The function g is given in three equivalent forms.
Which form most quickly reveals the zeros (or "roots") of the function?

A.g(x)=3(x+1)^2 −12
B.g(x)=3x^2+6x−9
C.g(x)=3(x+3)(x−1)

AND WRITE ONE OF THE ZEROS
X=

Answer: c, 84

Step-by-step explanation:

The scaling property of the Fourier transforms states that if we scale the function g(t) by a constant factor c, then its Fourier transform G(jw) will be scaled by a factor of 1/|c| and shifted by a factor of c.

This property can be expressed mathematically as follows:

F{g(ct)} = ∫ g(ct) \(e^{(-jw t)}\) dt

Let u = ct, then du/dt = c, and dt = du/c

Substituting this in the above equation, we get:

F{g(ct)} = ∫ g(u) \(e^{(-jw u/c)}\) du/c

= (1/c) ∫ g(u) e^(-jw u/c) du

= G(jw/c) / |c|

Therefore, we can conclude that the Fourier transform of a scaled function is obtained by scaling the Fourier transform of the original function by a factor of 1/|c|. This property is useful in signal processing and communication systems where signals are often scaled before transmission or processing.

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Answer: y = (5x)^2

Step-by-step explanation: You're finding the inverse.

Answer:

Could you repost this question with a picture of the circle? I'd like to help, but I can't answer without seeing the picture.

The exponential function that satisfies the given conditions is given as follows:

\(f(t) = 4e^{1.099t}\)

The format of the exponential function for this problem is given as follows:

f(t) = 4e^(kt).

In which k is the exponential growth rate.

After five hours, there was 972 bacteria, meaning that when t = 5, f(t) = 972, hence the growth rate is obtained as follows:

\(972 = 4e^{5k}\)

\(e^{5k} = 243\)

5k = ln(243)

k = ln(243)/5

k = 1.099.

Meaning that the function is defined as follows:

\(f(t) = 4e^{1.099t}\)

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The half-range cosine expansion of f(x) = sin(x), for 0 < x < π, simplifies to f(x) = (2/π).

To find the half-range cosine expansion of the function f(x) = sin(x) for 0 < x < π, we can utilize the half-range Fourier series expansion. The half-range expansion represents the function as a sum of cosine terms.

The half-range Fourier series expansion of f(x) can be expressed as:

f(x) = a₀/2 + ∑[n=1 to ∞] (aₙ * cos(nx))

To find the coefficients a₀ and aₙ, we can use the following formulas:

a₀ = (2/π) ∫[0 to π] f(x) dx

aₙ = (2/π) ∫[0 to π] f(x) * cos(nx) dx

Let's calculate the coefficients:

a₀ = (2/π) ∫[0 to π] sin(x) dx

= (2/π) [-cos(x)] [0 to π]

= (2/π) [-cos(π) + cos(0)]

= (2/π) [1 + 1]

= 4/π

For aₙ, we have:

aₙ = (2/π) ∫[0 to π] sin(x) * cos(nx) dx

= 0 [since the integrand is an odd function integrated over a symmetric interval]

Now, we can rewrite the half-range cosine expansion of f(x):

f(x) = (4/π) * (1/2) + ∑[n=1 to ∞] (0 * cos(nx))

= (2/π) + 0

Therefore, the half-range cosine expansion of f(x) = sin(x), for 0 < x < π, simplifies to:

f(x) = (2/π)

In this expansion, all the cosine terms have coefficients of zero, and the function is represented solely by the constant term (2/π).

It's worth noting that the half-range cosine expansion is valid for the given interval (0 < x < π), and outside this interval, the function would need to be extended or expressed differently.

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Answer:

10 6/10

Step-by-step explanation:

since the 6 is in the tenths place we know the denomiter is going to be 10. The 10 infront of the 6 is a whole number

Answer:

ik this

Step-by-step explanation:

i believe its 180

Answer: B) 115

Step-by-step explanation: i hop this help if not sorry :(

Answer:

the one that looks like a v

Step-by-step explanation:

bc for every y-input, there is only one output-x

Answer:

The correct option is a) 3n - 4 = 15

Step-by-step explanation:

The product of 3 and a number means 3 multiplied by a number (n)

So it'll be 3*n or simply 3n

Now, it says 4 less than the product

So 4 less than 3n

That is equal to 3n minus 4 or 3n -4

So we come to the conclusion that

3n - 4 = 15

Hope this helps!

The polynomial function \(\(f(x) = 2(x^2+3)(x+1)^2\)\) has zeros at -3 with multiplicity 1, and -1 with multiplicity 2. The graph of the function crosses the x-axis at -3 and -1.

To find the zeros and their multiplicities, we set \(\(f(x)\)\) equal to zero and solve for \(\(x\).\)

Setting \(\(f(x) = 0\),\) we have:

\(\[2(x^2+3)(x+1)^2 = 0\]\)

Since the product of two factors is zero, at least one of the factors must be zero. Thus, we solve for \(\(x\)\) in each factor separately:

1. \(\(x^2 + 3 = 0\):\)

  This equation does not have real solutions since the square of a real number is always non-negative. Therefore, this factor does not contribute any real zeros.

2. \(\(x + 1 = 0\):\)

  Solving for \(\(x\), we find \(x = -1\).\) This gives us a zero at -1 with multiplicity 1.

Since the factor \(\((x+1)^2\)\) is squared, the zero -1 has a multiplicity of 2.

Therefore, the zeros for the polynomial function are -3 with multiplicity 1 and -1 with multiplicity 2. The graph of the function crosses the x-axis at both zeros.

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97.04 mg Initial mass = 48 mg, Mass after 7 weeks = 48 mg * (1/2)^(12.25) Half-life of the goo in minutes = 120 / (log(37/296) / log(1/2)) The artifact was made approximately 22920 years ago.

Question 26:

The half-life of Radium-226 is 1590 years. To determine how many milligrams will remain after 3000 years, we can use the formula:

N(t) = N₀ * (1/2)^(t/T),

where:

N(t) is the remaining amount after time t,

N₀ is the initial amount,

t is the elapsed time, and

T is the half-life.

Given that the initial amount is 200 mg, the elapsed time is 3000 years, and the half-life is 1590 years, we can substitute these values into the formula:

N(3000) = 200 * (1/2)^(3000/1590).

Calculating this, we find:

N(3000) ≈ 200 * (1/2)^(1.8862) ≈ 200 * 0.4852 ≈ 97.04.

Therefore, approximately 97.04 mg of Radium-226 will remain after 3000 years.

Question 27:

The half-life of Palladium-100 is 4 days. We can use the half-life formula again to determine the initial mass and the mass after 7 weeks.

1. Initial mass:

After 12 days, the sample of Palladium-100 has been reduced to 6 mg. We need to determine how many half-lives have passed in 12 days to find the initial mass.

t = (12 days) / (4 days/half-life) = 3 half-lives.

Let's denote the initial mass as M₀. We can use the formula:

M(t) = M₀ * (1/2)^(t/T).

Substituting the values, we have:

6 mg = M₀ * (1/2)^(3).

Solving for M₀:

M₀ = 6 mg * 2^3 = 48 mg.

Therefore, the initial mass of the sample was 48 mg.

2. Mass after 7 weeks (49 days):

To find the mass after 7 weeks, we need to determine how many half-lives have passed in 49 days:

t = (49 days) / (4 days/half-life) = 12.25 half-lives.

Using the formula, we can calculate the mass after 7 weeks:

M(49 days) = M₀ * (1/2)^(12.25).

Substituting the initial mass we found earlier:

M(49 days) = 48 mg * (1/2)^(12.25).

Calculating this value will give us the mass after 7 weeks.

Question 28:

To find the half-life of the radioactive goo, we can use the formula:

N(t) = N₀ * (1/2)^(t/T),

where N(t) is the remaining amount at time t, N₀ is the initial amount, t is the elapsed time, and T is the half-life.

Given that the initial amount is 296 grams and the amount after 120 minutes is 37 grams, we can substitute these values into the formula:

37 g = 296 g * (1/2)^(120/T).

To find the half-life T, we can rearrange the equation:

(1/2)^(120/T) = 37/296.

Taking the logarithm of both sides, we have:

120/T * log(1/2) = log(37/296).

Solving for T:

T = 120 / (log(37/296) / log(1/2)).

Calculate the value of T using this equation to find the half-life of the radioactive goo in minutes.

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It would be closest rounded to about 30.25/30.26. Would be better to know the radius rather than the circumference.

Answer:

DG = 31.75

Step-by-step explanation:

The question is incomplete; however, I'll answer your question using attached image.

From the attachment,

<G = 72° and DO = 8.2

Required

DG?

To get the length of side DG, We have to look for a trigonometric ratio that relates DG, DO and <G together.

DG represents the hypothenus of the triangle;

DO represents the opposite of the triangle;

The two sides are bound by the sine function.

i.e.

Sin72° = DO/DG

Sin72° = 8.2/DG

Multiply both sides by DG

DG * Sin72 = 8.2/DG * DG

DG * Sin72 = 8.2

Sin72 = 0.2538

So, DG * Sin72 = 8.2 becomes

DG * 0.2538 = 8.2

Divide both sides by 0.2583

DG * 0.2583/0.2583 = 8.2/0.2583

DG = 8.2/0.2583

DG = 31.746031746

DG = 31.75 --- Approximated

Answer:

Step-by-step explanation:

30  30 x 3 = 90

x 3

90  

first  multiply 4 x 5 = 20 bring down 0 then multiply 4 x 2 = 8 then add+2= 10

25 x 4 = 100

12 x 15 = 180

Answer:

6 dollars

Step-by-step explanation:

Lets say the price of a single hamburger is some variable h, and the price of a drink is some variable d. We can make a system of equations with the prices:

5h+d=17

2h+6d=25

Now, you can multiply the first equation by 6 to leave you with a new system of equations:

30h+6d=102

2h+6d=25

Subtracting the second equation from the first, you are left with:

28h=77

h=2.75

Plugging this back into the first equation gives:

5(2.75)+d=17

13.75+d=17

d=3.25

Now that you know the price of an individual hamburger and drink, you know that the total combined cost is:

h+d=2.75+3.25=$6

First we find the slope of the line 2x−3y+8=0 by placing it into slope intercept form:

2x−3y+8=0

⇒−3y=−2x−8

⇒3y=2x+8

⇒y=  

3

2

​

x+  

3

8

​

Therefore, the slope of the line is m=  

3

2

​

.

Now since the equation of the line with slope m passing through a point (x  

1

​

,y  

1

​

) is

y−y  

1

​

=m(x−x  

1

​

)

Here the point is (2,3) and slope is m=  

3

2

​

, therefore, the equation of the line is:

y−3=  

3

2

​

(x−2)

⇒3(y−3)=2(x−2)

⇒3y−9=2x−4

⇒2x−3y=−9+4

⇒2x−3y=−5

Hence, the equation of the line is 2x−3y=−5.

Answer:

y=2/3x-11/3

Step-by-step explanation:

Hi there!

We are given the equation 2x-3y=9 and we want to write an equation that is parallel to it and that passes through (4,-1)

Parallel lines have the same slopes

So we need to first find the slope of 2x-3y=9

We can do this by converting the equation of the line from standard form (ax+by=c where a, b, and c are integers) to slope-intercept form (y=mx+b, where m is the slope and b is the y intercept)

To do this, we need to isolate y on one side

2x-3y=9

subtract 2x from both sides

-3y=-2x+9

divide both sides by -3

y=2/3x-3

as 2/3 is in the place where m is, 2/3 is the slope of the line

It's also the slope of the line parallel to it that passes through (4,-1).

Here's the equation of that line so far:

y=2/3x+b

now we need to find b

as the line will pass through the point (4,-1), we can  4 as x and -1 as y in order to solve for b

-1=2/3(4)+b

multiply

-1=8/3+b

subtract 8/3 to both sides

-11/3=b

Substitute -11/3 as b into the equation

y=2/3x-11/3

There's the equation

Hope this helps!

The empirical formula of the uranium chloride is UCl₁.

To determine the empirical formula of the uranium chloride, we need to calculate the mole ratio of uranium to chloride in the compound.

First, we need to find the moles of uranium and chloride in the given sample.

Mass of uranium (U) = 0.176 g

Atomic mass of uranium (U) = 238.03 g/mol

Moles of uranium (U) = mass / atomic mass = 0.176 g / 238.03 g/mol ≈ 0.0007387 mol

Since the molar ratio between uranium and chloride is 1:1 in the empirical formula, the moles of chloride will also be approximately 0.0007387 mol.

Next, we can convert the moles of chloride to grams using the molar mass of chloride.

Mass of chloride (Cl) = 0.255 g - 0.176 g = 0.079 g

Now, we can calculate the molar mass of chloride (Cl).

Molar mass of chloride (Cl) = mass / moles = 0.079 g / 0.0007387 mol ≈ 107 g/mol

The empirical formula of the uranium chloride can be determined by dividing the subscripts of each element by their greatest common divisor (GCD). In this case, the GCD of 1 and 1 is 1.

Therefore, the empirical formula of the uranium chloride is UCl₁.

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Aggregate Demand (AD) is a macroeconomic concept that represents the total demand for goods and services in an economy. The X factor in the AD equation represents exports, which are an important part of the economy.

AD is calculated by adding up the individual components of demand, which include consumer spending (C), investment spending (I), government spending (G), and net exports (X-M). The X-M component represents the difference between exports (X) and imports (M).

The X component in the equation represents exports, which are the goods and services produced domestically and sold to foreign countries. Exports are an important part of the economy as they generate income and create jobs. The M component in the equation represents imports, which are the goods and services purchased from foreign countries and consumed domestically. Imports can have a negative impact on the economy as they represent a drain on resources and can lead to a trade deficit. The X factor in the equation is used to represent exports because it is a variable that can change over time. Factors that can affect exports include exchange rates, tariffs, and global demand for certain products. If the exchange rate between two currencies changes, it can make exports more or less expensive for foreign buyers, which can affect the level of exports. Tariffs are taxes on imports, which can make domestic products more competitive in foreign markets.

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Answer:

359 is her payment

Step-by-step explanation:.

Answer:

359 in total :)

The solution of the system using elimination method is x = 3 and y = 3

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

To solve this problem we must establish the equations according to the given data and solve the operations:

4x + 2y = 18       (1)

2x + 3y = 15      (2)

We have two equations with two unknowns, using the elimination method we have to multiply the (2) by -2 and we get:

-2*(2x + 3y) = 15

-4x - 6y = -30    

Now we solve the system:

4x  + 2y   = 18       (1)

-4x - 6y   = -30      (2)

0x   -4y   = -12

Clearing the variable:

-4y = -12

Multiply by (-1) we have:

4y = 12

y = 12/4

y = 3

Replacing the value of y in equation (1) we get the value of x:

4x + 2y = 18       (1)

4x +2*3 = 18

4x + 6 = 18

4x = 18-6

4x = 12

x = 12/4

x = 3

Both x and y are equal to 3 = (3 , 3)

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Correctly written question:

What is the solution of the system? Use the elimination method.

4x + 2y = 18

2x + 3y = 15

If no two men are to sit next to each other, there are 144 ways to arrange four men and four women at a round table.

Combinations are mathematical operations that count how many possible combinations there are for a given set of components, regardless of the order in which they were chosen. One can choose the components of combos in any order.

First, arrange the four women so that there is a free seat between each pair of them at the round table. These four women can be seated at the round table in 3 different ways, for a total of 6 possible arrangements. This is written as 3! = 6.

Then, the four vacant seats will be occupied by the four men and this is written as ⁴P₄=4!=24. Then, the required number of ways to seat the two men who are not adjacent to each other is 6×24=144 ways.

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To make the function continuous on the interval (-infinity,infinity), we need to make sure that the two expressions for f(x) match at x=7. In other words, we need to have:

lim as x approaches 7 from the left of f(x) = lim as x approaches 7 from the right of f(x)

Using the given expressions for f(x), we can calculate these limits as:

lim as x approaches 7^- of f(x) = lim as x approaches 7^- of (cx+8) = 7c + 8
lim as x approaches 7^+ of f(x) = lim as x approaches 7^+ of (cx^2-8) = c(7^2)-8 = 49c - 8

Setting these equal to each other and solving for c, we get:

7c + 8 = 49c - 8
56c = 16
c = 2/7

Therefore, the value of the constant c that makes the function continuous on (-infinity,infinity) is c = 2/7.

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In this case, 0 is contained in the intervals [0, 5),and [0, 5]

In the given intervals, we can determine which ones contain the specified numbers as follows:

a) 0 is contained in the intervals [0, 5) and [0, 5] because the square bracket [ ] indicates the endpoint is included.

b) 1 is contained in the intervals (0, 5), (0, 5], [0, 5), [0, 5], (1, 4], and (2, 3) because it lies within the range of these intervals.

c) 2 is contained in the intervals (0, 5), (0, 5], [0, 5), [0, 5], (1, 4], [2, 3], and (2, 3) because it either lies within the range or is an included endpoint.

d) 3 is contained in the intervals (0, 5), (0, 5], [0, 5), [0, 5], (1, 4], [2, 3], and (2, 3) for the same reasons as 2.

e) 4 is contained in the intervals (0, 5), (0, 5], [0, 5), [0, 5], and (1, 4] because it lies within the range or is an included endpoint.

f) 5 is contained in the intervals (0, 5] and [0, 5] because the square bracket [ ] indicates the endpoint is included.

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So

Diagonals of Rhombus intercect at 90°.

So

Using angle sum property

\(\\ \tt\longmapsto 90+27+<RUS=180\)

\(\\ \tt\longmapsto <RUS=180-117=63°\)

Answer:

Step-by-step explanation:

The diagonals of the kite are perpendicular: RT ⊥ SU

RT is angle bisector of ∠SRU

∠RSU and ∠RUS are equal angles and are complementary with ∠SRT:

Katy's house is 8 kilometers from Pedro's house.Using the Pythagorean theorem, we can calculate the distance between Katy's house and Pedro's house

Since Katy would have to walk due north to get to Pedro's house and due east to get to Austen's house, we can visualize a right-angled triangle with Katy's house as the right angle. Let's label the distance between Katy's house and Pedro's house as x. According to the given information, the distance between Katy's house and Austen's house is 10 kilometers, and the distance between Austen's house and Pedro's house is 6 kilometers. Using the Pythagorean theorem, we can calculate the distance between Katy's house and Pedro's house:

x^2 + 6^2 = 10^2

x^2 + 36 = 100

x^2 = 100 - 36

x^2 = 64

x = √64

x = 8

Katy's house is 8 kilometers away from Pedro's house.we can visualize a right-angled triangle with Katy's house as the right angle.Using the Pythagorean theorem, we can calculate the distance between Katy's house and Pedro's house

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For this exercise we must correct the error of the given fraction, differentiating the properties of addition and multiplication, so:

1)This error occurs frequently because when simplifying in a multiplication or division it cannot be done in the operations of subtraction and addition.

2)As this error is very common, it has probably already occurred. But one way to resolve this is to pay attention and redo the math.

to understand this error we have to:

\(\frac{(3)(5)}{3} = 5\)

In the case of multiplication the 3 of the numerator can be simplified with the 3 of the denominator, the other case will be:

\(\frac{3+5}{3} = \frac{8}{5}\)

In the case of addition or subtraction, you should always keep the denominator.

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Fifty-three centimeters is equal to approximately 20.87 inches. To convert centimeters to inches, you need to multiply the number of centimeters by 0.3937.

Centimeters and inches are both units of measurement used to measure length. One centimeter is equal to 0.3937 inches, so to convert centimeters to inches you need to multiply the number of centimeters by 0.3937. For example, if you wanted to convert 10 centimeters to inches, you would multiply 10 by 0.3937, which would give you 3.937 inches. The same formula can be used to convert any number of centimeters to inches. In this example, we are converting 53 centimeters to inches. To do this, we would multiply 53 by 0.3937, which gives us 20.87 inches. This means that 53 centimeters is equal to approximately 20.87 inches. It is important to keep in mind that this conversion is an estimate, as the exact conversion may vary slightly due to rounding.

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Answer: Yes, all horizontal lines have slope of 0

Reason:

Recall that slope = rise/run

The rise tells us how far to go up or down. A horizontal line does neither. There's no change in y value.

So we have slope = rise/run = 0/run = 0, where "run" is any positive number you want. The run is how far to the right we go each time moving up or down.

Answer: Yes

Step-by-step explanation:

When you have a horizontal line it is flat and has no slope at all

____________________________________

So the slope = 0