In Exercises 1-6, find the orthogonal complement W⊥ of W and give a basis for W⊥.
w = {[x,y]} : 2x-y = 0}

Answer:

x= -5, 2

Step-by-step explanation:

set them equal to each other: \(x^{2}+5x-9=2x+1\)

subtract 2x from both sides: \(x^{2} +3x-9=1\)

subtract 1 from both sides to make it equal to zero: \(x^{2} +3x-10=0\)

find which 2 factors of -10 equal 3: 5 and -2

plug it into: \((x +?)\):  \((x+5) (x -2)\)

set both equations to zero: \(x +5=0\)         \(x-2=0\)

solve:  {x| x=-5, 2}

Answer:

1.6

Step-by-step explanation:

12.8/8 = 1.6

15.2/9.5 = 1.6

Scale factor = 1.6

Answer:

\(5^{17}\cdot \:32768\)

Step-by-step explanation:

explanation in image below

In order to see if the differences between time zones are significant,  Customer Satisfaction Score test will have to be run.

A customer satisfaction score (CSAT score) is the measurement of customer satisfaction level through a one-question survey. It ask from users to rate their experience with the brand’s products or services.

Customers answer based on the scale from “extremely dissatisfied” to “extremely satisfied.” Businesses can use the score so that they can determine their satisfaction levels at the crucial touchpoints like the store visit, point of sale, product use, or the digital conversation with customer support staff.

Hence, the test which will have to run is Customer Satisfaction Score(CSAT).

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By using the statements AE = EB, ∠CAB = ∠CBA, and mCB = mCAB, we can prove that triangle ABC is isosceles. The following statements can be used to prove that triangle ABC is isosceles:

AE = EB

∠CAB = ∠CBA

mCB = mCAB

To prove that AE = EB, we can use the fact that an altitude of a triangle bisects the base. This means that AD divides BC into two segments of equal length, BD and CD. Since AE and EB are the projections of AD onto AB and AC respectively, they must also be equal in length.

To prove that ∠CAB = ∠CBA, we can use the fact that the angles opposite equal sides of a triangle are equal. Since AE = EB, we know that ∆AED and ∆CEB are congruent by SSS. This means that ∠AED = ∠CEB, and since ∠AED + ∠CEB = ∠CAB + ∠CBA, we have ∠CAB = ∠CBA.

To prove that mCB = mCAB, we can use the fact that the base angles of an isosceles triangle are equal. Since ∠CAB = ∠CBA, we know that ∆ABC is isosceles, and therefore mCB = mCAB.

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Answer:

Step-by-step explanation:

The simplified form of the expression 1/5 divied by 2 as a fraction is 1/10.

Given the expression in the question;

1/5 divied by 2

1/5 ÷ 2

To simplify, multiply 1/2 by the reciprocal of 2

1/5 ÷ 2

1/5 × 1/2

Simplify

( 1 × 1 ) / ( 5 × 2 )

( 1 ) / ( 5 × 2 )

Multiply 5 and 2

( 1 ) / ( 10 )

1/10

Therefore, the simplified form is 1/10.

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the nearest whole number, the projected number of new cases for 2014 is 31,077.

What is Linear regression equation?

Linear regression equation is a mathematical formula that represents the relationship between two variables in a linear manner. It is used to model the relationship between a dependent variable (usually denoted as y) and one or more independent variables (usually denoted as x). The equation takes the form of y = mx + b, where m is the slope of the line, and b is the y-intercept. The slope (m) represents the change in the value of y for a unit change in x, while the y-intercept (b) represents the value of y when x is equal to zero. Linear regression equations are commonly used in statistics and machine learning to make predictions and analyze data.

To find the linear regression equation, we need to calculate the slope and y-intercept of the line that best fits the data. We can use the formula for slope:

Now we can use the slope-intercept form of a linear equation, y = mx + b, to find the y-intercept b. We can use any point from the table; let's use the first one, (0, 1077):

Therefore, the linear regression equation is y = 2030x + 1077. To find the projected number of new cases for 2014, we need to substitute x = 10 into the equation:

Rounded to the nearest whole number, the projected number of new cases for 2014 is 31,077.

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In statistical hypothesis testing, we compare the p-value of a test to the level of significance (α) to determine whether to reject or fail to reject the null hypothesis.

a) α=0.10, P-value=0.05: Since the p-value is greater than the level of significance, we fail to reject the null hypothesis.

b) α=0.061, P-value=0.027: Similar to situation a), the p-value is greater than the level of significance, so we fail to reject the null hypothesis.

c) α=0.01, P-value=0.034: Here, the p-value is less than the level of significance, so we reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis.

d) α=0.01, P-value=0.023: In this case, the p-value is less than the level of significance, so we reject the null hypothesis and conclude that there is significant evidence to support the alternative hypothesis.

Therefore, we reject the null hypothesis in situations c and d as the p-values are less than the level of significance. While in situations a and b, we fail to reject the null hypothesis as the p-values are greater than the level of significance.

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Answer:

x = 15

Step-by-step explanation:

sin = opp/hyp

sin37 = x / 25

Multiply both sides by 25

25 * sin37 = x

Use calculator

15.045375578801207 = x

Rounded

x = 15

D

Step-by-step explanation:

the answer is 12

if we add 25+12 =37

if we subtract 37-25 =12

Both Zola and Amir are correct in writing the area of the rectangle. They have simply used different ways of expressing the same value.

Zola and Amir have both written the area of a rectangle using different algebraic expressions.

Zola wrote the area of the rectangle as `2a + 3a + 4a`, which can be simplified using the distributive property of multiplication:

2a + 3a + 4a = (2 + 3 + 4)a

Therefore, Zola's expression simplifies to `(2 + 3 + 4)a`, which is the same as Amir's expression.

Amir wrote the area of the rectangle as `(2 + 3 + 4) a`, which can also be simplified:

(2 + 3 + 4) a = 9a

Therefore, Amir's expression simplifies to `9a`, which is the same as the sum of the terms in Zola's expression.

Therefore, both Zola and Amir are correct in writing the area of the rectangle. They have simply used different ways of expressing the same value.

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The given matrix A is diagonalizable, and the matrix P such that P⁻¹AP = D is:

P = [[1, 1],

    [0, 1]

D = [[2, 0],

    [0, 3]]

To determine whether a given matrix is diagonalizable, we need to check if it has a full set of linearly independent eigenvectors. If it does, then it is diagonalizable.
To determine if a matrix is diagonalizable and find the diagonal matrix D:
1. Compute the eigenvalues of matrix A by solving the characteristic equation det(A - λI) = 0, where λ is an eigenvalue and I is the identity matrix.
2. For each eigenvalue λ, find the corresponding eigenvectors by solving the equation (A - λI)X = 0, where X is a vector.
3. If the number of linearly independent eigenvectors is equal to the size of the matrix (i.e., the matrix has n linearly independent eigenvectors), then the matrix A is diagonalizable.
4. Once you have found a set of linearly independent eigenvectors, construct the matrix P using these eigenvectors as columns.
5. Find the inverse of matrix P, denoted as P⁻¹.
6. Compute the diagonal matrix D by using the equation D = P⁻¹AP.
If the matrix A is diagonalizable, then matrix P will be the matrix of eigenvectors, and D will be a diagonal matrix consisting of the corresponding eigenvalues on the diagonal.

Example:
Let's say we have a matrix A:
A = [[2, 1],
    [0, 3]]
1. Compute the eigenvalues:
  The characteristic equation is det(A - λI) = 0:
  |2-λ  1   |
  |0    3-λ |
  Setting this determinant equal to zero, we get:
  (2-λ)(3-λ) - 0 = 0
  Expanding and simplifying, we have:
  λ² - 5λ + 6 = 0
  Factoring, we get:
  (λ - 2)(λ - 3) = 0
  So, the eigenvalues are λ = 2 and λ = 3.

2. Find the eigenvectors:
  For λ = 2, we solve the equation (A - 2I)X = 0:
  |0  1| |x1|   |0|
  |0  1| |x2| = |0|
  Solving this system of equations, we get one eigenvector:
  X1 = [1, 0]
  For λ = 3, we solve the equation (A - 3I)X = 0:
  |-1  1| |x1|   |0|
  |0   0| |x2| = |0|
  Solving this system of equations, we get one eigenvector:
  X2 = [1, 1]
3. Since we have found two linearly independent eigenvectors (X1 and X2) and the matrix A is a 2x2 matrix, it is diagonalizable.
4. Construct matrix P:
  P = [X1, X2] = [[1, 1],
                  [0, 1]]
5. Find the inverse of matrix P:
  P⁻¹ = [[1, -1],
          [0,  1]]
6. Compute the diagonal matrix D:
  D = P⁻¹AP = [[2, 0],
                [0, 3]]
Therefore, the given matrix A is diagonalizable, and the matrix P such that P⁻¹AP = D is:
P = [[1, 1],
    [0, 1]]
D = [[2, 0],
    [0, 3]]

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Answer:

68°+47°+ x = 180°

115°+ x = 180°

115°-115°+x = 180°-115°

x = 65°

hope it's helpful ❤❤❤❤

THANK YOU.

Answer:

6 1/10

Step-by-step explanation:

Convert the mixed numbers into improper fractions (denominator × whole number + numerator / denominator):

9 2/5 = 47/5

3 3/10 = 33/10

Convert improper fractions to have the same denominator:

47/5 × 2/2 = 94/10

Find the difference by subtracting the numerators:

94/10 - 33/10 = 61/10

Convert the answer into a mixed number:

61/10 = 6 1/10

Answer:

14:1:5

because of \(\frac{70}{5} =14\\\\\frac{5}{5}=1\\ \\\frac{25}{5}=5\)

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

\(y=mx+b\)

\(m\) - slope

\(b\) - y-intercept

Given

\(m=-\dfrac{8}{7}\)

and point \((7;\ -5)\)

Substitute the value of the slope and the coordinates of the point ot the equation of a line:

\(-5=-\dfrac{8}{7\!\!\!\!\diagup}\cdot7\!\!\!\!\diagup+b\)     cancel 7

\(-5=-8+b\)           add 8 to both sides

\(-5+8=-8+8+b\)

\(3=b\to b=3\)

Therefore we have the equation of the line:

\(y=-\dfrac{8}{7}x+3\)

Substitute (x, 3) to the equation:

\(3=-\dfrac{8}{7}x+3\)          subtract 3 from both sides

\(3-3=-\dfrac{8}{7}x+3-3\)

\(0=-\dfrac{8}{7}x\)           divide both sides by (-8/7)

\(0=x\to x=0\)

The property descriptions which the township is located in is 9 North and Range 6 West

The townships serve as the main elements in the government's rectangular survey approach for identifying the position of properties. A township comprises a square region of six miles on all its four sides.

In order to ascertain the exact township where the property is situated, it is necessary to compute the township coordinates using the specified distance.

From the information given, we have to convert the distance to township units.

We have;

57 miles north / 6 miles = 9.5 townships north

38 miles west / 6 miles = 6.33 townships west

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Riboflavin is similar to thiamin in that option d: both riboflavin and thiamin serve as coenzymes in energy metabolism.

Riboflavin is similar to thiamin in that both serve as coenzymes in energy metabolism. Coenzymes are molecules that assist enzymes in carrying out their biological functions. In the case of riboflavin and thiamin, they play vital roles in the conversion of carbohydrates, fats, and proteins into usable energy for the body.

Riboflavin, also known as vitamin B2, is an essential nutrient found in various foods such as dairy products, meat, eggs, and leafy green vegetables. It is a water-soluble vitamin, meaning it dissolves in water and is not stored in the body to a significant extent. Therefore, it needs to be regularly replenished through the diet.

Thiamin, also called vitamin B1, is another water-soluble vitamin that plays a crucial role in energy metabolism. It is involved in converting glucose into energy and is found in foods like whole grains, legumes, nuts, and seeds.

Both riboflavin and thiamin work as coenzymes by participating in specific enzymatic reactions. They assist enzymes in catalyzing chemical reactions necessary for energy production. Riboflavin, in the form of its coenzyme derivatives flavin adenine dinucleotide (FAD) and flavin mononucleotide (FMN), acts as a carrier of hydrogen atoms in metabolic reactions. Thiamin, on the other hand, is converted into its active form, thiamin pyrophosphate (TPP), which plays a crucial role in the metabolism of carbohydrates.

Now, let's address the options mentioned in the question to understand how riboflavin is similar to thiamin:

a. both are easily destroyed by heat: While it is true that riboflavin and thiamin can be degraded by heat, riboflavin is more sensitive to heat than thiamin. Riboflavin is easily destroyed when exposed to high temperatures, such as during cooking or food processing. Thiamin, although also susceptible to heat, is relatively more stable.

b. both are easily destroyed by ultraviolet light: This statement is incorrect. Riboflavin is indeed sensitive to ultraviolet (UV) light, which is why it is often stored in opaque containers to protect it from light exposure. However, thiamin is not particularly affected by UV light.

c. though rare, both can be toxic when consumed in high amounts: While excessive intake of any nutrient can potentially be harmful, toxicity from riboflavin and thiamin is rare. These vitamins are considered safe for consumption in recommended amounts, and any excess is typically excreted in the urine.

d. both serve as coenzymes in energy metabolism: This statement is correct, as explained earlier. Both riboflavin and thiamin are essential coenzymes involved in energy metabolism.

e. both are found in abundant amounts in pork: While pork is a source of several nutrients, neither riboflavin nor thiamin is found in exceptionally high amounts in pork. Riboflavin is more commonly found in dairy products, while thiamin is abundant in whole grains and legumes.

In summary, the correct answer is option d: both riboflavin and thiamin serve as coenzymes in energy metabolism. They play important roles in converting food into energy and are essential for overall health and well-being.

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The Number of Gallons drained per minute from the pool is; 931.5 gallons drained per minute

Constant rate is simply a rate that remains unchanged regardless of change in parameters.

Now, we are told that One hundred three and one half gallons drained in the last 9 minutes from a pool. Thus;

Amount of gallons that drained from pool = 103¹/₂ gallons = 207/2 gallons

Time it took to drain = 9 minutes

Thus;

Number of Gallons drained per minute from the pool = (207/2)/9

Number of Gallons drained per minute from the pool = (207 * 9)/2

Number of Gallons drained per minute from the pool = 931.5 gallons drained per minute

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Answer:1.) To write the equation 4x + y = 10 in slope-intercept form, we need to isolate the y-term on one side of the equation. Subtracting 4x from both sides of the equation gives us y = -4x + 10. This is the slope-intercept form, where the slope is -4 and the y-intercept is 10.

2.) To write the equation 3x - y = 7 in slope-intercept form, we need to isolate the y-term on one side of the equation. Adding y to both sides of the equation gives us 3x = y + 7. Dividing both sides of the equation by 3 gives us x = (1/3)y + 7/3. This is the slope-intercept form, where the slope is 1/3 and the y-intercept is 7/3.

By analyzing when the piecewise function increases and when it decreases, we can conclude that the true statement is:

"The function is increasing over the interval −8≤x≤−2."

We know that our function is made of straight lines that connect:

(to see if it increases or decreases, compare the y-value of the second and first point. If the second is larger, then the line increases).

Then the statement that is true is:

3) "The function is increasing over the interval −8≤x≤−2."

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Answer:

55°

Step-by-step explanation:

If angle 1 is 35°, angle 2 is also 35° because vertical angles are congruent.

Since complementary angpes add to 90°, angle 3 is 55°.

The given fractions have equal value, so Liam is correct.

Equivalent fractions are defined as fractions that have different numerators and denominators but the same value. For example, 2/4 and 3/6 are equivalent fractions because they are both equal to 1/2. A fraction is part of a whole. Equivalent fractions represent the same part of a whole.  

Liam is claiming that the fraction -(5/12) is equivalent to 5/-12.

Thus, we can say that:

The fraction  -(5/12) can be described as the opposite of a positive number divided by a positive number. A positive number divided by a positive number always results in a positive quotient and its' opposite is always negative.

The fraction 5/-12 can be described as a positive number divided by a negative number which always results in a negative quotient

The fractions have equal value, so Liam is correct

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Answer:

Step-by-step explanation:

1 is a very special number

Let's check some speciality

Answer:

8) Obtuse triangle

9) Right triangle

12) Equilateral triangle

Step-by-step explanation:

8)

x + 48 + 32 = 180

x + 80 = 180

x = 100

Answer:

4 ^3√7m^2

Step-by-step explanation:

^3√64×7m^2

^3√4^3×7m^3

^3√4^3 3^√7m^2

= 4^3√7m^2

Answer:

\( \boxed{ \tt = 4 \sqrt[3]{7m {}^{2} } }\)

Step-by-step explanation:

Given,

\( \sqrt[3]{448m {}^{2} } \)

Solution:

\( = \sqrt{4 {}^{3 } \times 7 \: m {}^{2} } \)

\( \tt = 4 \sqrt[3]{7m {}^{2} } \)

\( \rule{225pt}{2pt}\)

Answer:

(x + 2)^2 + (y - 6.5)^2 = 25.25

Step-by-step explanation:

We can the equation of the circle in standard form, whose general equation is:

\((x-h)^2+(y-k)^2=r^2\), where

Step 1:  We know that the diameter is simply 2 * the radius.  Thus, we can find the radius by first finding the length of the diameter.  To do this, we'll need the distance formula, which is:

\(d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\), where

We can allow (-7, 7) to be our (x1, y1) and (3, 6) to be our (x2, y2) point and plug these into the formula to find d, the distance between the points and the length of the diameter:

\(d=\sqrt{(3-(-7))^2+(6-7)^2} \\d=\sqrt{(3+7)^2+(-1)^2}\\ d=\sqrt{(10)^2+1}\\ d=\sqrt{100+1}\\ d=\sqrt{101}\)

Now we can multiply our diameter by 1/2 to find the length of the radius:

r = 1/2√101

Step 2:  We know that the center lies at the middle of the circle and therefore represents the midpoint of the diameter.  The midpoint formula is

\(m=(\frac{x_{1}+x_{2} }{2}),(\frac{y_{1}+y_{2} }{2})\), where

We can allow (-7, 7) to be our (x1, y1) point and (3, 6) to be our (x2, y2) point:

\(m=(\frac{-7+3}{2}),(\frac{7+6}{2})\\ m=(\frac{-4}{2}),(\frac{13}{2})\\ m=(-2,6.5)\)

Thus, the coordinate for the center are (-2, 6.5).

Step 3:  Now, we can create the equation of the circle and simplify:

(x - (-2)^2 + (y - 6.5)^2 = (1/2√101)^2

(x + 2)^2 + (y - 6.5)^2 = 25.25

Based on the given information that it costs $20 for every 4 tickets, we can determine the cost per ticket by dividing the total cost by the number of tickets. The cost per ticket is $20 divided by 4, which equals $5.

Let's set up the proportion:

20 / 4 = X / 9

Cross-multiplying, we get:

4X = 20 * 9

Simplifying, we have:

4X = 180

Dividing both sides by 4, we find:

X = 45

Therefore, the cost for 9 tickets would be $45.

Using the same approach, we can complete the table:

Cost ($)    | Number of tickets

20           | 4

35           | 6

50           | 8

0             | 0

45           | 9

Thus, the cost for 8 tickets would be $50, and the cost for 0 tickets would be $0.

Please note that the value for 9 tickets does not result in a whole number, indicating that it does not fit the given pricing scheme of $20 for every 4 tickets.

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