so for given expression x⁴-2x³-x²-2x+1 = (x-1)² - (2x+1)
Define Equation.The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Define Algebraic expression.An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.
we can start by squaring the equation x²+(1/x)=3
so we have x⁴ + 2x² + (1/x)² = 9
x⁴ + 2x² + 1 = 9x²
x⁴ - 7x² + 1 = 0
Now we can factor it
(x²-1)(x²-1) = 0
so x² = 1
now we can substitute x² = 1 in the equation x⁴-2x³-x²-2x+1
x⁴-2x³-x²-2x+1 = x⁴-2x³-1-2x+1
= x⁴-2x³-2x-1
= (x⁴-2x³) - (2x+1)
= x⁴-2x³-2x-1
= (x²-x)² - (2x+1)
= (x-1)² - (2x+1)
so x⁴-2x³-x²-2x+1 = (x-1)² - (2x+1)
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What is the best definition of a decimal?
A) Decimals are ratios out of one hundred
B) Decimals are whole counting numbers
C) Decimals are ratios relating one integer to another
D) Decimals are integers followed by a decimal point and a number less than one
Answer:
D
Step-by-step explanation:
I think it would be D hope this helps!
The best definition of a decimal is decimals are whole counting numbers.
How can we express numbers belonging to decimal numeral system?Suppose that the number is abcdefg and belongs to the decimal numerical system.
Remember one thing that the place on the left of decimal point is called ones. Move one-one places to right, and divide by 10 and 10 more and more.
Move one-one places to left, and multiply (un-divide) by 10 and 10 more and more.
Thus, we write abcd.efg as:
[tex]a \times 10^3 + b \times 10^2 + c \times 10^1 + d \times 10^{0} + e \times 10^{-1} + f \times 10^{-2} + g \times 10^{-3}[/tex]
We will call d as ones digit, c as tens digit (it get multiplied by 10), b as hundreds digit etc.
We call e as digit at 10th place (division by 10), f as digit at hundredth place and so on.
Therefore, the definition will be Decimals are whole counting numbers,
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1. Are the triangles shown below similar? Explain.
Answer:
Step-by-step explanation:
These are the tests for similar triangles:
AA - if 2 pairs of corresponding angles are equal.
SSS - if corresponding sides have the same ratio.
SAS - if 2 pairs of corresponding sides have the same ratio and the included angles are equal.
This diagram does not indicate any of these relationships exist.
Therefore the triangles are not similar.
if you are traveling at 60 mph you will travel almost the length of a football field in how many seconds
Time taken to cross the field will be 3.36 seconds.
What does physics mean by speed?Velocity is the rate and direction of an object's movement, whereas speed is the time rate at which an object is moving along a path. In other words, velocity is a vector, whereas speed is a scalar value. There are four different types of speed. constant speed, varying speed, an average rate, instantaneous speed.
Solution,
Given,
speed=60 mph
length of football field=0.056 miles
time taken to cross it = distance/speed
time=0.056/60=0.00093 hour = 3.36 seconds.
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Coach Taylor asked his team to record the distance they ran during practice. It’s a dot plot so someone plssss help me I’ll give them 10 points!
The range between 3/16 & 3/8 is where the line plot with the difference of daily mileage logged by each racer in a group is still most obvious.
Line plot: what is it?A line graph, liner plot, or line chart is a graph that uses lines to link the individual data points. For a specific time period, quantitative values are displayed as a line graph. Line graphs are widely used in finance to depict the past market movements of a securities or asset.
Here,
calculation
The number line indicates that there's more than or equal to 3 marks when there are 7 markings either on or to the right of 3. The fraction must first have the same denominators.
=> 3/8 x 2 = 6/16
=> 1/2 x 8 = 8/16, 3/8 x 2 = 6/16
=> 5/8 x 2 = 10/16, 1/2 x 8 = 8/16
Since they all have the same numerator, we can now compare them.
=> 3/16 - 1/16 = 2/16
=> 6/16 - 3/16 = 3/16
=> 8/16 - 6/16 - 2/16
=> 10/16 - 8/16 = 2/16
The largest distinction is between 3/16 and 3/8 (6/16 vs. 3/16).
The range between 3/16 and 3/8 is where the line plot with the difference in daily mileage logged by each runner in a group is most obvious.
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The complete question is " Coach Taylor asked his team to record the distance they ran during practice The line plot shows the number of miles the individual members in a group of runners run each day. How many runners run at least 3 miles per day?."
Find the length of the third side. If necessary, round to the nearest tenth
Answer:
Step-by-step explanation:
Let AB = 3 units , BC = 1 unit and AC = ? (TO BE CALCULATED)
By Pythagoras theorem:
(AC)²=(AB)²+(BC)²
therefore, (AC)²= 3²+1²
(AC)²=9+1
(AC)²=10
(AC) = √10 = 3.03 cm
Michael has a bag of marbles. The frequency of selecting each color is recorded in the table below.
Outcome Frequency
Green 4
Black 6
Orange 5
Based on the given frequency, determine the experimental probability of selecting a green marble.
0.27
0.33
0.40
0.73
0.27 is the experimental probability of selecting a green marble.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given that Michael has a bag of marbles.
The frequency of selecting each color is recorded
Outcome Frequency
Green 4
Black 6
Orange 5
The total number of marbles are 4+6+5=15 marbles.
We need to find the experimental probability of selecting a green marble.
We need to select green marbles (4) from total marbles (15).
Probability=4/15=0.266=0.27
Hence, 0.27 is the experimental probability of selecting a green marble.
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Can anyone help please
The graph of the following equation will be a Parabola. The y=1 will be the line of symmetry.
Which four types of parabolas are there?Three different parabolas exist. Vertex form, standard form, and intercept form are the three forms. You can access a unique key feature for the graph on each form.
What distinguishes a hyperbola from a parabola?A set of points in a plane that are equally spaced apart from a directrix or focus are known as parabolas. The difference in distances between a group of points that are situated in a plane and two fixed points—which is a positive constant—is what is referred to as the hyperbola.
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Look down below for the question
Answer:
1.centre
2.chord
3.chord
4.radius
5.diameter
BRAINLY ME PLEASE IF HELPFUL!!!
A. What must the side length of each square represent for the rectangle to correctly represent (0. 3). (0. 5)?
The side length of each square represent for the rectangle to correctly represent (0, 3) · (0, 5) is 1 units.
A rectangle represented by (0, 3) · (0, 5) has length 3 units and breadth 5 units. To represent that rectangles with minimum number of squares of same size, we calculate the highest common factor.
Highest Common Factor is a mathematical concept used to find the greatest number that divides two or more numbers without leaving a remainder. It is also known as the greatest common divisor (GCD) or the greatest common factor (GCF).
Highest common factor of 3 and 5 is 1 as both are prime numbers. So squares with side length 1 unit best represent the rectangle to correctly represent (0, 3) · (0, 5).
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12. Find T in the diagram, if R = 110° and S = 60°.
Answer:
∠T = 130°
Step-by-step explanation:
The figure we are given is a quadrilateral, a 4 sided shape.
There are many different types of quadrilaterals, such as a rhombus, rectangle, etc.
How will we know which quadrilateral the given figure is?
We will have to look at the given properties of the figure to find out.
We are given that there are two adjacent pairs of congruent sides.
RS = RU, and ST = UT.
Thus, the given quadrilateral is a kite.
Now that we know that the given figure is a kite, we can utilize a kite's angle properties to find out ∠T.
In a kite, the non-vertex angles (∠S and ∠U) are congruent.
If ∠S = 60°, then ∠U = 60°.
In a kite, the sum of the interior angles is 360°.
Hence:
∠R + ∠S + ∠T + ∠U = 360°
Therefore, we can substitute the angles we know into the equation and solve for ∠T.
∠R + ∠S + ∠T + ∠U = 360°
110 + 60 + ∠T + 60 = 360
110 + 120 + ∠T = 360
230 + ∠T = 360
∴ ∠T = 130°
if this response helped you, please mark it the brainliest :)
The sum of four consecutive multiples of 7 is 406.
Work out the values of these four numbers.
Examples of four consecutive multiples of 7 are: 7, 14, 21, 28
The value of all four numbers will be 91, 98, 105, 112 respectively.
Let the first multiple be 7x
As the multiple of any number can be determined by simply multiplying the given number by the natural number or the counting numbers.
So, the value of the second multiple of 7 will be 7(x+1)
The value of third multiple of 7 will be = 7(x+2)
The value of fourth multiple of 7 will be = 7(x+3)
As all the multiple are consecutive so we have taken the multiplying factor as x, (x+1), (x+2) and (x+3)
From the data given in the question:
Sum = 7x+7x+7+7x+14+7x+21 = 406
=>28x+42=406
=>28x=364
=>x=(364/28)=13
So, the value of first multiple = 7x = (7*13) =91
So, the value of the second multiple of 7 will be 7(13+1)=98
The value of third multiple of 7 will be = 7(x+2)=7(13+2)=105
The value of fourth multiple of 7 will be = 7(x+3)=7(13+3)=112
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In 2017 the Hindu festival of Diwali occurred on Thursday, 19 October. What fraction of the year was this
The Diwali occurred on 0.408 or 40.8% of the year in 2017.
To find the fraction of the year that Diwali occurred in 2017, we need to divide the number of days between Diwali and the start of the year by the total number of days in the year.
Diwali occurred on Thursday, October 19, 2017. The start of the year 2017 is January 1, 2017 which is a Sunday.
There are 365 days in a non-leap year. Since 2017 is not a leap year, there are 365 days in that year.
So the fraction of the year that Diwali occurred in 2017 can be calculated as: (days between Diwali and the start of the year) / (total days in the year) = ( 19 + 31 + 30 + 31 + 30 + 19 ) / 365 = (148) / 365 = 0.408
So, the Diwali occurred on 0.408 or 40.8% of the year in 2017.
Therefore, Diwali occurred on 0.408 or 40.8%
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Rectangle A is similar to rectangle B by scale factor r. The length of rectangle A is 1. 5r+2. 25 units. The length of rectangle B is 3 unite. What is the scale factor
The scale factor of the two rectangles is 1.5
Describe the rectangle.According to Euclidean Plane Geometry, a rectangle is a quadrilateral with equal opposed sides and four right angles. In other words, a rectangle is a parallelogram with a right angle of 90 degrees or an equiangular quadrilateral (i.e., 360°/4 = 90°). A rectangle is referred to as a square if its four sides are all the same length.
The ratio of the matching side lengths of two comparable figures is known as the scale factor. We know that the ratio of the respective side lengths of the two rectangles equals equivalent to r since Rectangle A and Rectangle B are similar to one another by the scale factor r.
We can set up the following ratio to determine the scale factor if the lengths of rectangles A and B are 1.5r+2.25 units and 3 units, respectively.
(1.5r+2.25) / 3 = r
Solving for r, we get:
r = (1.5r + 2.25) / 3
multiply both sides of the equation by 3
3r = 1.5r + 2.25
Subtract 1.5r from both sides
1.5r = 2.25
divide both sides by 1.5
r = 2.25/1.5
r = 1.5
Therefore, the scale factor of the two rectangles is 1.5.
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A grocer makes a display of cans in which the top row has one can and each lower row has two more cans than the row above it. If the display contains $100$ cans, how many rows does it contain
A grocer makes a display of cans in which there are 10 rows.
The top row has one can and each lower row has two more cans than the row above it.
We can write it as sequence:
1, 3, 5, 7, . . .
We can observe that it's an arithmetic sequence: 1, 3, 5, 7, . . . , 2n-1
We know that the formula for the sum of n-terms of arithmetic sequence:
S(n) = (n/2)(1 + 2n-1)
Here, Sn = 100
So, (n/2)[1 + 2n-1] = 100
n(1 + 2n + 1)
n(2n) = 200
2n^2 = 200
n^2 = 100
n = 10
Hence, the number of rows = 10
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How do you find the domain of a function with two variables?
The domain of a function with two variables is the set of all possible inputs (x-values and y-values) that make the function defined. To find the domain, first identify all of the restrictions on the x-values and y-values, then combine them into a single set of restrictions.
The domain of a function with two variables is the set of all possible inputs (x-values and y-values) that make the function defined. To find the domain, first identify all of the restrictions on the x-values and y-values. These restrictions may come from the function itself, such as any values that would make the function undefined, or from outside sources, such as boundaries placed on the function’s input. Once all of the restrictions are identified, they must be combined into a single set of restrictions. This set of restrictions defines the domain. For example, if the function is defined for all x-values between 1 and 5 and all y-values between -3 and 7, then the domain is all x-values between 1 and 5 and all y-values between -3 and 7. The domain of a function with two variables is an important part of understanding how the function behaves, as it defines the range of inputs for which the function is valid.
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The surface area of a sphere with the radius r is 4 pi r^2. Including the area of its circular base, what is the total surface area of a hemisphere with the radius 6 cm? Express your answer in terms of pi.
The total surface area of the hemisphere is 108 pi cm^2.
Surface area is the amount of space covering the outside of a three-dimensional shape. We calculate the surface area for three dimensional objects. The surface area of a 3-D object is not same as its volume.
The surface area of a sphere with the radius r is 4 pi r^2
The surface area of a hemisphere with the radius r = 2 pi r^2 + pi r^2
where pi r^2 represents the area of the circular base of the hemisphere of radius r.
The surface area of a hemisphere sphere with the radius r is 3 pi r^2
For radius r=6cm
TSA of the hemisphere is 3 pi (6x6) cm^2
TSA = 108 pi cm^2
108 pi cm^2 is the total surface area of a hemisphere with the radius 6 cm.
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Don’t know need help
I think that the answer would be 14
how to subtract 3 1/2 - 1/4 as a fraction (I NEED IT TOMORROW)
Answer:
13/4 as an improper fraction
3 1/4 as a mixed number fraction
Step-by-step explanation:
Turn 3 1/2 into an improper fraction
7/2 - 1/4
To write 7/2 as a fraction with a common denominator, multiply by 2/2
7/2 x 2/2 = 14/4
14/4 - 1/4 = 13/4
Can you help me with this
Answer:
I have graphed a line with a slope of 3/5 and attached a screenshot in the explanation.
Step-by-step explanation:
how do i anser this question
The graph that is not a straight line does not represent a direct variation.
What is direct variation?Direct variation of a quantity {y} with respect quantity {x} means that the value of {y} increases as the the value of {x} increases. Mathematically -
y = Kx
K = y/x
where -
{K} is scale factor.
Given are the graphs representing direct variation.
Direct variation is represented by the equation -
y = kx
The graphs representing the direct variation are straight lines. Since all the graphs are not given, any graph that is not a straight line does not represent a direct variation.
Therefore, the graph that is not a straight line does not represent a direct variation.
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28.2, 27.22, 27.62 , 27.54 , 27.5 in Greatest to Least
Answer:
28.2, 27.63, 27.54, 27.5, 27.22
Answer: 28.2, 27.62,27.5,27.22
Step-by-step explanation:
An object is moving at a speed of 11 yards every 6 months. Express this speed in centimeters per hour.
Speed of the given object in centimeters per hour
= 0.23 cm / hour
What is unit conversion?Unit conversion is a process with multiple steps that involves multiplication or division by a numerical factor or, particularly a conversion factor. The process may also require selection of the correct number of significant digits, and rounding. Different units of conversion are used to measure different parameters.
Like 1 yard = 91.44 cm
1 month = 730 hrs.
Given,
Distance covered by the object = 11 yards
Distance covered in cm = 11 × 91.44 = 1005.84 cm
Time taken to cover 11 yards = 6 months
Time taken in hours = 6 × 730 = 4380 hrs.
Speed of the object = distance covered by the object / Time taken
Speed of the object = 1005.84/4380 = 0.2296 ≈ 0.23 cm per hour
Hence, in centimeters per hour,
the speed of the object is 0.23 cm / hour.
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Plot all of the points of the reflected figure.
You may click a plotted point to delete it.
y
-10 9 8 7 6 5
-4 3
-2
-1
10
9
8
7
6
сл
2
↓
$
co
4
-5
ન
19
N
3
4
5
6
7
8 9
10
-x
Just re dot the points like mirror it on where ever on the graph
How do you plot a reflection on a point?Use the same x-coordinate and the y-opposite coordinate's to reflect a point on the x-axis. Use the same y-coordinate and the x-opposite coordinate's to reflect a point on the y-axis.
A point can be reflected in the x-axis, y-axis, or both axes.
Due to identical x-coordinates and opposing y-coordinates, the red spots on the x-axis are mirror reflections of one another. Thus, in opposing directions and 3 units away from the x-axis, are the red spots. A reflection in the x-axis is shown by the red spots.
Due to the identical y-coordinates and opposing x-coordinates, the blue spots on the y-axis are mirror reflections of one another. the blue points are thus
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What is the missing reason for line 2 in this proof?
Definition of a rectangle
Explanation:
A rectangle has two sets of parallel sides, and those opposite sides are the same length. This is simply the definition of what it means to be a rectangle. Because ABCD is a rectangle, we have these two pairs of congruent opposite sides:
AB = CDAD = BCIn a middle-school mentoring program, a number of the sixth graders are paired with a ninth-grade student as a buddy. No ninth grader is assigned more than one sixth-grade buddy. If 13 of all the ninth graders are paired with 25 of all the sixth graders, what fraction of the total number of sixth and ninth graders have a buddy
Answer:
13/25
I hope this is the correct answer.
Word Problems
1) Sandy has 22 books in her library. She bought several books at a yard
over the weekend. She now has 61 books in her library. How many be
did she buy at the yard sale?
) How many ink cartridges can you buy with 143 dollars if
one cartridge costs 11 dollars ?
) Melanie is baking a cake. The recipe calls for 6 cups of flour. She alre
4 cups. How many more cups does she need to add ?
Answer:
1) 39
2) 13
3) 2
Step-by-step explanation:
1) She had 22 books, she now has 61 books, so she bought 61-22 = 39 books at the yard sale.
2) 143/11 = 13
3) 6-4 = 2
solve for x : 4x-6=x+9
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here's the solution ~
[tex]\qquad \sf \dashrightarrow \: 4x - 6 = x + 9[/tex]
[tex]\qquad \sf \dashrightarrow \: 4x - x = 9 + 6[/tex]
[tex]\qquad \sf \dashrightarrow \: 3x = 15[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 15 \div 3[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 5[/tex]
Answer:
Step-by-step explanation:
4x-6=x+9
4x-x=9+6
3x=15
Final answer: x = 5
What is the largest positive multiple of $12$ that is less than $350?$
Answer: 348
Step-by-step explanation: 12*29 = 348, which is the largest multiple less than 350.
28. Anael cut several boards to build a deck.
The boards must be 100 in. ± 0.25 in. Her
measurements of the boards after cutting
them are shown in the graph. Which boards,
if any, can she not use?
Anael can not use the fourth board measurement. This can be solved by using the concept of inch scale.
What is inch scale?A centimeter is smaller than an inch. On the other side of the centimeter ruler, inches are denoted by the large, continuous hash marks that are inscribed above the digits. On a ruler, the inch is the largest unit and is denoted by the longest line. There is a number next to each 1-inch line on the ruler that designates.
Since the international yard was adopted in the 1950's and 1960's, standards for the precise length of an inch have fluctuated, but the inch is now based on the metric system and is defined as precisely 25.4 mm.
The question given here,
the first board measurement: [tex]99\frac{3}{4} =[/tex] 99 inch ± 0.75 inch
the second board measurement: [tex]99\frac{7}{8} =[/tex] 99 inch ± 0.875 inch
the third board measurement: [tex]100\frac{1}{6} =[/tex] 100 inch ± 0.16 inch
the fourth board measurement: [tex]100\frac{5}{16} =[/tex] 100 inch ± 0.3125 inch
the fifth board measurement: [tex]99\frac{13}{16} =[/tex] 99 inch ± 0.8125 inch
Thus, Anael can not use the fourth board measurement.
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(m² - 7m - 11) ÷ (m-8)
By diving polynomials