5) which expression is equivalent to
(3x² - 6x - 12)

A) X²-2x - 4
B) x² + 5x - 8
C) 2x²- 4x - 8
D) 2x² - 5x - 4​

The one example of absolute value function is x =|y| , and the graph is sketched below .

What is Absolut value Function ?

The absolute value function is defined as a function in algebra that consists of the variable in the absolute value bars. The general form of absolute value function is written as f(y) = a |y - h| + k .

let the absolute value function be : x = |y|  ;

we put y = -1 , we get ⇒ x = 1  ;

we put y = 1 , we get ⇒ x = 1 ;

we put y = 0 , we get ⇒ x = 0 ;

from the above points we observe that , what ever we put in the function , the result "x" is always positive .

Therefore , the graph of the function x = |y| , is a V shaped graph that faces Right .

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The needed coordinate of Y when the sequence of transformations, R90° ° Tx-axis, is used on  ΔXYZ to make ΔX''Y''Z' is (0, 3)

The process of transformation involves the implementation of a fresh range of mathematical coordinates which are expressed as alternative functions of the initial coordinates.

A rotation 90 can be represented by the formula (x, y) —>  (-y, x)

Note that the there in the question, the coordinate Y is (3, 0)  Of the coordinate is transformed by 90degrees, the given new coordinate will be (0, 3) to (3,0)

So:

3 is the x point.

0 is the y point.

When you replace these two points (switch places) Hence, the x coordinate is 0 and the y coordinate is 3 giving us  (3,0)

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If the coordinates of Y'' are (3, 0), then the coordinates of Y is (0, 3)

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

The sequence of transformations:

This means that we rotate by 90 degrees and we reflect the triangle across the x-axis

The rule of 90° clockwise rotation is (x,y) = (y,-x)

The rule fo rx-axis is (x, -y)

When combined, we have

(x,y) = (y,-x) = (y, x)

using the above as a guide, we have the following:

If the coordinates of Y'' are (3, 0), then the coordinates of Y is (0, 3)

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The correct answer is option A. 2 1/8 when reduced to the lowest terms.

To subtract 3 1/4 - 1 1/8, we need to convert the fractions to a common denominator. The common denominator for 3 1/4 and 1 1/8 is 8. To convert 3 1/4 to 8, we multiply both the numerator and denominator by 2, resulting in 6/8. To convert 1 1/8 to 8, we multiply both the numerator and denominator by 8, resulting in 8/8.

Now we have two fractions with a common denominator of 8. To subtract them, we subtract the numerators and keep the same denominator. We have 6/8 - 8/8, which is -2/8. To reduce this fraction to the lowest terms, we divide the numerator and denominator by the greatest common factor (GCF), which is 2. -2/8 divided by 2 is -1/4. Finally, we add -1/4 to 1 1/8 to get the answer 2 1/8.

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All subjects or objects whose characteristics are being studied.

In statistics, a population consists of all subjects or objects whose characteristics are being studied. This means that a population can be defined as a group of individuals, objects, or events that have something in common.

For example, if you are conducting a survey on the opinions of people in a city, the population would be all the people living in the city. If you are studying the behavior of cats, then your population would be all cats. In short, the population is the group of individuals or objects that you are interested in studying.

In addition, the population can be further broken down into subgroups, such as males and females, different age groups, geographical regions, and so on. This is known as stratifying the population and can help researchers to better understand the characteristics of their population and make more accurate conclusions.

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Answer:

Give brainliest first then I’ll give the answer

Step-by-step explanation:

The solution to the system is x = 2 and y = 6, represented as the ordered pair (2, 6). This corresponds to option (B) in the answer choices.

To solve the system using substitution, we'll substitute the value of one variable from one equation into the other equation and solve for the remaining variable.

Given the system:

x + y = 8

y = 3x

Substituting the value of y from the second equation into the first equation, we have:

x + (3x) = 8

4x = 8

x = 2

Now, substitute the value of x into the second equation to solve for y:

y = 3(2)

y = 6

Therefore, the solution to the system is (2, 6). Option (B) is the correct answer.

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Answer:

\(\large\boxed{\tt 18a+42}\)

Step-by-step explanation:

\(\textsf{We are asked to simplify the given expression.}\)

\(\textsf{Per similar problems, we should use the \underline{Distributive Property}.}\)

\(\large\underline{\textsf{What is the Distributive Property?}}\)

\(\boxed{\begin{minipage}{25 em} \\ \underline{\textsf{\large Distributive Property;}} \\ \\ \textsf{Distributive Property is a property that allows us to multiply the term to the left of the parentheses into the terms inside the parentheses.} \\ \\ \underline{\textsf{\large Example;}} \\ \tt a(b+c)=ab+ac \\ \textsf{Per this example, a will multiply with the terms b and c.}\end{minipage}}\)

\(\large\underline{\textsf{Simplifying the Expression;}}\)

\(\textsf{For our given expression, let's use the Distributive Property.}\)

\(\underline{\textsf{Use the Distributive Property;}}\)

\(\tt 6 (3a + 7) \rightarrow (6 \times 3a) + (6 \times 7) \rightarrow \large\boxed{\tt 18a+42}\)

Hello and greetings AtticusR9000.

To solve this exercise, we apply the distributive property, which is a mathematical rule that establishes that the multiplication of a number by the addition or subtraction of two or more numbers is equal to the addition or subtraction of the multiplication of that number by each of the numbers. that are being added or subtracted. In other words, if we have three numbers a, b and c, then the distributive property can be written as:

a × (b + c) = (a × b) + (a × c)

or also as:

a × (b - c) = (a × b) - (a × c)

This means that the multiplication of the number "a" can be distributed through the addition or subtraction of the numbers "b" and "c" to obtain the same result as if "a" were multiplied by "b" and "a" by "c" and then add or subtract the results. The distributive property is fundamental in mathematics and is used in numerous algebraic and arithmetic operations.

Now we solve by applying the distributive property:

a × (b + c) = (a × b) + (a × c)

6(3a + 7) = (6 × 3a) + (6 × 7)

18a + 42

Therefore, the solution of exercise 6(3a+7) is 18a+42.

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Step-by-step explanation:

22000

.

.

.

.

.

is the correct answer

Answer:

21,000

Step-by-step explanation:

254 is less than 500 so you would round downwards. Or you can look at is as 2 (representing the 254) is less than 5 (500)

Answer:

I think it’s independent

Step-by-step explanation:

Answer:

Step-by-step explanation:

perpendicular is 90 degrees or inverse slope of that point

y = -1/4x -1

so the inverse slope of -1/4 is 4

now the other equation is

y = 4x - 1

So the two equations are

y = -1/4x -1

y = 4x - 1

Answer:

Step-by-step explanation:

All lines perpendicular to the line y =  -¹/₄ x - 1 will have a gradient that is the negative reciprocal (4).

∴ any line with a gradient of 4 would be perpendicular

examples include but are not limited to:

    y = 4 x - 1

    y = 4 x - 10

    y = 4 x - 11

The height of the cylinder is \(3 inch\)

Based on the attached figure,

Volume of the cylinder = 282.7 square inches

Radius of the cylinder =5 inches.

The height of the cylinder = ?

The volume of the cylinder  can be found with the formula as :

\(V=pi r^{2} h\)

\(h=\frac{V}{pi r^{2} } \\\\h = \frac{282.7}{3.142 * 5^{2} } \\\\=3 inch\)

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The corresponding graph is attached below

Answer:

(8 * 4) - 1/2(12 + 10 + 16)

Step-by-step explanation:

To determine the area of the triangle RST;

Draw a rectangle to enclose the triangle RST, after drawing the rectangle, 3 other triangles are formed. The sum of the areas of the 3 triangles formed is then subtracted from the area of the rectangle ;

The area of the rectangle depicts the entire area of the entire figure.

Area of rectangle = (length * width)

Area of triangle = 1/2 * base * height

Area of rectangle = (8 * 4)

Area of triangle 1 = 1/2 (3*4) = 1/2 * 12

Area of triangle 2 = 1/2 (2*5) = 1/2 * 10

Area of triangle 1 = 1/2 (2*8) = 1/2 * 16

Hence, Area of RST ;

Area of rectangle - (area of (triangle 1 + triangle 2 + triangle 3))

(8 * 4) - [(1/2 * 12) + (1/2 * 10) + (1/2 * 16)]

(8 * 4) - 1/2(12 + 10 + 16)

Answer:

C----(8 * 4) - 1/2(12 + 10 + 16)

Step-by-step explanation:

trust

Answer:

b. 5.

Step-by-step explanation:

There are 7 numbers in the data set so the mean =

=  (9 + 4 + 9 + 2 + 8 + 2 + 1) / 7

= 35/7

= 5.

Answer:

Ummm

Step-by-step explanation:

So what do you need help with?

Answer:

100

Step-by-step explanation:

Area of a triangle is b*h/2

So it's 10*20/2 which is 100

The possible values of two consecutive even integers, of which the sum of their squares is 1684, are 28 and 30 for positive integers, while for negative integers, they are  -28 and -30.

The difference between two consecutive even integers is 2.

Let the integers be a and (a+2). Then,

a² + (a + 2)² = 1684

a² + a² + 4a + 4 = 1684

2a² + 4a - 1680 = 0

a² + 2a -840 = 0

Hence, we get a quadratic equation.

There are three methods of solving a quadratic equations: by factoring, completing the square, and by using the abc formula.

Use the factoring method:

a² + 2a -840 = (a - 28) (a + 30)

a = 28  and a = -30

Hence, if the integers are positive, they are: 28 and 30.

If the integers are negative, they are -28 and -30.

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Answer:

78

Step-by-step explanation:

because I know everything

(a) The real discrete Fourier transform (DFT) is calculated for the given data set to analyze the helicopter's acoustic signature.

(b) To obtain the ck values and illustrate the relative size of each term in the Fourier series, we calculate the magnitude of each coefficient and plot their amplitudes on a bar graph against the corresponding frequency component, k.

To analyze the helicopter's acoustic signature, the real DFT is computed for the provided data set. The DFT transforms the time-domain measurements of acoustic pressure into the frequency domain, revealing the different frequencies present and their corresponding amplitudes. This analysis helps in understanding the spectral characteristics of the helicopter's acoustic signature and identifying prominent frequency components.

Using the Fourier series representation, the amplitudes (ck's) of the different frequency components in the Fourier series are determined. These amplitudes represent the relative sizes of each term in the series, indicating the contribution of each frequency component to the overall acoustic signature. By plotting the amplitudes on a bar graph, the relative strengths of different frequency components become visually apparent, enabling a clear comparison of their importance in characterizing the helicopter's acoustic signature.

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Answer:

  A.  60 ft·lb

Step-by-step explanation:

You want the work done lifting a 15-lb flower pot to a height of 4 ft.

Work is the product of force and distance. When the pot is raised 4 ft, the work done is ...

  W = F·d

  W = (15 lb)(4 ft) = 60 ft·lb

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The largest positive integer $n$ for which the given equation holds true for all real numbers $a_1, a_2, \dots, a_{n-1}$ (where $a_{n-1} \neq 0$) is $n = 3$.

We are given the equation $a_{n-1}x^2 - 2x\sqrt{a_1^2a_2^2\dots a_{n-1}^2}(a_1a_2\dots a_{n-1}) = 0$, and we want to determine the largest $n$ for which this equation holds true for any choice of $a_1, a_2, \dots, a_{n-1}$.

If we simplify the equation, we can rewrite it as $x^2 - 2x\left|a_1a_2\dots a_{n-1}\right| = 0$. From this equation, we can observe for any non-zero value of $a_1a_2\dots a_{n-1}$, the equation will always hold true, regardless of the value of $x$. However, when $a_1a_2\dots a_{n-1} = 0$, the equation becomes $x^2 = 0$, which implies that $x = 0$.

Therefore, for $n > 3$, we can find values of $a_1, a_2, \dots, a_{n-1}$ for which the equation does not hold true, making $n = 3$ the largest positive integer for which the equation holds true for all $a_1, a_2, \dots, a_{n-1}$.

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Answer:

\(Density = 1.094g/cm^3\)

Step-by-step explanation:

Given

\(Length = 17.7cm\)

\(Width = 8.3cm\)

\(Height = 13.0cm\)

\(Mass = 2090g\)

See attachment

Required

Determine the density of the wood

First, we calculate the volume of the wood.

\(Volume = Length * Width * Height\)

Substitute values for Length, Width and Height

\(Volume = 17.7cm * 8.3cm * 13.0cm\)

\(Volume = 1909.83cm^3\)

The density is:

\(Density = \frac{Mass}{Volume}\)

\(Density = \frac{2090g}{1909.83cm^3}\)

\(Density = 1.094g/cm^3\) --- approximated

Answer:

164.6 degrees

Step-by-step explanation:

The Angles add up to 180 degrees so do 180-15.4

Answer:

there the same ratio because there both offering the same ratio of of there number

3x10=30 ratio : 10

2x10=20 ratio: 10

Step-by-step explanation:

Answer:

7.17 + 25.8 = 32.97

Answer:

7.17+25.8= 32.97

the answer is above

The probability value of (m, n) is (1, 2^1005).

Let n be a positive odd integer. We are asked to find the probability that its reciprocal gives a terminating decimal. This is equivalent to saying that the only prime factors of n are 2 and 5 because any other prime factor will yield a repeating decimal.

If n is less than 2010, then its only possible prime factors are 3, 7, 11, ..., 2009, since all primes greater than 2009 are greater than n. We want n to have no prime factors other than 2 and 5. There are 1005 odd integers less than 2010.

We want to count how many of these have no odd prime factors other than 3, 7, 11, ..., 2009. This is equivalent to counting how many subsets there are of {3, 7, 11, ..., 2009}. There are 1004 primes greater than 2 and less than 2010. Each of these primes is either in a subset or not in a subset. Thus, there are 2^1004 subsets of {3, 7, 11, ..., 2009}, including the empty set.

Thus, the probability is:

P = (number of subsets with no odd primes other than 3, 7, 11, ..., 2009) / 2^1004

We can count this number using the inclusion-exclusion principle. Let S be the set of odd integers less than 2010. Let Pi be the set of odd integers in S that are divisible by the prime pi, where pi is a prime greater than 2 and less than 2010. Let Pi,j be the set of odd integers in S that are divisible by both pi and pj, where i < j.

Then, the number of odd integers in S that have no prime factors other than 2 and 5 is:

|S - ⋃ Pi + ⋃ Pi,j - ⋃ Pi,j,k + ...|

where the union is taken over all sets of primes with at least one element and less than or equal to 1005 elements.

By the inclusion-exclusion principle:

|S - ⋃ Pi + ⋃ Pi,j - ⋃ Pi,j,k + ...| = ∑ (-1)^k ⋅ (∑ |Pi1,i2,...,ik|)

where the outer summation is from k = 0 to 1005, and the inner summation is taken over all combinations of primes with k elements.

This simplifies to:

(1/2) ⋅ (2^1004 + (-1)^1005)

Thus, the probability is: P = (1/2^1004) ⋅ (1/2) ⋅ (2^1004 + (-1)^1005) = 1/2 + 1/2^1005. Hence, (m, n) = (1, 2^1005).

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Complete question:

If m/n is the probability that the reciprocal of a randomly selected positive odd integer less than 2010 gives a terminating decimal, with m and n being relatively prime positive integers. what is probability value of m and n?

The probability value of (m, n) is (1, 2^1005).This is equivalent to saying that the only prime factors of n are 2 and 5 because any other prime factor will yield a repeating decimal.

Let n be a positive odd integer. We are asked to find the probability that its reciprocal gives a terminating decimal. This is equivalent to saying that the only prime factors of n are 2 and 5 because any other prime factor will yield a repeating decimal.

If n is less than 2010, then its only possible prime factors are 3, 7, 11, ..., 2009, since all primes greater than 2009 are greater than n. We want n to have no prime factors other than 2 and 5. There are 1005 odd integers less than 2010.

We want to count how many of these have no odd prime factors other than 3, 7, 11, ..., 2009. This is equivalent to counting how many subsets there are of {3, 7, 11, ..., 2009}. There are 1004 primes greater than 2 and less than 2010. Each of these primes is either in a subset or not in a subset. Thus, there are 2^1004 subsets of {3, 7, 11, ..., 2009}, including the empty set.

Thus, the probability is:

P = (number of subsets with no odd primes other than 3, 7, 11, ..., 2009) / 2^1004

We can count this number using the inclusion-exclusion principle. Let S be the set of odd integers less than 2010. Let Pi be the set of odd integers in S that are divisible by the prime pi, where pi is a prime greater than 2 and less than 2010. Let Pi,j be the set of odd integers in S that are divisible by both pi and pj, where i < j.

Then, the number of odd integers in S that have no prime factors other than 2 and 5 is:

|S - ⋃ Pi + ⋃ Pi,j - ⋃ Pi,j,k + ...|

where the union is taken over all sets of primes with at least one element and less than or equal to 1005 elements.

By the inclusion-exclusion principle:

|S - ⋃ Pi + ⋃ Pi,j - ⋃ Pi,j,k + ...| = ∑ (-1)^k ⋅ (∑ |Pi1,i2,...,ik|)

where the outer summation is from k = 0 to 1005, and the inner summation is taken over all combinations of primes with k elements.

This simplifies to:

\((1/2) * (2^{1004} + (-1)^1005)\)

Thus, the probability is: P = \((1/2)^{1004}* (1/2) *(2^{1004} + (-1)^{1005}) = 1/2 + 1/2^{1005}.\)

Hence, (m, n) = (\(1, 2^{1005\)).

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Answer:

Answer: $17.22 was spent on a pass and $8.94 on lunch for each student and that implies a total of $26.16 was spent on each student

Tell me if wrong. :) Hope it helps!

Step-by-step explanation:

Answer:

C y = 3/4x + 12

Step-by-step explanation:

The probability of getting 2 tails is option (b) 37.5%

The event of "2 tails" can occur in three possible outcomes: {htt, tht, tth}, so the probability of getting 2 tails is the sum of the probabilities of these three outcomes.

Each toss of a fair coin is independent and has a 50% chance of landing tails. Therefore, the probability of each of these three outcomes is:

P(htt) = 1/2 × 1/2 × 1/2 = 1/8

P(tht) = 1/2 × 1/2 × 1/2 = 1/8

P(tth) = 1/2 × 1/2 × 1/2 = 1/8

So, the probability of getting 2 tails is:

P(2 tails) = P(htt) + P(tht) + P(tth) = 1/8 + 1/8 + 1/8 = 3/8

= 0.375

0.375 multiplied by 100% gives:

P(2 tails) = 37.5%

Therefore, the correct option is (b) 37.5%

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Answer:

Part 1: \(P(t)=3(1.4142)^t\)

Part 2: There are 24 people infected

Part 3: P(48)=50,331,648

More than 50 million people are infected after 2 days

Step-by-step explanation:

Exponential Growth

The natural growth of some magnitudes can be modeled by the equation:

\(P(t)=P_o(1+r)^t\)

Where P(t) is the actual amount of the magnitude, Po is its initial amount, r is the growth rate and t is the time.

We know the Zika virus started with Po=3 people infected. The number of people infected doubles every 2 hours, which means that for t=2 hours, P(2)=6, thus:

\(6=3(1+r)^2\)

Dividing by 3:

\((1+r)^2=2\)

Solving for 1+r:

\(1+r=\sqrt{2}\)

1+r=1.4142

Part 1:

The equation to model the situation is:

\(\boxed{P(t)=3(1.4142)^t}\)

Part 2:

After t=6 hours:

\(P(6)=3(1.4142)^6\)

P(6)=24

There are 24 people infected

Part 3:

After 2 days, t=2*24 = 48 hours:

\(P(48)=3(1.4142)^48\)

P(48)=50,331,648

More than 50 million people are infected after 2 days