The roots of the quadratic equation x^5 - x^2 = 0 are x = 0 and x = ±√2, which can be found by factoring and setting each factor equal to 0. The quadratic can be factored into (x^2)(x^3 - 1) = 0 and then the factors can be set equal to 0, resulting in x = 0 and x = ±√2.
To find the roots of the quadratic equation x^5 - x^2 = 0, first we must factor the equation. To do this, we can recognize that there are two terms, x^5 and x^2, and that the exponents are both greater than 1, so we can factor out an x^2 from both terms. When we do this, we get (x^2)(x^3 - 1) = 0. Now we can set each factor equal to 0, so that x^2 = 0 and x^3 - 1 = 0. Solving for x in the first equation, we get x = 0. To solve for x in the second equation, we can add 1 to both sides, so that x^3 = 1. Taking the cube root of both sides, we get x = ±√2. Therefore, the roots of the quadratic equation x^5 - x^2 = 0 are x = 0 and x = ±√2.
x^5 - x^2 = 0
x^2(x^3 - 1) = 0
x^2 = 0 → x = 0
x^3 - 1 = 0 → x^3 = 1 → x = ±√2
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What is set grade 3 math?
Set grade 3 math is a subject that helps children to develop a fundamental understanding of mathematics.
What is grade?Grade is a measure of academic progress. It is typically expressed as a letter or numerical score that reflects the level of achievement in a course or program. Grade is an important factor for measuring student performance and can be used to make decisions about placement, academic standing, and course selection. Grade is also used to inform students and parents about how well students are doing in their studies. Grade is often the most important factor in determining a student's overall academic success.
Set grade 3 maths covers topics such as addition, subtraction, multiplication, division, fractions, decimals, shapes, measurement, and problem-solving. This subject is important for the development of a child's critical thinking and reasoning skills. It encourages students to think logically, observe patterns, and use math operations to solve problems. Set grade 3 math also provides students with the opportunity to learn important mathematical concepts in a fun and engaging way.
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Answer:
Set grade math is a mathematical model for a collection of different things a set contains elements or members which can be mathematical objects of any kind numbers and symbols points in space.
What is expressions Class 8 maths?
Expression is a constant, variable or constant multiplied by a variable separated by operator.
What is algebraic expression and identity?Identity, as we all know, is equality, which holds true regardless of the variable's value. These identities are algebraic formulas that show that for all possible values of the variable, the Left-Hand Side (LHS) and the Right-Hand Side (RHS) of the equation are equal. A phrase that can have any value is called a variable.
What are the types of algebraic expressions?Monomial, polynomial and binomial are the three types of algebraic expression.
An expression with variables, constants, and algebraic operations is known as an algebraic expression (like subtraction, addition, multiplication, etc.). Terms comprise expressions. For instance: 5x+20y, 6-8x.
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Here are the first four terms of a sequence
4 , 11 , 22 , 37
find an expression, in terms of n, for the nth term of this sequence
Answer:
Step-by-step explanation:
Determine an algebraic expression for the nth term of the following sequence.
A set of 3 figures are connected squares. Figure 1 is a column of 5 squares next to a column of 3 shaded squares. Figure 2 is figure 1 with an additional column of 3 shaded squares to the right. Figure 3 is figure 2 with an addition column of 3 shaded squares to the right to make 9 shaded squares.
to guarantee that cans of soda are properly filled, some cans are sampled and the amounts measured. the overall average for the samples is 12 ounces. each sample contains 10 cans. the average range is 0.4 ounces. the lower control chart limit for the sample averages would be
Energy sources that are non renewable include coal, natural gas, oil, and nuclear power.
What is Nonrenewable Resources?Since we currently rely on these resources to meet the majority of our energy needs, their exhaustion and inability to be replenished poses a serious issue for humanity.Human society depends on both nonrenewable and renewable resources for its everyday energy needs. Renewable resources can naturally replenish themselves, but nonrenewable resources cannot. This is the main distinction between these two types of resources. Due to their finite availability, nonrenewable resources cannot be used responsibly.Nuclear energy, coal, natural gas, and oil are the four main categories of nonrenewable resources. Fossil fuels refer to the three fuels that make up coal, natural gas, and oil. The name "fossil" comes from the fact that fossil fuels were created deep inside the Earth over the course of millions of years from decomposing plants and animals. They are discovered in the silt and rock layers below the earth's surface. Crude oil, also known as petroleum, coal, and natural gas were produced by the pressure and heat combined with the remains of plants and animals.The Complete Question is Nonrenewable Resources.
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What is the median of the following numbers 24 23 25 21 24 27?
The median for the data is 24.
Median is the middle value of the set of data when the data is arranged in an ascending order.
The median of a data has a higher frequency if the data is distributed symmetrically.
We will arrange the given data in ascending order as 21, 23, 24, 25 and 27.
Also, the number of values here is 5, which is an odd number. As we know if the number of values is odd in a data, then the middle value will be the median.
For 5 numbers, the middle value will be the number from either side.
In the given data, as we can see that the value is 24, so 24 will be the median for the data.
Hence, the median for the data is 24.
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Is there algebra in 7th grade?
Answer:
probably simple basic algebra
Step-by-step explanation:
It is 1.4 kilometers from Jim’s house to his grandmother’s house. How far does Jim walk going to and from his grandmothers house once every day for 5 days?
Jim has to walk 7 km going to his grandmother's house once per day for 5 days.
What is an arithmetic operation?The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers.
Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per the data given in the question,
Distance between Jim and his grandmother's house = 1.4 km.
Jim travels once to his grandmother's house every day then,
Total distance traveled by him = 5 × 1.4 km = 7 km.
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Your friend is training for a triathlon. On one training day she swam 1500 m, rode a bike for 47 000 m and ran 14 km. How many kilometers were completed?
She completed one training day in a triathlon- 62.5 km.
Convert meter to kilometer :
1 kilometer = 1000 meter
⇒ 1 meter = [tex]\frac{1}{1000}[/tex] kilometer
On a training day, she swam = 1500 meter
= [tex]\frac{1500}{1000}[/tex] kilometer
= 1.5 kilometer
She rode a bike = 47000 meter
= [tex]\frac{47000}{1000}[/tex] kilometer
= 47 kilometer
She ran = 14 km
We may get the total distance by adding the distances she covered with swimming, riding, and running.
∴ Total distance she covered for a triathlon = ( 1.5 + 47 +14) km
= 62.5 km
She completed one training day in a triathlon - 62.5 km.
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The weight of 2apple i 400 gram. I ate one apple of 150 gram. Find the weight of the other apple
The weight of the other apple is 250 grams.
As per the given data:
The weight of 2 apples is 400 gram.
The weight of 1 apple is 150 grams which I ate.
We have to determine the weight of the other apple.
Subtract the weight of 1 apple from weight of 2 apples
Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers
One value is 400 and the other value is 150.
Means subtract 150 from 400.
The weight of the other apple = Weight of 2 apples - The weight of 1 apple
= 400 - 150
= 250 grams
Therefore the answer is 250 grams.
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If m/RXU = 52°, then what is m/SXU?
2
X
UA
The measure of angle SXU is m ∠SXU = 128°.
What is linear angles?
If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. These are also referred to as supplementary angles. Angles that share a vertex are said to be adjacent.
Given: m ∠RXU = 52°
We have to find the measure of angle m ∠SXU.
Let RS and VW are two lines intersects by a transversal TU.
∠3 and ∠4 are adjacent to each other after the intersection of the two lines.
Since the sum of angles of a linear pair is always equal to 180°.
⇒ ∠3 + ∠4 = 180°
52° + ∠4 = 180°
∠4 = 180° - 52°
∠4 = 128°
Hence, the measure of angle SXU is m ∠SXU = 128°.
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Aaron estimated that 148% of 333 is 495. is his estimate reasonable?
a. no, because his calculation should be 140% of 340.
b. no, because his calculation should be 150% of 340.
c. yes, because his calculation should be 140% of 330.
d. yes, because his calculation should be 150% of 330.
Yes, His computation should be 150% of 330, thus his estimate is accurate. So option D is true.
By dividing the desired value by the entire value and multiplying by 100, the percentage may be computed.
Example:
Required percentage value = a
total value = b
Percentage = [tex]\dfrac{a}{b} \times 100[/tex]
We have,
Aaron estimated the value, of 148% of 333 is 495.
This can be written as,
[tex]\dfrac{148}{100} \times 333[/tex]
[tex]= 492.84[/tex]
[tex]= 493\\\\[/tex]
Estimating the number, this should be equal to the,
148% ≈ 150%
333 ≈ 330
So it is equal to,
150% of 330
This can be written as,
[tex]\dfrac{150}{100} \times 330[/tex]
[tex]= 495[/tex]
Therefore, his estimate is reasonable because his calculation should be 150% of 330. So option D is true.
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Luisa began walking up a hill at a spot where the elevation is 0.9 km. After she walked
3 km, she saw a sign giving the elevation as 0.95 km. How far will she have walked when she
reaches and elevation of 1.1 km?
Answer:
3.82 km
Step-by-step explanation:
Assuming that the change in elevation is linear, we can calculate the elevation change per km traveled. The known values are the start (0km) and the sign (3km). The elevation gain over that interval is (0.95-9.0)km = 0.5km. That was for an distance interval of 3km, so we can write:
(0.5km elevation gain)/(3km distance)
We can use this as a rate change and and use it in a linear equation to predict the elevation as a function of distance.
Let y be the elevation and x the distance, both in km.
y = (0.183)(x)+b, where b is the elevation at the start of the trail. We can find b by using this equation and entering one of the two data points. Lets use the elevation of 0.95m at 3km distance:
y = (0.183)(x)+b
0.95 = (0.183)(3)+b
b = 0.4km
The full equation is :
y = (0.1833)X + 0.4
Enter 1.1 km for y and calculate x, the distance to reach 1.1 km altitude.
1.1 = (0.1833)X + 0.4
X = 3.82 km
What are the advantages of being a multinational corporation? check all that apply. Expansion into new marketsaccess to cheaper laborcreation of a trade surplusreliance on unskilled workerslower tax payments.
The advantages of being a multinational corporation are mentioned below.
Multinational corporations (MNCs) have several advantages:
Expansion into new markets: MNCs can expand their operations into new markets around the world, which can increase their revenues and profits.
Access to cheaper labor: MNCs can take advantage of lower labor costs in different countries by setting up operations in those countries. This can help them reduce their overall production costs and increase their competitiveness.
Creation of a trade surplus: MNCs can create a trade surplus by exporting more than they import. This can benefit the economies of the countries where they operate by generating foreign exchange and creating jobs.
Lower tax payments: MNCs can reduce their tax payments by taking advantage of lower tax rates in different countries and by using tax havens.
Note that relying on unskilled workers is not necessarily an advantage of being an MNC, as it may not be the most efficient or effective way to operate. In fact, many MNCs rely on skilled workers in order to produce high-quality products and services.
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Below are some benefits of working for a multinational firm.
Multinational businesses (MNCs) benefit from a number of factors:
Expansion into new markets: MNCs can broaden their business activities into other geographies, which can boost their earnings.
Access to cheaper labor: By establishing operations there, MNCs can benefit from lower labor costs in other nations. They can become more competitive and lower their overall production costs as a result.
Making a trade surplus: By exporting more than they import, MNCs can make a trade surplus. Through the production of foreign exchange and the creation of jobs, this can help the economy of the nations where they are present.
Lower tax obligations: MNCs can lower their tax obligations by utilizing tax havens and nations with lower tax obligations.
If the m<2 = 58° and the m<13 = 111°, find the measures of angles 1, 5, 8, 14, 18.
Note: x || m and z || y
Answer:
Angle 1: 58°
Angle 5: 58°
Angle 8: 111°
Angle 14: 111°
Angle 18: 58°
Step-by-step explanation:
A new road that connects uniontown to springville is 413 miles long. What is the change in distance when using the new road instead of the dirt roads? write your answer as a mixed number.
In mixed number form, the change in the distance when using the new road instead of the dirt roads is 2 1/12 miles lesser.
To determine the change in the distance when using the new road instead of the dirt roads, we need to find the difference between the distance of the new road and the distance of the dirt roads.
The distance of the dirt roads is the sum of the two measurements given, which is 2 3/8 + 3 5/6 = 5 15/24 miles.
The change in the distance when using the new road instead of the dirt roads is the difference between the distance of the new road and the distance of the dirt roads, which is 4 1/3 - 5 15/24 = -2 2/24 miles.
In mixed number form, the change in the distance when using the new road instead of the dirt roads is -2 and 2/24 = -2 1/12 miles.
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For the complex number z = negative startfraction startroot 21 endroot over 2 endfraction minus startfraction startroot 7 endroot over 2 endfraction i, what is arg(z)?.
Answer:
arg(z) = 7π/6
Step-by-step explanation:
You want the argument of the complex number -√21/2 -√7/2i.
ArgumentThe argument of the complex number is the angle it makes with respect to the positive real axis. It can be found using the arctangent function, paying attention to quadrant.
The number can be written as ...
[tex]z=-\dfrac{\sqrt{21}}{2}-\dfrac{\sqrt{7}}{2}i=\dfrac{\sqrt{7}}{2}(-\sqrt{3}-i)\\\\\arg{(z)}=\arctan{\dfrac{-1}{-\sqrt{3}}}\\\\\boxed{\arg{(z)}=\dfrac{7\pi}{6}}[/tex]
Answer: B. 210°
Step-by-step explanation:
What is the minimum value of the function f x )= 16x 2 )- 16x 28?
The minimum value of the given function f(x) = 16x² −16x+28 is 24.
What are the Maxima and Minima of a Function?The curve of a function has peaks and troughs called maxima and minima. A function may have any number of maxima and minima. Calculus allows us to determine any function's maximum and lowest values without ever consulting the function's graph.
To find the minimum value of the function f(x) = 16x² −16x+28 using the derivative method, you can start by taking the derivative of the function. The derivative of a quadratic function is given by:
f'(x) = 2ax + b
In this case, the derivative of the function f(x) is:
f'(x) = 2×16x - 16
To find the minimum value, we need to find the x value that makes the derivative equal to zero. Setting the derivative equal to zero and solving for x gives us:
216x - 16 = 0
32x = 16
x = 0.5
Now that we have the value of x that minimizes the function, we can plug this value back into the original function to find the minimum value:
f(0.5) = 16×(0.5)² - 16(0.5) + 28 = 4 - 8 + 28 = 24
Therefore, the minimum value of the function is 24.
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Match the equation with the correct form.
Slope-Intercept Form
Point-Slope Form
Standard Form
1. ax + by = c
2. y+y₁ = m(x + x1)
3. y = mx + b
4. y - y₁ = m(x − x₁)
The equation of a line in different forms are:
1. The slope-intercept form: y = mx + b.
2. The point-slope form: y - y₁ = m(x − x₁).
3. The standard form: ax + by = c.
What is the Equation of a Line?There are three ways that an equation that represents a line can be written in, they are as follows:
1. The slope-intercept form: this is expressed as y = mx + b. In this form, we have the following values and what they each represent:
m = the slope of the line.
b = the y-intercept of the line,
x and y are the coordinates of a point on the line.
2. The point-slope form: this is expressed as y - y₁ = m(x − x₁). In this form, the variables represented are:
m = the slope of the line.
x₁ and y₁ are the coordinates of a point that the line passes through.
3. The standard form: this is expressed as ax + by = c. In this form, the variables a, b, and c are integers.
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What is the slope of 5x y =- 7?
Answer:
-5
Step-by-step explanation:
The slope is -5
5x + Y = -7
-5x
=
Y= -5x - 7
What is the sample variance of the following numbers 6 4 2 7 1?
6.50 is the sample variance of the following numbers.
How to interpret a standard deviation?
The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean.
Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.
X = ∑x/n
= 3 + 4 + 2 + 7 + 1/5
= 20/5 = 4
s² = [∑(Xi - x)²/N-1]
= (6-4)² + ( 4 - 4 )²+ ( 4 - 4 )² + ( 7 - 4 )² + ( 1 - 4 )²/5 - 1
= 26/4
= 6.50
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a data set was graphed using a scatterplot. the correlation coefficient, r, is 0.813. which of the following statements explains how the correlation is affected? a.) it is not affected. b.) it is affected by an influential point. c.) it is affected by inappropriate grouping. d.) it is affected by non-linearity.
The correlation coefficient is increasing, which may have an effect on the influential points. Thus, option (a) is correct.
The correlation coefficient, in general, quantifies the strength of the association between two variables.
To find non-linearity, influential spots, or improper grouping in a dataset, for example. A scatter plot is used to graph the data set.
Here, the correlation coefficient is r = 0.813.
Linearity is evident since there is a significant link between the two variables. As a result, non-linearity has no effect on it. It is not influenced by incorrect categorization when it appears that type of case correlation may be lower.
The correlation coefficient is increasing, which may have an effect on the influential points.
Thus, option (a) is correct.
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Which expressions are equivalent to the one below? Check all that apply.
4^3 x 4^x
Answer:
d
Step-by-step explanation:
[tex]{4}^{3} . {4}^{x} [/tex]
In the following we make multiple not sum to the power
How do you draw a linear inequality?
To draw a linear inequality in graph the steps are mentioned below.
What are the steps to graphing an inequality?The graph of a two-variable inequality is the set of points that describe all solutions to the inequality. The coordinate plane is split in half by a boundary line created by a linear inequality, with one-half representing the solutions to the inequality.
Steps are described below:
Step 1: Always begin by separating the variable y from the inequality's left side.
Step 2: Replace the symbol for inequality with that for equality.
Step 3: In the xy plane, graph the boundary line from step 2. You are creating the boundary line that would divide or cut the xy-plane into two sections in this stage.
Step 4: Shading one side or area of the boundary line is the final step.
Step 5: Use this optional step to check or confirm that you have shaded the boundary line's side appropriately.
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Simplify: (-8) x (6)-(5)x(-2)
Answer: Answer -38
Simplified version: -48 + 10
Step-by-step explanation: Sorry If I'm wrong.
Identify the sample space of the probability experiment and determine the number of outcomes in the sample space Randomly choosing an even number between 1 and 10, inclusive
The sample space is______. (Use a comma to separate answers as needed. Use ascending order) There are________outcome(s) in the sample space.
Answer:
Step-by-step explanation:
Sample Space
off even numbers
= {2,4,6,8,10}.
There are 5 outcomes in the sample space,
What is the answer for 2 to the power of 1?
Answer:
2
Step-by-step explanation:
Any number to the power of 1 is that number itself, thus 2 to the power of 1 is 2.
Step-by-step explanation:
an exponent always means how often the base (or base number) is multiplied by itself.
like
3⁴ = 3×3×3×3
5³ = 5×5×5
x⁵ = x×x×x×x×x
so,
x¹ = x
for every value of x.
and therefore
2¹ = 2
How do you divide whole numbers step by step?
Divide the dividend's leading digit by the divisor. Divide the first two digits of the dividend by the divisor, and so on, if the divisor is greater than the dividend's first digit.
Step 2: Type the dividend's quotient above it.
what is divide?divide into parts; be divided into parts. cause one to disagree with .a significant difference between two groups that usually results in antagonism or conflict. the act or process of dividing; the condition of being divided; the act, process, or occurrence of distributing among many: distribution. : one of the segments or groups into which a whole is divided or is subdivided.
Divide the dividend's leading digit by the divisor. Divide the first two digits of the dividend by the divisor, and so on, if the divisor is greater than the dividend's first digit.
Step 2: Type the dividend's quotient above it.
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What is the slope angle of Y 3x 1?
The level of a line's slope indicates its steepness, here θ = [tex]tan^{-1/3}[/tex] is the slope angle of Y = 3x + 1.
How do one find the slope of a graph?The slope is computed mathematically as "rise over run" (change in y divided by change in x).
In accordance with the slope equation, the slope of such a line may be determined by dividing the rise of the line between two positions by the run of the same line between the same two sites.
Now, given that,
Y = 3x + 1 ........ (1)
slope intercept form equation is: y = mx+c ........... (2)
next, if we compare (1) and (2)
it comes out to be
m = 3 representing slope
and c = 1 representing y-intercept.
now, slope angle: tan θ = m (slope)
tan θ = 3 [putting the value of m]
θ = [tex]tan^{-1/3}[/tex]
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The complete question is as follows:
What is the slope angle of Y = 3x + 1?
Triangles RST and XYZ are drawn below. If RS= 6, ST=14, XY = 9, YZ=21, and ZSZY, is ARST similar to AXYZ? Justify your answer.
Answer:
yes, ∆RST ~ ∆XYZ
Step-by-step explanation:
You want to know if ∆RST is similar to ∆XYZ when RS=6, ST=14, XY=9, YZ=21 and ∠S≅∠Y.
SAS similarityTwo triangles are similar by the SAS theorem if corresponding sides have the same ratio, and the angles between them are congruent.
ApplicationCorresponding sides are ...
RS : XY = 6 : 9 = 2 : 3
ST : YZ = 14 : 21 = 2 : 3 . . . . same ratio
The angles between them are ...
∠S, ∠Y . . . . . given as congruent
Corresponding sides have the same ratios, and the angles between them are congruent, so the triangles are similar.
What is the vertical asymptote of y 1x − 5?
The vertical asymptote of y = 1x - 5 is x = 5, since the denominator becomes zero when x = 5 and the function is undefined at this point.
The vertical asymptote of y = 1x - 5 is x = 5. This is because when x = 5, the denominator of the function (1x - 5) becomes zero, and the function is undefined at this point. As a result, the vertical asymptote is x = 5. This can be seen by taking the limit of the function as x approaches 5 from either side. As x approaches 5 from the left, the limit of the function is negative infinity, and as x approaches 5 from the right, the limit of the function is positive infinity. Thus, the vertical asymptote of y = 1x - 5 is x = 5, since the denominator becomes zero when x = 5 and the function is undefined at this point.
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