The 3 different polynomial equations are linear polynomial equations, quadratic polynomial equations, and cubic polynomial equations.
A polynomial equation is one where a polynomial is set equal to zero. i.e., it is an equation created with variables, non-negative integer exponents, and coefficients together with operations and an equal sign.
A polynomial equation is always like "polynomial = 0". Algebraically, it is of the form p(x) = aₙ xⁿ + aₙ₋₁ xⁿ⁻¹ + ... + a₁ x¹ + a₀x⁰ = 0, where
aₙ, aₙ₋₁, ...., a₁, a₀ are coefficients and all these numbers are real numbers.
'x' is the variable.
p(x) means "polynomial in terms of variable x"
'n' is a non-negative integer, it is the degree of p(x).
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Write the coordinates of the vertices after a rotation 90 degrees counterclockwise around the origin.
Answer: J' (8, -9); K' (8, -2); L' (3, -2); M' (3, -9)
Step-by-step explanation:
A rotation of 90 degrees counterclockwise is (x, y) -> (-y, x), so
J (-9, -8) -> J' (8, -9)
First, you take negative 8 (y) of J and make it positive 8 for the x of J'. Then, take -9 (y) of J and switch it to x of J'.
You repeat this process for the rest of the points. X switches to Y with the opposite sign and Y switches to X but stays the same.
K (-2, -8) -> K' (8, -2)
L (-2, -3) -> (3, -2)
M (-9, -3) -> (3, -9)
6x + 11= 21 tape diagram
Answer:
x = 5/3
Step-by-step explanation:
6x + 11 = 21
6x = 10
x = 10/6
x = 5/3
Let's check
6(5/3) + 11 = 21
30/3 + 11 = 21
10 + 11 = 21
21 = 21
So, x = 5/3 is correct!
How do you find the 3rd side of a triangle?
Answer:
a2 = b2 + c2 2bc cos(0)
Step-by-step explanation:
Please help with this question I’m confused on it
PLEASE HELPP
A. Triangle ABC is similar to triangle DEF.
B. The value of x is 21.
What are similar triangles?
If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable. Similar figures are items that feature more than two figures that are the same shape but different sizes.
Here, we have
Given a triangle and we have to show both triangles are similar.
A. ABC will be similar to DEF if two sides along with their corresponding angle of ABC is equal to two sides and their corresponding angle of DEF. ABC will be similar to DEF if the corresponding ratios of all sides of both triangles are equal to each other.
Hence, triangle ABC is similar to triangle DEF.
B. By the property of similar triangles,
= AB/DE = AC/DF
= 14/x = 10/15
x = 21.
Hence, the value of x is 21.
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Because milk tea is flourishing in their town, Mathilda decided to sell Wintermelon milk tea (WMT) powder at Php 1 per gram and Okinawa milk tea (OMT) powder at Php 2 per gram. To increase her profit, she plans to mix the two milk tea powders. How much OMT should she mix with 300 grams of WMT so that she can sell the resulting mixture at Php 1.80 per gram?
So, Mathilda should mix 600 grams of OMT with 300 grams of WMT to sell the resulting mixture at Php 1.80 per gram.
Define the unitary method.The unitary approach involves calculating the value of a single unit, from which we may calculate the values of the necessary number of units.
The unitary method's formula is to identify the value of a single unit, then multiply that value by the number of units to obtain the required value.
What is a unit?A unit is a quantity with a fixed magnitude that is used to gauge the sizes of other quantities that behave similarly.
The terms millimeter (mm), centimeter (cm), meter (m), and kilometer (km) are used to describe length (km). The weight is measured in kilograms (kg) and grams (g). Milliliter (ml) and liter are used to measure volume (L).
Let x be the amount of OMT powder in grams. We know that the total amount of powder in the mixture is x + 300 grams since Mathilda is mixing x grams of OMT with 300 grams of WMT.
(x * Php 2 + 300 * Php 1) / (x + 300) = Php 1.80
Solving for x, we can get the amount of OMT powder in grams:
x = (300 * Php 1.80 - 300 * Php 1) / (Php 2 - Php 1.80) = 300 * (Php 1.80 - Php 1) / (Php 2 - Php 1.80) = 600
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Solve 345°=
Please help me ASAP
the due date of my assignment is tomorrow
The answer to ur question is 1
The function
h
defined by
h(t) = (49 + 4. 9t)(10 – t)
models the height, in meters, of an object
t
seconds after it is dropped from a helicopter.
1. Find or approximate the time when the object hits the ground. Explain or show your
reasoning
2. From what height is the object dropped? Explain or show your reasoning.
Answer:
55555555546776546567
Is a solution of pair of equations 3x 2y 4 and 2x y 5?
The solution of this pair of equations is (2, 3).
To solve this pair of equations, we can use the substitution method.
First, we solve the first equation for y:
3x + 2y = 4
2y = 4 - 3x
y = (4 - 3x) / 2
Next, we substitute this expression for y in the second equation:
2x + (4 - 3x) / 2 = 5
2x + 2 - 3x = 10
-x = 8
x = -8
Finally, we substitute this value for x in the expression for y to find the value of y:
y = (4 - 3(-8)) / 2
y = (4 + 24) / 2
y = 28 / 2
y = 14
Therefore, the solution of this pair of equations is (x, y) = (-8, 14).
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Help please! Thank you
Answer:
the answer is z^2-9. Using the box method line up equation. Then multiple numbers outside of the box and put numbers inside. Lastly combine like terms.
The endpoints of a line segment AB are (1, -6) and (5, -6). The equation of a line BC is
y=x-11. Is triangle ABC a right triangle? Justify your answer.
No, triangle ABC is not a right triangle. The equation of a line BC "y=x-11" is a line with slope of 1, which means it has an angle of 45 degrees with respect to the x-axis. The segment AB has a slope of 0, which means it is parallel to the x-axis. A right triangle's legs must be perpendicular, therefore a line with a slope of 1 and a line with a slope of 0 cannot be the legs of a right triangle.
A RIGHT TRIANGLEA right triangle is a triangle in which one of the angles is 90 degrees. In order for a triangle to be a right triangle, the two sides (or legs) that form the 90-degree angle must be perpendicular to each other. Perpendicular lines have slopes that are negative reciprocals of each other.
In this case, the equation of the line segment AB is "y = -6", which means it is parallel to the x-axis. The slope of a line parallel to the x-axis is 0. On the other hand, the equation of the line BC is "y = x - 11", which means it has a slope of 1. A slope of 1 means that the line is at a 45 degree angle with respect to the x-axis.
Since the slopes of the two lines are not negative reciprocals of each other (0 and 1), the legs of the triangle cannot be perpendicular. Therefore, triangle ABC cannot be a right triangle.
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A town has a population of 4000 and grows at 2% every year. To the nearest year, how long will it be until the population will reach 4500?
=========================================================
Work Shown:
x = number of years
y = population
y = 4000*1.02^x
4500 = 4000*1.02^x
4500/4000 = 1.02^x
1.125 = 1.02^x
log(1.125) = log(1.02^x)
log(1.125) = x*log(1.02)
x = log(1.125)/log(1.02)
x = 5.94784893412128
Rounding to the nearest year, it takes about 6 years for the population to reach 4500 people.
---------------
Check:
Plug in x = 5
y = 4000*1.02^x
y = 4000*1.02^5
y = 4416.3232128
y = 4416
We come up a bit short. Now try x = 6
y = 4000*1.02^x
y = 4000*1.02^6
y = 4504.649677056
y = 4505
We go a bit over the target, but it's better to go over rather than come up short.
This confirms the answer is approximately 6 years.
what is the coefficient for x in 8+ x/2
Answer: x= 8+ x over 2 = x over 2 + 8
Step-by-step explanation:
the function f(x)=80(0.5)^ represents the distance after a pendulum begins swinging,where x is the number of swings
It looks like there may be a typo in the function you provided. It appears that you meant to write "f(x) = 80(0.5)^x", which would represent the distance after a pendulum begins swinging, where x is the number of swings.
This function indicates that the distance traveled by the pendulum decreases by half with each swing. For example, after the first swing, the distance traveled would be 80(0.5)^1 = 40 units. After the second swing, the distance traveled would be 80(0.5)^2 = 20 units. And so on.
The exponent x in the function represents the number of swings, so the distance traveled by the pendulum can be calculated by plugging in the desired value of x into the function. For example, to calculate the distance traveled after 10 swings, we can plug in x = 10:
f(10) = 80(0.5)^10 = 0.390625 units
This indicates that the pendulum has traveled a distance of approximately 0.39 units after 10 swings.
Gorilla
Sophia
George
Nancy
Hank
Paula
Gavin
Weight
(pounds)
318
417
310
136
62
24
Plugged
into
3c+9=417
True or
False?
A company is loading recliners and sofas onto a trailer that has a volume of about 3800 cubic feet. Each recliner takes up about 40 cubic feet and each sofa takes up about 80 cubic feet. The company wants the shipment to have at least 30 recliners and more than 25 sofas. Identify and interpret the ordered pair in the solution region.
The ordered pair that would be needed by the company for shipment can be loaded in the trailer as the pair will take only 3200ft³ of the volume of the trailer which is 3800 cubic feet.
How to calculate the ordered pair for shipment?The total volume of the trailer = 3800 cubic feet
The volume of each recliner = 40 cubic feet
The volume of each sofa = 80 cubic feet
The number of recliner needed = 30
The number of sofas needed = 25
The volume that the sofa will cover = 25 × 80 = 2000
The volume that the recliner will cover= 30 × 40 = 1200
Therefore the total volume both will take = 3200 cubic feet.
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The continuous random variable N has a normal distribution with mean 7.5 and standard deviation 2.5. For which of the following is the probability equal to 0 ?
(A) P(N = 8) (B) P(N > 8) (C) P(N < 8) (D) P(7 < N < 8) (E) P(N < 7) or P(N > 8)
The probability for all five answers is greater than 0.
The normal distribution is a type of continuous probability distribution, and probability can never equal 0 for a continuous distribution. The probability of a particular value (in this case, 8) is the area under the normal curve at that point. Since the area under a continuous distribution is always greater than 0, the probability of a specific value (A) is not 0.
The probability of a range of values (D) is calculated by subtracting the area under the normal curve to the left of the lower value, from the area under the normal curve to the right of the higher value. This calculation would produce a value greater than 0.
The probability of values greater than a given number (B) is calculated by subtracting the area under the normal curve to the left of the given number, from the area under the normal curve to the right of the given number. This calculation would produce a value greater than 0.
The probability of values less than a given number (C) is calculated by subtracting the area under the normal curve to the right of the given number, from the area under the normal curve to the left of the given number. This calculation would produce a value greater than 0.
Finally, the probability of values less than one number or greater than another number (E) is calculated by subtracting the area under the normal curve to the left of the lower number, from the area under the normal curve to the right of the higher number. Again, this calculation would produce a value greater than 0.
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A certain United States flag has a perimeter of 58 feet. The length of the flag is 9 feet longer
than the width. What are the dimensions of the flag?
The dimensions of the flag are:
length = 19 feet and width = 10 feet
Let 'l' be the length of the flag and 'w' be the width of the flag.
The length of the flag is 9 feet longer than the width.
So, we get an equation
l = 9 + w ............(1)
The flag has a perimeter of 58 feet.
We know that the formula for the perimeter of rectangle:
P = 2(l + w) ..............(2)
Here, P = 58 feet
Substitute the value of P in equation (2)
58 = 2(l + w)
29 = (9 + w) + w ..........(from (1))
29 - 9 = 2w
2w = 20
w = 10
Substitute this value in equation (1),
l = 9 + 10
l = 19 feet
Therefore, length = 19 ft and width = 10 ft
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If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a Question 18 options: A) kite. B) trapezoid. C) hexagon. D) parallelogram.
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Option (d) is the correct choice.
A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.
A parallelogram has the following qualities:
The opposing sides are equally spaced and parallel.
Angles on either side are equal.
The following or neighboring angles are supplemental.
All of the angles will be at right angles if any one of them is a right angle.
The two diagonals cut across one another.
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A rigid body exists in an n-dimensional space. How many coordinates are needed to specify the position and orientation of this body in this space
The number of coordinates needed to specify the position and orientation of a rigid body in an n-dimensional space is n.
A rigid body is an object that maintains its shape and size while in motion. In order to specify the position and orientation of a rigid body in an n-dimensional space, we need to know its coordinates in each of the n dimensions. The coordinates describe the location of the body in the space and the orientation of the body relative to the space's coordinate system. Thus, n coordinates are required to fully specify the position and orientation of a rigid body in an n-dimensional space.
However, it is important to note that if the rigid body is placed in a space that's non-Euclidean, other parameters could be necessary to fully describe the rigid body position and orientation.
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What is the greatest possible quotient of any two distinct members of the set $\left\{\frac{2}{5}, \frac{1}{2},5,10\right\}$? Specifically, we wish to maximize $\frac{x}{y}$, where $x$ and $y$ are chosen from the previous set.
The greatest possible quotient of any two distinct members of the set; { 2 / 5, 1 / 2, 5, 10 } as required is; 25.
What is the maximum possible quotient of any pair of numbers from the set?It follows from the task content that the set from which the two numbers whose quotient is to be maximised is; { 2 / 5, 1 / 2, 5, 10 }.
On this note, since the quotient which is to be maximised is hypothetically; x / y;
To maximize the result of the quotient; it follows that the numerator, x must be as great as possible and the denominator, y must be as less as possible.
On this note, since the maximum number in the set is 10 and the minimum is 2 / 5; we have that;
10 / (2 / 5)
= ( 10 × 5 ) / 2
= 25.
Ultimately, the greatest possible quotient as required is; 25.
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What is the result of adding the system of equations 2x y 4 3x y 6?
The addition of terms [tex]2x+y^4[/tex] and [tex]3x+y^6[/tex] will be [tex]5x+y^4+y^6[/tex]
A polynomial is an equation made up of variables, constants, and exponents that are mixed using mathematical operations including addition, subtraction, multiplication, and division (No division operation by a variable).
Simply add the coefficients of each phrase to add polynomials.
You may remove polynomials by subtracting the coefficients.
To add polynomials, just combine any like terms.
Step 1: Arrange each polynomial in decreasing order of degree, starting with the term with the highest degree.
Step 2: Sort the words that are similar. Similar phrases have the same variables and exponents.
So, the addition of terms [tex]2x+y^4[/tex] and [tex]3x+y^6[/tex] will be (2x+3x) (As here both are only the like terms, so they will be added together)
So, the sum will be: [tex]5x+y^4+y^6[/tex]
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The correct question should be:
What is the result of adding the system of equations:
[tex]2x+y^4[/tex] and [tex]3x+y^6[/tex]
Find the value of x in the figure
Answer:
x=40º
Step-by-step explanation:
A straight line is 180º
180-40=140º
180-140=40º
x=40º
Hope this helps :)
Is x2 16 a perfect square trinomial?
No, x2 16 is not a perfect square trinomial.
What is perfect squares?Perfect squares are numbers that are the product of a number multiplied by itself. Examples of perfect squares include 4 (2 x 2), 9 (3 x 3), 16 (4 x 4), 25 (5 x 5), 36 (6 x 6), 49 (7 x 7), and 64 (8 x 8). Perfect squares are also referred to as "square numbers" or "whole-number squares."
A perfect square trinomial is a polynomial of the form a2+2ab+b2, where a and b are constants. This trinomial does not have the same pattern of constant coefficients. It is simply the product of two linear expressions, x2 and 16.
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567854+98723=?
Let's see who knows the correct answer
How do you describe rational and irrational?
Rational and Irrational numbers can described as the number that can be expressed as [tex]\frac{p}{q}[/tex] are rational and which cannot be expressed are called as Irrational Numbers .
The Rational Numbers are defined as a number that can be represented in the form of [tex]\frac{p}{q}[/tex] where [tex]q\neq 0[/tex].
We can also , say that the fraction where the denominator and the numerator are integers and the denominator is not equal to zero are called as Rational Numbers .
For Example : [tex]\frac{2}{3} , \frac{4}{9}[/tex] represents a rational numbers .
The Irrational Numbers are defined as a real number that cannot be expressed as a ratio of integers .
For Example : [tex]\sqrt{2} , \sqrt{5}[/tex] represents a Irrational number .
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Write two equations that can be solved using the double 7+7
Using doubles plus one fact the sum of 7 + 7 is equal to 15 it is done by simply adding 1 to the given number.
What is Doubles plus ?When we add two of the same number, we add using the “doubles fact”. For example, 1 + 1 and 2 + 2 are both doubles facts. Look at the example below: 4 + 4 = 8 is a doubles fact. Doubles fact can help us know other additional strategies like doubles plus one
A double is a number or an amount that is twice as large as the given number or amount. So, if we multiply a number by 2 or if we add a number to itself we say that the number is doubled
The sum of 7 + 7 can be determined by using doubles plus one fact as:
Simply add 1 in 7 + 7 to get the result required.
Therefore by using doubles plus one fact the sum of 7 + 7 is equal to 15.
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write as complete square root 3√5
need help with this screenshot
The quadratic equation in vertex form is y = -(x - h)² + k
The parabola passed through points (-1, -3), (0, 0), (1, 1), (2, 0) and so on
How to write the equation of parabola in vertex formFor a vertical parabola, the vertex form of the equation is written as
y = a(x - h)² + k
where:
a = 1/4p
h and k are points of the vertex = v(h, k)
The vertex
v (h, k) = (1, 1)
h = 1
k = 1
y = a(x - 1)² + 1
using point (0, 0)
0 = a(0 - 1)² + 1
-1 = a
hence a = -1
the equation is written as y = -(x - h)² + k
The points the graph passed is read from the graph to be
(-1, -3), (0, 0), (1, 1), (2, 0) and so on
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Solve the following system of equations. Enter the y-coordinate of the
solution. Round your answer to the nearest tenth.
5x+2y=21
- 21+ 6v=-34
To find the y-coordinate of the solution, we can substitute in this value for y and round it to the nearest tenth: y = -2.2
What exactly does a coordinate system mean?system of coordinates, Arrangement of reference lines or curves for locating points in space The Cartesian (named for René Descartes) system is the most popular one in two dimensions.
To solve for y in the equation 5x + 2y = 21, we can start by isolating y on one side of the equation. To do this, we can subtract 5x from both sides of the equation:
5x + 2y = 21
5x - 5x + 2y = 21 - 5x
2y = 21 - 5x
To solve for y, we can then divide both sides of the equation by 2:
2y = 21 - 5x
y = (21 - 5x) / 2
To solve for y in the equation -21 + 6y = -34, we can start by isolating y on one side of the equation. To do this, we can add 21 to both sides of the equation:
-21 + 6y = -34
-21 + 21 + 6y = -34 + 21
6y = -13
To solve for y, we can then divide both sides of the equation by 6:
6y = -13
y = -13/6
y = -2.1666666666666665
To find the y-coordinate of the solution, we can substitute in this value for y and round it to the nearest tenth:
y = -2.2
So, the y-coordinate of the solution is -2.2.
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"Suppose Dave purchases a puzzle having 650 pieces. Predict the lenght of time it will take him to compleate the puzzle."
a) Attached at the end.
b) Strong positive linear correlation.
c) The length of time is 220 minutes.
What is Scatter plot?A set of dots plotted on a horizontal and vertical axis is known as a scatter plot. Because they can demonstrate the degree of connection, if any, between the values of observed quantities or events, scatter plots are crucial in statistics (called variables).
Given:
a) The Scatter plot Associated with data is attached below.
b) The Scatter plot shows the positive linear correlation between number of pieces in a jigsaw puzzle and time required for a person to complete it.
c) To complete the puzzle with 650 pieces it will take 220 minutes.
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Answer:
a) See attachment.
b) Strong positive correlation.
c) 247 minutes
Step-by-step explanation:
Part aPlot the points from the given table on the given coordinate plane.
Draw a line of best fit.
(See attachment).
Part bAs the line of best fit has a positive gradient, the two variables are positively correlated.
As the line of best fit lies close to most of the points, this indicates there may be a strong correlation.
Part cTo predict the length of time it will take Dave to complete a 650-piece puzzle, locate 650 on the x-axis of the scatter plot, trace up to the line of best fit and read the y-value:
(650, 247)Therefore, it will take Dave approximately 247 minutes to complete a 650-piece puzzle.