The statement that in the Orthogonal Decomposition Theorem, each term in formula (2) for Å, is itself an orthogonal projection of y onto a subspace of W is true .
What is Orthogonal Decomposition Theorem?The orthogonal decomposition of the vector of is the sum of the vectors of the subspaces of and the vectors of the orthogonal complements of . The orthogonal decomposition theorem states that each vector in can be uniquely described in the form , if W is a subspace of V then ecah vector in can be written in uniquely. Therefore z belongs to W⊥ because it is orthogonal to the spanning set of W. To keep the decomposition y = p + z unique, assume another decomposition y = q + w such that q ∈ W and w ∈ W⊥. Both decompositions are equal to y, so we have p − q = w − z. where p − q is in W and w − z is in W⊥.
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Question 3 Write a method that solves for x in the quadratic equation. The parameters are a, b, c, and boolean flag that indicates whether it will solve the equation with addition or subtraction in the numerator. 2-4ac ㄨㄧ- 2a Source: Wikipedia The method will return the value of x
On solving the providewd question we can say that, public static double solve(double a, double b, double c, boolean flag )
What is quadratic equation?A quadratic equation is a quadratic polynomial in one variable that looks like this: x = ax2 + bx + c. a 0. This polynomial has at least one solution since it is a second-order polynomial, according to the Fundamental Theorem of Algebra. The answer can actually work or be difficult.
public static double solve(double a, double b, double c, boolean flag)
{ double d = Math.sqrt(b*b - 4*a*c); if(flag)
{ return (-b + d) / (2*a); }
else { return (-b - d) / (2*a); } }
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Select the correct answer. Consider the following equation. − 16 p + 37 = 49 − 21 p Select the equation that has the same solution as the given equation. A. − 55 + 12 p = 5 p + 16 B. − 14 + 6 p = − 9 − 6 p C. 2 + 1.25 p = − 3.75 p + 10 D. 3 2 p − 5 + 9 4 p = 7 − 5 4 p
The equation that has the same solution as − 16 p + 37 = 49 − 21 p is (3/2)p - 5 + (9/4)p = 7 - (5/4)p thus option (C) is correct.
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
More than one variable may be present inside a linear equation.
As per the given equation,
− 16 p + 37 = 49 − 21 p
-16p + 21p = 49 - 37
5p = 12
p = 12/5 = 2.4
In the equation,(3/2)p - 5 + (9/4)p = 7 - (5/4)p
(3/2)p + (9/4)p + (5/4)p = 7 + 5
5p = 12
p = 2.4
Hence "The equation (3/2)p - 5 + (9/4)p = 7 - (5/4)p has the same solution as − 16 p + 37 = 49 − 21 p ".
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1. What is the vertical distance between (5, –12) to (5, 17)?
2. What is the volume of a rectangular prism with a length of fourteen and one-fifth yards, a width of 7 yards, and a height of 8 yards?
3. The point (–7, 6) was reflected over an axis to become the point (7, 6). Which axis was it reflected over? Explain.
The required solutions for each of the questions are obtained as 29 units, 235.2 cubic yards and y axis respectively.
What is the distance formula?The distance formula in coordinate geometry is used to find the distance between two points whose coordinates are given as (x₁, y₁) and (x₂, y₂) as √((x₁ - x₂)^2 + (y₁ - y₂)^2).
By knowing the sides, the area of different polygons can be found.
(1) The vertical distance between points (5, –12) and (5, 17) is given by distance formula as below,
√((5 - 5)² + (-12 - 17)²) = 17
(2) The volume of the rectangular prism is given as,
Volume = Area of base × Height of the prism
= 14(¹/₅) × 7 × 8
= 21/5 × 56 = 235.2
(3) The given points are (–7, 6) and (7, 6).
It is clear that after reflection y coordinate does not change.
Which implies that the axis of symmetry is y axis.
Thus, the axis of reflection is y axis.
Hence, the vertical distance between points, the volume of the prism and the axis of reflection are 29 units, 235.2 cubic yards and y axis respectively.
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Mr Jenkins runs a large arable farm.
He grows three times as much wheat than barley,
and three times as much barley than corn. Farmer
Jenkins grows twice as much corn as pumpkins.
Mr Jenkins's farm has an area of 270 acres.
Set
that
x acres.
wood to
then
2x
are
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used
to grow barley.
and
16x
acres
Ore
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where.
§ set up
riddles
according
to quation
x +
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+6
x
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{total oven is
270
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252
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1. Find the slope of a line that passes through (3,-5) and (6,-6)
m=____
2. y=7 x+2
m=___
5. Find the slope of a line that passes through ( 4.5, 3.5) and (9.5, 5.5)
m=_____
6. y=-3 x-4
m=_____
The slope the lines in the given functions are -1/3, 7, 0.4 and -3
Slope of a LineThe is the ratio of the rise to run of the graph or the ratio of change in y- coordinate to the change in the x-coordinate.
The formula of slope is given as;
m = y₂ - y₁ / x₂ - x₁
1)
The points are
A = (3, -5)B = (6, -6)Applying the formula of slope of a line
m = -6 - (-5) / 6 - 3)
m = -6 + 5 / 3
m = -1/3
slope is - 1/3
2) The equation 7x + 2 is a linear equation which is modeled as y = mx + c
where m is the slope and c is the y - intercept
The slope of the linear equation y = 7x + 2 is 7
slope is 7
5) Using the formula of slope of a line
m = y₂ - y₁ / x₂ - x₁
m = 5.5 - 3.5 / 9.5 - 4.5
m = 0.4
Slope is 0.4
6) The linear function y = -3x - 4
Comparing the function with y = mx + c
The slope is -3
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{20 PTS}
4/6 = ??? x 1/6
what number makes this equation true? fill in the blank
Choose the function whose graph is given by:
A. y=-3.5cos x
B. y=3.5sin x
C. y=sin(3x)
D. y=2.5sin x
Answer:
A a option is right because cause 3 is near to zero that's value one and y 3.5 x 1near equal to 3 something
I'm not sure about this question DO NOT MIND THE TEXT IN THE BOX JUST ANSWER PLEASEEE!!
DONT ASNWER IF YOU DONT KNOW!
Answer:
You had it right, now all you have to do it add 18 and 30 and 4 and 3 and you should get your answer, than you take the answer and write 48r+7w=55rw
Step-by-step explanation:
I added 18, 30, 4, and 3. I got 48 for the 18 and 30 and 7 for the 4 and 3
6and 3/4 divided by 1 and 1/18
Answer:
Your answer is 6.
Step-by-step explanation:
If this is correct can i get branilest? Hope this helps :)
Realiza las siguientes potencias
The powers is 5 - 1/2³.
What is Exponents and Powers?Exponents and powers can be used to represent extremely big or extremely small numbers in a more straightforward fashion.
The number of times a number has been multiplied by itself is referred to as an exponent.
Given:
(5 - [tex]2^{-3}[/tex])
As, we know that
[tex]a^{-m[/tex] = 1/ [tex]a^m[/tex]
Then, (5 - [tex]2^{-3}[/tex])
= 5 - 1/2³
= 5-1/8
= 40-1/8
= 39/8
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The Translation of attached question is
Make the following powers
A rectangle is split into four triangle as shown. What is the area of shade triangle?
Answer:
First of all u need to find the rectangle area then subtract the area of three triangles.
step1 : 3×4=12
step2: 1×4/2 + 2×3/2 + 3×1/2 = 6.5
Answer = 12 - 6.5 = 5.5
Solve the following equation:
3x^2= -12
a.
X = 2
b. x=-2
C.
No real solutions
d.
X = ‡2
3x^2= -12
Divide each side by factors that do NOT contain the variable
This means X = +/- 2 (with imaginary number)
Find the missing fraction
_+ 1/16=3/2
Answer:
23/16?
Step-by-step explanation:
23/16 + 1/16 = 3/2
A large rectangular prism is 12 inches long, 9 inches wide, and 6 inches tall. A small rectangular prism is also 12 inches long, but it's only 3 inches wide and 3 inches tall.
How many small prisms would it take to fill the large prism?
The required number of small prism that would be fill in the large prism is given as 6
As mentioned in the question, a large rectangular prism is 12 inches long, 9 inches wide, and 6 inches tall. A small rectangular prism is also 12 inches long, but it's only 3 inches wide and 3 inches tall.
Here,
The volume of the large prism = 12 × 9 × 6
= 648 inches cube
The volume of the small prism = 12 × 3 × 3
= 108 inches cube,
The ratio of the volume of the large prism to a small prism will give the number of small prisms needed to fill the large prism. So,
n = 648 / 108 = 6 / 1
Thus, the required number of small prism that would be filled in the large prism is given as 6.
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Find the z-score such that the area under the standard normal curve to its left is 0.2
The z-score such that the area under standard normal curve to its left is 0.2 is found as -0.84.
Explain the term Z-score?A mathematical table known as the Z table, also known as the Z-score table or the standard normal table, is used to determine the likelihood that the z-score number is below, above, or in between the values just on standard normal distribution.
Z-scores are the most used name for standard scores. Its similar concepts, like as z-values, standardized factors, and normal scores, are utilized in this article.A positive Z score score implies that the raw score is higher than the distribution's mean.For instance, a z-score of 2 indicates that the result is two standard deviations above the mean.If the Z score is negative, the distribution's mean is below the raw score value.For the stated question,
You simply need to discover the location of 0.2 on the z-score table and then its z-score. (The area to the left of a z-score is shown in the table)
Our z-score is -(0.8 + 0.04) = - 0.84 as a result.
Thus, the z-score such that the area under the standard normal curve to its left is 0.2 is found as -0.84.
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Let ƒ(x) = 8(1/4)^X+³ — 4.
The graph of f(x) is translated 4 units down to form the graph of g(x).
The function f(x) is translated by 4 units down to form a function g(x) will be written below.
[tex]g(x) = 8 \times \left (\dfrac{1}{4} \right )^{3x} - 8\\[/tex]
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The function is given below.
[tex]f(x) = 8 \times \left (\dfrac{1}{4} \right )^{x^3} - 4[/tex]
Simplify the equation, then we have
[tex]f(x) = 8 \times \left (\dfrac{1}{4} \right )^{x^3} - 4\\\\\\f(x) = 8 \times \left (\dfrac{1}{4} \right )^{3x} - 4[/tex]
The function f(x) is translated by 4 units down to form a function g(x) will be given as,
[tex]g(x) = 8 \times \left (\dfrac{1}{4} \right )^{3x} - 4-4\\\\\\g(x) = 8 \times \left (\dfrac{1}{4} \right )^{3x} - 8[/tex]
The function f(x) is translated by 4 units down to form a function g(x) will be [tex]g(x) = 8 \times \left (\dfrac{1}{4} \right )^{3x} - 8\\[/tex]. The graph is drawn below.
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The greatest common factor of 250 and 300 is?
Answer:
250 / 50 = 5
300 / 50 = 6
Therefore, the greatest common factor of 250 and 300 is 50.its also known as a number to be divided so you can get the lowest fractionStep-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-The greatest common factor of 250 and 300 is 50
What is the greatest common factor of two numbers?The greatest common factor is the greatest factor that divides both numbers. To find the greatest common factor, first list the prime factors of each number.
Given here: The numbers as 250 and 350
Steps to find GCF
Find the prime factorization of 250
250 = 2 × 5 × 5 × 5
Find the prime factorization of 300
300 = 2 × 2 × 3 × 5 × 5
To find the GCF, multiply all the prime factors common to both numbers
Hence, GCF = 2 × 5 × 5 GCF = 50
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Find the multiplicative inverse of −1/2.
Answer:
2
Step-by-step explanation:
To determine the multiplicative inverse of a number, we use the following rule: The multiplicative inverse of a number a/b is b/a.
Rocky spends 1 3/4 hours working out
on Monday, 2½ hours on Wednesday and 5/6 of
an hour on Friday. How much time did he spend
working out this week.
Answer:
5 1/12 hours
Step-by-step explanation:
You need a common denominator and that would be 12
1 [tex]\frac{9}{12}[/tex] ([tex]\frac{3}{4}[/tex] x [tex]\frac{3}{3}[/tex]) another name for [tex]\frac{3}{3}[/tex] is 1. You are making an equivalent fraction
2 [tex]\frac{6}{12}[/tex] ([tex]\frac{1}{2}[/tex] x [tex]\frac{6}{6}[/tex])
[tex]\frac{10}{12}[/tex] ([tex]\frac{5}{6}[/tex] x [tex]\frac{2}{2}[/tex])
1 [tex]\frac{9}{12}[/tex] + 2 [tex]\frac{6}{12}[/tex] + [tex]\frac{10}{12}[/tex] = 3 [tex]\frac{25}{12}[/tex]
I can break [tex]\frac{25}{12}[/tex] into [tex]\frac{12}{12}[/tex] + [tex]\frac{12}{12}[/tex] + [tex]\frac{1}{12}[/tex] Another name for [tex]\frac{12}{12}[/tex] is 1
3 + 1 + 1 + [tex]\frac{1}{12}[/tex]
5 [tex]\frac{1}{12}[/tex]
Olivia and liam paint their houses. Olivia can paint her house in 9 hours while liam paints his in 7 hours. If olivia and liam painted together, write an equation that would find the time in hours t it. would take them to paint a house.
Answer:
t = 7/9 * 9 + 7/9 * 7 = 14 hours
Step-by-step explanation:
Are there any circles for which the relationship between the diameter and the circumference cannot be represented by π? explain
Well, the diameter and circumference scale perfectly. Therefore, the ratio will remain the same regardless of how big or tiny the circle is. For all circles, circumference is equal to x diameter. There are no exceptions because this is the definition of.
Give an example of diameter.
If you look at the cycle wheel, the spikes that run through the center from one end to the other are an illustration of diameter. This is comparable to a circle's diameter, which is a line segment that extends from one end of the circle to the other end while passing through the center.
What is a circle's circumference?
A circle's diameter is multiplied by to determine its circumference (pi). You can also determine the circumference by multiplying 2radius by pi (=3.14).
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Question 1 of 10
What is the slope formula?
OA. ₂-₁,
Y/₂-1/₁
OB. -
X₂-X₁
O c. 2-₁
X₂-1/₁
D. +₁
Y/₂+1/₁
SUBMIT
Answer:
(y2-y1)/(x2/x1)
Step-by-step explanation:
Well uh I hope you get it
determine the equation of the parabola that opens up, has vertex (7,7) and a focal diameter of 16.
The equation of a parabola that opens up and has a vertex at (7,7) can be written in the form
y = a(x - 7)^2 + 7.The focal diameter of the parabola is 16, which means that the distance from the vertex to the focus is 8 (since the focal diameter is the sum of the distances from the vertex to the focus and from the vertex to the directrix).
To find the equation of the parabola, we need to determine the value of a that will give us the correct focal diameter. The distance from the vertex to the focus is given by the equation sqrt(4a(y - 7)), so we can set this equal to 8 and solve for a:
sqrt(4a(y - 7)) = 8
4a(y - 7) = 64
a(y - 7) = 16
a = 16 / (y - 7)
Substituting this value of a back into the equation for the parabola gives us:
y = (16 / (y - 7))(x - 7)^2 + 7
This is the equation of the parabola that opens up, has a vertex at (7,7), and a focal diameter of 16.
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What is the volume of this figure?
The Volume of the given figure is 264 cubic units
What is Volume?
Volume is a measurement of three-dimensional space that is occupied. It is frequently mathematically quantified using SI-derived units or different imperial or US customary units. The concept of length is linked to the definition of volume.
Solution:
Volume of Cuboid = Length * Breadth * Height
Volume of Cuboid 1 = 8*5*5 = 200 cubic units
Volume of Cuboid 2 = 8*8*1 = 64 cubic units
Total Volume = 200 + 64 = 264 cubic units
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The sum of heart rate readings taken five times for of Kundaval and Kulazhi are 400 and 360 respectively. And their projected deviations are 3,16 and 2.0 respectively. If you were. a doctor, who would you treat immediately?.
If i were a doctor, the person I would treat immediately is; Kundaval because he has higher heart rate and larger projected deviation.
We are given that;
Sum of heart rates taken 5 times for Kundaval = 400
Sum of heart rates taken 5 times for Kulazhi = 360
Projected deviation for Kundaval = 3.16
Projected deviation for Kulazhi = 2.0
Now, mean simply means the average of a set of given data while standard deviation is defined as a measure of how dispersed the data is in relation to the mean.
Thus, as a doctor, I would prioritize the treatment of the patient that has higher heart rate and larger projected deviation. Thus, we would conclude that Kundaval, whose sum of heart rate readings is 400 and whose projected deviation is 3.16 would be the one that should be treated first.
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Kimberly’s whole family has colds so she makes a 6-quart pot of chicken noodle soup and serves everyone a bowl. Her family has a total of 4 people. If each of Kimberly’s bowls hold about 2 cups how many bowls of soup are left in the pot
The quantity of bowls of soup are left in the pot aftee serving her family is 16 cups
How many cups are left?Quantity of chicken noodle soup made = 6-quartNumber of people in Kimberly's family = 4Volume of bowl = 2 cupsConvert quarts to cups:
1 quarts = 4 cups6 quarts = 24 cupsTotal quantity of soup served = Number of people in Kimberly's family × Volume of bowl
= 4 × 2
= 8 cups
Quantity of bowls of soup are left in the pot = Quantity of chicken noodle soup made - Total quantity of soup served
= 24 cups - 8 cups
= 16 cups
In conclusion, 16 cups of soup are left in the pot after serving.
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Evaluate the expression when y=6 and x=9.
5y-x
Answer:
21
Step-by-step explanation:
y=6 and x=9.
5y – x
= 5(6) – 9
= 30 – 9
= 21
i hope this helped
Charlie starts to sove a system of linear equations graphically. he puts both equations into slope-intercept form and notices that the lines have the same slope. based on this information only, which of the following statements is true?A. The system could have no solution, one solution, or infinitely mani solutionsB. The system has no solution because two equations with the same slope never intersectC. The system has either no solution or infinitely many solutions, depending on the y-interceptsD. The system has infinitely many solutions because two equations with the same slope represent the same lineHx - 4y = -10Kx + 3y = -15
C. The system has either no solution or infinitely many solutions, depending on the y-intercepts
what is linear equation?
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.
If the slopes of both lines are same then the lines are parallel. Now, both the equations can represent same line or two different lines. If the equations represent the same line, then they are coincident and have infinite number of solutions, else if the equations represent two different lines with same slope then they are parallel and hence will never intersect, and therefore won't have any solution
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The system has either no solution or infinitely many solutions, depending on the y-intercepts
If the slopes of both lines are same then the lines are parallel. Now, both the equations can represent same line or two different lines. If the equations represent the same line, then they are coincident and have infinite number of solutions, else if the equations represent two different lines with same slope then they are parallel and hence will never intersect, and therefore won't have any solution
Using - your favorite statistics software package, you generate scatter plot which displays a linear form You find regression equation and the standard deviation for both variablesThe standard deviation for X is 1.34, and the standard deviation for y is 3.6. The regression equation is reported 4 1.891 What fraction of the variation in y can be explained by the variation in the values of x? (
The regression line is yˆ = 4 + 1.891x , the coefficient of determination of two variables or the fraction of the variation in y that can be explained by the variation in the values of x is 0.51..
Here the fitted regression equation of y on x is
yˆ = 4 + 1.891x ---(*)
where, x --> Independent variable
yˆ --> predicted value of the dependent variable
Now, b₁ = slope cofficient = 1.891 ~ 1.91
(estimated from least squares method)
We have given that,
Standard deviations for X = 1.34 = sₓ say
Standard deviations for Y = 3.6 = sᵧ say
we know, b₁ = r₀( sₓ/sᵧ ) where ro is corr(X,Y)
=> 1.91 = r₀ (3.6/1.34)
=> 1.91×1.34/ 3.6 = r₀
=> r₀ = 0.71944
Defining, R² = cofficient of determination of two variables = Proportion of variation in Y , explained by the variation in the value of X, through the regression model.
= (r₀)² = (0.71944)² = 0.505442
R² = 0.505442 ~ 0.51 (in two decimals)
Hence, the cofficient of determination is 0.51..
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Complete question:
Using your favorite statistics software package, you generate a scatter plot which displays a linear form. You find a regression equation and the standard deviation for both variables. The standard deviation for x is 1.34 , and the standard deviation for y is 3.6 . The regression equation is reported as y = 4 + 1.891x . What fraction of the variation in y can be explained by the variation in the values of x? (Enter your answer as a decimal between 1 and 2.)
Can somebody please tell me how do i solves these. Thank you.
1. The statement is false, as the differential equation is of the second order but it is nonlinear.
2. The statement is false, as the differential equation is linear.
3. The third statement is correct, as the differential equation is of the fourth order and nonlinear.
How to classify the differential equations?Regarding to linearity, the differential equations are classified as follows:
Linear: the derivatives of y are multiplied only by terms that do not contain the variable y.Non-linear: the derivatives of y are multiplied by terms that contain the variable y.Regarding the order, it is given by the order of the highest derivative in the differential equation.
For question 1, the differential equation y''y + (y')² = sin(x) is in fact of the second order, as the highest derivative is y'' (second derivative), but it is nonlinear, due to the multiplication of y by y''.
Hence the differential equation for question 2 is linear, as the multipliers to the derivatives are of x and -1, neither of which contains the variable y.
For question 3, we have that:
The differential equation is of the fourth order, as y''' x y' = y''''.The differential equation is nonlinear, due to the multiplication of y by xy'''.More can be learned about differential equations at https://brainly.com/question/18760518
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