The angle at the center of the circle will be;
⇒ θ = 0.5 radian
What is Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
A sector of a circle of radius 10 cm and has an area of 25 cm².
Now,
Since, We know that;
⇒ A = 1/2 r²θ
Where, A is area of circle , r is radius of circle and θ is the angle at the center of the circle.
Here, A sector of a circle of radius 10 cm and has an area of 25 cm².
Substitute all the given values, we get;
⇒ A = 1/2 r²θ
⇒ 25 = 1/2 × 10² × θ
⇒ 25 = 50 × θ
⇒ θ = 25 / 50
⇒ θ = 0.5 radian
Thus, The angle at the center of the circle = 0.5 radian
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A recreational area is formed by a rectangular shaped pool and a cement patio surrounding the pool. the pool has a length of 3x-3 meters and a width of 2x+7 meters. The patio extends x meters around to pool, on all sides of the pool. Write a polynomial expression that gives the total area of the recreational area.
The total area of the recreational area can be represented by the polynomial expression 26x² + 57x + 35.
What is the area of the rectangle?The area of a rectangle is defined as the product of the length and width.
The area of a rectangle = L × W
Where W is the width of the rectangle and L is the length of the rectangle
The area of the rectangular pool is given by its length times its width, so the area of the pool is (3x - 3) meters × (2x + 7) meters = (6x² + x - 21) square meters.
The area of the patio is given by the length of the pool plus twice the extension (x) on each side, times the width of the pool plus twice the extension on each side, so the area of the patio is (3x - 3 + 2x) meters × (2x + 7 + 2x) meters = (5x + 4) × (4x + 14) = 20x² + 56x + 56 square meters.
The total area of the recreational area is the sum of the areas of the pool and the patio, so it can be represented by the polynomial expression:
20x² + 56x + 56 + 6x² + x - 21 = 26x² + 57x + 35
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Which of the following statements must be true based on the diagram below?
Select all that apply. (Diagram is not to scale.)
The following statements are true based on the diagram below
I is a vertex of right angleK is a vertex of right angleWhat is vertex?When two or more curves, lines, or edges come together, it is called a vertex (plural: vertices or vertexes) in geometry. As a result of this definition, polygonal and polyhedral corners as well as the intersection of two lines to form an angle are referred to as vertices.
The vertex of an angle is the point at which two rays start or meet, where two line segments join or meet, where two lines intersect (cross), or any other suitable arrangement of rays, segments, and lines that results in two straight "sides" coming together at one location.
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To prevent deer from running across highways, researchers are investigating sound-emitting devices that would frighten deer before they reach the highway. As part of the investigation, the researchers set up 20 devices along a two-mile stretch of road. When a deer approached a device, the device would activate and emit a sound. The researchers recorded whether the deer moved toward the highway (positive response), away from the highway (negative response), or did not move (neutral response).
The researchers kept the loudness of the sound constant at 60 decibels. However, they varied the pitch of the sound. There were 6 treatment levels, all measured in kilohertz (kHz): 0, 0.28, 1, 8, 15, and 28. The order of the treatments was randomly assigned.
(a) The control in the experiment was 0 kHz, or no sound. What information is gained by using the control with no sound that could not be obtained if no control were used?
(b)(i) What is one advantage to keeping the loudness at a constant 60 decibels for all treatments?
(b)(ii) What is one disadvantage to keeping the loudness at a constant 60 decibels for all treatments?
(c) The results of the experiment are shown in the following bar chart.
Based on the results, would you recommend using a sound-emitting device to keep deer from running across highways? Explain your answer.
Answer: a) The control in the experiment, 0 kHz, or no sound, serves as a baseline against which to compare the other treatments. By using the control with no sound, researchers can determine whether the deer's response to the sound-emitting devices is due to the sound itself or some other factor. Without the control, it would be unclear what caused any differences in the deer's responses to the different sound treatments.
(b)(i) One advantage to keeping the loudness at a constant 60 decibels for all treatments is that it allows researchers to directly compare the deer's responses to the different sound pitches without the added variable of loudness.
(b)(ii) One disadvantage to keeping the loudness at a constant 60 decibels for all treatments is that loudness may also play a role in deer's response. So, it would be unclear if the different in deer's responses are due to sound frequency only or also caused by sound loudness
(c) Based on the results shown in the bar chart, it can be seen that the deer's response to the sound-emitting devices varies depending on the pitch of the sound. At lower pitches, around 0.28 kHz, the deer's response is more likely to be negative or neutral, indicating that they move away from or don't move towards the highway. At higher pitches, around 15 kHz, the deer's response is more likely to be positive, indicating that they move towards the highway. It suggests that the frequency of sound has an impact on the deer's response. So, based on this data, we cannot recommend using a sound-emitting device to keep deer from running across highways without further research on the optimal frequency and loudness that should be used to make sure that it is effective and safe for the deer.
Step-by-step explanation:
The sound-emitting device may have both advantages and disadvantages depending on the pitch. More research is necessary to find the optimal frequency and volume for the device to be effective and safe.
Explanation:Based on the results of the experiment, it would not be advisable to use a sound-emitting device to prevent deer from running across highways without further research. The experiment showed that the deer's response varied depending on the pitch of the sound. Although the device showed some advantages, such as moving deer away from the highway at lower pitches, it also presented potential disadvantages. At higher pitches, the deer had a tendency to move towards the highway, which could increase the risk of accidents. More research would be needed to determine the optimal frequency and volume to use for the device to be both effective and safe for the deer.
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A line passes through the point (-10,1) and has a slope of 3/2. Write an equation in point-slope form for this line.
The line passes through the point (-10,1) and has a slope of 3/20 has the equation as: y - 1 = 3/2 (x + 10)
How to write the equation of the lineThe general form of a linear equation is y - y₁ = m (x - x₁).
It draws attention to the line's slope and one of the line's points (that is not the y-intercept)
The point slope formula is given by y - y₁ = m (x - x₁), where:
y = output value
y₁= the given y coordinate point
m = slope
x = input value
x₁ = the given x coordinate
substituting the point (-10,1) and slope 3/2
y - y₁ = m (x - x₁)
y - 1 = 3/2 (x + 10)
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Name the image of p (9, 1.5) after being translated along the vector <3, -0.5>
The image for P(9, 1.5) after Translation is P'( 12, 1).
What is Translation?Each point in a figure is moved the same distance in the same direction using a type of transformation known as translation.
For example, this transformation moves the parallelogram to the right 5 units and up 3 units. It is written ( x , y ) → ( x + 5 , y + 3 ) .
Given:
P(9, 1.5) with Translating Vector (3, -0.5).
So, Applying the Translation we get
P(9 + 3, 1.5 + (-0.5))
= P(12 , 1.5- 0.5)
= P(12, 1)
hence, the image is P'( 12, 1).
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19,22,25,28 the 11nth term
Answer:
31 hecause the èattern is adding 3
Step-by-step explanation:
WHAT IS THE RECIPOCAL OF 6/5
Answer: 5/6
Step-by-step explanation:
The reciprocal of a number is 1 divided by that number. The reciprocal of 6/5 is 5/6.
Answer:
5/6
Step-by-step explanation:
Well to find a fraction's reciprocal all you need is to flop it like this
6/5 => 5/6
so 5 takes the place of 6 and 6 takes the place of 5
that's how 6/5 turns into 5/6
hence, the reciprocal is 5/6 .A rope 15 inches long has been divided into the greatest possible number of pieces in such a way that each piece has a different length, and each of these lengths in inches is expressed by a whole number. How many cuts were made?
A.3
B.4
C.5
D.6
E.7
Answer:
Below
Step-by-step explanation:
1+2+3+4+5 =15 5 lengths will require 4 cuts
what is the evaluation for 4-4y+y-3
Answer:
1-3 y
Step-by-step explanation:
Subtract the numbers 4 AND 3 WHICH WOULD EQUAL REWRITING THE ADDITON SO IT CHANGES THE MINUS SIGN TO A PLUS.
Find the range of values of k for which the equation 4x² + 12x + k = 0 has no real roots.
Hello there!
Answer:
[tex](9, +\infty)[/tex]
Step-by-step explanation:
It has no real roots only if
[tex] \sqrt{b {}^{2} - 4ac } [/tex]
has no roots. That means that b² - 4ac is smaller than 0:
[tex]b {}^{2} - 4ac < 0 \\ 12 {}^{2} - 4 \times 4 \times k < 0 \\ 144 - 16k < 0 \\ 144 - 144 - 16k < - 144 \\ - 16k < - 144 \\ k > 9 \\ k \: \: \: in \: \: \: (9, +\infty)[/tex]
we can approach this from the standpoint of the discriminant, if the discriminant is negative then we only get complex roots or namely "imaginary" solutions or values, well, let's check before that happens, when the discriminant is 0.
[tex]\qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ y=\stackrel{\stackrel{a}{\downarrow }}{4}x^2\stackrel{\stackrel{b}{\downarrow }}{+12}x\stackrel{\stackrel{c}{\downarrow }}{+k} ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases}[/tex]
[tex]0=(12)^2 - 4(4)(k)\implies 0=144-16k\implies 16k=144 \\\\\\ k=\cfrac{144}{16}\implies k=9\hspace{5em} \stackrel{if~k > 9\textit{, then we land on negative territory}}{{\Large \begin{array}{llll} k > 9 \end{array}}}[/tex]
Solve 7 cos(2x) = 7 cos² (x) - 4 for all solutions
value of x for all solution is 49.11° or 50° and 230°
Which trigonometry topics should I learn first?Before mastering trigonometry, you should have a working knowledge of algebra and geometry. You ought to be able to work with algebraic expressions and equations without any trouble. The Pythagorean theorem, similar triangles, and a few other concepts from geometry should be familiar to you, but not a lot.
7 cos(2x) = 7 cos² (x) - 4
7 cos² (x) - 7 (2cos² (x)-1)- 4=0
7 cos² (x)- 14 cos² (x)+7-4=0
cos² (x)= 3/7
range given from 0 to 360°.
x=49.11° or 50° and 230°
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Please help me please
can anyone help me out with this question
Answer:
[tex] \sf \: b) \: 45[/tex]
Step-by-step explanation:
The values given are,
→ u = 7
→ d = 10
→ e = 3.2
Now the expression is,
→ 15(d - u)
Evaluating the expression,
→ 15(d - u)
→ 15(10 - 7)
→ 15 × 3
→ 45
Hence, option (b) is correct.
Answer:45
Step-by-step explanation:
15(10-7)
15(3)
multiply and get 45
Determine if each of the following statements are true or false (HELP!!! ARE MY ANSWERS CORRECT?)
Answer:
yes
Step-by-step explanation:
find the order pairs for y=-5x-4
Answer:
(0,-4),(1,1)(2,6)
Step-by-step explanation:
Please help with homework
Solve
2(x+4)=3(-2+x)
Answer:
x = 14
Step-by-step explanation:
2(x + 4) = 3( -2 + x) distribute the 2 and the 3.
2(x) + 2(4) = 3(-2) + 3(x)
2x + 8 = -6 + 3x Subtract 2x from both sides
2x - 2x + 8 = -6 +3x -2x
8 = -6 +x Add 6 to both sides
8 + 6 = 6 - 6 + x
14 = x
Visually estimate the location of the centroid of the region shown. Then find the exact coordinates of the centroid.
y=49-x², y = 0
Therefore exact coordinates of Centroid = (0,3/2)
Define Centroid.The centroid of a flat figure or solid figure, also known as the geometric center or center of figure, in mathematics and physics, is the arithmetic mean position of all the points on the figure's surface. Any n-dimensional Euclidean object is included by the same definition.
What is Triangle?A polygon having three edges and three vertices is called a triangle. It is one of the fundamental geometric forms. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
This region is a parabola opening downward, with vertex at (0, 49) and a range of y values from 0 to 49. The region is symmetric about the y-axis, This means that the x-coordinate of the centroid is at 0.
To find the y-coordinate:
Integral from -√(49) to √(49) of (49-x²) x dx = [x²(49-x²)/3] from -√(49) to √(49) = (492√(49))/3 = (98√(49))/3
The area is integral from -√(49) to √(49) of (49-x²) dx = [x(49-x²)/2] from -√(49) to √(49) = (49*(2√(49)) - (2/3)(49^(3/2)))/2 = (49*(2*√(49)) - (98√(49))/3)/2
Therefore Centroid = (0, (98√(49))/(49*(2*√(49)) - (98√(49))/3)) = (0,3/2)
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PLEASE HURRY BE FAST
A fishing map is laid out on a coordinate plane with each unit equal to 1 mile. The boat is launched from the point (−3, 0) and goes to point (−3, 3) to fish. From there, the boat travels to (0, 0) to fish and then goes back to the launch point.
Determine the total number of miles traveled. Round to the nearest mile.
3 miles
6 miles
10 miles
24 miles
Answer:
24 miles
Step-by-step explanation:
each distance between points is 6.
6+6+6+6=24 miles
Select all the relations which represent a function.
- (1,3), (2,5), (2,7), (4,9) (1,3), (1,5), (1,7), (4,9) 0 (1,2), (2,5), (2,1), (4,5)
(1,3), (2,5), (3,7), (4,9) (1,3), (2,3), (3,3), (4,3)
Therefore , (1, 3), (2, 5), (3, 7) (4, 9) and (1, 3), (2, 3), (3, 3) (4, 3) are the relations that represent a function.
Function is what?According to a function's rule, every x value in the domain has one and only one range of y values. Definition. A one-to-one function exists when there is just one and only one value of x such that f(x) = y.
Here,
The relationship is (1, 3), (2, 5), and (2, 7) (4, 9)
Given that 2 is repeated, the connection is not a function.
The relationship is (1, 3), (2, 5), and (3, 7) (4, 9)
Since there are no repeating numbers, the relation is a function.
The relationship stated is (1, 3), (1, 5), and (1, 7). (4, 9)
The relationship is not a 1 repeated function.
The relationships are (1, 3), (2, 3), and (3, 3). (4, 3)
Since there are no repeating numbers, the relation is a function.
The relationship stated is (1, 2), (2, 5), and (2, 1) (4, 5)
As 2 repeated, the relationship is not a function.
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Factor the expression y^2+8x+12
Answer: y^2+8x+12
Step-by-step explanation:
A group of children played a balloon dart game at the county fair. The children took turns at the game, and the first 9 players scored
230, 540, 420, 430, 540, 560, 275, 50, 250
Joey is the 10th player, and his score is recorded with the first 9 scores after his turn. If Joey wants his score to be higher than the 70th percentile of all 10 scores, at least how many points does Joey need to score?
Joey needs to score more than 540 points, to be higher than
70th percentile of all scores.
What is percentile?Percentile is defined as the value below which a given percentage falls under.
Example: In a group of 20 children, Ben is the 4th tallest and 80% of the children are shorter than you. Hence, it means that Ben is at the 80th percentile.
The percentile formula determines the performance of a person over others. The percentile formula is used in finding where a student stands in the test compared to other candidates. A percentile is a number where a certain percentage of scores fall below the given number.
Given,
Scores of first 9 players:
230, 540, 420, 430, 540, 560, 275, 50, 250
let the score of joey be x.
Scores of all 10 players
230, 540, 420, 430, 540, 560, 275, 50, 250
Dataset in ascending order =
50, 230, 250, 275, 420, 430, 540, 540, 560
70th percentile of the dataset
k = 70
i = the index
n = total number of given data values = 10
i = k/100(n+1)
i = 70/100 (9+1)
i = 70 × 10/100
i = 7
The index of 70th percentile = 7
value of 70th percentile = value of data on index 7.
value of 70th percentile = 540.
Hence, To be higher than 70th percentile of all scores,
Joey should score more than 540.
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Please help me solve
[tex]~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill[/tex]
[tex](-6x^3 y^5 + 11x^3 y^2) \div (-2x^2 y^3)\implies \cfrac{-6x^3 y^5 + 11x^3 y^2}{-2x^2 y^3} \\\\\\ \cfrac{-6x^3 y^5}{-2x^2 y^3}+\cfrac{11x^3 y^2}{-2x^2 y^3}\implies \cfrac{-6}{-2}\cdot \cfrac{x^3 y^5}{x^2 y^3}+\cfrac{11}{-2}\cdot \cfrac{x^3 y^2}{x^2 y^3} \\\\\\ 3\cdot x^3 x^{-2}y^5 y^{-3}+\cfrac{11}{-2}\cdot \cfrac{x^3 x^{-2}}{y^3 y^{-2}}\implies 3x^{3-2}y^{5-3}-\cfrac{11}{2}\cdot \cfrac{x^{3-2}}{y^{3-2}} \\\\\\ ~\hfill {\Large \begin{array}{llll} 3x y^2 -\cfrac{11x}{2y} \end{array}}~\hfill[/tex]
what is the domain of y=2(x+1)-(3x-2)
Answer:
Domain is all real numbers (basically any number)
Step-by-step explanation:
Step 1: Simplify the expression first
y = 2(x+1)-(3x-2)
y = 2x + 2 -3x + 2
y = -x + 4
Step 2: Observe the graph
y = -x + 4 is simply a linear graph with a negative fixed gradient of -1, with a y-intercept of 4.
Step 3: Identify the domain
For linear graphs, domain is all real numbers.
(No restrictions on the graph according to question)
whats the answer??
its math related
Answer:
30
Step-by-step explanation:
x + 2x + 3x = 180 (the total angle of a triangle)
6x = 180
x = 180 : 6 = 30
Answer:
x = 30°
2x = 60°
3x = 90°
Step-by-step explanation:
Internal angles of a triangle sum 180°
Then:
x + 2x +3x = 180
6x = 180
x = 180/6
x = 30°
2x = 60°
3x = 90°
1.) The acceleration of a particle moving along the x-axis at time t is given by a(t) = 6t-2. If the position is 10 when
t= 1, then which of the following could be the function for position x(t) = ?
The function for position x(t) could be x(t) = 3t^2 - 2t + 10.
What is function?In mathematics, a function is a relation between two sets that assigns to each element of the first set exactly one element of the second set. In other words, it is a rule that describes how one set of values is related to another set of values. Functions are used to model real-world scenarios and to solve mathematical problems. Examples of functions include linear equations, polynomials, and trigonometric functions.
This is determined by using the equation x'(t) = a(t). Differentiating both sides of the equation, we get x'(t) = 6t - 2. Integrating this equation, we get x(t) = 3t^2 - 2t + C, where C is the constant of integration. Since x(1) = 10, we can substitute this value into the equation and solve for the constant of integration. Therefore, we get x(t) = 3t^2 - 2t + 10.
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What are the origins of matrices?
Answer: The origins of matrices can be traced back to the 18th century, with the work of mathematicians such as Gabriel Cramer, Leonhard Euler, and Joseph-Louis Lagrange. These mathematicians developed the idea of using arrays of numbers to represent systems of linear equations, which led to the development of the concept of matrices.
The term "matrix" itself was first used by James Joseph Sylvester in 1850, although it had been in use informally for some time before then. In 1858, the English mathematician Arthur Cayley first published a systematic theory of matrices, which further developed the field.
Matrix theory was primarily used in the early days to solve systems of linear equations, but it soon found applications in areas such as linear algebra, multivariate statistics, and even quantum mechanics.
In summary, the origins of matrices can be traced back to the 18th century as an idea to represent systems of linear equations, which developed over time with contributions of many mathematicians over the centuries, and now it plays an important role in many field of mathematics and science.
Step-by-step explanation:
a) calculer: f(1,5); f(2,5); f(2)
Answer:
Step-by-step explanation:
you should give the function, if i haven't it, how can i help you.
i can give u some tips, put 1.5, 2.5, 2 in function respectively. then calculate them, u will get the answer.
You buy 4 pounds of steak at Store A for $25.50. Your friend buys 6 pounds
of steak at Store B for $40.25. Which store is cheaper?
O No answer text provided.
O They're the same
O Store A
O Store B
Question 3
Answer: To determine which store has the cheaper steak, you need to compare the price per pound of steak at each store. To do this, divide the total price by the number of pounds of steak at each store.
At Store A, the price per pound of steak is $6.38 because 25.50 / 4 = <<25.50/4=6.375>>6.375.
At Store B, the price per pound of steak is $6.71 because 40.25 / 6 = <<40.25/6=6.708>>6.708.
Therefore, Store A is cheaper because it has a lower price per pound of steak. The correct answer is Store A.
Step-by-step explanation:
ABC is an equilateral triangle. A circle with radius 1 is tangent to the line
AB at the point B and to the line AC at point C. What is the side length of
ABC? Show your work?
The equilateral triangle ABC have a side length of 2 units of the radius length of the circle tangent to the line AB.
How to evaluate for the side length of the triangleAn equilateral triangle have all its side lengths equal so;
line AB = line BC = line AC
At points B and C where the lines AB and AC are tangent to the circle is the a side length BC of the equilateral triangle
Line BC form the diameter of the circle which is 2 radius of the circle so;
line BC = 2 × radius of the circle
line BC = 2 × 1
line BC = 2
Therefore, the side length of the equilateral triangle is 2 units of the radius of the circle tangent at point B and C.
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type an (x,y) ordered pair to put a point on this line.
The ordered pair (x, y) for the given line can be obtained from the graph as (-4, 1).
What is the equation for a straight line?A straight line can be written in the form of an equation as, y = mx + c.
Two straight lines intersect each other only at one point.
When two straight lines are parallel to each other the angle between them is zero.
The graph of the line is given.
In order to find the coordinate of a point do as follows,
Draw a perpendicular line from any point on the line to the x-axis.
The intersection of this line with the x-axis will give the x-coordinate.
Similarly, find the y-coordinate by drawing a perpendicular line to the y-axis.
Applying the above procedure, a point is obtained as (-4, 1).
Hence, the ordered pair for the line shown in the graph is (-4, 1).
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