What is the value of the X in this triangle?

Enter your answer

X=?

If all the second partial derivatives of a function exist and are continuous, then the order of taking derivatives does not matter for second derivatives. This statement is true.

1. The statement is a consequence of a mathematical concept known as Clairaut's theorem or Schwarz's theorem. According to this theorem, if a function f(x, y) has continuous second partial derivatives in a region, the order of taking the second partial derivatives with respect to x and y does not affect the result.

2. In other words, if f(x, y) is a function with continuous second partial derivatives, it implies that ∂²f/∂x² = ∂²f/∂y². This means that the mixed partial derivatives (∂²f/∂x∂y and ∂²f/∂y∂x) are equal.

3. The continuity of the second partial derivatives is crucial for this result to hold. If the second partial derivatives are not continuous, the order of taking derivatives may indeed affect the result. However, when all second partial derivatives exist and are continuous, the order of taking derivatives for second derivatives does not matter.

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a. To determine the limiting factor, we need to find the values of y when dy/dx = 0. Setting dy/dx = 0, we have:

y/8(6 - y) = 0

This equation is satisfied when y = 0 or y = 6. Thus, the limiting factors are 0 and 6.

b. Using Euler's method, we can approximate f(1) as follows:

We are given f(0) = 8, so we start with x0 = 0 and y0 = 8. Let h be the step size, which is the same for both steps. Then:

x1 = 0 + h = h

y1 = 8 + h(dy/dx)x0,y0 = 8 + h(f(0)/8(6 - f(0))) = 8 + h(f(0)/40 - f(0)^2/320)

Using f(0) = 8 and h = 1/2, we get:

x1 = 1/2

y1 = 8 + (1/2)(8/40 - 8^2/320) = 8 + 1/10 - 2 = 6.8

Using these values, we can repeat the process to find an approximate value of f(1):

x2 = 1/2 + h = 1

y2 = 6.8 + (1/2)(6.8/40 - 6.8^2/320) = 6.8 + 0.017 - 0.578 = 6.239

Therefore, an approximate value of f(1) using Euler's method with two steps of equal size is 6.239.

c. To determine the range of f for t > 0, we need to analyze the behavior of the logistic equation. The equation has two equilibrium points, y = 0 and y = 6, which are stable and unstable, respectively. This means that solutions starting below y = 6 will approach 0 as t increases, while solutions starting above y = 6 will increase without bound.

Since f(0) = 8 is above the unstable equilibrium point, we expect f(t) to increase without bound as t increases. Therefore, the range of f for t > 0 is (6, ∞).

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The equivalent fraction is 2/3. Option C

Fractions are simply described as expressions that are used for representing the part of a whole variable, a whole number or a whole element.

There are different types of fractions listed as;

Examples of these fractions are;

Mixed fractions are written as whole numbers attached to fractions, mostly proper fractions

2 1/3

Proper fractions are given as 2/3

Improper fractions are given as 4/3 , 5/6

From the information given, we have that;

4/6

Divide by a common  value

2/3

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The evidence from the text that supports the conclusion that Brutus and Cassius are in conflict are:

“Brutus, bay not me. / I’ll not endure it.”

“Away, slight man!”

We have,

“Brutus, bay not me. / I’ll not endure it.”

“Away, slight man!”

Both these lines show that Brutus and Cassius are having a heated argument and are in conflict.

The first line is Cassius telling Brutus not to attack him, and the second line is Cassius insulting Brutus by calling him a "slight man".

Thus,

The evidence from the text that supports the conclusion that Brutus and Cassius are in conflict are:

“Brutus, bay not me. / I’ll not endure it.”

“Away, slight man!”

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The length of JK in the triangle is 66.

There can be many different ways, one can include arc way, one can include angle bisector and perpendicular, and we can even try to discover some. But usually, (for the angle bisector and perpendiculars), we do the following:

Divide one of the angles in half.

Divide another angle in half.

The incenter, or point where they cross, is the inscribed circle's center.

Construct a perpendicular from the triangle's center point to one of its sides.

Draw an inscribed circle by placing the compass on the center point and adjusting the length to where the perpendicular crosses the triangle.

We are given that;

JA=9 AL=10 and CK=14

Now,

Adding them together

=10+9

=19.

CK is 14, so LK is 14.

Adding them together = 28.

The other side of the triangle is the same as JA plus AL, 19.

Hence, 19+19+28=66

Therefore, by the inscribed circle the answer will be 66

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The scale factors for the dilation that would result in an image that was smaller than the original figure 1/2 and 8/9.

As, Dilation is a transformation that produces an image that is similar to the original figure, but it may be larger or smaller depending on the scale factor.

If the scale factor is greater than 1, the image will be larger than the original figure, and if the scale factor is less than 1, the image will be smaller than the original figure.

Therefore, the scale factors that would result in an image that was smaller than the original triangle are:

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Answer:

48

Step-by-step explanation:

since this is a linear Angle, the total sum will be 180. Given Angle is 132. so answer will be:

180-132= 48

Answer:

Step-by-step explanation:

The sum of adjacent angles on a straight line is 180°. i.e. In the figure, we are given is a straight line, then n and 132° are the adjacent angles.

n + 132° = 180

n = 180 - 132

n = 48

Hence, the measure of the unknown angle is 48°.

The set of variables that is most likely to have a cause-and-effect relationship is option C: the weight of a box and the postage rate we have to pay to ship the box to California.

Based on the given sets of variables, the set most likely to have a cause-and-effect relationship is:
B. The height of a person and the weight of a person

This is because there is a general correlation between a person's height and their weight, as taller individuals tend to have higher weights. While this is not an absolute rule, there is a stronger cause-and-effect relationship in this set compared to the other options.

This is because the weight of the box is a likely cause of the postage rate, as the heavier the box, the more postage we will have to pay to ship it. In options A and B, there may be a correlation between the variables, but it is less likely that there is a direct cause-and-effect relationship. In option D, the make of a car is not a likely cause of its mileage, as there are many other factors that can affect a car's mileage.

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Answer:5/8) * (4/7) + ( 3/8)* (2/7) = 13/28

Step-by-step explanation:

The explanation for my answer could go a bit longer but it’s pretty easy to understand the concept & a good approach to hit such questions right in few seconds. Hope it helps !!!!!!

(Remember: we always multiply for AND case & do addition for OR case)

Selection would be in 2 ways possible i.e ( WHITE AND WHITE ball “OR” BLACK AND BLACK ball ) because we have been asked to choose two balls of same color. You cant pick White & White AND Black & Black because in this way u ll end up picking 4 balls which is wrong. so we used “OR”

Now,,,,,Think it like , what is the probability of getting 1 white ball on your first selection out of all balls….???

(Most imp approach)- Don’t consider both selection only in one go !!! so just think it one by one. …..O.K!

Hopefully u too thought it = 5/8 ( i.e there are 5 white balls and you selected one from total 8 balls) ……………………………………….GOOD :)

Now, what about the next ball being white…………..is the most common mistake many could do.

Problem is we have 5 white balls & we have chosen 1 ball out from that,,,, Right?

So, there are only 7 balls left for next selection & How many are there white balls left to select now??? = 4 ( because we have already selected one, out from 5)….. :)

2. PROBABILITY OF GETTING WHITE BALL AGAIN IN SECOND CHANCE = 4/7

PROBABILITY OF GETTING BOTH WHITE = (5/8) * (4/7) (remember, getting the first ball changes the probability of another, since we wanted a white AND a white ball so we ll multiply them both )

3. Similarly, for black we have 2 scenarios, hopefully u thought =(3/8)

4. Can u tell me probability of getting another black now???? = (2/7) ( LIKE WE DID FOR WHITE BALLS)

ANSWER……Probability of getting white & white OR black & black =

= (5/8) * (4/7) + ( 3/8)* (2/7) = 13/28 (& - multiply, OR -addition )

Hope, my long explanation helped you to understand the easy approach for such questions. :)

Thanks for reading! :) have a good day :)

Answer:

4 because 2 quarts mean one-forth part of 8 which is 2 she buys 2 quarts of cup means 4 so the cups that will be left are 8-4=4

Answer:

2 cups of orange juice

Step-by-step explanation:

The value of solution of the system of equations is,

⇒ x = 5, y = 0

We have to given that;

The system of equations are,

x - y = 5      .. (i)

3x - 2y = 12  .. (ii)

From (i);

x = y + 5

Substitute above value in (ii);

3x - 2y = 12

3 (y + 5) - 2y = 12

3y + 12 - 2y = 12

y = 0

And, x = y + 5

x = 0 + 5

x = 5

Thus, The value of solution of the system of equations is,

⇒ x = 5, y = 0

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The law of sines is solved for the triangle and C =28.7 units

Given data ,

Let the triangle be represented as ABC

Now , the measures of angles and sides are given as

Trigonometry's law of sines can be expressed as a/sinA = b/sinB = c/sinC, where a, b, and c are the lengths of the triangle's sides, and A, B, and C are the triangle's respective opposite angles.

Law of Sines :

a / sin A = b / sin B = c / sin C

c / sin ( 60 )° = 14 / sin ( 25 )°

Multiply by sin 60° on both sides , we get

c = 0.86602540378 ( 14 / 0.42261826174 )

On simplifying , we get

c = 28.688 units

Hence , the measure of c of triangle is c = 28.7 units

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The Complete sentence is 9 + (7 + 14).

We have the number (9 + 7)+ 14

We know from the Associative Property

(a+ b)+ c = a + (b+ c )

Here a = 9, b = 7 and c= 14.

Then, using the Associative property

(9 + 7) + 14

= 9 + (7 + 14)

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Answer:

3/4 would be c

Step-by-step explanation:

You have very four variables and you're looking for 3/4 so what you need is the third variable out of the four .

Answer:

D) same side interior angles are supplementary

Step-by-step explanation:

In the attachment, yellow is what we're given and need to prove.

Green are the 2 angles that are congruent.

Blue are the 2 angles that we are given that are supplementary, with the reason that 2 angles forming a linear pair sum to 180 degrees.

Red are the 2 angles that are supplementary also, but have to find the reaosn.

We can use process of elimination as one way.

Option A is incorrect because we can see that the red angles aren't vertical.

Option B and C are incorrect because the statement isn't asking for congruency, it's asking for supplementary angles.

Option D is correct because it has to do with supplementary angles.

Also, these 2 angles are supplementary because they are same side interior angles with a transversal cutting through the 2 parallel lines.

Thus, option D is correct.

Hope this helps! :)

The population in 2010 was 55.5M.

Given that;

The country's population in 1992 =  50 million

The country's population in 2002 =  53 million

It is a positive exponential function because the population is growing

Let 1992 be the beginning of time, or t=0.

Thereore,

P = P₀[tex]e^{kt}[/tex]

⇒P = 50[tex]e^{kt}[/tex]

In 2002 the value of t = 10

⇒ 53 = 50[tex]e^{10t}[/tex]

⇒10k = log(53/50)

⇒   k =  0.00583

Number of years ⇒ t = 2010-1992 = 18

So population in 2010 is,

⇒P(20) = 50[tex]e^{18(0.00583)}[/tex]

⇒ 55.5

Answer be 55.5 M.

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The complete question is;

A country's population in 1992 was 50 million. In 2002 it was 53 million. Estimate the population in 2010 using the exponential growth formula. Round your answer to the nearest million. P = Aekt

The length of one side of the cube is approximately 6.75 feet.

The possible dimensions of the cube are 6.75 feet, 6.75 feet, and 6.75 feet, corresponds to option D: 6.75, 6.75, 6.75.

A cube's surface area, use the formula SA = 6s2, s is one of the cube's sides' lengths.

The surface area of the cube is 273.375 square feet, which enables us to formulate the equation shown below:

273.375 = 6s²

Divide both sides by 6 to get the following result: 45.5625 = s2.

Either -6.75 or 6.75 is the result of calculating the square root of both sides.

The answer is false since a length can never be zero.

Use the formula SA = 6s2 to get a cube's surface area, s denotes one of the cube's side lengths.

The cube has a surface area of 273.375 square feet, allowing us to create the equation below:

273.375 = 6s²

6 divided by both sides. get: 45.5625 = s2.

The result of taking the square root of both sides is either 6.75 or -6.75.

Since a length cannot be negative, the answer is negative.

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When the area is doubled, the number of species increases by a magnitude of 8.

a. To solve the equation for S, we have:

log S = log c + k log A

To remove the logarithms, use the property a^(log a(x)) = x, so we have:

S = 10^(log c + k log A)

S = 10^(log c) * 10^(k log A)

Since 10^(log x) = x, we get:

S = c * A^k

b. Using part (a), if k = 3 and the area is doubled, we need to find the magnitude by which the number of species is increased:

Let A1 be the initial area and A2 be the doubled area (A2 = 2A1). Find the ratio of the number of species in A2 to the number of species in A1:

S2/S1 = (c * (2A1)^3) / (c * A1^3)

S2/S1 = (c * 8 * A1^3) / (c * A1^3)

S2/S1 = 8

So, when the area is doubled, the number of species increases by a magnitude of 8.

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Answer:

b 16.4 ft

Step-by-step explanation:

To solve this problem using a graphing calculator, we need to plug in the value of q (which is given as 7) into the equation y = 2 csc e, and then graph the resulting equation.

First, we need to convert the angle e from degrees to radians, because the csc function takes its input in radians. We can use the conversion formula:

radians = degrees x (π/180)

So for e = 2, we have:

e (in radians) = 2 x (π/180) = 0.0349 radians

Now we can plug this value into the equation y = 2 csc e:

y = 2 csc(0.0349) ≈ 103.8 feet

This tells us that the length of the rafters needed to make the roof is approximately 103.8 feet. However, the question asks us to round to the nearest tenth of a foot, so the answer is:

y ≈ 103.8 feet ≈ 103.8 rounded to the nearest tenth of a foot

Therefore, the length of the rafters needed to make the roof for q 7" is approximately 103.8 feet, rounded to the nearest tenth of a foot.

So the correct answer is (b) 16.4 feet.

Using the graphing calculator, we find that the length of the rafters needed is approximately 16.4 feet, Therefore, the correct answer is option B, 16.4 feet.

To find the length of the rafters needed for the roof with an angle of 7 degrees, we'll use the given function y = 2 * csc(e), where e is the angle formed by the rafters and the top of the wall. Here's a step-by-step explanation:

1. Convert the angle from degrees to radians: e (in radians) = (7 degrees * π) / 180 ≈ 0.1222 radians.

2. Calculate the cosecant  (csc) of the angle e: csc(0.1222) ≈ 8.185.

3. Plug the value of csc(e) into the function: y = 2 * 8.185 ≈ 16.37.
Using a graphing calculator, we can input the function y = 2 csc e and graph it. Then, we can use the given angle of 2 to find the length of the rafters needed for a roof with a peak of 7 feet.

4. Round the length to the nearest tenth of a foot: 16.37 ≈ 16.4 feet.
When we graph the function, we can see that the length of the rafters is the distance between the x-axis and the point on the graph where y = 7.
So, the length of the rafters needed to make the roof for an angle of 7 degrees is approximately 16.4 feet (Option b).

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The number that we have to add for completing the square is 25, that is square of half of the coefficient of x.

To use the method of completing the square to solve the quadratic equation x² - 10x + 21 = 0, we can first rearrange it to isolate the x² and x terms,

x² - 10x = -21

We then need to find a number to add to both sides of the equation to "complete the square". To do this, we take half of the coefficient of the x term (-10 in this case), square it, and add it to both sides of the equation. Half of -10 is -5, so we have,

x² - 10x + (-5)² = -21 + (-5)²

Simplifying the right-hand side, we get,

x² - 10x + 25 = -4

The left-hand side is now a perfect square trinomial, which we can write as,

(x - 5)² = -4

We can then take the square root of both sides, remembering to include both positive and negative roots,

x - 5 = ±√(-4)

x - 5 = ±2i (where i is the imaginary unit, √(-1))

Adding 5 to both sides, we get,

x = 5 ± 2i

Therefore, the number we would have to add to "complete the square" is (half of the coefficient of the x term) squared, which is (-5)² = 25.

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Complete question - If using the method of completing the square to solve the quadratic equation x² - 10x + 21 = 0, which number would have to be added to "complete the square"?

This means that the remaining categories must add up to 40%.

A relative frequency table shows the proportion or percentage of observations that fall into each category. The sum of all the relative frequencies in the table should add up to 1 or 100%.

If a is 40% and b is 4%, the total relative frequency is:

a + b = 40% + 4% = 44%

Since the relative frequencies should add up to 100%, we know that the remaining categories must add up to 56%. Without more information about the survey results, we can't determine what those other categories are.

Similarly, if a is 41% and b is 3%, the total relative frequency is:

a + b = 41% + 3% = 44%

Again, the remaining categories must add up to 56%.

If a is 47% and b is 3%, the total relative frequency is:

a + b = 47% + 3% = 50%

This means that the remaining categories must add up to 50%.

If a is 41% and b is 19%, the total relative frequency is:

a + b = 41% + 19% = 60%

This means that the remaining categories must add up to 40%.

Without more information about the survey results or the other categories in the table, we can't determine which of these values for a and b is correct.

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Step-by-step explanation:

in science notation 17,500 is expressed as 1.75 ×10^4

Answer: The value of x is 12

Definition of equation : In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

An equation combines two expressions connected by an equal sign (“=”). These two expressions on either side of the equals sign are called the “left-hand side” and “right-hand side” of the equation. We generally assume the right-hand side of an equation is zero. This will not reduce the generality since we can balance this by subtracting the right-hand side expression from both sides’ expressions.

EXPLANATION : Given: to solve for X:

[tex]x -\frac{x+7}{x - 10} = \frac{5}{x -10}[/tex]

Solution: [tex]x - \frac{x+7}{x -10} = \frac{5}{x -10}[/tex]

[tex]= > x^{2} -11x -7 = 5[/tex]

[tex]= > x^{2} -11x-7-5=0[/tex]

[tex]= > x^{2} -11x -12 =0[/tex]

[tex]= > x^{2} -12x+x-12 =0[/tex]

[tex]= > x(x-12) +1(x-12)= 0[/tex]

[tex]= > (x-12) (x+1)=0[/tex]

[tex]x =12 , x\neq -1[/tex]

Final answer: The value of x is 12

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True. An annuity due is a series of equal payments made at the beginning of each period, while an ordinary annuity is a series of equal payments made at the end of each period.

Because payments made at the beginning of each period earn interest for one additional period, annuity due payments are worth more than equivalent ordinary annuity payments. This means that the present value of an annuity due must be larger than the present value of an equivalent ordinary annuity, assuming the same interest rate and number of payments.

Therefore, if we compare two annuities with the same payment amount, interest rate, and number of payments, the annuity due will always have a larger present value than the ordinary annuity. It is important to understand the difference between these two types of annuities as it can impact the amount of money you receive or need to save for your retirement.

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Therefore, the long-run aggregate supply curve is a vertical line that is not influenced by changes in aggregate demand or short-run economic conditions.

The long-run aggregate supply curve is represented by the vertical line at the potential output level, which indicates that in the long run, the economy will produce at its full capacity without any increase in inflation or decrease in unemployment.

In other words, the long-run aggregate supply curve is not affected by temporary fluctuations in prices or output levels, and instead represents the economy's natural rate of output in the absence of any short-term disturbances. Therefore, the long-run aggregate supply curve is a vertical line that is not influenced by changes in aggregate demand or short-run economic conditions.

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It has been proved that the matrix A has two distinct real eigenvalues if and only if k > 0.

Let's first define what eigenvalues and eigenvectors are:

Eigenvalues are scalars that represent how a linear transformation changes an eigenvector.

Eigenvectors are non-zero vectors that remain in the same direction when a linear transformation is applied to them.

Now, to find the eigenvalues of a matrix, we need to solve the characteristic equation:

det(A - λI) = 0

where A is the matrix, I is the identity matrix, and λ is the eigenvalue we want to find.

In our case, the matrix A is:

A = [-6 k     -1 -1]

So, the characteristic equation is:

det(A - λI) = (-6-λ)(-1-λ) - k = λ² + 7λ + 6 - k = 0

Now, we can use the quadratic formula to solve for λ:

[tex]\lambda = (-7 \pm \sqrt{(49 - 4(1)(6 - k)))} / 2[/tex]

Simplifying this expression gives:

[tex]\lambda = (-7 \pm \sqrt{(25 + 4k))} / 2[/tex]

We can see that this expression will only have distinct real roots if the discriminant (25 + 4k) is positive.

So, we have:

25 + 4k > 0

4k > -25

k > -25/4

Therefore, matrix A has two distinct real eigenvalues if and only if k > -25/4. However, we need to check whether these eigenvalues are positive or not.

Recall that the eigenvalues are:

[tex]\lambda_1 = (-7+ \sqrt{(25 + 4k))} / 2[/tex]

[tex]\lambda_2 = (-7 - \sqrt{(25 + 4k))} / 2[/tex]

If k > 0, then both λ₁ and λ₂ will be positive.

If k = 0, then λ₁ = -3.5 and λ₂ = 0, which means they are not both positive.

If k < 0, then λ₁ will be positive and λ₂ will be negative, which also means they are not both positive.

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The length of a side of the equilateral triangle is 22 inches.

Let's denote the side length of the equilateral triangle as x inches.

According to the given information, the side length of the square is 2 inches longer than the side length of the triangle, so the side length of the square is (x + 2) inches.

The perimeter of the equilateral triangle is given by P_triangle = 3x inches.

The perimeter of the square is given by P_square = 4(x + 2) inches.

It is also given that the perimeter of the square is 30 inches more than the perimeter of the triangle, so we can set up the following equation:

P_square = P_triangle + 30

Substituting the values of the perimeters, we get:

4(x + 2) = 3x + 30

Simplifying the equation:

4x + 8 = 3x + 30

x = 22

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The winning raffle ticket to losing raffle ticket ratio is 4 to 9. Mr. Ticket buys 117 raffle tickets, he expect to have 36 winning tickets.

We know the ratio of winning to loosing ticket is 4:9

Sum of ratio = 4 + 9 = 13

Winning tickets = (4 / 13) × 117

= 4 × 9

= 36

In mathematics, a ratio is a phrase used to compare two or more numbers. It is used to express how large or tiny an amount is in comparison to another. A ratio compares two quantities by dividing them. The dividend is referred to as the "antecedent," while the divisor is referred to as the "consequent."

Ratios are divided into two sorts. The first is a part-to-part ratio, and the second is a part-to-whole ratio. The part-to-part ratio expresses the relationship between two distinct entities or groupings.

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