what is distance between C(−5,−2) and D(0,−4)

For f'(a) is given by f'(a) = 6a + 2 and equation of the line tangent to the graph is y = -10x - 12.

f(x) = 3x² + 2x

f'(x) = 6x + 2

So f'(a) = f'(-2) = -12+2 = -10

In order to find tangent line , we need a slope and a point. We have the x-co-ordinate for our point, so we can plug that in to find Y-coordinate.

F(-2) = 8

The slope of tangent line is the derivative at this point  , f'(-2) = -10

Equation of line tangent,

y - 8 = -10(x - (-2))

y = -10x - 12.

The limit of a function in mathematics is a key idea in calculus and analysis regarding the behavior of that function close to a specific input.

Informally, a function f gives each input x an output f(x). If f(x) approaches L as x approaches input p, we say that the function has a limit L at that location. More specifically, any input that is sufficiently close to p when f is applied forces the output value arbitrarily close to L.

The concept of limit is specifically used in the various definitions of continuity. Roughly speaking, a function is continuous if all of its limits agree with the values of the function. The term "limit" is also used in the definition of the mathematical term "derivative," which in one-variable calculus refers to the maximum value of the slope of secant lines on a function's graph.

To learn more about Limits:

brainly.com/question/282767

#SPJ4

Answer:

so sweethope you have an amazing day as well

Answer:

Sorry Good Afternoon, I also Love you and wishing you a great day and weekend.Bye

2. Using proportion, the value of x = 38, the length of FC = 36 in.

3. Applying the angle bisection theorem, the value of x = 13. The length of CD = 39 cm.

The Angle Bisector Theorem states that in a triangle, an angle bisector divides the opposite side into segments that are proportional to the lengths of the other two sides of the triangle.

2. The proportion we would set up to find x is:

(x - 2) / 4 = 27 / 3

Solve for x:

3 * (x - 2) = 4 * 27

3x - 6 = 108

3x = 108 + 6

Simplifying:

3x = 114

x = 114 / 3

x = 38

Length of FC = x - 2 = 38 - 2

FC = 36 in.

3. The proportion we would set up to find x based on the angle bisector theorem is:

13 / 3x = 7 / (2x - 5)

Cross multiply:

13 * (2x - 5) = 7 * 3x

26x - 65 = 21x

26x - 21x - 65 = 0

5x - 65 = 0

5x = 65

x = 65 / 5

x = 13

Length of CD = 3x = 3(13)

CD = 39 cm

Learn more about Angle Bisector Theorem on:

https://brainly.com/question/30459648

#SPJ1

Answer:

(-0.5 , 0.5)

Step-by-step explanation:

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

               \(= (\frac{-3+2}{2},\frac{4-3}{2})\\\\=(\frac{-1}{2},\frac{1}{2})\\\\=(-0.5, 0.5)\)

Answer:

$1361.68

Step-by-step explanation:

15000 > 10000

so she gets the 8.5%

so she gets 108.5% of her salary

x/1255 = 108.5/100

1255(108.5) = 136,167.5

136,167.5/100 = 1361.68

To find the determinant of a matrix, we can use several methods such as cofactor expansion, row reduction, or triangularization.

However, for the given matrix A with 6's on the diagonal, 1's above the diagonal, and 0's below the diagonal, we can easily use the fact that it is a triangular matrix and its determinant is the product of its diagonal entries.

Since all the diagonal entries of A are 6, the determinant of A is simply 6 times itself n times, where n is the dimension of the matrix. Therefore, the determinant of A is 6^n.

It is worth noting that triangular matrices are very useful in numerical linear algebra because they are easy to solve and their determinant can be easily computed. In addition, diagonal matrices are a special case of triangular matrices, and their determinant is simply the product of their diagonal entries. This property is useful in many applications, such as computing eigenvalues and eigenvectors, solving systems of linear equations, and finding the inverse of a matrix.

Learn more about matrix here:

https://brainly.com/question/29861416

#SPJ11

Answer:

A'= (0,-4)

B'= (2,-1)

C'= (4,-3)

Step-by-step explanation:

After you flip it over the x-axis, it would be

A'= (0,-4)

B'= (2,-1)

C'= (4,-3)

Answer:

\(x=-7\)

Step-by-step explanation:

Remember that:

We want to find the value of x such that \(\overline{BC}\parallel\overline{DE}\).

Therefore, the slopes of BC and DE must be equivalent.

So, let's find the slope of BC first.

BC)

We can use the slope formula:

\(\displaystyle m=\frac{y_2-y_1}{x_2-x_1}\)

Let B(17, 5) be (x₁, y₁) and let C(11, -3) be (x₂, y₂). Substitute:

\(\displaystyle m=\frac{-3-5}{11-17}\)

Subtract:

\(m=-8/-6=4/3\)

So, the slope of BC is 4/3.

DE)

Let D(-1, 2) be (x₁, y₁) and let E(x, -6) be (x, y₂). Substitute:

\(\displaystyle m=\frac{-6-2}{x-(-1)}\)

We know that the two slopes must be equal. So, the slope of DE must also be 4/3. Substitute 4/3 for m:

\(\displaystyle \frac{4}{3}=\frac{-6-2}{x-(-1)}\)

Solve for x. Simplify the right:

\(\displaystyle \frac{4}{3}=\frac{-8}{x+1}\)

Cross multiply:

\(4(x+1)=-8(3)\)

Multiply on the right:

\(4(x+1)=-24\)

Divide both sides by 4:

\(x+1=-6\)

Subtract 1 from both sides:

\(x=-7\)

So, the value of x is -7.

And we're done!

The probability that a randomly selected month's number of order is more than 150 is 0.13%

Given, shawn finds that the monthly number of take-out orders at a restaurant is normally distributed with mean 132 and standard deviation 6.

⇒ mean = 132

⇒ standard deviation = 6

Analysis:

Set the monthly number of take out order as x.

From the question, we know:

P(x > 150) = P(x-132/ > 150-132/6)

= P(x=132/6 > 3)

= 1 - P(x-132/6 ≤ 3)

≈ 1 - 0.9987 {standard normal distribution table}

≈ 0.0013

= 0.13%

Hence we get the probability as 0.13%.

Learn more about Normal distribution here:

brainly.com/question/4079902

#SPJ4

ANSWER:

AAA Similarity Theorem

STEP-BY-STEP EXPLANATION:

We can see that the two triangles have the same interior angles and are corresponding.

Therefore, we can state that these two triangles are congruent using the AAA Similarity Theorem, where if two triangles have equal corresponding angles, then their corresponding sides are proportional and the triangles are similar.

To yield $26,000 in the future, compounded semiannually at an interest rate of 6%, a lump sum investment needs to be made today. The correct amount to invest can be calculated using the present value formula.

The present value formula can be used to calculate the amount that should be invested today to achieve a specific future value. The formula is given by:

PV = FV / (1 + r/n)^(n*t)

In this case, the future value (FV) is $26,000, the interest rate (r) is 6%, and the compounding is semiannually (n = 2). We need to solve for the present value (PV).

Using the formula and substituting the given values:

PV = 26,000 / \((1 + 0.06/2)^(2*1)\)

PV = 26,000 / \((1.03)^2\)

PV = 26,000 / 1.0609

PV ≈ $24,490.92

Therefore, the correct lump sum to invest today, at 6% compounded semiannually, to yield $26,000 in the future is approximately $24,490.92.

Learn more about compounded semiannually here:

https://brainly.com/question/28971900

#SPJ11

76 is the missing value in the table. We can calculate it in the following manner:

Since earning and hours are in direct variation so this ratio will be constant. Therefore,

Earning/ Hours= Constant

19/2 = x/8 (According to the provided formula)

x= 76

Therefore 76 is the missing value in the table.

The term "constant" has several meanings in mathematics. When used as a noun, it can have any of the following two meanings: a constant, well defined number or another immutable mathematical entity. A constant has a fixed value and does not change over time. For instance, the size of a shoe, a piece of clothing, or any other article of clothing will never alter. \(\frac{a^{m} }{a^{n}} =a^{m-n}\)  is an algebraic equation, and 8 is a constant that cannot be altered.

To know more about constant :

brainly.com/question/14159361

#SPJ4

This statistic is misleading because Howard surveys only his department and not members of all the departments that the company has.

When studying anything from a population, it is usual practice in statistics to identify a sample of that group.

However, the sample has to be representative.

For example: I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So I ask, let's say, 1000 randomly selected Buffalo residents whether they are Buffalo Bills fans, and expand this to the entire population of New York State residents. This is not representative of all New York State residents, just Buffalo residents.

Howard wants to know the proportion of employees of a company who use the company's healthcare. He asks only his department. However, a company as multiple departments, which leads to the statistics found in Howard's survey being misleading.

To know more about sample visit: brainly.com/question/11045407

#SPJ4

Answer:

1.  7\(\frac{1}{2}\) = \(\sqrt{7}\)

2. 4\(\frac{7}{2}\) = \(\sqrt{4} x^{7}\)

3. 7\(\frac{1}{4}\) = \(\sqrt[4]{7}\)

4. 4\(\frac{1}{7}\) = \(\sqrt[7]{4}\)

Step-by-step explanation:

Answer:

20 is wrong but 100 is correct.

Step-by-step explanation:

He is correct about 100, because 5 x 100 is greater than 100, but he's wrong about the 20, because 5 x 20 = 100 is not greater than 100. It's the same.

The equation of the parabola in vertex form is y = (-1/12)(x + 3)^2 + 2, which opens downwards since the leading coefficient is negative.

The equation of the given parabola in vertex form is y = a(x + 3)^2 + 2, where a is a constant that depends on whether the parabola opens up or down.

To determine the value of a, we can use the fact that the parabola passes through (-7, 2/3). Substituting these values into the equation, we get:

2/3 = a(-7 + 3)^2 + 2

2/3 = 16a + 2

16a = -4/3

a = -1/12

Therefore, the equation of the parabola in vertex form is

y = (-1/12)(x + 3)^2 + 2.

The vertex form of a parabola is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. In this case, we are given that the vertex is (-3, 2), so we can write the equation as y = a(x + 3)^2 + 2.

To find the value of a, we use the fact that the parabola passes through (-7, 2/3). Substituting these values into the equation, we get 2/3 = a(-7 + 3)^2 + 2. Simplifying this equation, we get 2/3 = 16a + 2, which we can solve for a to get a = -1/12.

Therefore, the final equation of the parabola in vertex form is y = (-1/12)(x + 3)^2 + 2, which opens downwards since the leading coefficient is negative.

Learn more about parabola:

brainly.com/question/31142122

#SPJ11

Answer:

120 square feet

Step-by-step explanation:

they are similar so they are in a ratio 20/10=2 so smaller triangle is twice the larger one 6×2=12ft

area of triangle =1/2×base×height

=1/2×20×12

=120 square feet

The product of √x and 4√x can be simplified into a single radical expression in simplest form.

To begin, we can use the product rule of radicals, which states that √a • √b = √(ab). Applying this rule to the expression √x • 4√x, we get:

√x • 4√x = √(x • 4x)

Next, we can simplify the product inside the radical by multiplying the coefficients and combining the variables with the same exponent.

√(x • 4x) = √(4x^2)

Now, we can simplify the expression inside the radical by factoring out the perfect square factor of 4:

√(4x^2) = √(4 • x • x) = √4 • √x • √x = 2√x • 2√x = 4x

Therefore, the simplified form of √x • 4√x is 4x.

To learn more about  radical expression, click here:

brainly.com/question/31941585

#SPJ11

Answer:

x=5

Step-by-step explanation:

you need to do dirty math stuff for these kind of Q. not hard you just need to do it, or use computer graphs to solve them.

Answer:

What do you mean backward?

Step-by-step explanation:

I'm not really sure what you are meaning

The correct option for the demand requirement constraint in a production scheduling LP is option (c): beginning inventory + production - ending inventory = demand.

In a production scheduling LP, the demand requirement constraint represents the balance between the available inventory and the demand for the product. The constraint ensures that the production and inventory levels are sufficient to meet the specified demand.

Option (c) represents this relationship accurately by stating that the beginning inventory, production, and ending inventory, when subtracted from each other, should equal the demand. This equation reflects the concept of maintaining a balance between the production output and inventory changes to meet the demand

Option (a) is incorrect because it uses the greater than or equal to (≥) symbol, which does not accurately represent the constraint.

Option (b) is also incorrect because it uses the equality (=) symbol, which implies an exact balance between the inventory and demand, disregarding the changes in inventory.

Option (d) is incorrect because it uses the greater than or equal to (≥) symbol, which does not accurately represent the constraint.

Therefore, option (c) is the correct representation of the demand requirement constraint in a production scheduling LP.

Learn more about Inventory here: brainly.com/question/31500521

#SPJ11

The new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees are approximately (4.993, 2.048).

To find the new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees, we can use the rotation formula:

x' = x * cos(theta) - y * sin(theta)

y' = x * sin(theta) + y * cos(theta)

Where (x, y) are the original coordinates, (x', y') are the new coordinates after rotation, and theta is the angle of rotation in radians.

Converting the angle of rotation from degrees to radians:

theta = 5 degrees * (pi/180) ≈ 0.08727 radians

Plugging in the values into the rotation formula:

x' = 5 * cos(0.08727) - 2 * sin(0.08727)

y' = 5 * sin(0.08727) + 2 * cos(0.08727)

Evaluating the trigonometric functions and simplifying:

x' ≈ 4.993

y' ≈ 2.048

KLnow more about coordinates here;

https://brainly.com/question/32836021

#SPJ11

In order to simplify and verify trig identities, one needs to use the rules of trigonometry and algebra to manipulate the equation until it is in a simplified form.

The most common trig identities to remember include the Pythagorean identity, reciprocal identities, quotient identities, and sum and difference identities. When simplifying an equation, it is important to remember to include the negative sign when necessary and to factor out any common factors.

After simplifying, it is important to verify the equation. This can be done by plugging in known values for the variables and verifying that the equation is true. By utilizing the rules of trigonometry and algebra, one can simplify and verify trig identities. This process is essential for working with trigonometric functions.

know more about algebra here

https://brainly.com/question/24875240#

#SPJ11

Answer:

(-1,3) and (2,6)

Step-by-step explanation:

The solution to the system is where the two graphs intersect

The graphs intersect at x=-1 and y =3  and x = 2 y=6

(-1,3) and (2,6)

The sinusoidal equations for each of the six scenarios are listed below:

Case 1: h = 60 - 20 · cos 15t

Case 2: h = 60 - 30 · cos 15t

Case 3: h = 40 - 30 · cos 15t

Case 4: h = 40 - 30 · cos 18t

Case 5: h = 40 - 20 · cos 18t

Case 6: h = 60 - 20 cos 18t

In this problem we need to determine six sinusoidal equations, each associated with a scenario. The sinusoidal model is introduced below:

h = H - 0.5 · D · cos (2π · f · t)

Where:

Case 1

h = 60 - 20 · cos (5π · t)

h = 60 - 20 · cos 15.708t

h = 60 - 20 · cos 15t

Case 2

h = 60 - 30 · cos (5π · t)

h = 60 - 30 · cos 15.708t

h = 60 - 30 · cos 15t

Case 3

h = 40 - 30 · cos (5π · t)

h = 40 - 30 · cos 15.708t

h = 40 - 30 · cos 15t

Case 4

h = 40 - 30 · cos (6π · t)

h = 40 - 30 · cos 18.849t

h = 40 - 30 · cos 18t

Case 5

h = 40 - 20 · cos (6π · t)

h = 40 - 20 · cos 18.849t

h = 40 - 20 · cos 18t

Case 6

h = 60 - 20 · cos (6π · t)

h = 60 - 20 · cos 18.849t

h = 60 - 20 cos 18t

To learn more on sinusoidal equations: https://brainly.com/question/24331583

#SPJ1

Answer:

x = -4 1/2

Step-by-step explanation:

-2x/3 + 11 = 14

subtract 11 from each side of the equation:

-2x/3 = 3

multiply both sides by 3:

-2x = 9

divide both sides by -2:

x = -4 1/2

9514 1404 393

Answer:

  range

Step-by-step explanation:

An ordered pair is ...

  (element of domain, element of range)

Then the set of all "element of range" is the range.

_____

Additional comment

To understand math, it is helpful to understand the vocabulary of math. It is difficult to obtain any meaning from a communication when one doesn't know the language.

(a) The equation 5x^2 - 6xy^2z^2 = 7 in cylindrical coordinates can be expressed as:

ρ^2 cos^2(θ) - 6ρ^2 sin^2(θ)z^2 = 7,

where ρ represents the radial distance from the origin, θ denotes the azimuthal angle, and z represents the height coordinate.

(b) The equation z = 2x^2 - 2y^2 in cylindrical coordinates can be written as:

z = 2(ρ cos(θ))^2 - 2(ρ sin(θ))^2,

where ρ represents the radial distance from the origin, θ denotes the azimuthal angle, and z represents the height coordinate.

Cylindrical coordinates provide an alternative way to express points in three-dimensional space. In this system, a point is specified by its radial distance (ρ), azimuthal angle (θ), and height coordinate (z). These coordinates are related to the familiar Cartesian coordinates (x, y, z) through the following equations:

x = ρ cos(θ),

y = ρ sin(θ),

z = z.

The first equation relates the radial distance ρ and the azimuthal angle θ to the x-coordinate. The second equation relates them to the y-coordinate, and the third equation simply states that the z-coordinate remains the same. By substituting these equations into a given Cartesian equation, we can express it in cylindrical coordinates.

The transformation between Cartesian and cylindrical coordinates is widely used in various fields of science and engineering, particularly in problems involving rotational symmetry or cylindrical symmetry. Understanding these coordinate systems allows for more intuitive interpretations and simplifications of equations in different contexts.

Learn more about Equation

brainly.com/question/13763238

#SPJ11

An interaction occurs when the effect of one factor (such as factor A) depends on the level of another factor (such as factor B). This means that the effect of factor A is not constant across all levels of factor B, and vice versa.

For example, consider a study examining the effects of a new drug on blood pressure in two different age groups: younger adults (age 18-35) and older adults (age 60 and above). The study also includes a placebo group. The researchers found that the new drug has a significantly larger effect on reducing blood pressure in older adults compared to younger adults and that the placebo has no effect on blood pressure in either age group.

In this case, there is an interaction between the factors of age and the new drug, because the effect of the drug on blood pressure depends on the age of the participants. It would not be appropriate to interpret the individual effects of the drug or age, because the relationship between these two factors is complex and cannot be accurately captured by examining the effects of each factor in isolation.

To properly understand the relationship between the two factors, it is necessary to examine the interaction between them. This may involve conducting further statistical analyses or creating plots to visualize the data. It is important to consider the interaction when interpreting the results of the study, as it can provide important insights into the underlying mechanisms and help inform decisions about treatment or interventions.

To know more about the interaction of factors visit :

https://brainly.com/question/15925863?referrer=searchResults

#SPJ4