Find Tan A if Cos2A = 1/2

The value of function  (f + g)(x) is 7x² + x - 4.

Here the functions provided are,

f(x) = 4x² - 5x

g(x) = 3x² + 6x - 4

The p addition property of functions (f + g)(x) allows them to be written as,

(f + g)(x) = f(x) + g(x)

In the above equation, we can substitute the values of each function.

(f + g)(x) =  4x² - 5x + 3x² + 6x - 4

We have to combine the similar terms,

(f + g)(x) =  4x² - 5x + 3x² + 6x - 4

             = 7x² + x - 4

So (f + g)(x) = 7x² + x - 4

Therefore the correct answer is option B.

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The formula of rational function is [tex]R(x) = \frac{P(x)}{Q(x)}[/tex] , where P(x) and Q(x) are polynomial functions.

What is rational function ?

A rational function is one that can be written as a polynomial divided by a polynomial. Since polynomials are defined everywhere, the domain of a rational function is the set of all numbers except the zeros of the denominator. Example 1. f(x) = [tex]\frac{x}{x - 2}[/tex].

Rational functions are typically identified by the degrees of the numerator and denominator. For example, a quadratic for the numerator and a cubic for the denominator is identified as a quadratic/cubic rational function. A rational function model is a generalization of the polynomial model.

The formula of rational function is [tex]R(x) = \frac{P(x)}{Q(x)}[/tex] , where P(x) and Q(x) are polynomial functions.

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Answer:

  C.) The only extreme point is (-1, 18).

Step-by-step explanation:

You want the local and global extrema of f(x) = -2x² - 4x + 16.

Unless the domain is restricted to a particular interval, the extrema of a polynomial function will be its turning points. The number of possible turning points is 1 less than the degree of the equation.

An even-degree polynomial equation will always have at least one global extreme on the domain of all real numbers.

The given 2nd-degree equation will have exactly one extreme point: its vertex at (-1, 18).

__

Additional comment

The vertex of ax² +bx +c is located at x=-b/(2a). Here, that is x=-(-4)/(2(-2)) = -1. The value of f(-1) is -2 -(-4) +16 = 18, so the extreme point is (-1, 18). A graphing calculator finds it quickly.

Answer:

The answer for the question is 3.7

We determine the mean and standard deviation for a statistical observation by considering the available data set and size of data.

In the statistics, the mean value is the average value of all available data set.

The standard deviation is an estimation that implies how far each data is apart from the mean value.

Suppose we have a list of data. The data list is denoted by X and the total number of data is N. Now we will add all the data set and the result is denoted by ∑X

Mean value formula = the sum of data / number of data = ∑X/N

In the next, we will determine the square value of all data and the list is denoted by X². Finally, we add all the X² and the result is ∑X²

now, standard deviation is calculated by the formula,

  standard deviation = √[∑X²/N - (∑X/N)²]

hence, we can solve for mean and SD

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The median of the set of numbers 25 and 29 is 27. This is the average of the two middle numbers in the ordered set, and it is not affected by extreme values or outliers.

The median of a set of numbers is the value that is exactly in the middle of the set when it is ordered from least to greatest. In this case, the set of numbers is 25 and 29. When we order this set from least to greatest, we get 25, 29. There are two numbers in this set, so the median is the average of the two middle numbers, which is the only number in the set. The only number in this set is 27, so the median is 27.

To find the median, we first need to arrange the numbers in order from least to greatest. If there is an odd number of numbers in the set, the median is the middle number. If there is an even number of numbers in the set, the median is the average of the two middle numbers. In this case, there are two numbers in the set, so the median is the average of the two middle numbers.

In summary, the median of the set of numbers 25 and 29 is 27. This is the average of the two middle numbers in the ordered set, and it is not affected by extreme values or outliers.

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The circumcenter of a triangle is the point in the plane equidistant from the three vertices of the triangle.

In geometry, the circumscribed circle or circumcircle of a polygon is a circle that passes through all the vertices of the polygon. The center of this circle is called the circumcenter and its radius is called the circumradius.

Not every polygon has a circumscribed circle. A polygon that does have one is called a cyclic polygon, or sometimes a concyclic polygon because its vertices are concyclic. All triangles, all regular simple polygons, all rectangles, all isosceles trapezoids, and all right kites are cyclic.

A related notion is the one of a minimum bounding circle, which is the smallest circle that completely contains the polygon within it, if the circle's center is within the polygon. Every polygon has a unique minimum bounding circle, which may be constructed by a linear time algorithm.

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Using the AND rule of probability and percentage calculations, The answer is 0.0684.

Probability is the likelihood that something will occur. When we don't know how an event will turn out, we might discuss the likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.

Percentages are fractions with a 100 as the denominator. The percent symbol (%) is used next to the number to denote that it is a percentage.

62% goes to college.

% not going to college = 100%-62%

=38%

on that 38%, 18% gets employment,

probability =  0.38 * 0.18

=0.0684

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Answer:

  c. $350.24, the april balance plus the late fee

Step-by-step explanation:

You want to know the required total payment when the balance being repaid is $325.24 and a late fee of $25 is charged.

Arthur must pay both the balance due and the late fee. The total amount he must pay is ...

  balance + late fee = $325.24 +25.00 = $350.24

Therefore , the 6 year old children can able to  skip count to 1 to 100 counting by making them learn.

Mathematicians can add numbers using the counting-on technique. When using this method, a learner begins by adding the larger number, then "counts on" with the other addends to get the sum. The student will recognize 4 as the higher number and add three more numbers, such as integers "4... 5, 6, 7," if the number sentence is 4 + 3.

Here,

Around age 6, kids start to learn how to skip count. Skip counting teaches your youngster to count swiftly and gets them ready to grasp the fundamentals of multiplication.

The simplest way to count is in skip increments of 10, which are essentially identical to regular increments of 10 with the exception of an extra '0': 10, 20, 30,... 80, 90, 100.

Therefore , the 6 year old children can able to  skip count to 1 to 100 counting by making them learn.

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Answer:

y- intercept = - 1

Step-by-step explanation:

to find the y- intercept, let x = 0 in f(x) and evaluate

using rule of exponents

[tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]

given

f(x) =- 32[tex](2)^{x-3}[/tex] + 3 , then

f(0) = - 32 [tex](2)^{0-3}[/tex] + 3

     = - 32 [tex](2)^{-3}[/tex] + 3

    = - 32 × [tex]\frac{1}{2^3}[/tex] + 3

    = - 32 × [tex]\frac{1}{8}[/tex] + 3

    = - 4 + 3

    = - 1 ← y- intercept

The incorrect answer is b) The difference between their speeds is exactly 1.5 miles per hour.

What is distance?

The distance between two sites is the length of the route. The metre is the SI unit for distance.

What is speed?

The speed at which an object’s location changes in any direction. The distance travelled divided by the time it took to travel that distance is how fast something is moving.

What is time?

The amount of time that something happens, goes through a process, or remains the same.

Let distance be Y and time be X.

Distance (Y) travelled by William after X hours;

Y= 19X

Speed of Leo = [tex]\frac{distance}{time}[/tex]

= [tex]\frac{8}{0.5}[/tex]= 16 m/hr

Difference in speed= 19-16= 3m/hr

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If the spheres are connected by a long thin wire, then the two spheres are at the same potential.

In math, the term sphere refers a three dimensional solid, that has all its surface points at equal distances from the center.

Here we have given that the two conducting spheres, here one having twice the diameter of the other, that are separated by a distance large compared to their diameters. Then the smaller sphere (1) has charge q and the larger sphere (2) is uncharged.

And we need to find If the spheres are connected by a long thin wire.

While we looking into the given question when these two conducting spheres are connected together through a thin wire then charge from the smaller sphere will travel through the wire.

Therefore, here this charge will continue to travel towards the neutral sphere until the charge on both the spheres will become equal to each other.

Therefore, their potential will also become equal.

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No, the Square root of an integer is not always irrational because the square root of perfect squares is not irrational.

Any real number that cannot be written as p/q, where p and q are both integers, the quotient of two integers.

If a number is not a perfect square, the square root of that number is not rational.

For example, the square root is 4 is 2.

The square root of 9 is 3.

But whereas the square root of 5 is 2.23606797755555...... which is irrational

The square root of 8 is 2.8284271247555..... which is irrational.

So, therefore square root of a number is not irrational always it can be rational also.

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If you simply multiply the numerator, which is the top number on the bar, you can multiply a fraction by a full number.

A number that is not negative and doesn't have any fractional or decimal components. Anything that isn't a whole number is a fraction. most often expressed with a numerator (top) and denominator (bottom). All fractions should ideally be "correct" fractions, that is, less than 1.

You can multiply a fraction by a whole number by only multiplying the numerator which is the top number on the bar. for example:

E = 2 x 3/4

E = 6/4

E = 1²/₄

Hence, If you simply multiply the numerator, which is the top number on the bar, you can multiply a fraction by a full number.

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Answer:

x=3.25

Step-by-step explanation:

To solve this you would have to distribute the 3 to both numbers in the parenthesis and then you'd combine like terms. Once you combine like terms it'll be a bit easier to solve. When I distributed and combined like terms I got 3x-12-10=4-11x and then I solved and got x=3.25

Not sure if this is how your supposed to solve this problem for your assignment but for us it's usually like this...if it happens to be wrong then I'm sorry.

A theorem which is used to find the rational solutions of a polynomial equation is known as the rational root theorem.

A polynomial expression is given and after solving them we get the two values known as the roots of the function.

These are also known as the zeros of polynomial as after putting these values in the equation we get the result as 0 .

We should use the rational root theorem only when the value of coefficients are small.

The theorem states that each rational solution x = p ⁄ q, when on simplified satisfies the below mentioned points,

p is an integer factor of the constant term a0, and

q is an integer factor of the leading coefficient an.

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Answer:

a) 27.9069767442

b} 75.439%

Step-by-step explanation:

The answer is 40, by using addition.

Addition (usually signified by the plus symbol +) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division.The addition of two whole numbers results in the total amount or sum of those values combined. The example in the adjacent image shows a combination of three apples and two apples, making a total of five apples. This observation is equivalent to the mathematical expression "3 + 2 = 5" (that is, "3 plus 2 is equal to 5").

Besides counting items, addition can also be defined and executed without referring to concrete objects, using abstractions called numbers instead, such as integers, real numbers and complex numbers. Addition belongs to arithmetic, a branch of mathematics. In algebra, another area of mathematics, addition can also be performed on abstract objects such as vectors, matrices, subspaces and subgroups.

Here, what we can do is use addition to find the number one more than 39.

= 39 + 1

= 40

Hence, the number one more than 39 is 40.

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Addition (usually signified by the plus symbol +) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division.The addition of two whole numbers results in the total amount or sum of those values combined. The example in the adjacent image shows a combination of three apples and two apples, making a total of five apples. This observation is equivalent to the mathematical expression "3 + 2 = 5" (that is, "3 plus 2 is equal to 5").

Here, what we can do is use addition to find the number one more than 39.

= 39 + 1

= 40

The required sample interval in the given situation is 10.

The sampling interval is the space or period of time in which measurements or data collection occur.

This is known as the "nth selection" in research and occurs when we choose the nth participant (or sample unit) from the list; this sampling interval results in a random selection from the entire population.

Calculating the sampling interval involves dividing the population size by the desired sample size to arrive at the predetermined periodic interval.

So, have a population size of 500 people.

The number of members to be selected is only 50.

We already know that to find the sample interval, we should divide the population size bu the required sample size.

Now, calculate the sample interval as follows:

= 500/50

= 50/5

= 10

Therefore, the required sample interval in the given situation is 10.

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Units digit - 6

Step-by-step explanation:

A. 12004+ 32004 = 44008

B. 52004+72004 = 124008

Total - 44008+124008+ 92004 = 208016

Units digit - 6

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The point of intersection of these two lines is (2,1)

Point of intersection means the point at which two lines intersect.

These two lines are represented by the equation a1x + b1y + c1= 0 and    a2x + b2y + c2 = 0, respectively.

When the graphs of y = f(x) and y = g(x) intersect, both graphs have exactly the same x and y values.

So we can find the point or points of intersection by solving the equation f(x) = g(x)

We have been given that line l1  is horizontal and passes through the point (1,1). The line l2 is vertical and passes through points (2,2). We are asked to find a point of intersection between line l1 and line l2.  

Line l1 is a horizontal line so the y-coordinate will be 1 for any value of x. Line l2  is a vertical line, so the x-coordinate will be 2 for any value of y.

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Linear expressions or equations are expressions in which the highest power of the variable is one 5x+3= 13 in four steps

steps 5 x + 3 = 13. 5x+3=13. Subtract 3 from both sides. Subtract 3 from both sides.

5x=13-3. 5x=13−3. Subtract 3 from 13 to get 10. Subtract 3 from 13 to get 10.

5x=10. 5x=10. Divide both sides by 5. Divide both sides by 5.

x=\frac{10}{5} x=510​ Divide 10 by 5 to get 2. Divide 10 by 5 to get 2.

Linear expressions or equations are expressions in which the highest power of the variable is one.

Quadratic expressions or equations are expressions in which the highest power of the variable is two.

Cubic expressions or equations are expressions in which the highest power of the variable is three.

Quartic expressions or equations are expressions in which the highest power of the variable is four.

From the expression, 5x + 2 given,

the highest power of x is one. So it is a linear expression.

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The number that is 10 more than 21 is 31, using the concept of addition.

Addition (usually signified by the plus symbol +) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division.The addition of two whole numbers results in the total amount or sum of those values combined. The example in the adjacent image shows a combination of three apples and two apples, making a total of five apples. This observation is equivalent to the mathematical expression "3 + 2 = 5" (that is, "3 plus 2 is equal to 5").

Besides counting items, addition can also be defined and executed without referring to concrete objects, using abstractions called numbers instead, such as integers, real numbers and complex numbers. Addition belongs to arithmetic, a branch of mathematics. In algebra, another area of mathematics, addition can also be performed on abstract objects such as vectors, matrices, subspaces and subgroups.

Here, what we can do is use addition to find the number 10 more than 21.

= 21 + 10

= 31

Hence, the number 10 more than 21 is 31.

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The sum of the two Santa models is 24.

Given is math is a bit different at the north pole and a problem is shown in the image.

We can assume the three variables as : [x], [y] and [z]. So, we can write the equations as -

3x = 21                  ........ Eq[1]

y + z = 16              ........ Eq[2]

x + y - z = - 1          ........ Eq[3]

Now, it is given that -

3x = 21

x = 21/3

x = 7

and

y + z = 16

y = 16 - z

So, we can write the equation as -

x + y - z = - 1

7 + 16 - z - z = - 1

23 - 2z = - 1

2z = 24

z = 12

So, we can write -

[z] + [z] = 12 + 12 = 24

Therefore, the sum of the two Santa models is 24.

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Answer:

If each shopping trolley is 1 meter long, and each trolley in the stack adds 0.25 meters, then the total length of the stack will be equal to the length of each trolley plus the length added by each additional trolley in the stack. This means that the total length of the stack will be equal to 1 + 0.25 = 1.25 meters per trolley.

If the stack has a total length of 10 meters, and each trolley adds 1.25 meters to the stack, we can divide the total length by the length added by each trolley to find the number of trolleys that can be stacked in a single line of 10 meters:

10 / 1.25 = <<10/1.25=8>>8 trolleys

Therefore, if each shopping trolley is 1 meter long and each trolley in the stack adds 0.25 meters, a single line of 10 meters could hold a stack of 8 trolleys.

Step-by-step explanation:

Answer: 64.5 hours

Step-by-step explanation:

2580 divided by 40

Total surface area = 2(lb+bh+hl)

TSA = 2(25×20+20×15+15×25)

TSA= 2(500+300+375)

TSA= 2(1175)

TSA= 2350 cm²

Lateral surface area = 2(l+b)h

LSA= 2(25+20)15

LSA,= 2(45)15

LSA= 1350 cm²

h=25 cm

l=20 cm

b=15 cm

Total surface area is 2(lb+bh+hl)

2(20×15+15×25+25×20)

2(300+375+500)

2(1175)=2350 cm 2

The lines y = - 4x + 5 and y = x + 4y = - 40 is neither parallel nor perpendicular.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

Given, Are two lines y = - 4x + 5 and y = x + 4y = - 40.

Now,

x + 4y = 40

4y = - x + 40.

y = - (1/4)x + 10.

We know lines parallel to each other have the same slope and lines perpendicular to each other have a slope that is negative reciprocal of each other.

So, Line 1 is neither parallel nor perpendicular to line 2.

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