means that you can rearrange the real and imaginary parts separately.
So, the expression that demonstrates the use of the commutative property of addition in the first step of simplifying the expression [tex](-3+i)+(18+5i)[/tex]
would be:
[tex](-3+18)+(i+5i)[/tex]
Central High School plays Eastern High School in a basketball game. Eastern had double the score of Central before Central scored a three-pointer as the game ended.
The variable, c, represents Central's score before the three-pointer. Express the total points scored in the game as a variable expression. Check all that apply.
2c + c
3c + 3
2c + 3
2c + c – 3
2c – c + 3
2c + c + 3
The gasoline tax is a ______ tax
Answer:
Excise tax
Step-by-step explanation:
Correct me if I'm wrong <3
Hi can any one teach me this constant difference
The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).
How do you find the constant difference in a sequence of numbers?In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.
Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.
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what is 56 times 13 +44 times 13 in distributive property
Answer:
1300
Step-by-step explanation:
(56 · 13) + (44 · 13)
(728) + (572)
1300
So, the answer is 1300
An individual wants to bring multiple copies of two comic books to a convention this week. There are 50 copies of the comic book the individual wants to sell (S) and 13 copies of a comic book the individual wants appraised (A), with a combined weight of 133.4 oz. The individual can only fit around 100 oz. of comics in a bag. If the individual brings 35 copies of the comic book they want to sell (S) and 13 copies to be appraised (A), the combined weight would be 100.4 oz. Calculate how much each comic (S) weighs.
The correct answer is each comic book the individual wants to sell (S) weighs approximately 2.213 ounces.
Let's assume the weight of each comic book the individual wants to sell (S) is "x" ounces.
Given that there are 50 copies of the comic book the individual wants to sell (S) and their combined weight is 133.4 ounces, we can set up the equation:
50x + 13A = 133.4 ---(Equation 1)
Similarly, if the individual brings 35 copies of the comic book they want to sell (S) and 13 copies to be appraised (A), the combined weight would be 100.4 ounces:
35x + 13A = 100.4 ---(Equation 2)
We can solve this system of equations to find the weight of each comic book the individual wants to sell (S).
Multiplying Equation 1 by 35 and Equation 2 by 50 to eliminate the variable "A," we get:
1750x + 455A = 4679 ---(Equation 3)
1750x + 650A = 5020 ---(Equation 4)
Subtracting Equation 3 from Equation 4, we eliminate "x" and get:
195A = 341
Dividing both sides of the equation by 195, we find:
A = 341/195
A = 1.75
Now, substituting the value of A into Equation 1 or Equation 2, we can solve for "x":
50x + 13(1.75) = 133.4
50x + 22.75 = 133.4
50x = 133.4 - 22.75
50x = 110.65
x = 110.65/50
x = 2.213
Therefore, each comic book the individual wants to sell (S) weighs approximately 2.213 ounces.
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$9, $11, $13, $15, $20, $10, $12, $15, $10, $15 What is the mode allowance?
mode is the number or item that repeats most frequent so it's $15
PLEASE HELP!! I need to answer this photos
Answer: [m and n], and [o and p]
Step-by-step explanation:
The parallel groups of lines are m and n, and the group o and p.
some adults and children are watching a musical there are n children there are 25 fewer adults
According to the concept of algebraic expression and arithmetic, the correct answers are A) Number of adults = N - 25. B) Number of adults when N = 124: 124 - 25 = 99
A) Let's denote the number of children as N. Since there are 25 fewer adults than children, the number of adults can be expressed as N - 25.
B) If there are 124 children, we substitute N with 124 in the expression from part A. Thus, the number of adults would be 124 - 25 = 99.
To arrive at these answers, we used the given information that there are "N" children and 25 fewer adults than children. By substituting the value of N, we determined the number of adults in terms of N and then calculated the specific number of adults when N is equal to 124.
Note: The given question is incomplete. The complete question is:
Some adults and children are watching a musical. there are 'N' number of children. There are 25 fewer adults than children.
A) find the number of adults in terms of 'N'.
B) if there are 124 children how many adults are there?
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What are the outputs of the function below?
-6, -3, 1, 5
-6, -3, 4, 6
-8, 2, 4, 6
-8, 2, 1, 5
Answer:
[tex]5 { \times 54}^{2} [/tex]
which solution is extraneous
The extraneous solution for the rational expression 2 · x² - 2 = (x - 1) · (x - 2) is equal to x = 1.
Is there any solution extraneous to a rational expression?
In this problem we must determine whether an extraneous solution exist to a given rational expression. The procedure is now summarized. First, use algebra properties to eliminate denominators:
1 / (x - 1) = (x - 2) / (2 · x² - 2)
2 · x² - 2 = (x - 1) · (x - 2)
Second, expand and simplify the expression until a polynomial in standard form is found:
2 · x² - 2 = x² - 3 · x + 2
x² + 3 · x - 4 = 0
Third, factor the quadratic equation:
(x + 4) · (x - 1) = 0
x = - 4 or x = 1
Fifth, check in initial expression:
1 / (- 4 - 1) = (- 4 - 2) / [2 · (- 4)² - 2]
- 1 / 5 = - 6 / 30
- 1 / 5 = - 1 / 5
1 / (1 - 1) = (1 - 2) / (2 · 1² - 2)
1 / 0 = - 1 / 0 (EXTRANEOUS)
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14
Type the correct answer in the box. Round off your answer to the nearest integer.
Two planes, A and B, start from the same place and move in different directions, making an angle of 50° between them. The speed of plane A is
200 miles per hour, and the speed of plane B is 300 miles per hour.
The two planes are
miles apart after one hour.
The two planes are approximately 200 miles apart, rounded off to the nearest integer.
Using the Law of Cosines formula,
The distance between the two planes can be determined.
The formula for the Law of Cosines is as follows: c^2 = a^2 + b^2 - 2ab*cos(C), where c is the side opposite the angle C and a and b are the other two sides.
Using the formula, the distance between the two planes after one hour can be calculated as follows:
[tex]c^2[/tex] = [tex]200^2[/tex] + [tex]300^2[/tex] - 2(200)(300)cos(50°)[tex]c^2[/tex]
= 40,000 + 90,000 - 120,000cos(50°)[tex]c^2[/tex]
= 130,000 - 89,873.86c
= sqrt(40,126.14)c
= 200.315 miles
Therefore, after one hour, the two planes are approximately 200 miles apart, rounded off to the nearest integer.
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Carpet sells for $2 per square foot and will cost you $312 to recarpet your rectangular room. If your room is 12 feet long, how many feet wide is it?
Answer:
The room is 13 feet wide.
Step-by-step explanation:
Calculate for the Area of the room by dividing the cost by the price per square foot.
Area = $312 ÷ $2
Area = 156 ft²
Area of a rectangle = length x width
A = lw
Since we're given with 12 ft as the length then we can solve for the width 'w'
A = lw
Substitute
A = 156
l = 12
156 = 12w
Divide both sides of the equation by 12
156/12 = 12w/12
13 = w
w = 13ft
How many solutions does this system have? no solutions one unique solution O O two solutions O or an infinite number of solutions
Answer:
no solutions
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
equation of blue line is y = x + 2 , in slope- intercept form
with slope m = 1
equation of red line is y = x - 3 , in slope- intercept form
with slope m = 1
• Parallel lines have equal slopes
then the blue and red lines are parallel.
the solution to the system is at the point of intersection of the 2 lines
since the lines are parallel then they do not intersect each other.
thus the system shown has no solution.
A car travels 120 miles from A to B at 30 miles per hour but returns the same distance at 40 miles per hour. The average speed for the round trip is closest to?
The average speed formula is given by:
[tex]\displaystyle\sf \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}[/tex]
Let's calculate the total distance first. The car travels 120 miles from point A to point B, and then returns the same distance. Therefore, the total distance is [tex]\displaystyle\sf 2 \times 120 = 240[/tex] miles.
Now, let's calculate the total time. The time taken to travel from A to B can be calculated using the formula [tex]\displaystyle\sf \text{Time} = \frac{\text{Distance}}{\text{Speed}}[/tex].
For the journey from A to B:
[tex]\displaystyle\sf \text{Time}_1 = \frac{120}{30} = 4[/tex] hours
For the return journey from B to A:
[tex]\displaystyle\sf \text{Time}_2 = \frac{120}{40} = 3[/tex] hours
The total time for the round trip is the sum of the individual times:
[tex]\displaystyle\sf \text{Total Time} = \text{Time}_1 + \text{Time}_2 = 4 + 3 = 7[/tex] hours
Now, we can calculate the average speed:
[tex]\displaystyle\sf \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{240}{7} \approx 34.29[/tex] miles per hour.
Therefore, the average speed for the round trip is closest to 34.29 miles per hour.
The diameter of Jacob's circular tabletop is 6 feet. What is the area, in square feet, of Jacob's tabletop?
Answer:
approximately 28.26 square feet
Step-by-step explanation:
The formula for the area of a circle is A = pi(r)^2. So, the radius is half of the diameter, meaning it's 3 feet. Then we square it to get 9, and multiply by pi, or 3.14. This leads us to the approximated answer of 28.26 square feet.
The area is:
28.27 square feet
Work/explanation:
Since the tabletop is circular, we use the formula for a circle's area, which is: [tex]\bf{A=\pi r^2}[/tex].
We have the diameter, and to find the radius, we divide the diameter by 2, which gives us 6 ÷ 2 = 3 feet, so the radius of the tabletop is 3 feet.
Now, here's a diagram for you;
[tex]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 3\ ft}\end{picture}[/tex]
Plug in the data:
[tex]\sf{A=\pi\times3^2}[/tex]
[tex]\sf{A=\pi\times9}[/tex]
[tex]\sf{A=28.27\:ft^2}[/tex]
Hence, the area is 28.27 square feet.29.For n ≥ 3, a pattern can be made by overlapping n circles, each of circumference 1 unit, so that each circle passes through a central point and the resulting pattern has order-n rotational symmetry.
For instance, the diagram shows the pattern where n = 7.
If the total length of visible ares is 60 units, what is n?
The value of n can be determined by finding the number of visible arcs in the pattern, which is 30 in this case.
To determine the value of n, we need to find the relationship between the total length of visible areas and the number of circles (n).
In the given pattern, each circle contributes to the visible area twice: once as its circumference and once as the overlapping part with the adjacent circles. Since the circumference of each circle is 1 unit, the visible area contributed by each circle is 2 units.
Therefore, the total length of visible areas can be expressed as 2n. Given that the total length is 60 units, we can set up the equation:
2n = 60
Solving this equation, we find:
n = 60/2 = 30
Thus, the value of n is 30.
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Give at least 5 definitions that one should know if learning the *introduction* to algebra 1
1. Variable: A symbol or letter that represents an unknown value or quantity in algebraic expressions and equations.
2. Equation: A mathematical statement that shows the equality between two expressions, typically represented by an equal sign (=).
3. Coefficient: The numerical factor that is multiplied by a variable in a term.
4. Expression: A mathematical phrase that may contain variables, constants, and operations, but does not have an equal sign.
5. Linear Equation: An equation in which the highest power of the variable is 1, written in the form ax + b = 0, where a and b are constants and x is the variable.
Variable: In algebra, a variable is a symbol (usually a letter) that represents an unknown value or quantity. It allows us to express mathematical relationships and solve equations.
Equation: An equation is a mathematical statement that shows the equality between two expressions.
It consists of an equal sign (=) and can include variables, constants, and operations.
Solving equations involves finding the values of the variables that make the equation true.
Coefficient: A coefficient is the numerical factor that is multiplied by a variable in a term.
It represents the scale or magnitude of the variable.
For example, in the term 3x, the coefficient is 3.
Expression:
An expression is a mathematical phrase that can contain variables, constants, and operations, but does not have an equal sign.
Expressions can be evaluated or simplified, but they cannot be solved since they lack the equality found in equations.
Linear Equation:
A linear equation is an equation where the highest power of the variable is 1.
It can be written in the form ax + b = 0,
where a and b are constants and x is the variable.
Solving linear equations involves finding the value(s) of x that satisfy the equation.
These are just a few key definitions that form the foundation of understanding introductory algebra.
Mastering these concepts will provide a solid basis for further exploration and learning in algebraic principles and problem-solving.
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Four points partition the directed line segment from A to B.
• Point P partitions the directed line segment from A to B into a 3:4 ratio.
• Point Q partitions the directed line segment from A to B into a 4:3 ratio.
• Point R partitions the directed line segment from A to B into a 2:5 ratio.
• Point S partitions the directed line segment from A to B into a 5:2 ratio.
A number line has points A and B. A line is drawn from point A to point B.
Which distance measures 5 units?
A number line going from negative 8 to positive 8. A closed circle appears at negative 8 and is labeled W. A closed circle appears at negative 3 and is labeled X. A closed circle appears at positive 1 and is labeled Y. A closed circle appears at positive 5 and is labeled Z. An orange arrow line extends the length of the number line and contains all points.
the distance between points W and X
the distance between points X and Y
the distance between points X and Z
the distance between points Y and Z
The correct option is (iii) the distance between points X and Z. Distance between points Y and Z: 2 units
We can find the distance between points on the line segment by finding the difference between their coordinates.
The correct option is the distance between points X and Z, which is equal to 6.
There are four points that partition the directed line segment from A to B.
The partition ratio at each point is as follows:
Point P partitions the directed line segment from A to B into a 3:4 ratio.
Point Q partitions the directed line segment from A to B into a 4:3 ratio.Point R partitions the directed line segment from A to B into a 2:5 ratio.
Distance between points Y and Z:
Again, the number line does not provide the exact coordinates of the points Y and Z. However, the line segment from A to B is split 5:2 at point S, so the distance can be concluded as: Between Y and Z is 2 units.
So the distance between the given points is:
Distance between points W and X: 5 units
Distance between points X and Y: 4 units
Distance between points X and Z: 5 units
Distance between points Y and Z: 2 units
Point S partitions the directed line segment from A to B into a 5:2 ratio.
Here, we have to measure the distance of each of the following:
(i) The distance between points W and X
(ii) The distance between points X and Y
(iii) The distance between points X and Z
(iv) The distance between points Y and ZThe distance between points X and Z is 6 units.
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The distances are described as follows:
The distance between points W and X is 5 units.
The distance between points X and Y is 4 units.
The distance between points X and Z is 8 units.
The distance between points Y and Z is 4 units.
How do we calculate?The distance between points W and X is gotten:
We subtract the coordinates of point W from the coordinates of point X to get the distance
Distance = X - W = (-3) - (-8) = 5 units.
The distance between points X and Y shown as :
we will also subtract the coordinates of point X from the coordinates of point Y.
Distance = Y - X = 1 - (-3) = 4 units.
The distance between points X and Z is :
We also subtract the coordinates of point X from the coordinates of point Z.
Distance = Z - X = 5 - (-3) = 8 units.
The distance between points Y and Z:
Finally, we subtract the coordinates of point Y from the coordinates of point Z.
Distance = Z - Y = 5 - 1 = 4 units.
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Is ABC similar to A DEF? Why or why not?
OA. Yes, because the angles are congruent and the sides are
proportional.
OB. Yes, because the angles are close enough and the sides are
proportional.
OC. We cannot tell because the third side is not given.
D. No, because not all the angles are congruent.
The correct answer is A. Yes, because the angles are congruent and the sides are proportional.
Two triangles are considered similar if their corresponding angles are congruent and their corresponding sides are proportional. In this case, we are given the triangles ABC and ADEF.
To determine if ABC is similar to ADEF, we need to compare the angles and sides of the two triangles.
If all the angles of one triangle are congruent to the corresponding angles of the other triangle, and the sides of one triangle are proportional to the corresponding sides of the other triangle, then the triangles are similar.
we can say that if the angles of ABC are congruent to the angles of ADEF and the sides of ABC are proportional to the sides of ADEF, then ABC is similar to ADEF.
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1. Identify the terms, variables, & coefficients in the expression shown in the picture
(Ignore the “5.”, the expression is 5 - 4x - 8y)
2. Andrea solved this and she believes the terms are 5, 4x, and 8y
She believes the variables
are x and y
She believes the coefficients are 5 and 4x
3. Is Andrea correct? if not, correct her mistakes!
Therms are
5 , 4x , 8y
Variables are
x , y
coefficients are
4 , 8
In the similar triangles below , what is the measure of D
45
22.5
63
90
sum angel measure of angles in triangle is 180° according to this rule
(n-2)180 , n is the no. of sides
so E+D+F=180
72+D+63=180
135+D=180
D=180-135
D=45°
HOPE IT HELPS
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sin(x) = 5/7 and x is in quadrant 2, determine the exact value of each of the following. Use fractions and radicals only, no decimals. You do not need to rationalize the denominator. sin(x/2) = COS = tan(x/2) =
Using the given information sin(x) = 5/7 and x in quadrant 2, the exact values are:
sin(x/2) = √[(1 - √24/7)/2],
cos(x/2) = -√[(1 + √24/7)/2],
tan(x/2) = (√[(1 - √24/7)/2]) / (-√[(1 + √24/7)/2]).
To determine the exact values of sin(x/2), cos(x/2), and tan(x/2) when sin(x) = 5/7 and x is in quadrant 2, we can utilize the half-angle formulas. These formulas allow us to express the trigonometric functions of an angle in terms of the trigonometric functions of half that angle.
Given sin(x) = 5/7, we can find cos(x) using the Pythagorean identity:
cos(x) = √(1 - sin^2(x)) = √(1 - (5/7)^2) = √(1 - 25/49) = √(24/49) = √24/7.
To find sin(x/2), we use the half-angle formula for sine:
sin(x/2) = ±√[(1 - cos(x))/2] = ±√[(1 - √24/7)/2].
Since x is in quadrant 2, sin(x) is positive. Therefore, sin(x/2) is also positive. Thus, we have:
sin(x/2) = √[(1 - √24/7)/2].
Similarly, we can find cos(x/2) using the half-angle formula for cosine:
cos(x/2) = ±√[(1 + cos(x))/2] = ±√[(1 + √24/7)/2].
Since x is in quadrant 2, cos(x) is negative. Therefore, cos(x/2) is also negative. Thus, we have:
cos(x/2) = -√[(1 + √24/7)/2].
Lastly, we can find tan(x/2) using the half-angle formula for tangent:
tan(x/2) = sin(x/2) / cos(x/2) = (√[(1 - √24/7)/2]) / (-√[(1 + √24/7)/2]).
Combining these results, the exact values for sin(x/2), cos(x/2), and tan(x/2) when sin(x) = 5/7 and x is in quadrant 2 are:
sin(x/2) = √[(1 - √24/7)/2],
cos(x/2) = -√[(1 + √24/7)/2],
tan(x/2) = (√[(1 - √24/7)/2]) / (-√[(1 + √24/7)/2]).
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Puan Yani has RM24 700 in her saving account. Her husband has RM75 300 more money than Puan Yani. At the end of May, Puan Yani deposited RM1 300 in her account. What is the total savings they have now?
The total savings that the couple Puan Yani and her husband have now is A) RM126,000.
How the total savings are computed:The total savings of the couple can be determined by addition.
Addition is one of the four basic mathematical operations, including subtraction, divsion, and multiplication.
Let the amount that Puan Yani has in her savings account, a = RM24,700
Let the amount that her husband has than Puan Yani = RM75,300
The total amount that her husband has = a + 75,300
= RM100,000 (R24,700 + RM75,300)
The additional amount that Puan Yani deposited at the end of May = RM1,300
The total amount that Puan Yani has in her savings account at the end of May = RM26,000 (RM24,700 + RM1,300)
The total savings in the couple's accounts = RM126,000 (RM100,000 + RM26,000)
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For Mean = 73.19, Mode = 79.56 and Variance = 16, the Karl Pearson's Coefficient of Skewness will be -0.0256 -1.64 0.0256 0
Answer:
To calculate Karl Pearson's coefficient of skewness, we need to use the formula:
Skewness = 3 * (Mean - Mode) / Standard Deviation
Given the Mean = 73.19, Mode = 79.56, and Variance = 16, we need to find the Standard Deviation first.
Standard Deviation = √Variance = √16 = 4
Now we can substitute the values into the formula:
Skewness = 3 * (73.19 - 79.56) / 4
Skewness = -6.37 / 4
Skewness = -1.5925
Rounded to four decimal places, the Karl Pearson's coefficient of skewness for the given values is approximately -1.5925.
Anyone can help me plis for this 5 questions
The angles formed by the diagonals and sides of the regular geometric figures and polygons indicates;
6. m∠1 = m∠2 = 90°
m∠4 = 39°
7. m∠3 = 52°
m∠1 = 128°, m∠2 = 128°
8. x = 30°
9. The lines drawn are the median lines of the triangle
10. 120°
What is a polygon?A polygon is a geometric figure with three or more sides that form a loop.
6. The diagonals of a kite are perpendicular, therefore;
m∠1 = m∠2 = 90°
m∠3 = 51° (Corresponding angles of congruent triangles are congruent)
m∠4 = 90° - ∠3 (Acute angles in a right triangle)
m∠4 = 90° - 51° = 39°
Part 2
The base angles of an isosceles trapezoid are congruent, therefore;
m∠3 = 52° (Definition of congruent angles)
The angles ∠1 and ∠2 are congruent, therefore;
m∠1 + m∠2 + 52° + m∠3 = 360°
m∠1 + m∠2 = 360° - (52° + m∠3)
2 × m∠1 = 360° - (52° + 52°) = 256°
m∠1 = 256°/2 = 128°
m∠1 = m∠2 = 128°
8. The measure of an interior angle of a polygon is; θ = (n - 2) × 180/n
The polygon is a dodecagon, therefore, the measure of the interior angles of the 12 sided polygon is therefore;
θ = (12 - 2) × 180/12 = 150
The angle x and the interior angles of the dodecahedron are linear pair angles, therefore;
θ + x = 180°
x = 180° - θ
x = 180° - 150° = 30°
9. The lines drawn that bisect the facing sides are median lines, that are also the angle bisectors of the interior angles of the triangle. The point of intersection of the lines is the incenter and the centroid of the triangle.
10. The interior angle of a regular hexagon, which is a 6 sided polygon can be found as follows;
Interior angle of a regular polygon with n sides, θ = (n - 2) × 180/n
In a regular hexagon, n = 6, therefore;
θ = (6 - 2) × 180/6 = 120°
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