If f(x) = 5x, what is f¹(x)?

f¹(x) = -5x
ƒ¹(x) = -1/5 x
f¹(x) = 1/5x
f¹(x) = 5x

The given equation is equivalent to (4x²+9)*(4x²-9) or (4x²+9)*(2x-3)*(2x+3). And the zero of the function are: [tex]\pm \frac{3}{2}[/tex] and [tex]\pm \frac{3}{2}i[/tex].

The quadratic function can represent a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.

For solving a quadratic function you should find the discriminant: D=b²-4ac and after that use this variable in the formula: [tex]x=\frac{-b\pm\sqrt{D} }{2a}[/tex].

In math, factoring or factorization is used to write an algebraic expression in factors. There are some rules for factorization.  One of them is a factor out a common term for example: x²-x= x(x-1), where x is a common term.

The question gives: [tex]16x^4-81=0[/tex], you can factor this equation. See below.

(4x²+9)*(4x²-9)

(4x²+9)*(2x-3)*(2x+3)

Therefore, you should choose one of options: (4x²+9)*(4x²-9) or (4x²+9)*(2x-3)*(2x+3).

Next step is to solve the given equation. Solving for  (4x²+9)*(2x-3)*(2x+3)=0, then:

For 2x-3=0

      x=3/2

For 2x+3=0

      x= -3/2

For 4x²+9=0

      4x²=-9

       x²= -9/4

      x = [tex]\pm \sqrt{\frac{-9}{4} }[/tex]

      x   =[tex]\pm \frac{3}{2}*\sqrt{-1 }\\ \\ \pm \frac{3}{2}*i[/tex]

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Answer:

17.5 hours

I hope this helps and you can give a brainliest!

Step-by-step explanation:

Given: time spent per day follows the arithmetic sequence 1,1.5,2... (for 7 terms) with first term 1 and common difference 0.5 (in hours)

Concept used: the total study time is the partial sum S7of the given arithmetic series.

Calculation: As the number of terms is small, it can be calculated by hand.

S7 = 1+1.5+2+2.5+3+3.5+4

S7= 17.5 hours

Conclusion: Total time spent after one week is 17.5 hours

Answer:

17 and 1/2 hours.

Step-by-step explanation:

this is an arithmetic series  with common difference 0.5 hours.

Number of hours after 7 days

= (n/2)[2a + (n -1)d]

= (7/2)(2*1 + (7-1)0.5)

= 3.5 * 5

= 17.5 hours

The length of the segment [tex]pt[/tex]is [tex]10[/tex] if the coordinates of [tex]p[/tex] and [tex]t[/tex] is [tex](-6 )and( 4)[/tex]

How can find the length of the segment ?

The coordinate of [tex]p=-6[/tex]

The coordinate of [tex]t=4[/tex]

We can assume only [tex]x[/tex] coordinates given and [tex]y[/tex] coordinates is [tex]0[/tex]

so coordinate of [tex]p=(-6,0)\\[/tex]

And coordinate of [tex]t=(4,0)[/tex]

So the length of the segment

[tex]pt=x_{2} -x_{1} \\pt=4-(-6)\\pt=4+6\\pt=10[/tex]

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Answer:

Step-by-step explanation:

You have 2 x's.  I think the first one is for multiplication and the second one is a variable.

2x2 -1 = 7x  

4-1 = 7x (first multiple 2x2)

3=7x  (second 4-1)

0.428571429 = x (Divide both sides by 7.  On the left side, 3/7 is 0.428571429 and 7x/7 is just x because the 7s cancel out.

Since the answer needs to be to two decimal places, I have to decide if 0.428571429 is closer to 0.42 or 0.43 Since the digit after the 2 in the answer is 8, that makes the number closer to 0.43 than 0.42.  So, the final answer is 0.43

The value of f left parenthesis 3 right parenthesis is 45.

According to the statement

We have given that the F(x) = 5(x)^2

and we have to find the value when Sophia have a 3 right parenthesis.

So, Parenthesis are used in mathematical expressions to denote modifications to normal order of operations.

And now we have to find the value for 3 right parenthesis

And for this purpose we have to put the value X= 3 in the f(x) then

F(x) = 5(x)^2

F(3) = 5(3)^2

F(3) = 5*9

F(3) = 45.

here the value of 3 right parenthesis is 45.

So, The value of f left parenthesis 3 right parenthesis is 45.

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Answer:

d. 90

Step-by-step explanation:

z = (x - mean)/SD = (15 - 18)/5.4 = - 3/5.4 = -0.55555555... ≈

≈ -0.56

remember the z-table represents the rounded values.

the z-table at -0.56 gives us the p-value of 0.28774.

that is the probability to the left of 15 pounds, so, the probability to have lost 15 pounds or less.

to have lost at least 15 pounds, we have to get the right side of 15 pounds in the bell curve.

and that is 1 - 0.28774 = 0.71226

so, the probability to have lost at least 15 pounds is therefore 0.71226.

how many people are that ?

well, there were in total 128 people (with the total probability of 1 representing everything).

the number of people that lost at least 15 pounds are the proportionate share of 0.71226 of 1 (the whole) :

128 × 0.71226 = 91.16928...

so, the closest answer option is d. 90

Answer: 113.1 ft^3

Step-by-step explanation:

We know the radius is 3 so substitute it in the formula like this...

V = 4/3 π (3)^3

Solve for (3)^3 which is 27.

Next multiply 4/3 by π. Which equals 4.1887....

Then multiply that answer by 27.

And your answer is 113.1 ft^3.

Answer:

[tex]V=108ft^{3}[/tex]

Step-by-step explanation:

[tex]V=\frac{4}{3}(3)(3)^{3}[/tex]

[tex]V=\frac{4}{3}(3)(27)[/tex]

[tex]V=\frac{4}{3} (81)=\frac{324}{3}[/tex]

[tex]V=108[/tex]

Hope this helps

Answer:

Step-by-step explanation:

Formula

Area = 1/2 b* h

Givens

b = 25

h = 9

Solution

Area = 1/2 * 25 *  9     Substitute givens into formula

Area = 1/2 * 225         Combine

Answer

Area = 112.5 ft^2

Haven worked on an externship in a prosecutor’s office, the legal support position which you would be best suited for is: paralegal.

Paralegal can be defined as a person who has been trained in subsidiary legal matters (issues), but not fully qualified to act as an attorney or lawyer.

In this context, we can infer and logically deduce that paralegal is a legal support position which you would be best suited for a person who has worked on an externship in a prosecutor’s office.

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Complete Question:

If you had worked on an externship in a prosecutor’s office, and then you moved to another state, which of these legal support positions would be best suited for?

mediator

paralegal

legal secretary

court reporter

The equation of the new graph g(x) is expressed as g(x) = 4^x + 6

The standard exponential equation is expressed as y = ab^x. Exponential equation is inverse of logarithmic equation.

Translations is a transformation technique that changes the position of an object from one point on the plane to another.

Given the function f(x) = 4^x

If the function is shifted 6 units up, the function g(x) is derived by adding 4 to the function f(x). The resulting function is given as;

g(x) = f(x) + 6

g(x) = 4^x + 6

Hence the equation of the new graph g(x) is expressed as g(x) = 4^x + 6

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The confidence interval is from 3.44 to 4.06 minutes.

According to the statement

we have given that the mean length of songs is 3.75 minutes and standard deviation 0.5 minutes and the sample size n is 7. and the confidence interval is 90%

and we have to find the mean interval.

So, We know that the

A confidence interval is defined as the range of values that we observe in our sample and for which we expect to find the value that accurately reflects the population.

And A margin of error is a statistical measurement that accounts for the difference between actual and projected results in a random survey sample.

We know that the z value for 90% confidence interval is 1.64.

so, The formula to calculate margin of error is

MOE = Z*standard deviation/ (n)^1/2

put the values in it

MOE = Z*standard deviation/ (n)^1/2

MOE = 1.64*0.5/ (7)^1/2

MOE = 1.64*0.189

MOE = 0.310

And to find the interval the formula is

Confidence interval = sample mean ± margin of error

Confidence interval = 3.75 ± 0.310

Confidence interval = (4.06,3.44)

So, The confidence interval is from 3.44 to 4.06 minutes.

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Answer:

98, 27

Step-by-step explanation:

In the first figure, the two angles are supplementary, meaning that their sum would equal 180 degrees, giving the equation: b+82 = 180 --> b=98

In the second figure, the two angles are complementary, meaning that they add up to 90 degrees, giving the equation: b+63 = 90 --> b=27

Answer:

D

Step-by-step explanation:

simplified is 1 1/2, 1.5 or 3/2

Answer:

(8 , 5)

Step-by-step explanation:

• Marty would get the best view ,if he stood at the midpoint

of the line that connect the park to the high school .

• On the coordinates plane ,the park is located at (-4 , -11)

and the high school is located at (20 , 21) .

•• Calculating the midpoint (best position) :

Let M(x , y) be the midpoint.

[tex]x=\frac{-4+20}{2} =8[/tex]

[tex]y=\frac{-11+21}{2} =5[/tex]

Answer:

(8, 5)

Step-by-step explanation:

Given points:

To find the point that is between and equidistant from the High School and the park, use the formula for midpoint between two points.

Midpoint between two points

[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\quad \textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)[/tex]

Define the endpoints:

[tex]\textsf{Let }(x_1,y_1)=(20,21)[/tex]

[tex]\textsf{Let }(x_2,y_2)=(-4,-11)[/tex]

Substitute the endpoints into the formula:

[tex]\implies \textsf{Midpoint} =\left(\dfrac{-4+20}{2},\dfrac{-11+21}{2}\right) = (8,5)\end{aligned}[/tex]

Therefore, the point at which Marty would get the best view is (8, 5).

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Using the binomial distribution, there is a 0.265 = 26.5% probability that at least two of them have the same number.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

For this problem, the values of the parameters are:

p = 1/65 = 0.0154, n = 65.

The probability that at least two of them have the same number is:

[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]

In which:

P(X < 2) = P(X = 0) + P(X = 1)

Then:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{65,0}.(0.0154)^{0}.(0.9846)^{65} = 0.3647[/tex]

[tex]P(X = 1) = C_{65,1}.(0.0154)^{1}.(0.9846)^{64} = 0.3703[/tex]

So:

P(X < 2) = P(X = 0) + P(X = 1) = 0.3647 + 0.3703 = 0.735.

[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.735 = 0.265[/tex]

0.265 = 26.5% probability that at least two of them have the same number.

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Answer:

D

Step-by-step explanation:

You are looking for what you would need to cancel the yards in 800 yards.

800 yards (1 mile/ 1760 yards).  You have yards in the numerator of your original measurement.  You will cross cancel out the yard on the the top and the yards on the bottom.

By applying the definition of difference, we find that the average daily maximum temperature in Syracuse is 26.55 °C higher than the average daily minimum temperature.

Herein we must find the difference bewteen the two temperatures, defined as the subtraction of the minimum temperature from the maximum temperature:

x = 21.85 °C - (- 4.7 °C)

x = 26.55 °C

By applying the definition of difference, we find that the average daily maximum temperature in Syracuse is 26.55 °C higher than the average daily minimum temperature.

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The polynomial function in standard form that has the zeros listed. i and -i is  x² +1 = 0.

A quadratic, cubic, quartic, and other functions involving only non-negative integer powers of x are examples of polynomial functions.

The values of x that fulfil the formula f(x) = 0 are the zeros of a polynomial. The polynomial's zeros are the x values for which the function's value, f(x), equals zero in this case. The degree of the equation f(x) = 0 determines how many zeros a polynomial has.

Calculation for the polynomial function-

The general two degree/quadratic equation is given by-

ax² + bx + c = 0

Where a ≠ 0

If the two roots of the equation are x1 and x2.

Then the relation between roots and coefficients of the polynomial are -

         x1 + x2 = (-b)/a

        x1.x2 = c/a

From the above two relation the general equation can be written as-

x² -(x1 - x2)x + x1.x2 = 0

Lets say x1 = i and x2 = -i

Substitute the values of x1 and x2 in the general equation

x² -(i - i)x + (i).(-i) = 0

x² - i ² = 0

x² + 1 = 0

Therefore, the polynomial function in standard form that has the zeros listed. i and -i is x² + 1 = 0.

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The statement which is true about the translation is; The asymptote of g(x) is the asymptote of f(x) shifted six units down.

Since it follows from the task content that the function g(x) represents a 6 units vertical shift downward, it can then be concluded in the same regard that The asymptote of g(x) is the asymptote of f(x) shifted six units down.

Therefore, the true statement is; the asymptote of g(x) is the asymptote of f(x) shifted six units down.

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Answer:

See below

Step-by-step explanation:

Slope, m of given line = - 1/2

perpendicular slope is = -1/m = -1 / (-1/2) = +2

Point (6,9)  slope form of line

y -9 = 2(x-6)    expand and simplify

y - 9 = 2x -12

y = 2x -3

Considering the given functions in the graph, we have that:

We look at the graph, and find f(3) and g(3), then add them. Hence:

Then the addition is:

(f + g)(3) = f(3) + g(3) = 0 + 4 = 4.

Same logic, at the graph we have that:

Hence:

(f - g)(1) = f(1) - g(1) = -1 - 1 = -2.

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A state license plate consists of three letters followed by three digits. If repetition is allowed, the number of different ways in which license plates are possible is 17,576,000.

An arrangement of items in a specific order is referred to as a permutation. When the order of the arrangements counts, it is a mathematical technique that establishes the total number of alternative arrangements in a collection.

Calculation for the permutation -

Three letters are followed by three digits on a state license plate.

26 letters from a to z and 10 numbers from 0 to 9 make up the alphabet.

The potential of arrangements is due to the license plate's composition of three letters and three numerals.

Total ways = 26×26×26×10×10×10

                  = 17,576,000

Therefore, the number of different ways in which license plates are possible is 17,576,000.

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In order to avoid double counting, statisticians just count the final goods and services.

According to the statement

we have to find the procedure which is used by statisticians to avoid the double counting.

final goods and services are the type of way which is used to avoid the double counting.

In other words, statisticians count only the final results rather than the efforts.

So, In order to avoid double counting, statisticians just count the final goods and services.

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The probability of drawing two blue marbles if the first marble is not replaced is 1/5

The probability of tossing a head and drawing a red marble

The given parameters are:

White = 1

Blue =3

Red = 2

Total = 6

The probability of a head is

P(Head)= 1/2

The probability of drawing a red marble is

P(Red)= 2/6 = 1/3

The required probability is

P = P(Head) * P(Red)

This gives

P = 1/2 * 1/3

P =1/6

The probability of drawing two blue marbles if the first marble is not replaced.

Here, we have:

P(B1) = 3/6 = 1/2

P(B2) = 2/5

The required probability is

P = P(B1) * P(B2)

This gives

P = 1/2 * 2/5

P =1/5

Hence, the probability of drawing two blue marbles if the first marble is not replaced is 1/5

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Se calcula que la aceleración es - 8,35 m/s.

Ahora sabemos lo siguiente de la pregunta;

Velocidad inicial (u) = 60 km/h o 16,7 m/s

Tiempo empleado (t) = 2 s

Dado que;

v = tu + en

v = 0 m/s porque el carro se detenía

tu = -en

a = -(u/t)

 a= -1(6,7 m/s/2 s)

a =- 8,35 m/s

La aceleración es negativa porque la velocidad disminuye con el tiempo.

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Answer:

21+21+7+7+7+7+8+8+8+8+9+9

Step-by-step explanation:

amswer is 120

Answer:

Step-by-step explanation:

21+2=42.There are four sevens-which is  7x4=28.There are four eights meaning it is 8x4=32+28=60+42=102+(9+9)=102+18=120

Answer:

Step-by-step explanation:

144,72

Answer:

If you cut the rectangle in half, you have two squares of area 144 ft², or side length 12 ft.

The length of the rectangle is 24 ft; its width is 12 ft.

There are 17 hops in a hop, a skip, and a jump.

We have the relations:

How many hops are in a hop, a skip and a jump?

So we have:

1 hop + 1 skip + 1 jump.

First, using the second relation we rewrite:

1 hop + 1 skip + 3 skips = 1 hop + 4 skips.

Now, using the first relation:

1 hop + 4 skips = 1 hop + 4*(4 hops) = 1 hop + 16 hops = 17 hops.

There are 17 hops in a hop, a skip, and a jump.

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Answer:

Length= 50

Width=17

Step-by-step explanation:

length= n+8

Since n= 42, Just plug it in. So it would be 42+8 which is 50 for the length

Widith: 1/2n-4

basically since N is given for 42, you do 1/2 multipied by 42 which is 21.

Since you also have to subtract 4 inches it would be 17 for the length

The values of x and y from the given diagram are 47 ad 86 degrees respectively

From the given circle, the triangle HJL is a right triangle.

Determine the value of y

43 = 1/2 <y

<y = 43 * 2

<y = 86 degrees

Since the sum of angle on a straight line is 180 degrees, such that;

x+90+43 = 180

x + 133 = 180

x = 47 degrees

Hence the values of x and y from the given diagram are 47 ad 86 degrees respectively

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