The midpoint is at ([tex]-\sqrt{3} , 3 ,3\sqrt{2}[/tex])
In the given statement is
To find the midpoint of the line segment joining the pair of points
B(√3, 2,2√2) and C(-2√3, 4,4√2)
Midpoint:
The coordinates of the midpoint of a line segment are the average of the coordinates of the end points.
m = (A +B)/2
If we are given three points and we wish to find the midpoint of those points, we need to use the midpoint formula m =([tex]\frac{x_{1}+x_{2} }{2} , \frac{y_{1}+y_{2} }{2} , \frac{z_{1}+z_{2} }{2} ,[/tex] )
where:
(x1 , y1 ,z1) are the coordinates of the first point:
(x2 , y2 , z2) are the coordinates of the second point:
Now, We are given the three points B(√3, 2,2√2) and C(-2√3, 4,4√2)
Solving for the midpoint , we have,
m = ([tex]\frac{\sqrt{3}+(-2\sqrt{3} ) }{2}, \ \frac{2+4}{2}, \frac{2\sqrt{2} +4\sqrt{2} }{2}[/tex])
m = [tex]\frac{-2\sqrt{3} }{2} ,\frac{6}{2},\frac{6\sqrt{2} }{2}[/tex]
m = ([tex]-\sqrt{3} , 3 ,3\sqrt{2}[/tex])
Therefore, the midpoint is at( [tex]-\sqrt{3} , 3 ,3\sqrt{2}[/tex])
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How many fixed points are there for the function f(x)= x^5
To calculate the fixed point for the given function that is f(x)= x^5
The value of ‘x’ can take from one to infinity that means the range is (1,infinity)
Therefore,
The function can be represented as: [tex]f(x)= x^5[/tex]
The interval of the variable 'x' is: [tex]0 < x <[/tex]∝ (infinity)
And finally the range of the variable 'x' as: (1, 32,......,infinity)
What is the fixed point?
Fixed points are those points which do not change when they are mapped with different functions. It is also called as invariant points. The fixed point method is used for the calculation of those function which are in the form of constant.
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Determine whether the regular polygon will tessellate in the plane. Write yes or no. Explain.
pentagon
No, the regular polygon pentagon will not tessellate in the plane.
What is tessellation?A tessellation or tiling is the seamless application of one or more geometric shapes, known as tiles, to a surface, frequently a plane. Tessellation in mathematics can be expanded to include other geometries and higher dimensions.
A tiling constructed of materials like cemented ceramic hexagons or squares is referred to as a real-world tessellation. Such tilings may be ornamental designs or serve practical purposes such providing long-lasting and water-resistant pavement, floor, or wall coverings.
Tessellations were historically employed in Islamic art, such as the Moroccan architecture and the ornamental geometric tiling of the Alhambra palace. They were also used in Ancient Rome.
Regular polygons tessellate if their interior angles divide by 360° evenly or if the total of their interior angles is a factor of 360°. A tessellation is a pattern made of identical forms that fit together seamlessly.
So lets find out how pentagon won't tessellate.
First we find the measure of the interior angles of pentagon,
[tex]\frac{540\°}{5} = 108\°[/tex]
Now divide the interior angle by 360°
[tex]\frac{360\°}{108\°}[/tex] = 3.333
Hence, the measure of the interior angle does not divide by 360°.
Therefore, we conclude that the regular polygon pentagon will not tessellate in the plane.
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Arysville purchased new textbooks for its three elementary schools. about how many more books did they purchase for oak hill than elm street and woodland combined? textbooks purchased for marysville elementary schools elm street oak hill woodland 4,432 12,398 5,912
Using basic mathematical operations such as addition and subtraction, they purchase 2054 more books for Oak Hill than Elm Street and Woodland combined.
Elm Street = 4,432 books
Oak Hill = 12,398 books
Woodland = 5,912 books
Using addition, we can determine how many books are purchased for Elm Street and Woodland combined by adding their values.
Elm Street + Woodland
4,432 + 5,912 = 10,344
Using subtraction, determine how many more books did they purchase for Oak Hill than Elm Street and Woodland combined.
Oak Hill - (Elm Street + Woodland)
12,398 - 10,344 = 2054 books
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Select the expressions that are equivalent to -5(-9f + 7) - 7.
-42f + 45
-9f-42
(-9f + 7)-5-7
45f - 42
Answer:
The answers are 45f - 42 and -42+45f
Step-by-step explanation:
-5(-9f + 7) - 7
45f (-35 -7)
45f -42
also
-42 + 45f
Word problem involving average rate of change
Answer: A. -2.2 B. -2.7
Step-by-step explanation: To find the rate of change is y2-y1/x2-x1.
For A y2=184.3, y1=140.3 x2=0 and x1=20. 184.3-140.3 will give you 44. 0-20 is -20. So 44 divided by -20 is -2.7.
For B its the same thing: y2=109.3, y1=28.3, x2=30, and x1=60. 109.3-28.3 is 81 and 30-60 is -30. 81 divided by -30 is -2.7.
Let triangle ABC be a right triangle, and let H be the point on the side AB so that CH is perpendicular to AB.
Prove that (x+h)^2 + (y+h)^2 = (a+b)^2
(I would like a detailed answer)
Find following measure.
m DH
When an angle exists encircled by a circle, its measure exists equivalent to the intercepted arc's measure divided by two. The measure of m DH is 162.
What is meant by inscribed arc?
The arc that is inside the inscribed angle and whose endpoints are on the angle is known as the intercepted arc. Anywhere on the circle that the sides of an inscribed angle intersect to produce an intercepted arc can serve as the angle's vertex.
Angles with vertices on a circle and that cross an arc on the circle are said to be inscribed angles. Half of the intercepted arc's length and half of the central angle's length intersecting that same arc make up the measure of an inscribed angle. Congruent inscribed angles are those that intersect the same arc.
According to the Inscribed Angle Theorem, an inscribed angle's measure is equal to half of its intercepted arc's measure. Congruent inscribed angles are those that intersect the same arc.
An angle's measure is equal to the intercepted arc's measure divided by two when it is surrounded by a circle.
m DH = 2(m ∠F) = 162
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What is the value of cos(B) in the diagram?
Answer:
11/61
Step-by-step explanation:
Cos is equal to Adjacent over hypotenuse
For angle B, the adjacent side is side BC which is 11 units long
the hypotenuse is 61
11/61
Divide. State any restrictions on the variable. 5 x+15 / 10 x-10 ÷ x²+6 x+9 / 3 x² - 3
The restriction on the variable x for the expression 5x+15/10x-10÷x²+6 x+9/3x²-3 is x ≠ -3 .
Restriction in algebraic expression is defined as the value that makes the denominator as 0 or the whole expression as not defined.
For Example: 1/(x+2) , here the restriction is x ≠ -2 as -2 will make the denominator 0.
In the given question
[tex]=\frac{5x+15}{10x-10} \div\frac{x^{2} +6x+9}{3x^{2} -3}[/tex]
rewriting the expression
[tex]=\frac{5x+15}{10x-10} \times\frac{3x^{2} -3}{x^{2} +6x+9}[/tex]
Simplifying the numerator and denominator we get
=5(x+3)/10(x-1) x 3(x² -1)/(x²+3x+3x+9) ...( by splitting the middle term )
=5(x+3)/10(x-1) x 3(x-1)(x+1)/(x+3)(x+3) ...( using identity a²-b²=(a+b)(a-b) )
On further simplifying we get ,
=5*3*(x+1)/10(x+3)
=3(x+1)/2(x+3)
For finding restriction;
denominator, 2(x+3)≠0
means (x+3)≠0 ⇒ x ≠ -3.
Therefore , the restriction on the variable x is x ≠ -3 as -3 will make the expression not defined, and the value after division is 3(x+1)/2(x+3).
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Wall Ab is covered in a mirror. If you stand at point C and look at point D, what point on wall BF will you see in the mirror? Label the point E and determine the distance from B to E.
The distance from B to E is 4/3 when wall AB covered in a mirror.
The virtual image created by reflection in a plane mirror is the mirror image of an object or two-dimensional figure; it is the same size as the original but different, unless the object or figure has reflection symmetry.
Angle ∠1 = Angle ∠2
So Triangle ADC = Triangle EBD
A line of reflection is required to accomplish a geometry reflection; the two figures' consequent orientations are opposing. Comparable distances separate the corresponding regions of the figures from the line of reflection. Ordered pair rules appear on the x-axis as (x, -y), the y-axis as (-x, y), and the line y=x as follows (y, x).
tan ADC = AC / AD
= 2/3
tan EBD = BE/BD
= x/2
if Triangle ADC = Triangle EBD
than AC / AD = BE / BD
2/3 = x/2
x = 4/3
Thus , when wall AB is covered in mirrors, the distance from B to E is 4/3.For point E see the attachment below -
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The diameter of a tennis ball is 2.7 inches, and the diameter of a baseball is 2.9 inches. How many times as great is the volume of the baseball as the volume of the tennis ball?
Volume of baseball is 1.24 times greater than volume of tennis ball.
We are given the diameter of baseball and tennis ball. So, firstly we will calculate the volume of tennis ball and baseball.
Volume of ball = 4/3πr³, where r stands for radius of ball.
Taking value of π as 3.14.
Volume of tennis ball = 4/3×π×2.7³
Volume of tennis ball = 82.4 m³
Volume of baseball = 4/3×π×2.9³
Volume of baseball = 102.1 m³
Now, finding the number of times volume of baseball is greater than volume of tennis ball.
Comparison - volume of baseball ÷ volume of tennis ball
Comparison - 102.1 ÷ 82.4
Comparison - 1.24
Hence, volume of baseball is 1.24 times of volume of tennis ball.
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Consider the functions f (x) = 2x² - 3 and g (x) = -x + 6.
f (g (4)) =
g (f (4)) =
f (4) = 61
g (4) = 2
Step-by-step explanation:
f(4) = 2(4)² - 3
f(4) = 8² - 3
f(4) = 64 - 3
f(4) = 61
g (4) = -4 + 6
g (x) = 2
y varies directly with x .
If y=-7 when x=-3 , find y when x=9 .
The required value of y is 21.
What is the constant of proportion?
A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.
Solving for the value of y
let k be a constant of proportion
When a quantity varies directly with others, then we have a relation, y = kx, —-- 1
Now, find k for given x = 3 and y = 7, we need to put these values in equation 1, i.e.
7 = k(3)
k = 7/3
k = 7/3
Further calculate y for given x = 6 and constant of proportion = 7/3 i.e.
y = (9)(7/3)
y = 21
Hence, the required value of y is 21.
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A doggy daycare charges a $90 fee plus $15 each day to board a dog. the puppy palace charges $35 per day to board a dog. the cost to board the dog at each site is for a full day. how many days must someone board their dog for the total cost at a doggy daycare to be less expensive than puppy palace?
Answer:
5 days
Step-by-step explanation:
Answer:
All of theses are correct.
4.5
4 1/2
9/2
About 5.
The cost to download data for a certain mobile phone plan is modeled by c(x), where x represents the total number of gigabytes downloaded. The mobile phone company plans to raise the rate per gigabyte by $2. 50, and charge 20% more if the number of gigabytes downloaded is 5 or more. Identify a function for the new rates
The new cost function for downloading data is as follows:
C(x) = { 14.50x if 0 <= x < 2
20.50x if 2 <= x < 5
24.60x if x >= 5 }
Option D is correct.
Here, we have, the new cost function for downloading data based on the given conditions.
If 0 <= x < 2 gigabytes:
The original cost function is C(x) = 12x.
After raising the rate by $2.50, the new cost function for this range becomes C₁(x) = (12+ 2.50)x = 14.50x.
If x >= 2 gigabytes:
The original cost function is C(x) = 18x.
After raising the rate by $2.50, the new cost function for this range becomes C₂(x) = 18x + 2.50x = 20.50x.
If x >= 5 gigabytes (20% more):
The original cost function is C(x) = 18x.
After raising the rate by $2.50 and charging 20% more, the new cost function for this range becomes C₃(x) = [1.20 * (18+ 2.50)]x = 24.60x.
Now, we need to combine these functions to get a single function for the new rates:
For 0 <= x < 2 gigabytes: C(x) = C₁(x) = 14.50x
For 2 <= x < 5 gigabytes: C(x) = C₂(x) = 20.50x
For x >= 5 gigabytes: C(x) = C₃(x) = 24.60x
So, the new cost function for downloading data is as follows:
C(x) = { 14.50x if 0 <= x < 2
20.50x if 2 <= x < 5
24.60x if x >= 5 }
Option D is correct.
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Find the value of x?
Answer: 70º
Step-by-step explanation: isosceles triangle (2 equal sides) means 2 equal angles
Answer:
Hi,
Answer 111
Step-by-step explanation:
This shape (a kite) has an axis of horizontal symmetry
Begging for help atp!!!! PLEASE
The range of the graph is 0 <= y <= 12
How to determine the range of the graph?The graph represents the given parameter
On the graph, we have the following observations
Minimum y value = 0
Maximum y value = 12
The range of the graph is represented as
Minimum y value <= y <= Maximum y value
So, we have
0 <= y <= 12
Hence, the range of the graph is 0 <= y <= 12
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Find the measures of the angles or sides in each triangle.
The ratio of the three sides is 5: 3: 6 and the perimeter is 98 centimeters.
Interior angles in triangles are all equal to 180 degrees. A triangle's angles are equal to the sum of the angles at each of its three vertices. The sides of the triangle are 35cm, 21cm, and 42cm.
How to measures the angles of the triangle?
Due to the fact that one outside angle of a triangle is equal to the sum of its other two angles, all of its angles add up to 180 degrees. In other words, the third angle must be added to the other two angles in the triangle (the ones that add up to generate the outer angle) to form a 180-degree angle.
The perimeter of the triangle = 98cm
The ratio of the 3 sides is 5: 3: 6
Take it as 5x, 3x, 6x
where, x is the scaling factor
5x + 3x + 6x = 98
simplifying the above variables, we get
14x = 98
x = 7
The sides of the triangle are
5x = 5 × 7 = 35 cm
3x = 3 × 7 = 21 cm
6x = 6 × 7 = 42 cm
Therefore, the sides of the triangle exists 35 cm, 21 cm and 42 cm.
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Determine whether the events are independent or dependent. Explain. Alita's basketball team is in the final four. If they win, they will play in the championship game.
For given situation the events are dependent.
In this question,
Alita's basketball team is in the final four.
we have been given two events.
event A: Alita's basketball team win.
event B: Alita's basketball team play in the championship game.
From given condition, If they win, they will play in the championship game.
We can clearly observe that the occurrence of event B is dependent on the other event A.
If event A occurs only then event B would be true.
Therefore, for given situation the events are dependent.
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Divide.
46)532
Enter your answer by filling in the boxes.
please help me if u cannn <33
Exact Form:
23
266
Decimal Form:
0.08646616...
Make a scatter plot of each set of points and describe the correlation.
(1.2,1),(2.5,6),(2.5,7.5),(4.1,11),(7.9,19)
A scatter plot is a series of points plotted on horizontal and vertical axes. If there is no correlation between variables, the points appear randomly scattered on the coordinate plane. If the correlation is high, the points will be clustered around a straight line. A scatter chart is a data visualization tool that helps show trends.
The scatter plot shows not only the correlation's magnitude but also the correlation's direction.
As the vertical (or Y-axis) variable increases, the correlation is positive as the horizontal (or X-axis) variable increases.
The correlation is negative if the y-axis variable decreases and the x-axis variable increases, or vice versa.
The correlation is zero if none of the above criteria can be established.
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If you rotate point (4,2) 90°C and 180°C about the origin, how do the x - and y -coordinates change?
R (-90°) = (x, y) — > (y, -x) is the x - and y -coordinates change.
How is a point rotated with respect to the origin?
Rotational direction: clockwise or counterclockwise. Rotations that are positive are counterclockwise. Clockwise rotations are negative rotations. The following rule is used, for instance, to rotate the point (2, 5) 90 degrees counterclockwise around the origin.As it turns out, however, I don’t need to look at options. I can tell you that a clockwise rotation of 90° of a point about the origin is actually considered a rotation of -90°.
(For positive rotations are counterclockwise, while negative rotations are clockwise.) The rule for the type of rotation you speak of is
R (-90°) = (x, y) — > (y, -x)
One more point, if I may. It appears that you copied this problem verbatim right out of a textbook.
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Select the correct answer.
Based on the end behavior, which is the graph of function f?
f(x) = x³ x² – 2x
Answer:
The answer and explanations are in the pictures.
Step-by-step explanation:
given aright triangle with legs a and b, hypnoses c, find the length of side c if a=2(sqr)3, c=2b
The length of the hypotenuse c is 6
How to determine the length of c?The given parameters are
Legs = a and b
Hypotenuse = c
a = 2√3
c = 2b
Make b the subject in c = 2b
b = 1/2c
By Pythagoras theorem, we have:
c^2 = a^2 + b^2
This gives
c^2 = (2√3)^2 + (1/2c)^2
Evaluate the exponents
c^2 = 12 + 1/4c^2
Evaluate the like terms
1/3c^2 = 12
This gives
c^2 = 36
Take the square roots
c = 6
Hence, the length of the hypotenuse c is 6
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A rabbit population in a forest doubles each month. The Department of Natural Resources estimates that the forest contains 525 rabbits at the start of the first month. Write an explicit formula describing the number of rabbits an, in the forest n months later.
Answer: [tex]525(2)^{n-1}[/tex]
Step-by-step explanation:
We can represent this as a geometric sequence with first term 525 and common ratio 2.
Estimate the uncertainty in the momentum of an electron whose location is uncertain by a distance of 2 angstroms. what is the uncertainty in the momentum of a proton under the same conditions?
Δp≥5.2755∗10−25ms−1
According to the Heisenberg uncertainty principle, we have
δx∗δp≥ℏ2
Since Δx=1angstrom=10−10m,
Δp≥6.626∗10−344∗3.14∗10−10
Δp≥5.2755∗10−25ms−1
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Find the slope of the line through each pair of points. (-5,-7) and (0,10)
The slope of the line through each pair of points. (-5,-7) and (0,10) is 17 / 5
What is the slope of an equation?A line's slope often indicates the steepness and direction of the line. By calculating the difference between the coordinates of the two locations, (x1,y1) and (x2,y2), it is simple to calculate the slope of a straight line between them. The letter "m" is frequently used to denote slope.
The given points are (-5,-7) and (0,10)
Formula to calculate slope is - y2 - y2 / x2 - x1
= 10 + 7 / 0 + 5
= 17 / 5
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i need help with this
Find the slope of the line.
d. the line containing (-3,3) and (4,3)
The slope of the line containing (-3,3) and (4,3) is Zero (0).
The slope of a straight line can be written as follows,
m = [tex](y_{2} - y_{1} )/(x_{2} - x_{1} )[/tex] equation1
The line is containing the points (-3,3) and (4,3). So, we can write
[tex]y_{2}[/tex] = 3 , [tex]y_{1}[/tex] = 3 , [tex]x_{2}[/tex] = 4 , and [tex]x_{1}[/tex] = -3 .
On substituting the values of variables in equation1, we will get
m = ( 3-3 ) / ( 4-(-3) ) = (0/7) = 0.
As the slope of a line is Zero (0), so we can conclude that the given line is a straight line.
Here:
m = the slope of the line
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) are the first coordinates.
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )are the second coordinates.
The slope of the line containing (-3,3) and (4,3) is Zero (0).
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Find the slope of the line through each pair of points. (0,0) and (2,6)
The slope of the line through each pair of points (0,0) and (2,6) is 3.
What is the slope of the line?The increase divided by the run, or the ratio of the rise to the run, is how a line's slope is calculated. It gives information about the line's slope in the coordinate plane. Finding the slope between two locations and calculating the slope of a line are related tasks.
The following formula is used to determine slope:
The slope of the line between two points is given by y2 - y1 / x2 - x1.
Given the points are -
(0,0) and (2,6)
The slope of the line passing through the points is -
= 6 - 0 / 2 - 0
= 6/2
= 3
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