The solutions of x^2= 16x-28

To verify that the limit of the given function as x approaches 4 is 5 using the ε-δ definition of a limit, we need to show that for any ε > 0, there exists a δ > 0 such that whenever 0 < |x - 4| < δ, then |2x² + 1 - 5| < ε.

To begin, we can simplify the expression 2x² + 1 - 5 to obtain 2x² - 4. We want to find a δ > 0 such that |2x² - 4| < ε whenever 0 < |x - 4| < δ.

Let's choose δ = 1. Now, we need to show that whenever 0 < |x - 4| < 1, then |2x² - 4| < ε.

Notice that |2x² - 4| = |2(x - 2)(x + 2)|. For values of x near 4, we can see that |x + 2| will be less than 6. Hence, we have |2x² - 4| < 6|x - 2|.

Now, if we choose δ = min(1, ε/6), we can ensure that whenever 0 < |x - 4| < δ, we have |2x² - 4| < 6|x - 2| < 6δ ≤ ε.

Therefore, we have shown that for any ε > 0, there exists a δ > 0 such that whenever 0 < |x - 4| < δ, then |2x² + 1 - 5| < ε, which verifies that the limit of the function as x approaches 4 is 5.

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The greatest common factor for the following sets of numbers are as follows,

24, 34, 567 : 1

23, 36, 52, 11 : 1

37, 53, 72, 11², 13 : 1

1, 2, 3, 4, 6, 8, 12, and 24 make up the number 24.

1, 2, 17, and 34 make to the number 34.

1, 3, 7, 9, 21, 27, 63, 81, 189, and 567 make up the number 567.

Because of this, the case's greatest common factor is 1.

The elements of 11 are: 1, 11

The 23 factors are: 1, 23,

1, 2, 3, 4, 6, 9, 12, 18, and 36 make up the number 36.

The sum of 52's factors is: 1, 2, 4, 13, 26, and 52.

Therefore, 1 is the number that these numbers have the most in common, and thus, 1 is the greatest common factor here.

The elements of 13 are: 1, 13, and

These are the 37 factors: 1, 37

These are the components of 53: 1, 53

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72 make up the number 72.

1, 11, and 121 make up the number 121.

Thus, the greatest common factor for 37, 53, 72, 121, 13 is again 1.

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Answer:

The average was 259.24 in 1996.

Step-by-step explanation:

In order to find the year that the average, "y", is 259.24 we need to apply this value on the given expression, as done below:

\(259.24 = 0.15*x + 255.34\\0.15*x = 259.24 - 255.34\\0.15*x =3.9\\x = \frac{3.9}{0.15}\\x = 26\)

The average was 259.24 after 26 years, therefore it was in 1996.

The city that has the biggest difference between the maximum and minimum temperatures is Glasgow.

In order to determine which city has the biggest difference, subtract the difference between the minimum temperature from the maximum temperature.

Range = maximum temperature - minimum temperature

Range of Glasgow = 2 - (-8)

2 + 8 = 10

Range of Cardiff = 6 - (-1)

6 + 1 = 7

Range of Exeter = 8 - 0 = 8

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A/an database schema diagram can be used to show how the tables in a database are defined and related.

This type of diagram provides a visual representation of the structure and organization of the database. It illustrates the tables ,and  their attributes, and the relationships between them.

The database schema diagram helps in the  understanding the logical design of the database, including primary keys, for  foreign keys, and the connections between different tables. It allows developers, database administrators, and stakeholders to visualize the database structure and serves it as a reference for in  designing, modifying, and querying the database effectively.

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The questions for Third Angles Theorem is stated as:

1. Can you provide a counterexample.

2. Does the Third Angles Theorem specifically state that it applies only to triangles, or is it a general principle that can be extended to other polygons?

3. Are there any other theorems or properties specific to quadrilaterals that can be used to establish the congruence of angles?

Here are some additional questions to help your classmate decide if they can use the same strategy for quadrilaterals:

1. Can you provide a counterexample where two corresponding pairs of angles of two quadrilaterals are congruent, but the third pair is not congruent?

2. Does the Third Angles Theorem specifically state that it applies only to triangles, or is it a general principle that can be extended to other polygons?

3. Are there any other theorems or properties specific to quadrilaterals that can be used to establish the congruence of angles in a similar way as the Third Angles Theorem does for triangles?

4. Are there any additional conditions or constraints that need to be considered when applying the Third Angles Theorem to quadrilaterals, such as the type or properties of the quadrilaterals involved?

5. Have you explored other angle relationships and properties specific to quadrilaterals that could potentially support or contradict the congruence of angle pairs in the same way as the Third Angles Theorem?

By critically examining these questions and exploring the relevant properties and theorems, your classmate can gain a better understanding of whether the same strategy can be applied to quadrilaterals or if additional considerations are needed.

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Answer:

Step-by-step explanation:

Triangle DEF is triangle ABC rotated by 180°

So:

∠A is corresponding to ∠D

∠B is corresponding to ∠B

and ∠C is corresponding to ∠F

336 simple random samples of size 3 can be selected from a population of size 8 by the permutation concept as defined "The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply put, a permutation is a term that refers to the variety of possible arrangements or orders. The arrangement's order is important when using permutations".

The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply put, a permutation is a term that refers to the variety of possible arrangements or orders. The arrangement's order is important when using permutations. A permutation is a way to arrange each member in the proper order. The combination is a choice of components from a group. A permutation is the non-replaceable selection of r items from a set of n items in which the order is important. n Pr = (n!) / (n-r)!.

Here,

size 3 can be selected from a population of size 8

=8P3

=8!/(8-3)!

=8*7*6

=336

The permutation concept as defined allows for the selection of 336 small random samples of size 3 from a population of size 8. "Mathematical calculations are used to determine the number of possible configurations for a given set, and this procedure is referred to as permutation. A permutation is a term used to describe a variety of possible configurations or orders. When using permutations, the order of the arrangement is crucial ".

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Answer:

x = 61°

Step-by-step explanation:

In a rhombus, the diagonals bisect the angles, thus

∠ BAE = ∠ DAE = 29° , then ∠ A = 58°

∠ ADE = ∠ CDE = x , then ∠ D = 2x

In a rhombus, consecutive angles are supplementary

∠ A and ∠ D are consecutive angles , then

58 + 2x = 180 ( subtract 58 from both sides )

2x = 122 ( divide both sides by 2 )

x = 61°

Answer:

If x represents the number of laptops sold and y represents the total weekly income, our equation would be y = 55x + 150

Answer:

Step-by-step explanation:

Every week, the given or set in stone amount of money she receives $150. So automatically, the first part of the equation is 150x, because x represents the number of weeks, and 150 is $150. So for instance, if she works for two weeks, she will earn $300. Anyway, she has an additional amount of money she gets, which is $55 for every laptop she sells. This isn't a set in stone amount of money. She might not always earn the extra $55, because she might not sell a laptop for a certain week. So, the final equation would be 150x+55. Hope this helped :)

Answer:

90%

Step-by-step explanation:

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:

x<11

Interval Notation:

(−∞,11)

If a function is not continuous, it may or may not be differentiable.

The differentiability of a function is not determined solely by its continuity.

A continuous function is a function that can be drawn without picking up a pen. In mathematical terms, a function f(x) is continuous if, as x approaches a point a, f(x) approaches f(a).

For a function to be differentiable, it must be continuous. If a function is not continuous, it is not differentiable. However, the opposite is not always true; a function may be continuous but not differentiable.

In summary, a function that is not continuous may or may not be differentiable, while a function that is differentiable must be continuous.

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Answer:

I don't see anything but Perimeter is Length + Width × 2

Diameter is the length of the line segment that divides a circle in half, and circumference is the length of one complete "lap" around a circle.

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Answer:

4:8=1:2

3:9=1:3

10:2=5

3:18 is the same thing as 3:18

56 units are in the sum of the lengths of the three altitudes in a triangle with sides $7,$ $24,$ and $25$

Properties of triangles are:

A triangle has three sides and three angles.

The sum of the angles of a triangle is always 180 degrees.

The exterior angles of a triangle always add up to 360 degrees.

The sum of consecutive interior and exterior angle is supplementary.

Given:

Height: ha = 7

Height: hb = 24

Height: hc = 25

Sum to sides is:

25 +7 + 24 =56 units.

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Answer:

a) = 7x² + 4y²

b) = 3x + 7xy - 7

Step-by-step explanation:

a) = (9 - 2) x² + (-3 + 7) y²

= 7x² + 4y²

b) = (8 - 5) x + (3 + 4) xy - 7

= 3x + 7xy - 7

Answer:

1

Step-by-step explanation:

Given \(a\), half the length of the major axis, and \(b\), half the length of the minor axis for an ellipse, its eccentricity is \(\displaystyle e=\sqrt{1-\frac{b^2}{a^2}}\), which tells us how close the ellipse is to the shape of a circle or how flat and round it is. An infinitely long ellipse would have an infinitely long major axis, so the greater the \(a\) value, the eccentricity gets infinitely closer to 1.

It is a rectangular region with u and v values ranging from 1 to 2.

To find the Jacobian of the transformation x = 3u, y = 2uv, we need to compute the partial derivatives ∂x/∂u, ∂x/∂v, ∂y/∂u, and ∂y/∂v.

Given:

x = 3u

y = 2uv

Calculating the partial derivatives:

∂x/∂u = 3

∂x/∂v = 0 (since x does not depend on v)

∂y/∂u = 2v

∂y/∂v = 2u

Now, we can construct the Jacobian matrix J:

J = [∂x/∂u   ∂x/∂v]

   [∂y/∂u   ∂y/∂v]

Substituting the partial derivatives we calculated earlier:

J = [3   0]

   [2v  2u]

Therefore, the Jacobian of the transformation is:

J = [3   0]

   [2v  2u]

To sketch the region described by the inequalities g: 3 < 3u < 6, 2 < 2uv < 4, we can consider the ranges of u and v that satisfy these conditions.

From the inequality 3 < 3u < 6, we have:

1 < u < 2

From the inequality 2 < 2uv < 4, we can divide both sides by 2:

1 < uv < 2

Since u and v must both be greater than 1, we can determine the range of v:

1 < v < 2

Now, we can sketch the region in the u-v plane bounded by the conditions:

1 < u < 2

1 < v < 2

It is a rectangular region with u and v values ranging from 1 to 2.

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Answer:

Step-by-step explanation:

Answer:

a. 8

Step-by-step explanation:

use Pythagorean theorem to find the missing side

a^2 + b^2 = c^2

15^2 + b^2 = 17^2

b= 8

The mean for the number of people with the genetic mutation in a group of 800 is approximately 116.

For the mean for the number of people with the genetic mutation in groups of 800, we can multiply the proportion of the population with the mutation by the total number of people in each group.

We know that about 14.5% of the population has the genetic mutation, we can express this as a proportion by dividing 14.5 by 100: 0.145.

Next, we multiply this proportion by the total number of people in each group (800) to find the expected number of people with the genetic mutation in a group of 800:

Mean = Proportion × Total number of people

     = 0.145 × 800

     ≈ 116

Therefore, the mean for the number of people with the genetic mutation in a group of 800 is approximately 116.

This means that, on average, we would expect about 116 out of the 800 people randomly selected to have the genetic mutation where each eye has a different color.

However, it's important to note that this is an expected value and the actual number may vary in each group due to randomness.

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The correct answer is option B: Add row 1 to row 3 and replace row 3 with the result. The elementary row operation that transforms the first matrix into the second is adding row 1 to row 3 and replacing row 3 with the result.

To find the elementary row operation that transforms the first matrix into the second, and the reverse operation that transforms the second matrix into the first, we can compare the two matrices and observe the changes made. Let's analyze each option one by one:

1. Multiply row 1 by and add the result to row 3.

  This operation involves multiplying row 1 by a scalar and adding it to row 3. However, this operation does not match the transformation between the two matrices.

2. Add row 1 to row 3 and replace row 3 with the result.

  This operation adds row 1 to row 3 and replaces row 3 with the sum. This matches the transformation between the matrices, where the elements of row 1 in the first matrix are added to the corresponding elements in row 3 to obtain the second matrix.

3. Interchange row 2 and row 1.

  This operation swaps the positions of row 2 and row 1. However, this operation does not match the transformation between the two matrices.

4. Interchange row 3 and row 2.

  This operation swaps the positions of row 3 and row 2. However, this operation does not match the transformation between the two matrices.

Therefore, the correct answer is option B: Add row 1 to row 3 and replace row 3 with the result.

Now, let's find the reverse row operation that transforms the second matrix into the first. Since we have determined that adding row 1 to row 3 and replacing row 3 with the result is the transformation, the reverse operation is subtracting row 1 from row 3 and replacing row 3 with the result.

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Step-by-step explanation:

2y+3x=-5

2y= -3x -5

y= -3/2 (x) -5/2

y= MX +c

m= -3/2 and c = -5/2

Answer:

the first one and last one are true

Step-by-step explanation:

The approximate P-value for this test is D. 0.01267.

From the information, Mrs. Peterson claims to produce random numbers from 1 to 5 (inclusive) on her calculator, but you've been keeping track. In the past 80 selections, the number "five" has come up only 8 times.

The p(cap) will be:

= 8 / 80

= 0.1

The z score will be:

= (0.1 - 0.2) / (✓0.2(0.8)/80

= -0.1 / ✓0.0019

= -2.236

= -2.24

By using the distribution table after getting the z score, the p value is 0.01267.

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Answer:

305 cookies

Step-by-step explanation:

Well, we know that each cookie is $15.25( that is expensive!?) so we multiply it and get 305 (15.25 x 20)

YW!! Have a nice day!

To find the arc length of the curve defined by the parametric equations x = 8t^3 and y = 12t^2 on the interval [0, 1/3], we can use the arc length formula for parametric curves.

The arc length formula for a parametric curve defined by x = f(t) and y = g(t) on the interval [a, b] is given by: L = ∫[a,b] √[f'(t)^2 + g'(t)^2] dt. First, let's find the derivatives of x and y with respect to t: dx/dt = 24t^2, dy/dt = 24t

Next, we substitute the derivatives into the arc length formula and evaluate the integral over the given interval [0, 1/3]: L = ∫[0,1/3] √[(24t^2)^2 + (24t)^2] dt = ∫[0,1/3] √(576t^4 + 576t^2) dt = ∫[0,1/3] √(576t^2(t^2 + 1)) dt = ∫[0,1/3]√(576t^2) √(t^2 + 1) dt = ∫[0,1/3] 24t √(t^2 + 1) dt

Evaluating this integral will give us the arc length of the curve on the given interval [0, 1/3]. In conclusion, the arc length of the curve defined by x = 8t^3 and y = 12t^2 on the interval [0, 1/3] is given by the integral ∫[0,1/3] 24t √(t^2 + 1) dt. Evaluating this integral will provide the numerical value of the arc length.

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