Round 545 to the nearest hundred

(a) The limit lim f(x) as x approaches -2 = -12 + m. B) The limit  lim f(x) as x approaches ∞ = 0 , To find the limit of f(x) as x approaches -2, we substitute -2 into the function f(x) = 6x + m.  c) value of m that satisfies the condition is m = 38.

So, lim f(x) as x approaches -2 = 6(-2) + m = -12 + m.
(b) To find the limit of f(x) as x approaches ∞ (infinity), we need to consider the highest power of x in the function.
Since the highest power of x is x2, we divide every term in the function by x2 to find the limit.

So, lim f(x) as x approaches ∞ = lim (6x/x2) + (m/x^2) + (2 - 7x2)/x^2.
As x approaches ∞, the terms (6x/x2) and (m/x2) both approach 0, and the term (2 - 7x2)/x2 approaches 0 as well.
Therefore, lim f(x) as x approaches ∞ = 0 + 0 + 0 = 0.

(c) To find the values of m such that the limit of f(x) as x approaches 2 exists, we need to find the values of m for which the left-hand limit and the right-hand limit are equal.  Let's first find the left-hand limit, lim f(x) as x approaches 2- (from the left side).  Substituting x = 2 into the function f(x) = 6x + m, we have lim f(x) as x approaches 2- = 6(2) + m = 12 + m.

Now let's find the right-hand limit, lim f(x) as x approaches 2+ (from the right side). Substituting x = 2 into the function f(x) = 2 - 7x2 + 2m, we have lim f(x) as x approaches 2+ = 2 - 7(2)2 + 2m = 2 - 28 +2m = -26 + 2m.

To find the values of m such that the left-hand limit equals the right-hand limit, we equate the expressions:
12 + m = -26 + 2m. Solving this equation for m, we have m = 38. Therefore, the value of m that satisfies the condition is m = 38.

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the greatest possible product of a four-digit number and a three-digit number obtained from seven distinct digits is 2,463,534.

To find the greatest possible product of a four-digit number and a three-digit number obtained from seven distinct digits, we can start by considering the largest possible values for each digit.

Since we need to use seven distinct digits, let's assume we have the digits 1, 2, 3, 4, 5, 6, and 7 available.

To maximize the product, we want to use the largest digits in the higher place values and the smallest digits in the lower place values.

For the four-digit number, we can arrange the digits in descending order: 7, 6, 5, 4.

For the three-digit number, we can arrange the digits in descending order: 3, 2, 1.

Now, we multiply these two numbers to find the greatest possible product:

7,654 * 321 = 2,463,534

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The general integral is provided by y = C1e-t + C2te-t + (1/2)(t2)e-t.

(m + 1)2 =0 is the characteristic polynomial for the differential equation y" +2y' + y = e-t.

Roots -1, -1. yh = C1e-t + C2te-t is the answer to the homogeneous equation at that point.

Use the method of variation of parameters, taking into account the independent integrals y1 = e-t, y2 = te-t, and Wronskian

W(t) = e-2t, to derive the specific integral related to f(t) = e-t.

Then, use the conventional formula yp = - y1(t)(Integral of Y2(t)f(t)dt/W(t)) +y

Obtain yp = (1/2)(t2)e-t for the given situation.

As a result, the general integral is provided by

y = C1e-t + C2te-t + (1/2)(t2)e-t.

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Here is your Answer:-

4 = whole number 1 = numerator 7 = denominator To convert mixed number 4 1/7 to improper fraction, you follow these steps: Multiply the whole number by the denominator 4 × 7 = 28.

The improper fraction of the mixed number 4 1/7 is given by A = 29/7

A mixed number is a whole number, and a proper fraction represented together. A mixed number is formed by combining three parts: a whole number, a numerator, and a denominator. The numerator and denominator are part of the proper fraction that makes the mixed number.

Given data ,

Let the mixed number be represented as A

Now , the value of A is

A = 4 1/7   be equation (1)

On simplifying the equation , we get

To convert the mixed number to improper fraction ,

A = [ ( 4 x 7 ) + 1 ] / 7

On further simplification , we get

A = [ 28 + 1 ] / 7

A = 29 / 7

Hence , the improper fraction is 29/7

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Answer:

$83.75

Step-by-step explanation:

6.25 plus 7.00 plus 3.50 is 16.75.

16.75 per class.

times the 5 different classes is 83.75

Henry' distance is approximately 197 feet from the tree.

To determine Henry's distance from the tree

Use the Pythagorean theorem,

We know that the Pythagoras theorem for a right angled triangle:

(Hypotenuse)²= (Perpendicular)² + (Base)²

In this case,

The tree, Henry's starting point, and Henry's final position form a right triangle.

Let us designate the distance Henry goes north as "a," the distance he walks east as "b," and the distance he walks south as "c."

Then we have,

a = 180 feet (north)

b = 80 feet (east)

c = 80 feet (south)

Now use the following formula to calculate the distance from the tree to Henry's ultimate position,

Which is the hypotenuse of the right triangle:

d = √(a² + b²)

Put the values we have, we get:

⇒ d = √(180² + 80²)

⇒ d = √(32400 + 6400)

⇒ d = √38800

⇒ d ≈ 197.0 feet

Hence,

The distance be,

⇒ 197 feet

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1.  we can use the first equation to find y = 3x + 1 = 3(9) + 1 = 28 So, the larger integer is 28, (2).  The smaller integer is 9. The larger integer is 10, which is the next consecutive integer.

An integer is a whole number ,neither a fraction or a decimal, in mathematics. Integers can be zero, positive, or negative.

Integer examples include -3, -2, -1, 0, 1, 2, 3, and so forth.

The letter "Z" stands for the set of integers.

In mathematics and allied disciplines such as computer science, physics, and finance, integers are utilized extensively.

A whole number is a non-negative integer in mathematics, which indicates that it is either a positive integer or zero.

Negative and fractional numbers are not included in whole numbers. The full integers 0, 1, 2, 3, 4, and so on are examples.

In many different branches of mathematics as well as in other disciplines, such as arithmetic, algebra, and geometry, whole numbers are used. They are also employed in daily tasks like quantity calculations and object counts.

According to question :-

Let's call the smaller integer x and the larger integer y. We know that:

y = 3x + 1 (the largest of the two integers is one more than three times the smaller)

x + y = 37 (the sum of the two integers is 37)

We can use substitution to solve for y in terms of x:

x + (3x + 1) = 37

4x + 1 = 37

4x = 36

x = 9

Now we can use the first equation to find y:

y = 3x + 1 = 3(9) + 1 = 28

So the larger integer is 28.

Let's call the smaller integer x and the larger integer y. We know that:

y = x + 1 (the integers are consecutive)

x + 2y = 29 (the sum of the smaller and twice the larger is 29)

We can substitute y = x + 1 in the second equation:

x + 2(x + 1) = 29

Simplifying and solving for x:

3x + 2 = 29

3x = 27

x = 9

So the smaller integer is 9. The larger integer is 10, which is the next consecutive integer.

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An eigenvalue of a matrix is a scalar value that satisfies the equation ax = λx for some vector x. If a is an n × n matrix, then if ax = λx for some vector x, λ is an eigenvalue of a

An eigenvalue of a matrix is a scalar value that satisfies the equation ax = λx for some vector x. If a matrix a is an n × n matrix, then the equation ax = λx can be used to find the eigenvalues associated with the matrix. By taking the equation ax = λx and rearranging it, we can isolate the eigenvalue λ on the left side of the equation, leaving the vector x on the right side. λ is then the eigenvalue of the matrix a. For example, if we have a 2 x 2 matrix a, and we have an equation of the form ax = λx, where x is a 2-dimensional vector, then by rearranging the equation we can find the eigenvalue λ associated with the matrix a. In summary, if a is an n × n matrix and ax = λx for some vector x, then λ is an eigenvalue of a.

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Answer:

The two triangles are similar.

What is the value of x?

Enter your answer in the box.

x=

The value of x is 7 units.

Two triangles are said to be comparable if their two sides are in the same ratio as the two sides of another triangle and their two sides' angles inscribed in both triangles are equal.

Given :

AD = 6 units , BD = 8 units, m∠ABC = m∠DBE = 90° and              

∠DEB ≅ ∠ACB

Now, AB = AD + BD

              = 8 + 6 = 14 units

Now, In ΔABC and ΔDBE,

∠DBE = ∠ABC ( Each of 90° )

∠DEB = ∠ACB ( given )

So, By using AA postulate of similarity of triangles , ΔABC ~ ΔDBE

Now, proportion of the corresponding sides will be equal.

AD/ DB= BC/ BE

14/8 = 3x/ 2x-2

4x= 28

x= 7

Hence, the value of x is 7 units.

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Where the above are given,

(a) MLE of β: (nα + y₁ + y₂ + ... + yn)/n

(b) MLE of E(Y): (nα + y₁ + y₂ + ... + yn)/n

Maximum Likelihood Estimation (MLE) is   a statistical method used to estimate the parameters of a probability distribution by maximizing the likelihood function based on observed data.

(a) The MLE of β can be found by   maximizing the likelihood function. The likelihood function for  a gamma distribution is given by  -

L(β;  y₁, y₂, ..., yn) = (1/β^nαΓ(α))ⁿ * exp(-( y₁ + y₂ + ... + yn)/β)

Taking the logarithm of the likelihood function (log-likelihood) to simplify the calculations  -

log L(β;  y₁, y₂, ..., yn) =   n*log(1/β) + nα*log(β) - n*logΓ(α) - ( y₁ + y₂ + ... + yn)/β

To find the MLE of β, we differentiate the log-likelihood with respect to β, set it equal to zero, and solve for β  -

d/dβ(log L(β;  y₁, y₂, ..., yn)) = -n/β + nα/β² + ( y₁ + y₂ + ... + yn)/β² = 0

Simplifying the equation -

-n/β + nα/β^2 + ( y₁ + y₂ + ... + yn)/β² = 0

Multiplying through by β²

-nβ + nα + ( y₁ + y₂ + ... + yn) = 0

Rearranging  whave

nβ = nα + ( y₁ + y₂ + ... + yn)

Finally, solving for β -

β = (nα +  y₁ + y₂ + ... + yn)/n

Therefore, the MLE of β is (nα +  y₁ + y₂ + ... + yn)/n.

(b) The MLE of E(Y), the expected value of Y, is simply the MLE of β.

So, the MLE of E(Y) is (nα +  y₁ + y₂ + ... + yₙ)/n.

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Answer

The equation of the quadratic function that passes through (0, 1) and has a vertex at (1,4) is

y = -3x² + 6x + 1

Explanation

The general form of a quadratic equation is

y = ax² + bx + c

We are told that the function passes through (0, 1) and has its vertex (the highest or lowest point on the graph) at (1, 4).

We can obtain simultaneous equations by substituting these into the general form of a quadratic equation.

(0, 1)

when x = 0, y = 1

y = ax² + bx + c

1 = a(0²) + b(0) + c

1 = 0 + 0 + c

c = 1 ...... equation 1

(1, 4)

y = ax² + bx + c

4 = a(1²) + b(1) + c

4 = a + b + c

But c = 1, So

4 = a + b + 1

a + b = 4 - 1

a + b = 3 ....... equation 2

Then, the third one, at the vertex, the first derivative of the function is 0.

y = ax² + bx + c

(dy/dx) = 2ax + b = 0

At this point, x = 1

2ax + b = 0

2a(1) + b = 0

2a + b = 0 ...... equation 3

Writing these equations together

c = 1

a + b = 3

2a + b = 0

From equation 3, b= -2a

Substituting this into equation 2

a + b = 3

a - 2a = 3

-a = 3

a = -3

b = -2a = -2 (-3) = 6

So,

a = -3

b = 6

c = 1

y = -3x² + 6x + 1

Hope this Helps!!!

Answer:

its B

Step-by-step explanation:

I got a 100%

Answer:

Step-by-step explanation:

1.

\(-7x+16=58\\\\\mathrm{Subtract\:}16\mathrm{\:from\:both\:sides}\\-7x+16-16=58-16\\\\-7x=42\\\\\mathrm{Divide\:both\:sides\:by\:}-7\\\\\frac{-7x}{-7}=\frac{42}{-7}\\\\x =-6\)

2.

\(-2x+15=-9\\\\\mathrm{Subtract\:}15\mathrm{\:from\:both\:sides}\\\\-2x+15-15=-9-15\\\\-2x=-24\\\\\mathrm{Divide\:both\:sides\:by\:}-2\\\\\frac{-2x}{-2}=\frac{-24}{-2}\\\\x=12\\\)

3.

\(5x-4=36\\\\\mathrm{Add\:}4\mathrm{\:to\:both\:sides}\\\\5x-4+4=36+4\\\\5x=40\\\\\mathrm{Divide\:both\:sides\:by\:}5\\\\\frac{5x}{5}=\frac{40}{5}\\\\x=8\)

4.

\(25-3x=88\\\\\mathrm{Subtract\:}25\mathrm{\:from\:both\:sides}\\\\25-3x-25=88-25\\\\\mathrm{Divide\:both\:sides\:by\:}-3\\\\\frac{-3x}{-3}=\frac{63}{-3}\\\\x=-21\)

5.

\(-11=7-x\\\\\mathrm{Add\:}x\mathrm{\:to\:both\:sides}\\\\-11+x=7-x+x\\\\-11+x=7\\\\\mathrm{Add\:}11\mathrm{\:to\:both\:sides}\\\\-11+x+11=7+11\\\\x=18\)

6.

\(65+15x=35\\\\\mathrm{Subtract\:}65\mathrm{\:from\:both\:sides}\\\\65+15x-65=35-65\\\\\mathrm{Divide\:both\:sides\:by\:}15\\\\\frac{15x}{15}=\frac{-30}{15}\\\\x=-2\)

7.

\(\frac{1}{2} x-18=2\\\\\mathrm{Add\:}18\mathrm{\:to\:both\:sides}\\\\\frac{1}{2}x-18+18=2+18\\\\\frac{1}{2}x=20\\\\\mathrm{Multiply\:both\:sides\:by\:}2\\\\2\times\frac{1}{2}x=20\times \:2\\\\x=4\)

8.

\(\frac{2}{3}x-10=-12 \\\\\mathrm{Add\:}10\mathrm{\:to\:both\:sides}\\\\\frac{2}{3}x-10+10=-12+10\\\\\frac{2}{3}x=-2\\\\Divide\:both\:sides\:by\: 2/3\\\\\frac{2}{3}x\div \frac{2}{3} =-2\div \frac{2}{3} \\\\\frac{2}{3} x\times \frac{3}{2} =-2\times\frac{3}{2} \\\\x =-3\)

9.

\(6-\frac{1}{3}x=-1 \\\\\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}\\\\6-\frac{1}{3}x-6=-1-6\\\\-\frac{1}{3}x=-7\\\\\mathrm{Multiply\:both\:sides\:by\:}-3\\\\\left(-\frac{1}{3}x\right)\left(-3\right)=\left(-7\right)\left(-3\right)\\\\x=21\)

10.

\(4-9x=-14\\\\\mathrm{Subtract\:}4\mathrm{\:from\:both\:sides}\\\\4-9x-4=-14-4\\\\-9x=-18\\\\\mathrm{Divide\:both\:sides\:by\:}-9\\\\\frac{-9x}{-9}=\frac{-18}{-9}\\\\x=2\)

11.

\(11-x=29\\\\\mathrm{Subtract\:}11\mathrm{\:from\:both\:sides}\\\\-x=18\\\\\mathrm{Divide\:both\:sides\:by\:}-1\\\\\frac{-x}{-1}=\frac{18}{-1}\\\\x=-18\)

12.

\(-9-11x=68\\\\\mathrm{Add\:}9\mathrm{\:to\:both\:sides}\\\\-9-11x+9=68+9\\\\-11x=77\\\\\mathrm{Divide\:both\:sides\:by\:}-11\\\\\frac{-11x}{-11}=\frac{77}{-11}\\\\x=-7\)

13.

\(45+\frac{5}{6}x =50\\\\\mathrm{Subtract\:}45\mathrm{\:from\:both\:sides}\\\\45+\frac{5}{6}x-45=50-45\\\\\frac{5}{6}x=5\\\\\mathrm{Divide\:both\:sides\:by\:}5/6\\\\\frac{5}{6} x\div\frac{5}{6}=5\div\frac{5}{6}\\\\\frac{5}{6}x\times \frac{6}{5}= 5\times\frac{6}{5}\\\\ x=6\)

14.

\(-5x+17=-33\\\\\mathrm{Subtract\:}17\mathrm{\:from\:both\:sides}\\\\-5x+17-17=-33-17\\\\\mathrm{Divide\:both\:sides\:by\:}-5\\\\\frac{-5x}{-5}=\frac{-50}{-5}\\\\x=10\)

15.

\(95=-4+33x\\\\-4+33x=95\\\\\mathrm{Add\:}4\mathrm{\:to\:both\:sides}\\\\-4+33x+4=95+4\\\\\mathrm{Divide\:both\:sides\:by\:}33\\\\\frac{33x}{33}=\frac{99}{33}\\\\x=3\)

Answer:

17000 drops in the bottle

Answer:

9:002 8(8 this might be the answer for this and the answer im going for is this lemme show (7)

Step-by-step explanation:

Here's link to the answer:

cutt.us/tWGpn

Answer:

3 to 12 reduced 1 to 4

\(\frac{1}{4}\)

Step-by-step explanation:

Answer: there are 2 blue marbles

Step-by-step explanation:

10 / 2 = 5

If there are 5 to 1 then 5 + 5 = 10

So 1 + 1 = 2

(Sorry if that didn’t make much sense)

Answer:

I think total area=36

Step-by-step explanation:

By finding ar. of all 4 triangles separately by the formula 1/2×base×height

Answer:

a part of a line that has one endpoint and extends indefinitely in one direction

Step-by-step explanation:

a ray has one endpoint, then has an arrow going indefinitely in one direction.

Answer:

a

Step-by-step explanation:

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

To find the y-intercept , just need to put 0 ( zero ) instead of x in the equation.

Let's do it...

\(x + 2y = 4\)

\(0 + 2y = 4\)

\(2y = 4\)

Divide sides by 2

\( \frac{2y}{2} = \frac{4}{2} \\ \)

\(y = 2\)

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Answer:

You line up the decimals,

17.5

2.48

Step-by-step explanation:(optional) add a 0 the where the numbers don't line up, it would look like this

17.50

02.48

It will not change the total

The solution to the triangles using sine rule and cosine rule is as follows:

1. Q = 43°; P = 52°; QR = 15 units

2. C = 22°; BC = 21 units; DC = 11 units

3. Y = 39°; VX = 10.6 units; WX = 10.2 units

4. HF = 18.7 units; H = 29°; F = 15°

The triangles can be soved as follows:

Using sine rule:

1. 19/sin 85° = 13/sin Q

Q = sin⁻¹ (13 * sin 85°/19)

Q = 43°

P = 180 - (85 + 43)

P = 52°

QR = (19 * sin 52)/sin 85

QR = 15 units

2. C = 180 - (139 + 19)

C = 22°

BC = 21 units

DC = 11 units

3. Y = 180 - (100 + 41)

Y = 39°

VX =  (16 * sin 41)/sin 100

VX = 10.6 units

WX = (16 * sin 39)/sin 100

WX = 10.2 units

4. Using cosine rule:

HF = √(13² + 7² - 2 * 13 * 7 * cos 136°)

HF = 18.7 units

Using sine rule:

13/sin H = 18.7/sin 136

H = sin⁻¹ (13 * sin 136°/18.7)

H = 29°

F = 180°°- (29 + 136)°

F = 15°

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Answer:

For simple interest: $50, for compound interest: $56.25

Step-by-step explanation:

Year 1) 100+100(.25) = 125

Year 2) 125+125(.25) = 125+31.25 = $156.25

156.25 - 100 = $56.25

25 x 2

=50

I searched your question and here is what I found:

Step-by-step explanation:

L = 4 + 3W  (from the second condition)

L2 = 66 + LW (combining the first and third condition)

L2 = 66 + L(L-4)/3

3L2 = 198 + L2 -4L

2L2 + 4L -198 = 0

(2L - 18)(L + 11) = 0; discarding the negative root for lack of practicality , L = 9

from the first equation W = (L - 4)/3 = 5/3 = 1 2/3; 1.67

Hence the length of the rectangle is 9 cm and the width is 1.67 cm

check;        

2nd condition; L = 4 + 3*1.67 = 9 (proven)

1st and 3rd condition; 92 = 66 + 9*1.67 = 81 (proven)

The length of the rectangle is 9 cm.

The width of the rectangle is 5/3 cm.

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

Rectangle:

Length = 3w + 4

Width = w

Area = (3w + 4)w

Square:

Side = 3w + 4

Area = (3w + 4)²

Now,

The area of the square is 66 more than the area of the rectangle.

This means,

(3w + 4)² =  (3w + 4)w + 66

9w² + 16 + 24w = 3w² + 4w + 66

9w² - 3w² + 24w - 4w + 16 - 66 = 0

6w² + 20w - 50 = 0

2 (3w² + 10w - 25) = 0

3w² + 10w - 25 = 0

3w² + (15 - 5)w - 25 = 0

3w² + 15w - 5w - 25 = 0

3w(w + 5) - 5(w + 5) = 0

(3w - 5)(w + 5) = 0

w + 5 = 0 and 3w - 5 = 0

w + 5 = 0

w = -5 (rejected since its negative)

3w - 5 = 0

3w = 5

w = 5/3

Now,

Length.

= 3w + 4
= 3 x 5/3 + 4

= 5 + 4

= 9

Width = 5/3

Thus,

The length and width of the rectangle are 9 and 5/3.

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According to the Angle-Angle-Side Postulate (AAS), two triangles are congruent if two angles and the included side of one triangle are congruent with two angles and the included side of another triangle.

Angle-Angle-Side is abbreviated as AAS. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle. AAS congruence can be demonstrated with a few simple methods.

Triangles can be proved to be congruent using the methods SSS, SAS, ASA, and AAS, but SSA and AAA are invalid and cannot be utilized. The angle-angle-side theorem, or AAS, was discussed here. According to this theorem, triangles are congruent if two angles and any side of one triangle are congruent with two angles and any side of another triangle. An extension of angle-side-angle, or ASA, is this theorem.

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please write clear handwriting

Answer:

I hope the above image will be helpful