The solutions are 1+i and 1-i of the quadratic equation x²-2x+2=0
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
The quadratic formula to find solution of an equation is
x=-b±√b²-4ac/2a
The given equation is x²-2x+2=0
a=1, b=-2, c=2
x=2±√4-4(1)(2)/2(1)
x=2±√-4/2
x=2±2i/2
x=1+i, 1-i
Hence, the solutions are 1+i and 1-i of the quadratic equation x²-2x+2=0
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Answer this question Please
(70 points)
A 130
The red line meets the measuring tool at 155 and 25 therefore we get:
155-25 = 130
6. [3 marks ] Answer the question regarding the meaning of the given statement which contains a multiple negation. Stephen failed to avoid spoilers on the new Star Wars movie. Did Stephen see spoilers?
Answer: The statement "Stephen failed to avoid spoilers on the new Star Wars movie" contains a negative phrase "failed to avoid". When a sentence contains a negative phrase, it can sometimes be difficult to determine the meaning. However, in this case, the meaning of the sentence is that Stephen did see spoilers on the new Star Wars movie. The use of "failed to avoid" indicates that Stephen made an effort to avoid spoilers but was unsuccessful, which means that he saw them.
Step-by-step explanation:
The Unit Rate means how much of something per 1 unit of something else. true or flase
Answer:
true
Step-by-step explanation:
A unit rate is a price for one unit of anything. This is written as a ratio with a denominator of one.
Determine the area of each composite figure. Round to the nearest tenth if necessary.
The area of each composite figure is 828.96 cm².
What is Surface Area?A 3D object's surface area is the entire area that all of its faces cover. For instance, the surface area of a cube is its surface area if we need to determine how much paint is needed to paint it. It is consistently expressed in square units.
Given:
Surface area = SA of Cone + SA of Hemisphere
Cone:
radius = 8 cm
slant height = 17 cm
So, SA of Cone = πrl
= 3.14 x 8 x 17
= 427.04 cm²
Hemisphere:
radius = 8 cm
So, SA of Hemisphere = 2πr²
= 2 x 3.14 x 8 x 8
= 401.92 cm²
Thus, the SA of figure = 427.04 + 401.92 = 828.96 cm²
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use the pythagorean theorem to determine which of the following give the measures of the legs and hypotenuse of a right triangle.
The Pythagorean theorem states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse.
Therefore, for the given values of 3, 4, and 5, these lengths can indeed form a right triangle. Specifically, this triangle is a 3-4-5 triangle, which is a special type of right triangle whose sides have integral lengths and whose angles are all multiples of 30°.
Mathematically, this can be expressed as a^2 + b^2 = c^2, where a and b are the lengths of the two legs of the triangle and c is the length of the hypotenuse. The theorem is a fundamental result in geometry and has wide-ranging applications in mathematics, physics, engineering, and other fields.
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the range of x is the set {0,1,2,3,x}, where x is unknown. if each value is equally likely and the mean of x is 6, determine x.
If each value is equally likely and the mean of x is 6, x = 24.
The arithmetic mean (arithmetic average or simply the mean or average) in statistics is the sum of a collection of numbers divided by the count of numbers in the collection, which is is often a set of results from an experiment, a survey, or observational study.
The arithmetic mean A is defined to be the formula: [tex]A = \frac{1}{n} \sum_{i=1}^{n} a_i=\frac{a_1+ ... +a_n}{n}[/tex].
We're given a set of {0, 1, 2, 3, x} where x is unknown and the mean of x is 6. In order to find the value of x, we can plug all the known values in the formula first and then we're going to simplify the equation:
[tex]A = \frac{a_1+...+a_n}{n}\\\\6 = \frac{0+1+2+3+x}{5}\\\\6 = \frac{6+x}{5}\\\\30 = 6 + x\\\\30 - 6 = x\\\\x = 30 - 6\\\\x = 24[/tex]
We've confirmed that x is indeed equal to 24.
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Find the area of each triangle. Round to the nearest tenth.
The area of the triangle is 2. 6 square units
How to determine the area of the triangleThe formula for calculating the area of a triangle is expressed as;
A = 1/2bh
Given that the parameters are;
A is the area of the triangleb is the base of the triangleh is the height of the triangleusing the trigonometric identity, sine, we have;
sin 60 = h/4
substitute the values
0. 8660 (4) = h
h = 3.5
substitute the value
Area = 1/ 2 × 3. 5 × 1. 5
multiply the values
Area = 2. 6 square units
Hence, the value is 2. 6 square units
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for which of the following conditions is it not appropriate to assume that the sampling distribution of the sample mean is approximately normal? responses
It is not appropriate to assume that the sampling distribution of the sample mean is approximately normal when the sample size is small and the population distribution is skewed to the right or to the left. So, the options C and D are not appropriate. A and B are appropriate as the sample size is large and the population is normally distributed. E is also appropriate as the sample size is large.
The central limit theorem states that if we have a large enough sample size (typically n >= 30) from any population with a well-defined mean and finite variance, then the distribution of the sample mean approaches a normal distribution with mean equal to the population mean and variance equal to the population variance divided by the sample size.
However, if the population distribution is highly skewed, meaning it is not symmetric, then even a large sample size may not lead to a normal distribution of the sample mean.
In this case, it is not appropriate to assume that the sampling distribution of the sample mean is approximately normal. This is why options C and D are not appropriate as the sample size is large (10 and 75 respectively) but the population distribution is skewed to the right or to the left. On the other hand, options A and B are appropriate as the sample size is large and the population is normally distributed. Option E is also appropriate as the sample size is large, regardless of the shape of the population distribution.
The complete question is given below:
""
For which of the following conditions is it not appropriate to assume that the sampling distribution of the sample mean is approximately normal?
A) A random sample of 8 taken from a normally distributed population.
B) A random sample of 50 taken from a normally distributed population.
C) A random sample of 10 taken from a population distribution that is skewed to the right.
D) A random sample of 75 taken from a population distribution that is skewed to the left.
E) A random sample of 100 taken from a population that is uniform.
"
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find the slope of the line passing through the points (3, -9) and ( 1,-4)
Answer:
= [tex]-\frac{5}{2}[/tex]
= m = -2.5
Step-by-step explanation:
Hope it helps on your assignment/quiz/test/homework
Answer:-5/2
Step-by-step explanation:
(3,-9) and (1,-4)
(x1,y1) (x2,y2)
[tex]\frac{-4+9}{1-3\\}[/tex] = [tex]\frac{-5}{2}[/tex]
Suppose the average yearly salary of an individual whose final degree is a master's is $43 thousand less than twice that of an individual whose final degree is a bachelor's. Combined, two people with each of these educational attainments earn $110 thousand. Find the average yearly salary of an individual with each of these final degrees.
The average yearly salary of an individual with each of these final degrees is $22333 and $16666.6.
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form
Ax + B = 0.
Given;
The average yearly salary of an individual whose final degree is a master's is $43000 less than twice that of an individual whose final degree is a bachelor's.
Combined, two people with each of these educational attainments earn $110 thousand.
Now, let the salary of bachelors be x
Then salary of masters= 2x-43000
x+2x-43000=110000
3x=67000
x=22333.33
2x-43000=16666.66
Therefore, by solving equations answer will be $22333 and $16666.6.
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show that the sum of residuals (error) for any first order simple linear regression least squares line is zero (0). that is pn i
The sum of residuals (error) for any first order simple linear regression least squares line is zero (0).
To show that the sum of residuals (error) for any first order simple linear regression least squares line is zero (0), we can use the following equation:
∑i = 1n (yi − (b0 + b1xi)) = 0Where b0 is the intercept and b1 is the slope of the line, and xi and yi are the x and y values of the ith data point. This equation can be expanded by substituting the least squares solution for b0 and b1 into the equation:
∑i = 1n (yi − (∑i = 1n yi)/n − (∑i = 1n xiyi − (∑i = 1n xi)(∑i = 1n yi))/(∑i = 1n xi2 − (∑i = 1n xi)2/n)) = 0
Simplifying both sides of the equation, we get:
∑i = 1n (yi − (∑i = 1n xiyi)/(∑i = 1n xi2)) = 0
Therefore, the sum of residuals (error) for any first order simple linear regression least squares line is zero (0).
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Is this true or false?
Answer:
Step-by-step explanation:
you look it up, If that doesn't work, see if someone asked the same question on this, if not, I got nothing.
The probability of committing a Type I error ____.
1) cannot be controlled by the experimenter
2) is determined by the level of significance (α, alpha) that one chooses
3) is determined by the sample size that one selects
4) is determined solely by the size of the treatment effect
The experimenter cannot control the probability of a Type I error, but they can control the level of significance they set, and that will determine the probability of making this type of error.
The probability of committing a Type I error is determined by the level of significance (α, alpha) that one chooses. This is because the level of significance is the probability of rejecting the null hypothesis when it is actually true. In other words, the level of significance is the probability of making a Type I error (falsely rejecting the null hypothesis). For example, if the level of significance is set to 0.05, then the probability of making a Type I error is 0.05. This can be expressed mathematically as: P(Type I Error) = α. Therefore, the experimenter cannot control the probability of a Type I error, but they can control the level of significance they set, and that will the probability of making this type of error.
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Wrtie the slope intercept form of the inequality 9x-7y>-7
Answer:
Step-by-step explanation:
9x - 7y > -7
-7y > -9x - 7
y < 9/7x + 1
Roberto needs 6 feet and 8 inches of lumber to repair the deck. He has 54 inches of lumber. How many more inches of lumber does he need?
Answer:
26 inches, or 2 ft 2 in.
Step-by-step explanation:
1 ft = 12 in.
6 ft 8 in. = 6 ft + 8 in. =
= 6 ft × 12 ft / in. + 8 in.
= 72 in. + 8 in.
= 80 in.
He needs 80 inches.
80 - 54 = 26
Answer 26 inches or 2 ft 2 in.
Answer:
he needs 26 inches
Step-by-step explanation:
which ratio forms a proportion with 8 over 36
consider the following system below, assuming the pinion has negligible inertia. formulate two equations of motion in terms of x, theta, and theta a for the parameters shown. one should be written in terms of the rotational acceleration and the other in terms of the linear acceleration
The system shown consists of a rotational mass, a pinion, and a linear mass.
The equations of motion for this system can be formulated in terms of x, theta, and theta a in terms of rotational and linear acceleration.
The equation of motion for rotational acceleration is given by:
θ¨ = (1/J) * (T - (b*x¨))
Where J is the moment of inertia of the rotational mass, T is the torque applied to the pinion, and b is the coefficient of friction between the pinion and the linear mass.
The equation of motion for linear acceleration is given by:
x¨ = (1/m) * (T - (b*θ¨))
Where m is the mass of the linear mass, T is the torque applied to the pinion, and b is the coefficient of friction between the pinion and the linear mass.
The equations of motion for the system shown can be formulated in terms of rotational acceleration (θ¨) and linear acceleration (x¨) using the moment of inertia (J) and mass (m) of the rotational and linear masses, respectively, as well as the coefficient of friction (b) between the two.
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The dotplot below displays the number of math classes taken by a random sample of 35 students at a high school.
A dotplot titled Math Classes. A number line going from 2 to 6 is labeled number of math classes taken. 2, 1; 3, 6; 4, 18; 5, 7; 6, 1.
Which letter represents the approximate location of the mean number of math classes?
A. A
B. B
C. C
D. D
Answer:
Class B
Step-by-step explanation:
duh
Answer:
b
Step-by-step explanation:
A trailer weighs one and one-half tons. There are 200 pounds of hay on
Answer:
3200
Step-by-step explanation:
1 1/2 US tons is 3000 pounds. Add the 200 pounds of hay and you get 3200. Hope this helps.
In this figure, h = 6, and r = 8.
What is the exact surface area of the cone?
Enter your answer in the box.
[answer] units²
Cone oriented with vertex on top and base on bottom. The perpendicular distance between the vertex and the base is labeled h. The radius of the circular base is labeled r.
[tex]\textit{surface area of a cylinder}\\\\ SA=2\pi r(h+r)~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ h=6\\ r=8 \end{cases}\implies SA=2\pi (8)(6+8) \\\\\\ SA=16\pi (14)\implies SA=224\pi \implies SA\approx 703.72~units^2[/tex]
The values of data measured on this scale can be rank ordered and have meaningful differences between scale points. For this scale, there is also an absolute zero. It is called____________
The values of data measured on this scale can be a number or a name, but they can be rank ordered___________
The values of data measured on this scale can be rank ordered and have meaningful differences between scale points. For this scale, there is also an absolute zero. It is called interval scale.
The values of data measured on this scale can be a number or a name, but they can be rank ordered I'd called Ordinal scale.
Ordinal Scale CharacteristicsThe ordinal scale can be observed with a distinction that shows the order or level of the object being measured based on certain parameters.
The characteristics of the ordinal scale are
Determined based on the number of special characteristics possessed Has zeros which are not absolute Data is logical The data is separated from each other Ordinal scales have a zero that is used to represent a point on the scale, but this zero is not an absolute zero Definition of Interval ScaleInterval scale is a scale that uses fixed intervals in determining categories. So this scale is called an interval scale, this scale has characteristics similar to nominal and ordinal scales, but differs because of the intervals used as a guide.
Interval Scale feature
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83 cmp cut from 1.3 metres 1.3metres
The remaining length when 85 cm is cut from 1.3 meters is 0.45 meters.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
We know, 1.3 meters = 1.3×100 cm = 130 cm.
Now, 83 cm is cut from it.
Therefore, The remaining length is,
= (130 - 85) cm.
= 45 cm.
And 45 cm is equal to (45/100) meters.
= 0.45 meters.
Q. 83 cm is cut from 1.3 meters what would the remaining length in meters?
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surd in bracket √2(2+6)
The value of the expression given as √2(2+6) is 4
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
√2(2+6)
We start by evaluating the expression in the bracket
So, we have the following
√2(2+6) = √2(8)
Evaluate the products
This gives
√2(2+6) = √16
Lastly, we have
√2(2+6) = 4
Hence, the solution is 4
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AREA The area of the rectangle in the figure is 32xy square units. Find the width of the rectangle. Write any variables in alphabetical order.
8xy
Answer:
[tex]4y^{2}[/tex]
Step-by-step explanation:
A = Area
w = width
l = length
[tex]A=lw[/tex]
in this equation the area is [tex]32xy^{3}[/tex] and the length is [tex]8xy[/tex].
To find the equation we simply have to divide the area ([tex]32xy^{3}[/tex]) by the length ([tex]8xy[/tex]).
[tex]32xy^{3} =(8xy)w[/tex]
When dividing, it's important to remember two things:
A variable divided by itself is oneTo divide a variable by the same variable with a lower exponent we have to subtractUsing these two rules, we divide the common bases (number by number, x by x, y by y):
[tex]\frac{32}{8}=4[/tex]
[tex]\frac{x}{x}=1[/tex]
[tex]\frac{y^{3} }{y}=y^{2}[/tex]
Multiplying all of them together, we find that the width is:
[tex]4y^{2}[/tex]
PLEASE HELP 20 POINTS
Answer: 3 times 5 minus a number x
Step-by-step explanation:
What will be congruence criterion
They are congruent by the by the Angle-Side-Angle (ASA) congruence criterion.
What is an Angle-Side-Angle (ASA) congruence criterion?Angle-Side-Angle (ASA) congruence criterion states that if two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the two triangles are congruent. In this case, the angles angle E = angle I and EG=FI (a non-included side), so the triangles ADEF and AHIG are congruent by ASA.
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Select the correct answer. Sides of three square rooms measure 14 feet each, and sides of two square rooms measure 17 feet each. Which expression shows the total area of these five rooms? A. (3 × 14^2) + (2 × 17^2) B. (2 × 14^3) + (2 × 17^2) C. (3 × 17^2) + (2 × 14^2) D. (3 × 14^2) × (2 × 17^2)
The total area of the given 5 square rooms is (3×14²)+(2×17²). Therefore, option A is the correct answer.
Describe area.The area of a thing is the amount of space it occupies in two dimensions. It is the measurement of the quantity of metric squares that completely cover the entire surface of an enclosed figure. The square unit, which is frequently expressed as square inches, sq.ft, etc., is the accepted unit of area.
What in math is area?Area is the entire amount of space occupied by a plain (2-D) surface or an object's form. The area of a planar figure is the area that its perimeter encloses. The quantity of unit triangles that cover a closed figure's surface is its area. Area is measured in units like mm in diameter and m2.
Given that, sides of three square rooms measure 14 feet each, and sides of two square rooms measure 17 feet each.
We know that, area of square =a², where a is the side of square
Now, area of a square room with side 14 feet
= 14² square feet
The area of 3 square room with sides 14 feet
= 3×14² square feet
The area of a square room with side 17 feet
= 17² square feet
The area of 2 square room with sides 17 feet
= 2×17² square feet
So, total area of these five rooms
= (3×14²)+(2×17²) square feet
The total area is (3×14²)+(2×17²). Therefore, option A is the correct answer.
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A glass contains 320 cm³ of orange juice. The mass of the juice
is 370 g.
Calculate the density of the juice in kilograms per cubic metre
(kg/m³).
Give your answer to the nearest integer.
Therefore , the solution of the given problem of volume comes out to be density 1.15625 g/ cm³.
Describe volume.The volume of a three-dimensional item, which is measured in cubic units, describes how much room it occupies. Two examples of cubic units are cm3 and in3. The amount of matter in a thing is measured by its mass, on the other hand. The weight of an object is typically converted into mass quantities like pounds and kilograms.
Here,
Given:
Density = mass /volume
mass = 370 gm
volume = 320 cm³
Density = 370/320
=>Density = 1.15625 g/ cm³
thus , density 1.15625 g/ cm³
Therefore , the solution of the given problem of volume comes out to be density 1.15625 g/ cm³.
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true/false. the student knows that the relationship between the spring constant (k), the mass (m), and the period of oscillation (t) is given by the equation (19) this is not a linear equation, but it can be linearized using the same method used to linearize equation 10.
The statement “The relationship between the spring constant (k), the mass (m), and the period of oscillation (t) is given by the equation (19) this is not a linear equation, but it can be linearized using the same method used to linearize equation 10.” is true because equation 19 can indeed be linearized with the same method used to linearize equation 10.
Equation 10 is a non-linear equation and can be linearized by taking the natural logarithm of both sides. This will convert the equation into a linear form which can be used to calculate the parameters of the original equation.
Similarly, equation 19 can be linearized by taking the natural logarithm of both sides. The linearized form of equation 19 will also be useful in finding out the parameters of the original equation.
By linearizing the equations, it becomes easier to solve for the parameters of the equations. This is because linear equations are much simpler and can be solved using basic algebraic methods.
Linear equations can also be solved using matrix methods and can be used to solve for the parameters of the original equations more accurately.
Therefore, it is true that equation 19 can be linearized using the same method used to linearize equation 10. This will make it easier to solve for the parameters of the original equation.
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Draw The Congruence markings on ΔXYZ, so that ΔABC≅ΔXYZ by ASA
Angle B is equal to angle Y and angle A is equal to angle X. And AB is equal to side XY.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
The triangle ΔABC is congruent to the triangle ΔXYZ.
In triangles ΔABC and ΔXYZ, then we have
∠B = ∠Y (Corresponding angles)
∠A = ∠X (Corresponding angles)
AB = XY (Common side)
Angle B is equal to angle Y and angle A is equal to angle X. And AB is equal to side XY.
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