How do i derive the quadratic and cubic functions from
the point group

Answer:

Final Value = 58.50 × (1 + 10/100)

Final Value = 58.50 × (1 + 0.1)

Final Value = 58.50 × (1.1)

Final Value = 64.35

Answer:

64.35

Step-by-step explanation:

58.50 × 0.10 = 5.85

58.50 + 5.85 = 64.35

Answer:

im pretty sure its 24

Step-by-step explanation:

because 12+12=24

To eliminate the roots in 1.1 and 1.2, we can use trigonometric substitution. In 1.1, we can substitute x = 4 sin(theta) to eliminate the root of 4. In 1.2, we can substitute z = 7 sin(theta) to eliminate the root of 7.

1.1. V64+2 + 1 We can substitute x = 4 sin(theta) to eliminate the root of 4. This gives us:

V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3 1.2. V4z2 – 49

We can substitute z = 7 sin(theta) to eliminate the root of 7. This gives us:

V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta) (2 – 1) = 7 sin(theta)

Here is a more detailed explanation of the substitution:

In 1.1, we know that the root of 4 is 2. We can substitute x = 4 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 2.

When we substitute x = 4 sin(theta), the expression becomes V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3

In 1.2, we know that the root of 7 is 7/4. We can substitute z = 7 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 7/4.

When we substitute z = 7 sin(theta), the expression becomes: V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta)

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The missing coordinate of point P on the unit circle in the given quadrant is (5, -12). Point P has a positive x-coordinate and lies below the x-axis.

To find the missing coordinate of point P on the unit circle, we need to consider the given information. In the first case, the x-coordinate of P is positive, and the y-coordinate of P is -5. Since the point lies on the unit circle, we can use the Pythagorean theorem to find the missing coordinate. The Pythagorean theorem states that for any point (x, y) on the unit circle, x^2 + y^2 = 1. Plugging in the given values, we have x^2 + (-5)^2 = 1. Solving this equation, we get x^2 + 25 = 1, which leads to x^2 = -24. Since the x-coordinate must be positive, we discard the negative solution, giving us x = sqrt(24) = 2√6. Therefore, the missing coordinate of P is (2√6, -5).

In the second case, the x-coordinate of P is missing, but we know that P lies above the x-axis. Since the point lies on the unit circle, the y-coordinate can be found using the Pythagorean theorem. Since the x-coordinate is missing, we can represent it as x = sqrt(1 - y^2). Plugging in the given y-coordinate of -12, we have x = sqrt(1 - (-12)^2) = sqrt(1 - 144) = sqrt(-143). However, since the x-coordinate cannot be imaginary, we conclude that there is no point P with a positive x-coordinate lying above the x-axis for this case.

Therefore, based on the given information, the missing coordinate of point P on the unit circle is (5, -12), satisfying the conditions of a positive x-coordinate and lying below the x-axis.

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Anthony's "hiring process" or "recruitment period" was 30 days.

The blank can be filled with "hiring process" or "recruitment period" to indicate the duration between placing the advertisement for a new assistant on November 1 and hiring Marquis on December 1. This period represents the time it took Anthony to evaluate applicants, conduct interviews, and make the decision to hire Marquis.

The hiring process typically involves several steps, such as advertising the job opening, reviewing applications, conducting interviews, and finalizing the selection. The duration of this process can vary depending on various factors, including the number of applicants, the complexity of the position, and the efficiency of the hiring process.

In this case, the hiring process took 30 days, indicating the length of time it took for Anthony to complete the necessary steps and choose Marquis as the new assistant. This duration provides insight into the timeframe Anthony needed to assess candidates and make a hiring decision.

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Answer:

-5/3

Step-by-step explanation:

m=−9−6/10−1

m=−15/9

Slope=

−15/9=−5/3

Step-by-step explanation:

substitute the value of y

3x+2x+3=-2 (collect like term)

5x=-2-3 (calculate the difference)

5x=-5 (both side over 5)

x=-1

i hop it helps you❤

Answer:

Options C and D

Step-by-step explanation:

From the graph attached,

Coordinates of the vertices,

X → (0, 0)

Y → (-1, -2)

Z → (0, -2)

Rule for the rotation of a  point (h, k) by 180° about the origin is given by,

(h, k) → (-h, -k)

By this rule,

Coordinates of the image points will be,

X(0, 0) → X'(0, 0)

Y(-1, -2) → Y'(1, 2)

Z(0, -2) → Z'(0, 2)

Therefore, Option (C) and Option (D) are the correct options.

Answer

C/D

Step-by-step explanation:

The smallest possible area of the circle with the points (-3,-2) and (1,4) is 13π.

Given, the endpoints of the circle are given:

(-3,-2) = (x₁,y₁)

(1,4) = (x₂,y₂)

The circle with the smallest possible area that passes through the points (-3, -2) and (1, 4) is a circle with a diameter whose endpoints are these two points.

we are asked to determine the area of the circle = ?

first calculate the distance between the points:

distance  = √(x₁-x₂)²+(y₁-y₂)²

d = √(-3-1)²+(-2-4)²

d = √(-4)² + (-6)²

d = √16+36

d = √52

d = 2√13

Thus, the radius has a length of r = √13,

and the area of the circle is A = π x (√13)²

= 13π.

Hence we get the area of the circle as 13π..

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Answer:

A

Step-by-step explanation:

180⁰= a+b+81⁰

a=180⁰-117⁰=63⁰

b=180⁰-63⁰-81⁰=36⁰

A polynomial regression model is a good choice for this data, as it can fit the trend of increasing population growth over time.

A function is a mathematical concept that assigns a unique output value for each input value.

In mathematical notation, a function is usually expressed as "f(x)" where "x" is the input and "f(x)" is the corresponding output. For example, a function could be defined as f(x) = x^2, which means that for any value of x, the function will calculate and return the square of that value.

To model the world population data, we can use a mathematical function to fit the data points. A polynomial regression model is a good choice for this data, as it can fit the trend of increasing population growth over time.

To find the expected world population in 2017, we would need to estimate the polynomial regression model using the data points provided and then evaluate the model at the year 2017.

Research shows that the actual world population in 2017 was approximately 7.5 billion, which is higher than our estimated value based on the limited data points provided. This highlights the importance of considering additional factors and data when making predictions about the world population.

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The complete question is

As similarity theorem, the value of x that will make the triangles similar by SSS similarity theorem is 77.

Similarity theorem:

In math, similarity theorem refers the line segment splits two sides of a triangle into proportional segments if and only if the segment is parallel to the triangle's third side.

Given,

Here we need to find the t value of will make the triangles similar by the similarity theorem.

For example, we are told that the 2 triangles are similar by SSS theorem.

Here we know that, SSS means Side - Side -Side and it is a congruence theorem which states that the 3 corresponding sides of two triangles have same ratio, then we can say that the two triangles are congruent by SSS theorem

Therefore, in the triangles ,applying the SSS postulate gives;

=> x/35 = 44/20

Then by applying the multiplication property of equality, let us multiply both sides by 35 to get;

=> x = (44 * 35)/20

When we simplify this one then we get,

=> x = 77

Therefore, the value of x is 77.

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Answer: Point Form: (4,2)

Equation Form: x=4,y=2

Step-by-step explanation:

Answer:

Option C.

Step-by-step explanation:

For a given set of N elements:

{x₁, x₂, ..., xₙ}

The mean is given by:

\(M = \frac{x_1 + x_2 + ... + x_n}{N}\)

And the variance is given by:

\(v = \frac{(x_1 - M)^2 + (x_2 - M)^2 + ... + (x_n - M)^2}{N}\)

Then for our set:

{70, 80 ,75, 75, 80}

We have 5 elements, then N = 5

The first thing we need to find is the mean.

\(M = \frac{70 + 80 + 75 + 75 + 80}{5} = 76\)

Then the variance will be:

\(v = \frac{(70 - 76)^2 + (80 - 76)^2 + (75 - 76)^2 + (75 - 76)^2 + (80 - 76)^2}{5} = 14\)

The correct option is C, 14.

The Solomon four-group design includes two control groups: one that is not pretested and does not receive treatment, and another that is not pretested but receives treatment.

In the Solomon four-group design, there are two treatment groups and two control groups. The purpose of this design is to examine the interaction effect between pretesting and treatment.

The first control group does not receive any treatment, while the second control group also does not receive treatment but is pretested. These two control groups help to measure the impact of pretesting on the dependent variable.

The two treatment groups receive the treatment being studied, with one group being pretested and the other group not being pretested. By comparing the pretested and non-pretested treatment groups, researchers can determine if there is an interaction effect between pretesting and the treatment.

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The measure of the angle enclosed by the 19 inch and 23 inch sides is  81 degrees in the triangle.

In a triangle, the sum of the measures of the three angles is always 180 degrees.

Let the angle enclosed by the 19 inch and 23 inch sides x.

The Law of Cosines states that for a triangle with sides a, b, and c, and angle C opposite side c:

c² = a² + b² - 2ab cos(C)

Let's choose the 27 inch side as side c.

Then we have:

27² = 19² + 23²- 2(19)(23)cos(x)

729 = 850 - 874cos(x)

-121 = -874cos(x)

cos(x) = 0.1386

x=81 degrees

Hence, the measure of the angle enclosed by the 19 inch and 23 inch sides is  81 degrees.

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Answer:sine

Step-by-step explanation:

Answer:

1 Cups (US) = 0.24992635042 Quarts

either divide or multiply by 0.24992635042

52* 0.24992635042 = 13

13 /  0.24992635042 = 52

Step-by-step explanation:

Answer:

A) not congruent.    You only know one side and one angle to be congruent.

Step-by-step explanation:

Carol had originally invested 19,470.69 pound in the account when we have 2.5% compound interest per year.

According to the question,

We have the following information:

On the 1st January 2014 Carol invested some money in a bank account which gives 2.5% compound interest per year.

He withdrew 1000 pound from the account after 1 year.

Now, the amount left in Carol's account on 1st January 2016 is 23517.60 pound.

Compound amount = \(P(1+\frac{r}{100}) ^{t}\) where P is the principal amount, r is the rate of interest and t is the time in years

Let's take the amount invested to be x pound.

Now, after 1 year, the total amount in the bank will be:

x(1+2.5/100)

x(100+2.5)/100

112.5x/100

Now, when 1000 pound are withdrawn, the amount left is:

(112.5x/100)-1000

1.125x-1000

Now, this is the principal amount for the next year:

Amount = (1.125x-1000)(1+2.5/100)

Amount = (1.125x-1000)(112.5/100)

(1.125x-1000)1.125 = 23517.60

1.125x-1000 = 23517.60/1.125

1.125x-1000 = 20904.53

1.125x = 20904.53+1000

1.125x = 21904.53

x = 21904.53/1.125

x = 19470.69

Hence, the original amount invested by Carol is 19470.69 pound.

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Step-by-step explanation:

The slope of this line = (y₂ - y₁) ÷ (x₂ - x₁)

                                   =  (2 - (- 1 )) ÷  (-6 - (-4))

                                   =  3 ÷ (-2)

                                   =  - ³/₂

The equation of the line can be determined using the point-slope form:

y - y₁ = m(x - x₁)

⇒ y - 2 = -³/₂(x - (-6))

   y - 2 = -³/₂ (x + 6)

Answer:

7 (1-6)

Step-by-step explanation:

you find the greatest common factor of 7 and 42.

7

7x1

42

1x42

2x21

3x14

6x7

Answer:

one solution

Step-by-step explanation:

3x-1=3

Add 1 to each side

3x-1+1=3+1

3x = 4

Divide by 3

3x/3 = 4/3

x = 4/3

There is one solution

Answer:

One solution

Step-by-step explanation:

3x=4

x=4/3

no other answer

Using the law of cosines, the measures of the angles are given as follows:

The law of cosines states that we can find one of the sides or the angle C of a triangle according to the following equation:

c² = a² + b² - 2abcos(C)

In which:

For this problem, the parameters for the triangle are given as follows:

a = b = 12, c = 3.

We want to solve for the smallest angle C, hence:

c² = a² + b² - 2abcos(C)

9 = 288 - 288cos(C)

288cos(C) = 279

cos(C) = 279/288

C = arccos(279/288)

C = 14.36º.

The other two angles are congruent, and the sum of the internal angles of a triangle is of 180º, hence:

14.36 + x + x = 180

2x = 165.64

x = 165.64/2

x = 82.82º.

Then the measures of the angles are given as follows:

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Answer:

14

83

Step-by-step explanation:

i did it on edge

The calculated value of the tenth term, b₁₀ of the sequence is 78732

From the question, we have the following parameters that can be used in our computation:

b₁ = -4

bₙ = 3bₙ₋₁

The above means that

We multiply the current term by 4 to get the next term

So, we have

b₂ = 3 * 4 = 12

b₃ = 3 * 12 = 36

b₄ = 3 * 36 = 108

b₅ = 3 * 108 = 324

b₆ = 3 * 324 = 972

b₇ = 3 * 972 = 2916

b₈ = 3 * 2916 = 8748

b₉ = 3 * 8748 = 26244

b₁₀ = 3 * 26244 = 78732

Hence, the tenth term, b₁₀ of the sequence is 78732

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According to the given statement the given data is true.

we can see that the number 5 is a perfect square of 25.

Informally: When someone multiplies an integer (a "whole" number, positive, negative, or zero) by itself, mathematics resulting product is known as a square number, a perfect square, or simply "a square." So, 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on are all square numbers.

To check the accuracy of your square, simply calculate the exact square root of something like a given value. If the square root seems to be an integer, your number is the perfect square. Let's compute the squares of something like the following numbers: 49 and 53. 49 = 7 - 7 is an integer number 49 is a perfect square.

As can be seen, the calculated value is:

x²=25 , then x=5

While find the square root of the given number of:

x²=25

x = √25

x=5

So,

we can see that the number 5 is a perfect square of 25.

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STEP 1

Interpret question to make sense geometrically.

We have circular shapes, thus, we are dealing with circles and these circles have their area, however, we seek the angle with which when used to cut the circle will give us an area of 220 sq cm.

Note that this is a fraction of the total area of the circle.

This will be illustrated diagrammatically below

Area of a sector is given as:

STEP 2

Find unknown

The ci

The fourth-order accurate finite difference approximation is:

u00(x) = c−2u(x − 2h) + c−1u(x − h) + c0u(x) + c1u(x + h) + c2u(x + 2h) + O(h4).

Compute the coefficients using the matlab code fdstencil.m and check that they satisfy the system you determined in part (a).

Test this finite difference formula to approximate u

00(1) for u(x) = sin(2x) with values of h from the array hvals = log space(-1, -4, 13). Make a table of the error vs. h for several values of h and compare against the predicted error from the leading term of the expression printed by  fdstencils.

You should observe the predicted accuracy for larger values of h. For smaller values, numerical cancellation in computing the linear combination of u values impacts the accuracy observed.

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