By algebra properties, the roots of the quintic equation are approximately 541.159 with a multiplicity 5.
How to find the roots of polynomial by algebraic proceduresIn this problem we find a quintic equation, whose roots have to be found by using algebra rules:
33¹⁰ - 33 · x⁵ + 1 = 0
33 · x⁵ = 33¹⁰ + 1
x⁵ = (33¹⁰ + 1) / 33
x⁵ = 33⁹ + 33⁻¹
x = [tex]\sqrt[5]{33^{9}+33^{- 1}}[/tex]
x ≈ 541.159
By using algebra properties, the roots of the quintic equation are approximately 541.159 with a multiplicity 5.
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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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Determine whether the statement is always, sometimes, or never true. Explain you reasoning.
Lines p and q intersect in points M and N .
A line segment is also a line but a line with finite length and fixed endpoints. The given statement "Lines p and q intersect in points M and N" can never be true.
What is a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely.
A line segment is also a line but a line with finite length and fixed endpoints.
The given statement "Lines p and q intersect in points M and N" will never be true, this is because two straight lines can only bisect once, therefore, at only a single point.
Although, the line may also bisect each other at infinite points but only if the line overlap with one another.
Since it is given that bisect each other at two points M and N.
Hence, The given statement "Lines p and q intersect in points M and N" can never be true.
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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...
Find the slope and y -intercept of each line.. -(1/3)x - (2/3)y = 5/3
The slope is (-1/2) an y -intercept is (-5/2) in the line -(1/3)x - (2/3)y = 5/3
What is a slope of line?A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.
The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.
Therefore,
m = y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.
Be aware that tan ∅ = y/x
We also refer to this tan as the line's slope.
We know that the equation for slope(m) and y - intercept(c) of a line is given by :
y = mx + c
Here the equation is -(1/3)x - (2/3)y = 5/3
⇒ -(1/3)x - (2/3)y = 5/3
⇒ - (2/3)y = (1/3)x + 5/3
⇒ [tex]\frac{-2y}{3}[/tex] = [tex]\frac{x + 5}{3}[/tex]
⇒ -2y = x + 5
⇒ y = [tex]\frac{x + 5}{-2}[/tex]
⇒ y = [tex]\frac{-1}{2}x -\frac{5}{2}[/tex]
Hence, slope is (-1/2) and y - intercept is (-5/2)
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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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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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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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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.
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
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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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.
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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How much will you have, if you invest $4700 at 5.8%/ a compounding quarterly for 25 years?
Answer:$19,829.10
Step-by-step explanation:
Compounded quarterly so use [tex]A = P(1+\frac{r}{n})^{nt}[/tex]
-Quarterly means 4 times a year
Initial Amount (P) = $4700
Rate = 5.8%
Time = 25 years
Plug everything into equation
[tex]A = 4700(1+\frac{0.058}{4})^{4*25}[/tex]
Insert into calculator and get:
$19,829.0996305 which is approximately $19,829.10
Round to the nearest hundredth because when dealing with money there are only two decimal places.
Answer:
$19,829.10
Step-by-step explanation:
Compound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]
where:
A = Final amount.P = Principal amount.r = Interest rate (in decimal form).n = Number of times interest is applied per year.t = Time (in years).Given:
P = $4,700r = 5.8% = 0.058n = 4 (quarterly = 4 times a year)t = 25 yearsSubstitute the given values into the formula and solve for A:
[tex]\implies \sf A=4700\left(1+\dfrac{0.058}{4}\right)^{4 \times 25}[/tex]
[tex]\implies \sf A=4700\left(1+0.0145\right)^{100}[/tex]
[tex]\implies \sf A=4700\left(1.0145\right)^{100}[/tex]
[tex]\implies \sf A=4700(4.2189573...)[/tex]
[tex]\implies \sf A=19829.0996...[/tex]
Therefore, the account balance after 25 years will be $19,829.10 (nearest cent).
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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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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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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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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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The equation 2x-20/3
= 2x models temperature change, where x represents the difference in degrees in the last 24 hours. Solve for x.
3
The solution to the equation (2x - 20)/3 = 2x of temperature change gives x = -5.
What is defined as the temperature change?Temperature change - a change in the degree of hotness of the a body (or medium). Advection is the horizontal transmission of heat or even other atmospheric properties in meteorology.Temperature change definitions. a procedure for changing the degree of heat of a body (as well as medium).The given equation is;
(2x - 20)/3 = 2x
Simplify the equation;
2x - 20 = 6x
Bring variables together;
6x - 2x = -20
4x = -20
Divide by 4
x = -5
Therefore, the solution to the equation (2x - 20)/3 = 2x of temperature change gives x = -5.
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i need help with this
need help with this question x+12=2x-15
Answer: x=+27
Step-by-step explanation:
[tex]\huge\qquad\underline{{\tt answer : - }} [/tex]
[tex]x+12=2x-15 \\ x - 2x = - 12 - 15 \\ - x = - 27 \\ x = 27[/tex]
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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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What is the product of 6 and 13.5
Answer:
81
Step-by-step explanation:
6 multiplied by 13.5 gives the answer 81.
Answer: 81
Step-by-step explanation:
[tex]13.5*6=\\\\13.5*2*3=\\\\27*3=\\\\81[/tex]
You put $550 in an account that earns 4.4% simple interest per year. How much interest do you earn in 6 months
The simple interest earned on the principal of $550 is $12.1.
What is meant by simple interest?Simple interest is calculated on the loan principal or the first deposit into a savings account. Because simple interest does not compound, a creditor would only pay interest just on principal amount, and a borrower will never be required to pay more interest on previously accumulated interest. Simple Interest (S.I.) is a technique for determining the interest amount for such a given principal amount at a given interest rate.The formula for simple interest is;
SI = PRT/100
where,
P is principal amount = $550
R is rate of interest = 4.4%
T is the total time in year; 6 months = 0.5 years.
Put the values in formula;
SI = 550×4.4×0.5 / 100
On simplification;
SI = 12.1
Thus, the simple interest incurred on the deposited principal is $12.1.
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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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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
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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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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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)
In ΔIJK, j = 960 inches, i = 200 inches and ∠I=68°. Find all possible values of ∠J, to the nearest degree.
According to the question, the given parameters of a triangle Δ IJK is given below:
j = 960 inches, i = 200 inches and ∠I = 68 degree.
As we know, the sum of the angle of a triangle is 180 degree.
Therefore, ∠I + ∠J + ∠K = 180 degree
Substituting above values in the given expression, we get:
∠J + ∠K = 180 - 68 = 112 degree
For isosceles triangle, two sides are equal. Therefore, ∠J = 56 degree
Hence, the calculated value for the ∠J is 56 degree.
What is triangle?
In the geometry of mathematics, the triangle can be defined as a polygon shape which has three edges as well as three vertices. There are three different forms of triangle which are known as scalene, isosceles and equilateral triangle.
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