2.)
Given m
li
n, find the value of x and y.
40°
m
yº
n
I

Check the picture below.

Answer:

696 39/100 meters

Step-by-step explanation:

Ben needs to replace two sides of his fence. One side is 367 9/100 meters long, and the other is 329 3/10 meters long. How much fence does Ben need to buy?

Side A = 367 9/100 meters

Side B = 329 3/10 meters

How much fence does Ben need to buy?

Total fence Ben needs to buy = Side A + side B

= 367 9/100 + 329 3/10

= 36709/100 + 3293/10

= (36709+32930) / 100

= 69639/100

= 696 39/100 meters

Ben needs to buy 696 39/100 meters

Answer:

\(y = \frac{9}{2} x + \frac{9}{2} \)

Step-by-step explanation:

\(m = \frac{9 - ( - 9)}{1 - ( - 3)} = \frac{18}{4} = \frac{9}{2} \)

\(9 = \frac{9}{2} (1) + b\)

\( \frac{18}{2} = \frac{9}{2} + b\)

\(b = \frac{9}{2} \)

\(y = \frac{9}{2} x + \frac{9}{2} \)

By angle bisector theorem, the value of x is 5.625

What does the angle bisector theorem mean?

The angle bisector of a triangle divides the other side according to the Angle Bisector Theorem in a way that makes the ratio of the two line segments equal to the ratio of the other two sides.

According to angle bisector theorem

CB/DB = CA/DA

7.5/x = 4/3

x = 7.5•3/4

x = 22.5/4

x = 5.625

Hence, the value of x is 5.625

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Two of them have the same remaining. The proof using the pigeonhole principle is now complete.

When an integer is divided by 4, there are four potential remainders: 0, 1, 2, or 3. Take any set of five numbers as an example.

If at least three of them have the same remainder when divided by 4, then we are done, since two of them will have the same remainder. This is because if three integers have the same remainder, then we can subtract that remainder from all of them, and the resulting three integers will all be divisible by 4, which means that two of them will have the same remainder when divided by 4.

So suppose that at most two of the integers have the same remainder when divided by 4. Then there are at most two integers with remainder 0, at most two integers with remainder 1, at most two integers with remainder 2, and at most two integers with remainder 3. This means that there are at most 8 integers in total, which is a contradiction since we started with 5 integers. Therefore, there must be at least three integers with the same remainder when divided by 4, and hence there are two with the same remainder. This completes the proof by the pigeonhole principle.

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The ball traveled approximately \(26.27\) units in total.

To calculate the distance the ball traveled, we can use the distance formula between two points in a Cartesian coordinate system.

Distance = \(\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1} )^{2} }\)

Let's calculate the distance between Player A and Player B first:

Distance_AB =

\(\sqrt{((16-2)^{2}+(9-4)^{2}) }\)

\(= \sqrt{(14^{2}+5^{2} ) } \\= \sqrt{(196 +25)} \\= \sqrt{221} \\= 14.87\)

Now, let's calculate the distance between Player B and Player C:

Distance_BC =

\(\sqrt{ ((25 - 16)^2 + (16 - 9)^2)}\\= \sqrt{ (9^2 + 7^2)}\\= \sqrt{(81 + 49)}\\= \sqrt{130}\\=11.40\)

Finally, we can calculate the total distance traveled by adding the distances AB and BC:

Total distance = Distance_AB + Distance_BC

\(= 14.87 + 11.40 \\= 26.27\)

Starting from Player A at \((2, 4),\) it was thrown to Player B at \((16, 9),\) covering a distance of about \(14.87\) units. From Player B, the ball was then thrown to Player C at \((25, 16),\) covering an additional distance of approximately \(11.40\) units.

Combining these distances, the total distance the ball traveled was approximately \(26.27\) units.

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A. The units of these decision variables are in quantities (pieces).

B. Maximize Profit = 20x1 + 85x2 + 35x3

The objective function calculates the total revenue by multiplying the unit selling price of each product with its corresponding quantity (decision variable). The goal is to maximize this total profit.

a) Decision Variables:

Let's define the decision variables as follows:

x1: The number of fabric necklaces produced.

x2: The number of bags produced.

x3: The number of scarves produced.

The units of these decision variables are in quantities (pieces).

b) Objective Function:

The objective function represents the goal or objective to be optimized. In this case, the objective is to maximize the total profit generated from the sale of necklaces, bags, and scarves. The objective function can be written as follows:

Maximize Profit = 20x1 + 85x2 + 35x3

The objective function calculates the total revenue by multiplying the unit selling price of each product with its corresponding quantity (decision variable). The goal is to maximize this total profit.

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The value of the expression is 17/8.

Given is an expression, 7/8 - (-2+3/4) = ( ____+____) + 7/8, we need to solve it,

7/8-(-2+3/4)

= 7/8-(-8+3)/4

= 7/8 + 5/4

= 7+10 /8

= 17/8

Hence, the value of the expression is 17/8.

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If bx = by in the cross product or vector product, the unit-vector notation of the resulting vector would be (0, 0, 1) or simply k-hat.

In the cross product or vector product of two vectors, the resulting vector is perpendicular to both of the original vectors. The direction of the resulting vector is determined by the right-hand rule, where the thumb represents the direction of the cross product.

If bx = by, it means that the x-component of the first vector is equal to the y-component of the second vector. In this case, the resulting vector will have an x-component and y-component of zero.

Since the resulting vector must be perpendicular to both vectors, its z-component must be non-zero. Therefore, the unit-vector notation of the resulting vector would be (0, 0, 1), where the z-component (k-component) is 1.

If bx = by in the cross product, the resulting vector in unit-vector notation would be (0, 0, 1) or simply k-hat. This indicates that the resulting vector has zero components in the x and y directions and a non-zero component in the z direction.

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Answer:

C and E and F

Step-by-step explanation:

Integers are basically whole numbers. For example, 6.5 is not an integer since it is not a whole number and it is between 6 and 7. Also fractions that cannot be simplified to whole numbers are not integers. Also integers can be negative.

Answer:

regular 4 is correct

Step-by-step explanation:

Answer:

C. 4

Step-by-step explanation:

Rounding to three decimal places, the probability that exactly 7 Americans out of a sample of 15 own an answering machine is approximately 0.170.

To find the probability that exactly 7 of the 15 Americans selected at random own an answering machine, we can use the binomial distribution formula:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

where P(X = k) is the probability of getting exactly k successes, n is the sample size, p is the probability of success, and (n choose k) is the binomial coefficient which represents the number of ways to choose k successes out of n trials.

In this case, n = 15, p = 0.69 (the proportion of Americans who own an answering machine), and k = 7. Thus, the probability of getting exactly 7 Americans who own an answering machine out of a sample of 15 is:

P(X = 7) = (15 choose 7) * 0.69^7 * (1 - 0.69)^(15 - 7)

Using a calculator or statistical software, we can evaluate this expression to find:

P(X = 7) ≈ 0.170

This means that if we were to repeat this survey many times with samples of size 15, we would expect approximately 17% of the samples to have exactly 7 Americans who own an answering machine.

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The parametric equations for the line of intersection are:
x = 61 - 5t
y = 2t - 30
z = t

To find the parametric equations for the line of intersection of the given planes, we first need to solve the system of equations:

1. x + 2y + z = 1
2. 2x + 5y + 32 = 4

Step 1: Solve for x from equation 1:
x = 1 - 2y - z

Step 2: Substitute x in equation 2 with the expression found in step 1:
2(1 - 2y - z) + 5y + 32 = 4

Now we can use elimination to solve for one variable. Let's eliminate y by multiplying the first equation by 5 and subtracting it from the second equation:

Step 3: Simplify and solve for y:
2 - 4y - 2z + 5y + 32 = 4
y - 2z = -30

Step 4: Designate z as the parameter t:
z = t

Step 5: Substitute z with t in the expression for y:
y = 2t - 30

Step 6: Substitute z with t in the expression for x:
x = 1 - 2(2t - 30) - t
x = 1 - 4t + 60 - t
x = 61 - 5t

Now we have the parametric equations for the line of intersection:
x = 61 - 5t
y = 2t - 30
z = t

Note that we can choose any value of z for the parameter t, since z is unconstrained.

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If matrix A is positive definite and A = UΣV* is a singular value decomposition of A, then the left singular vectors U and the right singular vectors V are equal.

Let's assume A is a positive definite matrix, which means all its eigenvalues are positive. According to the singular value decomposition (SVD), any matrix A can be decomposed as A = UΣV*, where U and V are unitary matrices and Σ is a diagonal matrix containing the singular values of A.

Since A is positive definite, all its eigenvalues are positive, and hence, all the singular values in Σ are positive as well. In a singular value decomposition, the singular values are arranged in descending order along the diagonal of Σ. As a result, the singular values can be expressed as σ₁ ≥ σ₂ ≥ ... ≥ σₙ > 0, where n is the rank of A.

Now, consider the singular value decomposition A = UΣV*. The columns of U are the left singular vectors of A, and the columns of V are the right singular vectors of A. Since the singular values are positive and arranged in descending order, the maximum singular value corresponds to the first column of U and V, i.e., σ₁u₁ and σ₁v₁*.

Since σ₁ is positive, we can normalize both u₁ and v₁ to have a unit norm without changing their directions. Therefore, u₁ and v₁* are both unit vectors in the same direction. By extension, all the corresponding singular vectors u and v* are proportional to each other.

However, since U and V are both unitary matrices, their columns are orthonormal vectors. Therefore, the columns of U and V must be exactly equal in order to satisfy the orthonormality condition. Hence, we can conclude that U = V, meaning that the left singular vectors and the right singular vectors of a positive definite matrix A are identical.

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Answer:

Step-by-step explanation:

The graph is a line Then it has an equation of the form : y = my + p

where m is the slope and p is the y-intercept.

the line crosses the y-axis at the point (0,6) then

p = 6

the line is going down then

m is negative

the only provided equation that verify: m < 0 and p = 6 is  y = -2x + 6

Answer:

y = -2x + 6

Step-by-step explanation:

Answer:

D) (5x + 6)(5x + 6)

Step-by-step explanation:

area of square = 6 x 6 = 36

area of rectangle = 5x(5x + 12) = 25x² + 60x

total together = 25x² + 60x + 36

factored:

(5x + 6)(5x + 6)

By 20 percent the number of burglaries actually changed in the two-year period.

Here, The annual number of burglaries in a town rose by 50% in 2012

So, the annual number of burglaries in 2012 would be 150%

The annual number of burglaries in a town fell by 20% in 2013.since in 2013.

Now we find the 20 percentage of 150

20% of 150 is:

20/100 × 150 = 30

So, the annual number of burglaries in 2013 would be 150 - 30 = 120%

This means that the actual percentage increase of burglaries is 120% - 10% = 20% not 30%.

Therefore, the actual percentage increase = 20%

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The complete question is:

The annual number of burglaries in a town rose by 50% in 2012 and fell by 20% in 2013. hence the total number of burglaries increased by 30% over the two year period

a. by what percent has the number of burglaries actually changed in the two-year period?

Answer:tff

Step-by-step explanation:

Answer:

A)F(x)=1/(x+1)^2

Step-by-step explanation:

The rational functions which is graphed is f(x) =1/(x+1)², option A is correct.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

A relation is a function if it has only one y-value for each x-value.

Rational function is the ratio of two polynomial functions where the denominator polynomial is not equal to zero.

There are vertical asymptotes at -1.

Vertical asymptotes are present where x on the denominator is equal to 0

f(x) =1/(x+1)² is the rational function.

Hence, the  rational functions which is graphed is f(x) =1/(x+1)², option A is correct.

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Answer:

7/20 or 0.35

Step-by-step explanation:

The approximate enthalpy change, δhrxn, for the combustion of methane is approximately -1283.79 kJ/mol.

To calculate the approximate enthalpy change, δhrxn, for the combustion of methane, we can use Hess's Law and the enthalpies of formation.

The balanced equation for the combustion of methane is:

CH4 + 2O2 → CO2 + 2H2O

To calculate the enthalpy change, we need to find the difference between the sum of the enthalpies of formation of the products and the sum of the enthalpies of formation of the reactants.

The enthalpy of formation for methane (CH4) is -74.81 kJ/mol. The enthalpy of formation for carbon dioxide (CO2) is -393.5 kJ/mol, and the enthalpy of formation for water (H2O) is -285.8 kJ/mol.

Using these values, we can calculate the enthalpy change:

ΔHrxn = (2 * -393.5 kJ/mol) + (2 * -285.8 kJ/mol) - (-74.81 kJ/mol)

     = -787 kJ/mol - 571.6 kJ/mol + 74.81 kJ/mol

     = -1283.79 kJ/mol

Therefore, the approximate enthalpy change, δhrxn, for the combustion of methane is approximately -1283.79 kJ/mol.Please note that the values used for enthalpies of formation are approximate and may vary slightly depending on the source. Additionally, this calculation assumes standard conditions.

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Answer:

The algebraic expression which represents the phrase “two times the quantity of a number minus 12” is : 2x- 12

Step-by-step explanation:

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

for example :-

3x + 4y – 7,  4x – 10, etc.

These expressions are represented with the help of unknown variables, constants and coefficients. The combination of these three (as terms) is said to be an expression. It is to be noted that, unlike the algebraic equation, an algebraic expression has no sides or equal to sign

let the quantity mentioned in the question be 'x'

therefore according to the statement the algebraic expression which represents the phrase “two times the quantity of a number minus 12” is : 2x- 12 is

⇒2x - 12 (answer)

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The function is discontinuous at x = 5, i.e., the point of discontinuity is x = 5 for the given function.

The abrupt change in the function's value over a small change in its independent variable is known as discontinuity.

The following are the types of discontinuity:

Removable Discontinuity: When a function has a hole at a certain value of x, the discontinuity is known as removable discontinuity.

Jump Discontinuity: When a function has a sudden jump from one value to another at a certain value of x, the discontinuity is known as jump discontinuity.

Infinite Discontinuity: When a function has an infinite gap (vertical asymptote) at a certain value of x, the discontinuity is known as infinite discontinuity.

Other types of discontinuity are Oscillating Discontinuity and Essential Discontinuity.

Here, the function is continuous from both sides for x = 5.

But it is not continuous at x = 5 as the left and right-hand limits are not equal; the function has a jump discontinuity at x = 5.

The function is discontinuous at x = 5, i.e., the point of discontinuity is x = 5.

Hence, the result is S - if x < 5 if x ≥ 5.

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Answer:

The end point of a ray is A

Step-by-step explanation:

Hope this Helps

Answer:

yes, he gets 674 points

Step-by-step explanation:

12*58=696

22*1=22

696-22=674

Answer:

12

Step-by-step explanation:

uhh division

hope this helped! :)

Answer:

producers or consumers

Step-by-step explanation:

1. C. Gravity is a force that acts as an inversely proportional square law with respect to distance.

2. B. Type Ia supernovae

3. D. Downwards; towards the center of the Sun

The interpretation of the equations and the correct options for the given questions are as follows:

Question 1:

The equation interpretation is related to gravity. The equation states a relationship between gravity and distance. The correct option is:

C. Gravity is a force that acts as an inversely proportional square law with respect to distance.

Question 2:

To test how the constant G (gravitational constant) has changed over the evolution of the Universe, certain phenomena or objects are used. The correct option is:

B. Type Ia supernovae

Question 3:

Based on the excerpt, the direction of gravity from the Sun is described. The correct option is:

D. Downwards; towards the center of the Sun

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Therefore, the solution to the given differential equation is: y = -cos(x)(x + C), where C is the constant of integration.

To solve the differential equation using separation of variables, we will separate the variables and integrate.

e^(-y) sec(x) - dy/dx cos(x) = 0

Rearranging the equation:

e^(-y) sec(x) = dy/dx cos(x)

Divide both sides by e^(-y) sec(x) to isolate the variables:

dy/dx = cos(x) / (e^(-y) sec(x))

Now, we can separate the variables by multiplying both sides by dx:

dy / (cos(x) e^(-y)) = dx

Next, integrate both sides with respect to their respective variables:

∫ dy / (cos(x) e^(-y)) = ∫ dx

The integral of the left side can be simplified using substitution. Let u = e^(-y), then du = -e^(-y) dy:

∫ -du / (cos(x) u) = ∫ dx

Applying the integral:

ln|u| / cos(x) = x + C

Substituting back u = e^(-y):

ln|e^(-y)| / cos(x) = x + C

Using the property ln(e^a) = a, we have:

(-y) / cos(x) = x + C

Simplifying further:

y = -cos(x)(x + C)

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