f(x)=3(x+1)^2 -27 what two equations represent function f?

The expression representing a perfect square trinomial is given as follows:

y² - 15y + 56.25.

There are two formats of perfect square trinomial, given as follows:

For this problem, we have a subtraction sign, meaning that the value of a is obtained as follows:

2ay = 15y

2a = 15

a = 15/2

a = 7.5.

Then the square of a is given as follows:

a² = 7.5²

a² = 56.25.

Meaning that the expression is given as follows:

y² - 15y + 56.25.

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Answer:

Step-by-step explanation:

prime factorization of 60= 2*2*3*5 = [tex]2^{2} * 3^{1} * 5^{1}[/tex]

prime factorization of 150 = 2*3*5*5 = [tex]2^{1} * 3^{1} * 5^{2}[/tex]

greatest (highest) common factor (divisor), calculated

HCF = 2*3*5 = 30

For LCM, when you compare the prime factorization of these two numbers, you want to look for the highest power that each prime factor is raised to

LCM = [tex]2^{2} * 3^{1} * 5^{2}[/tex]=300

The requried first year in which Nina sees that investment exceeded investment B is 5th year.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
According to the given data,
Equation models for the given condition are,
For investment A

y = 50(1.08)ˣ

For investment B
y = 60 + 3x

Where y is the total amount after x years of passing.

When plotting the graph of both equations we can see Investment A will surplus the graph of Investment B at x = 5.56

Thus, the requried first year in which Nina sees that investment exceeded investment B is 5th year.

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Therefore , the solution of the given problem of unitary method comes out to be we have successfully created two groups of cards with the same sum.

After determining the dimensions of one tiny slice, multiply the sum by two to complete a work using unitary procedure. The unit variable methodology, which just requires an expression, can be used to distinguish a coded unit from a certain group or set of groups. 40 pens, for example, might cost Rs. 4,000, which would be equal to $1.01 and 4000 pounds. It's possible that one country will have total control over the method employed to do this. Virtually every living creature has a distinctive quality.

Here,

We can create two groups of cards with the same sum as follows:

Group 1: 1, 2, 5, 8, -4

Group 2: -2, -4, 5, 8, 2

To check that the two groups have the same sum, we can add up the values of each group:

Group 1 sum: 1 + 2 + 5 + 8 - 4 = 12

Group 2 sum: -2 - 4 + 5 + 8 + 2 = 9

We can see that the sum of Group 1 is 12, and the sum of Group 2 is 9. However, we want the sums to be the same. We can make them the same by adding 3 to the sum of Group 2, which gives:

Group 1 sum: 12

Group 2 sum: 12

Therefore, we have successfully created two groups of cards with the same sum, using as many cards as possible from the given set of card numbers.

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Answer:

Step-by-step explanation:

Black = 9, Blue = 6, Green = 1, Red = 4

Pr(Black) = 9/18 = 1/2 = 50%

Pr(Red or Green) = 5/18 = 28%

therefore it is 22% (50-28) more likely that Mrs. Devon will select a black pen than a red or green

Answer:

1. 9+6+1+4=20

Black 9/20 = 0.45 = 45%

Red or green = 5/20 = 0.25= 25%

selecting black is 45-25 = 20%

There is no true equation among the given equations.

An equation is a mathematical statement that proves the equality or equivalence of two or more mathematical expressions.

Mathematical expressions are constants, numbers, values, or variables written with algebraic operands, including addition, subtraction, division, and multiplication.

A. 34 − 12 = 14.  This equation is not true because (34 - 12 = 22).

B. 916 − 48 = 58. This equation is not true since (916 - 48 = 868).

C. 78 − 34 = 18. This equation is not true since (78 - 34 = 44).

D. 715 − 13 = 615. This equation is not true because (715 - 13 = 702).

E. 12 − 20 = 10. This equation is untrue since (12 - 20 = -8).

Thus, since the solutions to the equations are not the same values given, we can conclude that none of the equations is true.

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A. 34 − 12 = 14

B. 916 − 48 = 58

C. 78 − 34 = 18

D. 715 − 13 = 615

E. 12 − 20 = 10

The reliability of experts who interpret lie detector tests in criminal investigations can be determined by analyzing the results of the random sample of 280 cases that were studied. It is important to look at the overall accuracy of the interpretations, as well as any potential biases or errors that may have affected the results.

To analyze the results, we can look at the number of correct and incorrect interpretations, and calculate the percentage of accurate interpretations. This will give us an overall measure of the reliability of the experts.

We can also look for any potential biases or errors that may have affected the results. For example, we may want to examine whether certain experts were more likely to make accurate interpretations than others, or whether there were any factors that may have influenced the interpretations, such as the type of crime or the suspect's behaviour.

Overall, the reliability of experts who interpret lie detector tests in criminal investigations can be determined by analyzing the results of a random sample of cases and looking for any potential biases or errors that may have affected the results. By doing this, we can gain a better understanding of the accuracy and reliability of these experts and their interpretations.

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Answer:

5pi (use the pi character button on your screen)

Step-by-step explanation:

Arc length formula is the shortest formula in all of all math!

Arc length = r•theta

r is the radius. In your question, it is 6.

"theta" is the angle in radians, which was given in your question as 5pi/6.

Fill in these given values to the formula.

Arc length

= r • theta

= 6 • 5pi/6

Simplify (the 6's cancel)

= 5pi

Step-by-step explanation:

clearly, the price is marked down to $9.60.

so, the 1st and 4th answer options are wrong.

is it marked down by 12% or by 20% ?

the basic price was $12. = 100%

how much are 10% of that ? well, 12/10 = $1.20.

but we marked down by $2.40.

when you compare $1.20 and $2.40, what do to see ?

that the second number is exactly twice the first number.

10%×2 = 20%

therefore, the 3rd answer is correct.

Answer:

Step-by-step explanation:

2x³+54=2(x³+27)=2(x³+3³)

a³+b³=(a+b)(a²-ab+b²)

complete it

Answer:

are you trying to find the derivative if so the answer will be 0

Step-by-step explanation:

The reasonable domain of the growth function is [0, 8], the y-intercept is 3 cm and the average rate of change of the function is 0.40 cm per month.

The growth function, also called the shatter coefficient or the shattering number, measures the richness of a set family. It is especially used in the context of statistical learning theory, where it measures the complexity of a hypothesis class.

A marine biologist is studying the growth of a particular species of fish, given by the exponential equation,

f(m) = [tex]3(1.09)^{m}[/tex]

We need to find, reasonable domain to plot the growth function, the y-intercept of the graph of the function f(m) to represent and average rate of change of the function f(m) from m = 1 to m = 9,

f(m) = [tex]3(1.09)^{m}[/tex]

m = 0

f(0) = 3(1.09)⁰  = 3 cm

The length of the fish was approximately 5.98 cm.

5.98 = [tex]3(1.09)^{m}[/tex]

1.99 = [tex](1.09)^m[/tex]

m = 8

Domain = [0, 8]

Reasonable domain to plot the growth function = [0, 8]

The y-intercept of the graph of the function f(m) represent initial length of fish = 3 cm

The average rate of change of the function f(m) from m = 2 to m = 8

m = 2, f(2) = 3(1.09)² = 3.56  cm

m = 8, f(8) = 3(1.09)⁸ = 5.97 cm

Change in 8-2 = 6 months = 5.97-3.56 = 2.41 cm

The rate of change of the function f(m) from m = 2 to 8

= (2.41/6)

= 0.40 cm per month

Hence, the reasonable domain of the growth function is [0, 8], the y-intercept is 3 cm and the average rate of change of the function is 0.40 cm per month.

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Answer: TSA( TOTAL SURFACE AREA) of the cube of side 8 cm is 384 square cm.

Step-by-step explanation: We know,

the total surface area of a cube is = 6 a^2 where a is the length of the side of the cube.

Here, a = 8cm

thus TSA = 6* 8*8= 384 square cm.

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Answer:

Step-by-step explanation:

Let's call the regular price of the stereo "x".

The stereo is sold at a 10% discount, which means the selling price is 90% of the regular price:

Selling price after discount = 0.9x

Then, a 10% tax is added to the selling price, so the final sale price is:

Final sale price = (1 + 0.1)(0.9x) = 1.1(0.9x) = 0.99x + 0.1(0.9x) = 0.99x + 0.09x = 1.08x

We are given that the final sale price is $589.05, so we can set up the equation:

1.08x = 589.05

Solving for x, we get:

x = 589.05 ÷ 1.08

x = 545.83 (rounded to the nearest cent)

Therefore, the regular price of the stereo was $545.83.

The mean age of the 12 students is approximately 17.02 years, the variance is 37.41, and the standard deviation is approximately 6.117 years.

The statistic is the study of mathematics that deals with relations between comprehensive data.

Here,
To calculate the mean, variance, and standard deviation of the ages of the 12 students, we first need to find the sum of the ages:

Sum = 16 + 17 + 18 + (16/0.5) + 17 + 18 + 19 + 17 + 17 + 13 + (17/2/2) + 16

= 16 + 17 + 18 + 32 + 17 + 18 + 19 + 17 + 17 + 13 + 4.25 + 16

= 204.25

Mean = Sum / Number of students = 204.25 / 12 ≈ 17.02 years

To calculate the variance, we need to subtract the mean from each age, square the differences, add up the squares, and divide by the number of students minus one:

Variance = [ (16 - 17.02)² + (17 - 17.02)² + ... + (16 - 17.02)² ] / (12 - 1)

= [ 0.16 + 1.96 + ... + 0.16 ] / 11

= 37.41

Finally, we can calculate the standard deviation by taking the square root of the variance:

Standard deviation = √(Variance) ≈ 6.117

Therefore, the mean age of the 12 students is approximately 17.02 years, the variance is 37.41, and the standard deviation is approximately 6.117 years.

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The remainder theorem can be used to determine the volume of a cage with a 15-inch height since b = 15, which results in a volume of 2160 inch3.

The size of an item in 3 directions is the area that is covered by its boundaries. The amount of room an object occupies in three aspects is measured by its height, which is given in cubic inches. A few of illustrations of cubic units are cm3 and in3. On the other perspective, an item's mass is used to measure what more matter it contains. The typical method to ascertain an object's mass is to weigh it, either in pounds or kilograms. Unlike the fundamental equations for the area of a rectangular box, which is length, breadth, and height, the primary equation for volumes is length, width, and height.

given

Height is listed as b and is 18 inches.

B = 18 s= b-3 (from I = 18 - 3 s = 15 as a result.

Therefore, volume

volume of a rectangle = l x b x h V= 18 x 15 x 15 = 4,050 inch3

3) Height = 15 then b = 15 b -15 = 0 if height = 15.

The remaining theorem's definition is:

To get a smaller polynomial and a remainder, we divide a polynomial P(x) by the factor (x - a). The polynomial does not have to contain the factor.

= 2160

The remainder theorem can be used to determine the volume of a cage with a 15-inch height since b = 15, which results in a volume of 2160 inch3.

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The length of CG is approximately 5.4 units.

A triangle is a closed geometric figure that is formed by connecting three straight line segments called sides. These sides meet at three points called vertices. Triangles are one of the simplest and most fundamental shapes in geometry and can be found in many natural and man-made objects.

Triangles can be classified into different types based on their sides and angles.

By sides:

Equilateral triangle: all three sides are equal in length.

Isosceles triangle: two sides are equal in length.

Scalene triangle: all three sides are different in length.

By angles:

Acute triangle: all three angles are acute (less than 90 degrees).

Right triangle: one angle is a right angle (exactly 90 degrees).

Obtuse triangle: one angle is an obtuse angle (greater than 90 degrees).

Triangles have many properties and are used in various fields such as architecture, engineering, physics, and mathematics. They are also commonly used in trigonometry to solve problems involving angles and distances.

We can use the property of similar triangles to solve this problem.

First, let's label the intersection point of FG and BC as point H. Also, let's label the length of CG as x.

Since FG is parallel to AC, we can use the property of similar triangles to find that triangles ABF and HBG are similar.

Therefore, we can set up the proportion:

AB/FB = HG/GB

Plugging in the given values, we get:

10/63 = (x + 57)/57

Solving for x, we get:

x = 5.4

Therefore, the length of CG is approximately 5.4 units.

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The correct sketch is B

The liquid range of water refers to the temperature range at which water exists as a liquid. At standard atmospheric pressure (1 atm), the liquid range of water is from 0 degrees Celsius to 100 degrees Celsius, or from 32 degrees Fahrenheit to 212 degrees Fahrenheit.

This means that water can exist as a liquid within this temperature range, but if the temperature falls below 0 degrees Celsius or rises above 100 degrees Celsius, it will freeze into a solid or boil into a gas, respectively.

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Therefore , the solution of the given problem of range comes out to be  the range of the composite function f(g(h(x))) is [0, ∞).

By calculating the variable's maximum observed value and subtracting its minimum observed value, the variable range is obtained (minimum). Potential range or finite difference bounds include different steel pricing and various designs. A procedure or action's breadth or scope insight into the maximum or expected range of a weapon's projectile. The number between the minimum and maximum of a list and set is known as its range. You can locate the area by lining up all the numbers.

Here,

The range of a function is the set of all possible output values. Let's consider each function separately:

f(x) = |x-3|

The absolute value of any number is always non-negative, so the range of f(x) is [0, ∞).

g(x) = -(x-4)²-3

The square of any real number is always non-negative, so the range of the function -(x-4)² is (-∞, 0]. Subtracting 3 from this range gives the range of g(x) as (-∞, -3].

h(x) = -7

The output of h(x) is always -7, so the range of h(x) is {-7} (a singleton set containing only the number -7).

Putting it all together, the range of the composite function f(g(h(x))) is [0, ∞).

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Answer: 14.5734588364

Step-by-step explanation:

Answer:

Hope the picture helps! <3

Step-by-step explanation:

Answer:

Step-by-step explanation:

We can start by combining the two fractions by finding a common denominator:

sin(a)/(1+cos(a)) + (1+cos(a))/sin(a)

= sin^2(a)/(sin(a)(1+cos(a))) + (1+cos(a))^2/((1+cos(a))sin(a))

= sin^2(a) + (1+cos(a))^2 / (sin(a)(1+cos(a)))^2

= (sin^2(a) + 1 + 2cos(a) + cos^2(a)) / (sin^2(a) + 2sin(a)cos(a) + cos^2(a))

= (2 + 2cos(a)) / (sin(a) + cos(a))^2

= 2(1+cos(a)) / (sin(a) + cos(a))^2

= 2(cos^2(a/2)/sin^2(a/2)) / (sin(a/2) + cos(a/2))^2 (using the half-angle identities)

= 2tan^2(a/2) / (sin(a/2) + cos(a/2))^2

This expression cannot be simplified further without additional information or context.

Answer:

Step-by-step explanation: you need to rewrite the formula but with the numbers that are given to you so then you multiply and divide by 2 and BOOM you got your answer

The length of side x is approximately 9.05 cm.

What is law of sines ?

The Law of Sines, also known as the Sine Rule, is a formula used to find unknown angles or sides of a triangle, given some combination of angle and side measurements. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle. Mathematically, the Law of Sines can be expressed as follows:

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the angles opposite those sides, respectively.

Given by the question:

To find x, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides.

Let's use the sine function to find the length of side AB:

sin A / AB = sin C / BC

sin 45 / x = sin 40 / 12

Rearranging and solving for x:

x = sin 45 * 12 / sin 40

x ≈ 9.05 cm

Therefore, the length of side x is approximately 9.05 cm.

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The company had 32,500 employees a year ago.

Let x be the number of employees the company had a year ago.

According to the problem, the company now has 36% more employees than it did a year ago. This can be expressed mathematically as:

x + 0.36x = 44200

Simplifying the left-hand side of the equation:

1.36x = 44200

Dividing both sides by 1.36:

x = 32500

Therefore, the company had 32,500 employees a year ago.

Percentage is a way of expressing a portion or part of a whole as a fraction of 100. It is often represented by the symbol "%".

For example, if 20 out of 100 students in a class are absent, we can say that the percentage of absent students is 20%. This means that 20 out of every 100 students in the class are absent.

To calculate a percentage, you divide the part by the whole and multiply by 100. For example, if 30 out of 50 students passed a test, the percentage of students who passed the test is:

(30 ÷ 50) × 100 = 60%

This means that 60 out of every 100 students in the class passed the test.

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Using third-order Newton's interpolating a polynomial the value of f(2) is  (25ln(2))/9.

To estimate the value of f(2) using a third-order Newton's interpolating polynomial with the given data points, we first need to calculate the divided differences. The divided differences are defined as:

f[xi] = f(xi) for i = 1, 2, 3

f[x1,x2] = (f[x2] - f[x1]) / (x2 - x1) = (ln(4) - ln(1)) / (4 - 1) = ln(4) / 3

f[x2,x3] = (f[x3] - f[x2]) / (x3 - x2) = (ln(6) - ln(4)) / (6 - 4) = ln(3) / 2

f[x1,x2,x3] = (f[x2,x3] - f[x1,x2]) / (x3 - x1) = ((ln(3) / 2) - (ln(4) / 3)) / (6 - 1) = -0.018

Using these divided differences, we can write the third-order Newton's interpolating polynomial as:

f(x) = f[x1] + f[x1,x2](x - x1) + f[x1,x2,x3](x - x1)(x - x2) + f[x1,x2,x3,x4](x - x1)(x - x2)(x - x3)

Substituting the values of the data points and the divided differences we calculated, we get:

f(x) = ln(1) + ln(4)/3 (x - 1) - 0.018 (x - 1)(x - 4)

Simplifying this expression, we get:

f(x) = ln(1) + (ln(4)/3)x - (11ln(2)/9) + (ln(2)/9)x^2

To estimate f(2), we plug in x = 2:

f(2) = ln(1) + (ln(4)/3)(2) - (11ln(2)/9) + (ln(2)/9)(2)^2

f(2) = 2ln(2) - (11ln(2)/9) + (ln(2)/9)(4)

f(2) = (25ln(2))/9

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Answer: $3,700 or $90,650

Step-by-step explanation:

Answer:

3,700

Step-by-step explanation:

i thibk thisisthay answer

The cubic function is one where the coefficient a, b, c, and d are correlational the variable are real numbers and are polynomial numbers. The function is either one or three real roots. The graph of the function is a cubic curve.

The example of a cubic function is that of  the forms of y = ax3 + bx2 + cx + d, where the a, b, c, and d are constants. The cube root function is inverse to the cube function.  

Hence they are increasing option A is correct.

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Based on the choices, the ordered pairings that correspond to the graph are (2, 2), (2, 3), and (2, 4). (2, 4).

The x-coordinate of each point on the graph is always 2, since the vertical line passing through x=2 is a vertical asymptote, which implies the graph approaches but never reaches the line. Although the points where the graph crosses the y-axis are not shown, we may deduce from the curve's shape that the approximate y-coordinates of the first option, second choice, and third choice are 2, 3, and 4, respectively.

Hence, the suitable ordered pairings are (2, 2), (2, 3), and (2, 4).

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10352 grade point averages must be obtained. The solution has been obtained by using the concept of sample size.

What is sample size?

The sample size is the number of observations utilised to derive estimates for a certain population. By taking a sample from the population, the sample size was established. Sampling is the practise of selecting a subset of the population to infer characteristics about the complete population.

We know that for 99% confidence, the z- score is 2.5758

So, using this we get

N = (z * σ/E)²

N = (2.5758 * 0.79/0.02)²

N = 10351.86

Hence, 10,352 grade point averages must be obtained so that the sample mean is within 0.2 of the population mean.

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