The function f is given in three equivalent forms.
Which form most quickly reveals the zeros (or "roots") of the function?
Choose 1 answer:
a. f(x) = -1/2(x+3)^2+25/2
b. f(x)= -1/2(x-2)(x+8)
c. f(x)= -1/2x^2-3x+8

write one of the zeros.
x=

\(\huge\begin{array}{ccc}a_1=-2\\a_2=1\\a_3=6\\a_{10}=97\end{array}\)

\(a_n=n^2-3\)

Find the first 3 terms and the 10th term.

Substitute

n = 1, n = 2, n = 3 and n = 10:

\(a_1=1^2-3=1-2=-2\\\\a_2=2^2-3=4-3=1\\\\a_3=3^2-3=9-3=6\\\\a_{10}=10^2-3=100-3=97\)

Investment X earns the greater amount of interest over a period of 2 years.

Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,

SI = PRT

where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.

Let's consider that Ian invests in X, then:

Principle amount, P = $6,000
Time, T = 2 Years

Rate of Interest, R = 4.5% at simple Interest = 0.045

The interest earned is:

Interest = PRT = $6,000 × 0.045 × 2 = $540

Now, consider that Ian invests in Y, then:

Principle amount, P = $6,000
Time, n = 2 Years

Rate of Interest, R = 4% at Compound Interest = 0.04

The interest earned is:

Interest = P(1+R)ⁿ - P

            = $6,000(1+0.04)² - $6,000

            = $489.6

Since $540>$489.6, therefore, Investment X earns the greater amount of interest over a period of 2 years.

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The statement "System analysts define an object's attributes during the systems design process" is true because  defining object attributes is an essential part of the systems design process to ensure that the system meets the desired functional requirements.

In systems design, objects are used to represent real-world entities that are relevant to the system being developed. These objects have attributes that describe their characteristics or properties, which are used to identify and manipulate them within the system. System analysts define these attributes during the systems design process to ensure that the system meets the desired functional requirements.

For example, in a library system, a book object may have attributes such as title, author, publisher, and ISBN. Defining these attributes helps ensure that the system can properly manage and retrieve books as needed. Object-oriented design is a popular approach to systems design that relies heavily on defining objects and their attributes.

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Answer:

$4.04

Step-by-step explanation:

Since the ice cream is 15% off, that means you will have to subtract 0.15 from 1, since 1 is 100%, and 0.15 is 15%. If you do the math, then you will get 0.85, which translates to 85%. So now that we have found the percentage of the original price that we have to pay, we can do some more advanced calculations. Since we found the 1 - 0.15 = 0.85, we will multiply the original price, which is $4.75, by 0.85. You can do this by hand or by calculator. You will get 4.0375, which is your answer. Since this is about money, you will have to add a $ sign at the beginning, which would be $4.0375. Of course, you can't pay a percentage of a cent, so you would have to round that up to $4.04. In conclusion, the sale price of the half-gallon of ice cream is $4.04.

Coordinate plane with quadrilateral ABCD at A 0 comma 0, B 5 comma negative 1, C 3 comma negative 5, and D negative 2 comma negative 4, the correct answer is 19.1.

To find the perimeter of the quadrilateral ABCD, we need to calculate the sum of the lengths of its sides.

Let's find the length of each side using the distance formula:

Side AB:

\(Length AB = \sqrt((x2 - x1)^2 + (y2 - y1)^2)\)

        \(= \sqrt((5 - 0)^2 + (-1 - 0)^2)\)

       \(= \sqrt(25 + 1)\)

         \(= \sqrt(26)\)

Side BC:

\(Length BC = \sqrt((x2 - x1)^2 + (y2 - y1)^2)\)

        \(= \sqrt((3 - 5)^2 + (-5 - (-1))^2)\)

         \(= \sqrt(4 + 16)\)

         \(= \sqrt(20)\)

         \(= 2 * \sqrt(5)\)

Side CD:

\(Length CD = \sqrt((x2 - x1)^2 + (y2 - y1)^2)\)

         \(= \sqrt((-2 - 3)^2 + (-4 - (-5))^2)\)

         \(= \sqrt(25 + 1)\)

         \(= \sqrt(26)\)

Side DA:

\(Length DA = \sqrt((x2 - x1)^2 + (y2 - y1)^2)\)

         \(= \sqrt((0 - (-2))^2 + (0 - (-4))^2)\)

         \(= \sqrt(4 + 16)\)

         \(= \sqrt(20)\)

         \(= 2 * \sqrt(5)\)

Now, let's calculate the perimeter by summing up the lengths of all sides:

Perimeter = AB + BC + CD + DA

       \(= \sqrt(26) + 2 * \sqrt(5) + \sqrt(26) + 2 * \sqrt(5) = 2 * \sqrt(26) + 4 * \sqrt(5)\)

Rounded to the nearest tenth, the perimeter is approximately 19.1.

Therefore, the correct answer is 19.1.

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The correct answer of perimeter is 19.1.

To find the perimeter of the quadrilateral ABCD, we need to calculate the sum of the lengths of its four sides.

Using the distance formula, we can find the lengths of each side:

Side AB: \(\(\sqrt{(5-0)^2 + (-1-0)^2}\) = \(\sqrt{25+1}\) = \(\sqrt{26}\)\)

Side BC: \(\(\sqrt{(3-5)^2 + (-5-(-1))^2}\) = \(\sqrt{4+16}\) = \(\sqrt{20}\)\)

Side CD: \(\(\sqrt{(-2-3)^2 + (-4-(-5))^2}\) = \(\sqrt{25+1}\) = \(\sqrt{26}\)\)

Side DA: \(\(\sqrt{(0-(-2))^2 + (0-(-4))^2}\) = \(\sqrt{4+16}\) = \(\sqrt{20}\)\)

Now, we can calculate the perimeter by summing up the lengths of all sides:

Perimeter = AB + BC + CD + DA = \(\(\sqrt{26} + \sqrt{20} + \sqrt{26} + \sqrt{20}\)\)

Rounding the perimeter to the nearest tenth, we get:

Perimeter = 19.1

Therefore, the correct answer is 19.1.

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The greatest possible integer value of the radius of the circle is 7 inches.

The area of a circle is given by the equation\($A = \pi r^2$\). We know that the area is less than \($60\pi$\) square inches, so the equation can be written as \($60\pi > \pi r^2$\). We can solve for the radius by dividing both sides by \($\pi$\), which gives us \($60 > r^2$\). Taking the square root of both sides gives us \($r < \sqrt{60}$\), which is approximately 7.74 inches. Therefore, the greatest possible integer value of the radius of the circle is 7 inches.

To explain this further, we can start with the equation for the area of a circle, which is\($A = \pi r^2$\). Since the area is less than \($60\pi$\)square inches, this equation can be rewritten as\($60\pi > \pi r^2$\). We can then divide both sides by \($\pi$\) to get \($60 > r^2$\). Taking the square root of both sides gives us \($r < \sqrt{60}$\). This result can then be rounded down to the nearest integer, which is 7. Therefore, the greatest possible integer value of the radius of the circle is 7 inches.

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Given someone interested in reading, the individual will more likely take an interest in playing board games.

This can be referred to as the rate in which an event occurs over a given period of time and is usually dependent on certain factors based on the subject involved.

The relative frequency of people who love reading but dislike board game is 25/73 while the relative frequency of those who like either of them is 48/73.

Since the ratio 48/73 is greater than 25/73 then the individual will more likely take an interest in board games.

This therefore makes board games the most appropriate choice in this type of scenario.

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Answer:

not enough information to answer

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

$376.35 / 4 does equal to $94.0875 but when it comes to money, it should be rounded to the nearest cent being $94 and .08 cents.

Measurement of ∠ ABC is 90°

A linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°.

Given that ∠ CBD and ∠ ABC are linear pairs,

Therefore, m∠ CBD + m∠ ABC = 180°

m∠ ABC = 180° - 90° = 90°

Hence, Measurement of ∠ ABC is 90°

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The sample space of the experiment is 52.

The possibility that an event will occur among all potential events is known as probability. It ranges from 0 to 1. The probability is calculated by dividing the number of things by all of the items. Population includes the sample. When studying the entire population is challenging, it is studied.

52 cards in a deck

There are 12 face cards.

The experiment needs a sample space of 52 to find the face cards.

Given that a regular deck of cards is available.

The sample space required for the experiment to determine the probability of face cards must be found.

A face card may or may not be revealed when we pull a card from the deck. So, in order to rule out the possibility that a face card is present at the end of the deck, we must draw every card from a regular deck.

52 samples are therefore required for the experiment.

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Answer:

The extraneous solution is x = -5/6

Length = 4 ft

Width = 5 ft

Step-by-step explanation:

Length = 3x - 5 ft

Width = 2x - 1 ft

Height = 2 ft

Volume = 40 ft^3

Volume = length × width × height

40 = (3x - 5)(2x-1)(2)

40 = (6x^2 - 3x - 10x + 5)(2)

40 = 12x^2 - 6x - 20x + 10

12x^2 - 26x + 10 - 40 = 0

12x^2 - 26x - 30 = 0

Divide through by 2

6x^2 - 13x - 15 = 0

Solve using factorization method

(6x + 5) (x - 3) = 0

6x + 5 = 0

6x = -5

x = -5/6

Or

x - 3 = 0

x = 3

The extraneous solution is x = -5/6

Length = 3x - 5 ft

= 3(3) - 5

= 9 - 5

= 4 ft

Width = 2x - 1 ft

= 2(3) - 1

= 6 - 1

= 5 ft

The area of the preimage, the original square, before its dilation, is 33 units.

To find the area of the original square before dilation, we need to find the scale factor. We can determine the scale factor by comparing the areas of the preimage and the image.

The area of the preimage (original square) is denoted as A, and the area of the image (dilated square) is given as 132 units. The scale factor, denoted as k, represents how much the side lengths of the original square were multiplied by to obtain the image.

The relationship between the areas and the scale factor is as follows:

Area of Image = (Scale Factor)^2 x Area of Preimage

Plugging in the given values, we have:

132 = \(k^2\) x A

Since the problem states that the preimage was dilated by a scale factor of 2, we substitute k = 2 into the equation:

132 = \(2^2\) x A

132 = 4A

Now, solve for A:

A = 132 / 4

A = 33

Therefore, the area of the original square before dilation is 33 units.

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Answer:

1/3

Step-by-step explanation:

\(\frac{6}{9}*\frac{1}{2}\)

\(\frac{6*1}{9*2}\)

\(=\frac{6}{18}\)

Reduce by dividing both the numerator and denominator by the Greatest Common Factor GCF(6,18) = 6

\(\frac{6/6}{18/6}=\frac{1}{3}\)

Therefore:

\(\frac{6}{9}*\frac{1}{2}=\frac{1}{3}\)

[RevyBreeze]

Answer:

why are you running

Step-by-step explanation:

why are you running

Answer:

Step-by-step explanation:

The absolute difference is 77-(-8)=85. The only option that is equivalent is

|-8|+77

Answer:

-16?

Step-by-step explanation:

the correct answer  i

- 16

Answer:

3

The answer is 3 because:

4/5 of 3.75 is 3.

So, the answer should be 3.

Hope it helps!

Step-by-step explanation:

add the radii to get the diameter then multipy by pi

10 (3.14) =31.4

The slope of the line that passes through points (2, 8) and (-3, 14) is -1.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively.

Given:

The coordinates of point = (2, 8) and (-3, 14),

Calculate the slope of the line from the formula given below,

m = (y₂ - y₁) / (x₂ - x₁)

Here m is the slope.

Substitute the values,

m = (13 - 8) / (-3 - 2)

m = −1

Therefore, the slope of the line that passes through points (2, 8) and (-3, 14) is -1.

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Answer:

4%

Step-by-step explanation:

Sales tax over original price

12.80 / 320* 100 = 4%

Answer:

Either 9.71 (adjacent to 36°) or 7.05 (opposite 36°)

Step-by-step explanation:

The question doesn't specify which leg is under question.  Is it the adacent leg or the opposite leg?  I'll assume adjacent.

We can use the acronym

SOHCAHTOA which is a helpful mnemonic for remembering the definitions of the trigonometric functions.  For an angle other than the right angle, the following relationships are defined.

SOH:  S is sine = Opposite/Hypotenuse

CAH:  C is cosine = Adjacent/Hypotenuse

TOA:  T is tangent = Opposite/Adjacent

For a side adjacent (A) to the 36° angle, we can use

Cosine = Adjacent/Hypotenuse

Since we know the hypotenuse (12) we can find A:

Cosine(36) = A/12

A = Cosine(36)*12

A = (0.809)*12

Adjacent = 9.71

====================

If the opposite leg is calculated, we would use

Sine= Opposite/Hypotenuse

Sine(36) = Opposite/12

O = (0.5877)*12

Opposite = 7.053

The coefficient of variation (CV) is a measure of relative variability and is calculated by dividing the standard deviation by the mean, and then multiplying by 100 to express it as a percentage.

In this case, the mean weight is 340 grams, and the standard deviation is 5.2 grams.

CV = (Standard Deviation / Mean) * 100

CV = (5.2 / 340) * 100

CV ≈ 1.53%

Therefore, the correct answer is option B: 1.53%.

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The function which represents the cost to drive a car from this agency miles x a day is :

C(x) = 15, if 0 ≤ x ≤ 200

      = 15 + 0.05x, if x > 200

Given that,

A car rental agency charges $15 a day for driving a car 200 miles or less.

The function can be written as,

C(x) = 15 if 0 ≤ x ≤ 200

If a car is driven over 200 miles, the renter must pay $0.05 for each mile over 200 driven.

C(x) = 15 + 0.05x, if x > 200

Hence the correct option is D.

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The correct option is cone and plane. A conic section is the intersection of a plane and a cone. The best definition of a conic section is "cone and plane".

The definition of conic section is a conic section is a shape that is formed when a right circular cone intersects a plane. Depending on the angle of the plane concerning the center line of the cone, the conic sections are classified into four types. They are a circle, parabola, ellipse, and hyperbola. Each type of conic section has a unique shape and properties.

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5.1) The boundaries of Kcp for system stability are -∞ < Kcp < 1.2 and Kcp > 3.33. 5.2) For a peak time of 1 sec and 70% overshoot, the value of Kcp is approximately 2.14.


5.1) To determine the stability boundaries, we need to find the values of Kcp that make the characteristic equation’s roots have negative real parts. Using the quadratic formula, we find the discriminant Δ = 8^2 – 4(1)(20) = 24. The system is stable when the discriminant is positive, so Δ > 0, which leads to the condition 5Kcp – 24 > 0. Solving for Kcp, we get Kcp > 4.8. Additionally, to avoid complex roots, we need the condition 5Kcp – 24 > 0 to be true, resulting in Kcp < 4.8. Therefore, the stability boundaries are -∞ < Kcp < 1.2 and Kcp > 3.33.
5.2) To find the value of Kcp for a peak time (Tp) of 1 sec and a 70% overshoot, we can use empirical rules. For a 70% overshoot, the damping ratio (ζ) can be found using the formula ζ = (-ln(Overshoot/100)) / (√((π^2) + (ln(Overshoot/100))^2)). From ζ, we can calculate the natural frequency (ωn) using the formula ωn = (4 / (ζ * Tp)). Finally, we can determine the value of Kcp by equating ωn^2 = 5Kcp. By substituting the given values, Kcp is approximately 2.14.

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The total interest you will earn in 30 years is approximately $241.61.

To calculate the total interest earned in 30 years, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt) - P
Where:
A = the future value of the investment
P = the principal amount (initial deposit)
r = the annual interest rate (in decimal form)
n = the number of times the interest is compounded per year
t = the number of years
In this case, the principal amount is $200, the annual interest rate is 3% (or 0.03 as a decimal), the interest is compounded monthly (so n = 12), and the time period is 30 years (so t = 30).
Plugging in these values into the formula:
A = 200(1 + 0.03/12)^(12*30) - 200
Now we can simplify and calculate:
A = 200(1.0025)^(360) - 200
A = 200(2.208040033) - 200
A ≈ 441.6080066 - 200
A ≈ 241.6080066

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Answer:

the answer is 1

Step-by-step explanation:

x2 equal to 1 by 28 and xby 2root7 equal to 1by 28 so are neglected

Answer:

A

Step-by-step explanation:

Answer: A. -10

Step-by-step explanation: