find the value of each trigonometric ratio in simplist form

Answer:

y = 2(x + 1.5)² + 0.5

Step-by-step explanation:

"To convert the standard form y = ax² + bx + c to vertex form:

Extract a from the first two terms: y = a[x² + (b/a)x] + c.

Add and subtract (b/(2a))² inside the bracket: y = a[x² + (b/a)x + (b/(2a))² - (b/(2a))²] + c.

Use the short multiplication formula: y = a[(x + b/(2a))² - (b/(2a))²] + c.

Expand the bracket: y = a(x + b/(2a))² - b²/(4a) + c.

This is your vertex form with h = -b/(2a) and k = c - b²/(4a)."

^^ not my explanation!!

Answer:

C

Step-by-step explanation:

The theoretical probability of landing on A, B, C, or D is all 1/4. This would also mean the theoretical probability is 45/180. Statement C is the only one that is true.

A function with a vertex must switch from increasing to decreasing or vice versa at the vertex. So, the function cannot be only increasing or only decreasing over its entire domain.

Given data ,

A function with a vertex, also known as a vertex form of a quadratic function, is a function of the form f(x) = a(x-h)^2 + k, where (h, k) represents the vertex of the parabola. The vertex is the point on the parabola where it changes direction from increasing to decreasing or vice versa.

It is impossible for a function with a vertex to increase continuously if its whole domain shows an increase in the function. Similar to the last example, a function with a vertex cannot decrease throughout its whole domain because that would imply that the function is constantly decreasing.

Hence , a function with a vertex must switch from increasing to decreasing or vice versa at the vertex, and it cannot be only increasing or only decreasing over its entire domain.

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The given graph represents the function with the equation f(x) = 12(x - 1)/[(x + 2)(x - 3)].

To write an equation for the function, we first observe that the vertical asymptotes occur at x = -2 and x = 3, indicating that the denominator (Q(X)) has roots at x = -2 and x = 3. Hence, the equation of the denominator is:

Q(X) = (x + 2)(x - 3)

Furthermore, from the graph, we can see that the zero of the function occurs at x = 3, indicating that the numerator (P(X)) has the factor (x - 3). Let a be the leading coefficient of P(X), so we can write:

P(X) = a(x - 1)(x - 3)

To find the value of a, we use the fact that the y-intercept of the function is (0, -2). Substituting x = 0 and f(0) = -2 into the equation of the function, we get:

-2 = a(-1)/[(2)(-3)]

Simplifying this equation gives us:

a = -2/(2*3) = -1/3

Substituting this value of a into the equation for P(X), we get:

P(X) = (-1/3)(x - 1)(x - 3)

Substituting the equations for P(X) and Q(X) into the formula for f(x), we get:

f(x) = (-4)(x - 1)/[(x + 2)(x - 3)]

Simplifying this equation gives us:

f(x) = -4(x - 1)/[(x + 2)(x - 3)]

Therefore, the equation of the function graphed in the figure is f(x) = -4(x - 1)/[(x + 2)(x - 3)].

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Answer:

Let the three numbers be x, y, and z.

We are given that x + y = z + 4.

We are also given that x + y + z >= 20 and x + y + z <= 28.

Combining these two inequalities, we get:

z + 4 + z >= 20

2z >= 16

z >= 8

Since z is an integer, z can be 8, 9, 10, 11, 12, 13, 14, 15, 16, or 17.

For each value of z, we can find the corresponding values of x and y using the equation x + y = z + 4.

For example, if z = 8, then x + y = 12.

So, the three integral values satisfying the inequality are 8, 4, and 0.

Another example is z = 15.

In this case, x + y = 19.

So, the three integral values satisfying the inequality are 15, 2, and 2.

There are many other possible solutions.

The solution of the system of equations is given by the point of intersection of all the equations that compose the graph.

In this problem, the graph of the system of equations is given, hence we use it to obtain the solution.

The solution of the system of equations is given by the point of intersection of all the equations that compose the graph, that is, the point where all the curves cross each other.

The point of intersection represents the solution of the system of equations as it is the input values for which all the equations have the same output value.

The problem is incomplete, hence the procedure to obtain the solution of the system of equations from the graph is presented.

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Annual depreciation = ($37,800 - $2,400) / 3 years = $11,800 per year

Depreciation per unit = ($37,800 - $2,400) / 261,000 = $0.139 per unit

Depreciation rate = 2 / 3 = 0.667 or 66.7%

Method of the straight line:

Annual depreciation = (Cost - Residual value) / Useful life

Annual depreciation = ($37,800 - $2,400) / 3 years = $11,800 per year

Schedule of depreciation: shown in the below table

Units-of-production method:

Depreciation per unit = (Cost - Residual value) / Total units of production

Depreciation per unit = ($37,800 - $2,400) / 261,000 = $0.139 per unit

Depreciation schedule:

Double-declining-balance method:

Depreciation rate = 2 / Useful life

Depreciation rate = 2 / 3 = 0.667 or 66.7%

Depreciation schedule: shown in the below table

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Answer:
here is the graph for it

Step-by-step explanation:

The graph that represents the exponential function f(x) = 2^(x - 1) + 2 is given as follows:

Graph A.

An exponential function has the definition presented as follows:

y = ab^x.

In which the parameters are given as follows:

The function for this problem is defined as follows:

f(x) = 2^(x - 1) + 2

It has an horizontal asymptote at y = 2, which removes the option C.

The parameter b is of b = 2, meaning that the function is increasing, which removes option D.

The numeric value of the function when x = 0 is given as follows:

f(0) = 2^(0 - 1) + 2

f(0) = 1/2 + 2

f(0) = 5/2

f(0) = 2.5.

Hence graph A is correct.

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The error made by Tony is in Step 4, where he wrote "x + 2 = ± 81". The correct step should be:

Step 4: Take the square root of both sides to solve for x.

√((x + 2)^2) = √81

In this step, Tony should have taken the square root of both sides, but he made the mistake of only taking the square root of the right-hand side and neglected to take the square root of the left-hand side correctly.

The correct step should be:

x + 2 = ±9

Step 5: Solve for x.

x + 2 = 9 or x + 2 = -9

Step 6: Subtract 2 from both sides to isolate x.

x = 9 - 2 or x = -9 - 2

This will give the correct solutions:

x = 7 or x = -11

So, the error made by Tony occurred in Step 4 where he only took the square root of the right-hand side and neglected to take the square root of the left-hand side correctly.

Hope this helps!

Answer:

Step-by-step explanation:

y = 5x^3 - x

Slope of a secant

= (y2 - y1)/(x2-x1)     where (x1, y1) and (x2, y2) are the 2 points.

Slope for the interval (1, 2)

= [5(2)^3 - 2)- (5(1)^3 - 1)] / (2-1)

= 34

Slope for interval (1, 1.5)

=  [5(1.5)^3 - 1.5)- (5(1)^3 - 1)] / (1.5-1)

= 22.75

In the same way we get the slopes of the  intervals:

(1, 1.1):-  15.55

(1, 1,01):-  15.15

(1, 1.001):- 15.015

So the answer is 15.

The standard form of the hyperbola is:

(x-3)²/4 - (y+2)²/(64/35) = 1

Given vertices (1, -2) and (5, -2), the center is (3, -2) and the semi-major axis, a = 2.

The hyperbola is horizontal.

Using point (-3, 6), we find the semi-minor axis, b² = 64/35.

The standard form of the hyperbola is:

(x-3)²/4 - (y+2)²/(64/35) = 1

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Between 2226 and 3241 people are predicted to see an improvement in their baldness.

The expected amount of people expected to see improvement is obtained applying the proportions in the context of the problem.

The sample proportion is given as follows:

175/500 = 0.35.

Considering the margin of error, the bounds are given as follows:

Hence the amounts out of 7810 people are obtained as follows:

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its c please mark me as a brainliest

Answer:

below

Step-by-step explanation:

To show that (AB)^-1 = B^-1A^-1, we need to show that:

(AB)(B^-1A^-1) = (B^-1A^-1)(AB) = I

where I is the identity matrix.

Using the associative property of matrix multiplication, we can simplify the left-hand side of the equation as:

(AB)(B^-1A^-1) = A(BB^-1)A^-1 = AIA^-1 = AA^-1 = I

Similarly, using the associative property of matrix multiplication, we can simplify the right-hand side of the equation as:

(B^-1A^-1)(AB) = B^-1(A^-1A)B = B^-1IAB = BB^-1 = I

Therefore, we have shown that (AB)^-1 = B^-1A^-1.

To show this identity, we need to demonstrate that:

(AB)^-1 = B^-1 A^-1

To do this, we start by multiplying both sides of the equation by (AB):

(AB)^-1 (AB) = B^-1 A^-1 (AB)

On the left side, we know that (AB)^-1 is the inverse of AB. So we can simplify to:

I = B^-1 A^-1 (AB)

Where I is the identity matrix. We can now simplify the right side by rearranging the terms:

B^-1 A^-1 (AB) = B^-1 (A^-1 A) B

Since A^-1 A = I, we can simplify further to:

B^-1 (A^-1 A) B = B^-1 IB = B^-1 B = I

Therefore, we have shown that:

(AB)^-1 = B^-1 A^-1

Q.E.D.

Answer:

2800=1.4tons

Step-by-step explanation:

2000Ib=1ton

Option C) EG bisects ZFEH would prove that EFGH is a square.

In geometry, a quadrilateral is a polygon with four sides and four vertices (corners). It is a two-dimensional shape with four straight sides, and the sum of its interior angles is equal to 360 degrees. Some common types of quadrilaterals include squares, rectangles, parallelograms, trapezoids, and rhombuses. Each type of quadrilateral has its own unique set of properties, such as congruent sides and angles, parallel sides, or perpendicular diagonals. Quadrilaterals are used in many areas of mathematics, as well as in engineering, architecture, and other fields.

Here,

A rhombus has opposite sides congruent, but its angles are not necessarily right angles. However, if the diagonals of a rhombus are perpendicular bisectors of each other, then the rhombus is a square.

If EG bisects ZFEH, then the opposite angles of the rhombus are congruent and the diagonals of the rhombus are perpendicular bisectors of each other. This means that EFGH is a square, and all its sides and angles are congruent.

Options A), B), and D) do not provide any information about the shape of EFGH.

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Answer:

3cm

Step-by-step explanation:

triangle formula is height times base divided by two and divide base by two. then its 6 and divide 6 from 18. so the answer is 3cm

the total number of students in the group is (5/17)12B. We don't have a specific value for B, so we can't give a specific answer for the number of students,

How to solve the problem?

Let's use the following variables to represent the unknowns in the problem:

Let A be the area of area A

Let B be the area of area B

Let x be the number of students working in area B in the morning

Let 3x be the number of students working in area A in the morning

Let y be the total number of students in the group

From the problem statement, we know that A = 1.5B (since area A is 1.5 times area B). We also know that in the morning, the number of students working in area A is 3 times the number of students working in area B. This can be expressed as:

3x = y/2 (since half of the students work in the morning)

In the afternoon, 7/12 of the students work in area A, so the number of students working in area B is:

(1-7/12)y = 5/12y

At the end of the day, area A is done and area B still needs 4 more students to work for another day. This means that the amount of work done by the students in area B is (y/2 - 3x) + (5/12y - 4B) = B, since the total work needed to be done in area B is B and the amount of work done by the students in area A is y/2 - 3x.

Substituting A = 1.5B and 3x = y/2, we can solve for y:

(y/2 - 3x) + (5/12y - 4B) = B

y/2 - 3(y/2)/3 + 5/12y - 4B = B

y/2 - y/2 + 5/12y = 5B

17/12y = 5B

y = (5/17)12B

Therefore, the total number of students in the group is (5/17)12B. We don't have a specific value for B, so we can't give a specific answer for the number of students, but we can say that the number of students is proportional to the area of area B. If we know the area of area B, we can use the equation above to find the total number of students in the group.

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The probability that Mason does not arrive at work by 9 a.m. is given as follows:

p = 17/50.

A probability is calculated dividing the desired number of outcomes by the total number of outcomes.

The outcomes relating to the bus not arriving on time are divided as follows:

Hence the probability is given as follows:

p = 1/4 x 4/5 + 7/10 x 1/5

p = 1/5 + 7/50

p = 10/50 + 7/50

p = 17/50.

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The cost assigned to the ending inventory will cost or assigned based on the lifo method is attached.

Denoting the valuation of inventories a business owns at the completion of any accounting term – be it monthly, quarterly, or annually – ending inventory speaks to the cost of items that have yet to be sold or used in the creation of goods and services.

Checking a company's economic performance is contingent on examining its ending inventory since this element impacts cost of goods sold (COGS) substantially; many corporations' COGS are worked out by subtracting the cost of goods distributed over a period from the overall cost of goods available for sale during that same interval.

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Answer:

-----------------------

Tangent line is perpendicular to radius at the point of tangency.

Hence we have:

Therefore ΔMKJ is a right  triangle.

Radius is 11, so diameter is 22, this is one of legs and its hypotenuse is 25 units.

Use Pythagorean theorem to find the missing leg:

True, option (G) is which is - at least one of the numbers is positive.

A positive integer is a whole number greater than zero, i.e., any number that can be expressed without fractions or decimals, and is greater than zero.

If the difference of two numbers is less than the sum of the numbers, it is always true that at least one of the numbers is positive. As a result, "At least one of the numbers is positive" is the response, which is (G).

Here we assume that x and y are two numbers. The difference between the two numbers is |x - y|, which is always positive.

Now, according to the given condition:

|x - y| < x + y

Simplifying this inequality, we get:

-x + y < x + y

2y > 0

Dividing both sides by 2, we get:

y > 0

Therefore, we can conclude that at least one of the numbers (y) is positive. Note that it is possible for both numbers to be positive or for one number to be positive and the other to be zero.

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The bar chart showing the growth of the price per tone of ground nut over the years is attached accordingly.

A bar chart, sometimes known as a bar graph, is a type of chart or graph that displays categorical data using rectangular bars with heights or lengths proportionate to the values they represent. The bars can be plotted horizontally or vertically. A vertical bar chart is also known as a column chart.

From the bar chart, is clarer to see that the price of ground nut per tone increased steadily year on year.

By the year 2008, it had hit  record high of 100,000 per ton.

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The regression equation that fits the scenario will be y = 11.46 e1.107x

Utilizing this method with the provided information, we attain the regression equation:

ln y = 2.4502 + 0.0515x

It should be noted that to find the exponential equation, we can elevate both sides of the equation:

y = e^(2.4502 + 0.0515x) = 11.46 * e^(1.107x)

Consequently, the mathematical model that is most suitable for the mentioned data is:

y = 11.46 * e^(1.107x)

The coefficient of determination (R-squared) for said model is 0.994, thus indicating an incredibly strong fit.

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If "t" number of years the study started and "y" denote the forest cover area, then the exponential-function representing the relation between "y" and "t" is y = 1500 × [tex](0.9225)^{t}[/tex].

An "Exponential-Function" is a mathematical expression in which a constant (called the base) is raised to a variable power.

In this case, we want to find an exponential function that relates the area of a forest (y) to the number of years since the start of an environmental study (t).

We know that the forest is decreasing by 7.75% each year, which means that the area of the forest after "t years" will be some percentage of its original area.

The formula for an exponential function is y = a × [tex]b^{t}[/tex], where "a" = initial value and "b" = growth or decay factor.

In this case, the initial area of the forest is = 1500 km², and

The forest is decreasing by 7.75% each year.

So, the "decay-factor" is = 1 - 0.0775 = 0.9225,

The exponential function that relates the area of the forest (y) to the number of years since the start of the study (t) is:

⇒ y = 1500 × [tex](0.9225)^{t}[/tex],

Therefore, the required "exponential-function" is y = 1500 × [tex](0.9225)^{t}[/tex].

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Simplifying the expression √y⁶ for y is y³

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

sqrt y^6

Rewrite the expression using numbers and mathematical symbol

So, we have

√y⁶

Take the square root of both sides

So, we have

√y⁶ =  y³

Hence, the solution to the expression √y⁶ is  y³

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the probability of a major tornado in three consecutive years is 1/8000.   the probability of not having a major tornado in the next ten years is approximately 0.328. he probability of having at least one major tornado in the next ten years is approximately 0.672.

(a) The probability of a major tornado in any single year is 1/20. To find the probability of a major tornado in three consecutive years, we multiply the probabilities together:

P(major tornado in 3 consecutive years) = (1/20) * (1/20) * (1/20) = 1/8000

So the probability of a major tornado in three consecutive years is 1/8000.

(b) The probability of not having a major tornado in any single year is 19/20. To find the probability of not having a major tornado in the next ten years, we raise this probability to the power of 10:

P(no major tornado in next 10 years) = (19/20)^10 ≈ 0.328

So the probability of not having a major tornado in the next ten years is approximately 0.328.

(c) To find the probability of having at least one major tornado in the next ten years, we can subtract the probability of having no major tornadoes in the next ten years from 1:

P(at least one major tornado in next 10 years) = 1 - P(no major tornado in next 10 years)

P(at least one major tornado in next 10 years) = 1 - (19/20)^10 ≈ 0.672

So the probability of having at least one major tornado in the next ten years is approximately 0.672.

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