evaluate the integral. (use c for the constant of integration.) dx (ax)2 − b2 3/2

Answer:

$29.88

Step-by-step explanation:

We first would need to figure out what 20% of $37.35 is.

0.2 (or 0.20) × 37.35 = 7.47

This means that the discount price is $7.47

Now subtract that from the total.

37.35 - 7.47 = 29.88

Therefore, his total in dollars and cents after the discount and before tax is twenty-nine dollars and eighty-eight cents.

Answer:

[tex]P(x)=x^5+10x^4+75x^3+10x^2+74x[/tex]

Step-by-step explanation:

Given information:

For any complex number  [tex]z=a+bi[/tex], the complex conjugate of the number is defined as  [tex]z^*=a-bi[/tex].  

If f(z) is a polynomial with real coefficients, and z₁ is a root of f(z)=0, then its complex conjugate z₁* is also a root of f(z)=0.

Therefore, if P(x) is a polynomial, and i is a root of f(x)=0, then its complex conjugate -i is also a root of P(x)=0.

Similarly, if P(x) is a polynomial, and -5+7i is a root of f(x)=0, then its complex conjugate -5-7i is also a root of P(x)=0.

Therefore, the polynomial in factored form is:

[tex]P(x)=x(x-i)(x-(-i))(x-(-5+7i))(x-(-5-7i))[/tex]

[tex]P(x)=x(x-i)(x+i)(x+5-7i)(x+5+7i)[/tex]

Expand the polynomial:

[tex]P(x)=x(x^2-i^2)(x^2+10x+25-49i^2)[/tex]

[tex]P(x)=x(x^2-(-1))(x^2+10x+25-49(-1))[/tex]

[tex]P(x)=x(x^2+1)(x^2+10x+74)[/tex]

[tex]P(x)=x(x^4+10x^3+75x^2+10x+74)[/tex]

[tex]P(x)=x^5+10x^4+75x^3+10x^2+74x[/tex]

Alex came closer to their grade’s state record for the triple jump.

What is algebra?

The area of mathematics known as algebra is used to help express issues or circumstances into mathematical expressions.

Here, we have

Given:

Alex jumped 38 feet 11 2/3 inches the eighth-grade record is 40.17 feet.

Let's see how closer Alex jumped.

11 2/3 inches = 22* 0.083 = 1.826

38+ 1.826 = 39.826

40.17 -  39.826  = 0.344

Eric, a seventh grader, jumped 36.89 feet. The seventh-grade record is 38 feet 1 3/5 inches.

1 3/5 inches = 8/5*0.083 = 0.1328

38 + 0.1328 = 38.1328

Eric jump was

38.1328 - 36.89 = 1.2428

0.344 is smaller than 1.2428.

Hence, Alex came closer to their grade’s state record for the triple jump.

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The trigonometric ratios are;

We know that the trigonometric ratios would have to do with the ratios such as the sine the cosine and the tangent of the angle. In This case, we would need to obtain the side AB and this is by the Pythagoras theorem;

/AB/^2 = /AC/^2 + /BC/^2

/AB/ = √ /AC/^2 + /BC/^2

/AB/ = √(9)^2 + (12)^2

/AB/ = 15

Then;

Sin A = 12/15

Cos A = 9/15

Tan A = 9/12

These are the ratios for the right angle triangle

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The distance between the ball and pole is divided by the time taken to travel that distance to calculate the rate of shadow travel, which is 80 fps.

The shadow of the ball is moving at a rate of 80 feet per second (fps). This can be calculated as follows:

Distance Fallen = 16t^2

Distance Fallen in 0.5 Seconds

= 16(0.5)^2

= 4 feet

Distance Between Ball and Pole

= 50 feet - 4 feet

= 46 feet

Time Taken To Travel Distance

= 0.5 Seconds

Rate of Travel = 46/0.5

= 80 fps

The shadow of the ball is moving at a rate of 80 fps. This is calculated by taking the distance between the ball and pole (50 feet-4 feet=46 feet) and dividing it by the time taken to travel that distance (0.5 seconds). This results in 80 fps.

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A. The coefficient of x^4y^{12} in the expansion of (-4x+2y)^{16} is -8192.

B. The coefficient of x^4y^8z^7 in the expansion of (-4x+2y-1z)^{19} is -134217728.

For the first question, we can use the binomial theorem to expand the expression. The binomial theorem states that

(a+b)^n = C(n,0)a^nb^0 + C(n,1)a^{n-1}b^1 + C(n,2)a^{n-2}b^2 + ... + C(n,n)a^0b^n

Where C(n,k) = n!/(k!(n-k)!)

Applying this to the given expression, we get:

(-4x+2y)^{16} = C(16,0)(-4x)^{16}(2y)^0 + C(16,1)(-4x)^{15}(2y)^1 + C(16,2)(-4x)^{14}(2y)^2 + ... + C(16,16)(-4x)^0(2y)^16

The coefficient of x^4y^{12} is the coefficient of the term -4x^42y^{12} in this expansion, which is

C(16,4)(-4)^42^{12} = C(16,4)(-256)4096 = C(16,4)(-256)*4096 = -8192

For the second question, the same logic can be applied to:

(-4x+2y-1z)^{19} = C(19,0)(-4x)^{19}(2y)^0(-1z)^0 + C(19,1)(-4x)^{18}(2y)^1(-1z)^0 + C(19,2)(-4x)^{17}(2y)^2(-1z)^1 + ... + C(19,19)(-4x)^0(2y)^0(-1z)^19

The coefficient of x^4y^8z^7 is the coefficient of the term -4x^42y^8(-1z)^7 in this expansion, which is C(19,4)(-4)^42^8*(-1)^7 = C(19,4)256256*-1 = -134217728

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Answer: below :)

Step-by-step explanation:

1. Line AB

2. Ray AB

3. Line segment AB

4. Ray BA

The number of solutions the system have is 2. They will meet in 5 hours.

For that , we will try solving it first using the method of substitution in which we express one variable in other variable's form and then you can substitute this value in other equation to get linear equation in one variable.

If there comes a = a situation for any a, then there are infinite solutions.

If there comes wrong equality, say for example, 3=2, then there are no solutions, else there is one unique solution to the given system of equations.

Matt drives at a rate of 40 miles per hour. Matt drives 50 miles before Kylie begins traveling.

So the total distance for Matt is given by;

M(t)= 40t+50

Kylie drives at a rate of 50 miles per hour.

When he starts(at position 0), Matt will be already at 50. So Kylie's equation is given by:

K(t)= 50t

To find out how many hours until they meet?

K(t)= M(t)

So, 50t= 40t+50

10t= 50

t=5

Therefore the answer of the equation will be 2.

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There are approximately 3263 total albums and CDs are in the collection.

Percentage is defined as part of a whole expressed in hundredths or out of 100. It is usually written with the symbol "%".

let 'x' be the total albums and CDs in the collection

If the music fan has 2000 CDs, which comprise 61.3% of the total collection, then 61.3% of x is equal to 2000.

2000 albums and CDs = 61.3% of the total albums and CDs in the collection

2000 = 61.3% of x

2000 = 0.613x

Solving for x,

x = 3262.6

the total albums and CDs in the collection ≅ 3263

Therefore, the the total albums and CDs in the collection is approximately 3263.

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Answer:

Step-by-step explanation:

(-5,7)

The popular vote, which determines the winner of a presidential election, is simply the total number of voters from all 50 states. The popular vote is deemed to have been won by the candidate with the most votes cast nationally.

Every four years on the first Tuesday in November, the US holds its presidential election. The candidate must have at least 35 years of age, have been born in the US, and have resided in the US for the previous 14 years in order to be eligible.

Traditionally, candidates announce their intention to run for president one year prior to the election. Since there is no national body that organises elections, local authorities organise them with the aid of tens of thousands of administrators.

On January 20, the United States Capitol in Washington, D.C., will host Inauguration Day. The Vice President is sworn in first, then the President.

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By adding all the distances of the branches, we will conclude that Sylvester traveled a distance of 66.74 meters.

We know that Sylvester is a slug, and it travels for four branches, such that the length of each branch is:

To get the total distance that Sylvester travels, we just need to add these 4 numbers, then we will get:

Total distance = 9.01 m + 12.31m + 19.5m + 25.92m

Total distance = 66.74 meters.

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The inequalities that represent Chocolate and Saffron in a gift bag are

x + 2y<7 and x + y <5.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

Given, To'ak Chocolate is the rarest chocolate in the world with a cost of $5 per gram. Saffron is a spice used for flavoring and coloring foods and costs $10 per gram.

Let x be the number of grams of chocolate and y be the number of grams of saffron

Hence,

Cost of chocolate = 5x

Cost of spices = 10y

Also given She has to keep the cost to less than $35

Thus, the Linear equation

5x + 10y < 35

Divide by 5 into both sides

x = 2y < 7

Also given, A party planner for a celebrity event wants to include no more than 5 grams (g) of To'ak Chocolate and Saffron in a gift bag.

Thus, x + y < 5

therefore, The inequalities x + 2y < 7 and x + y < 5 depict the combination of chocolate and saffron in a gift bag.

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Complete question:

To'ak Chocolate is the rarest chocolate in the world with a cost of $5 per gram. Saffron is a spice used for flavoring and coloring foods and costs $10 per gram. A party planner for a celebrity event wants to include no more than 5 grams (g) of To'ak Chocolate and Saffron in a gift bag. She has to keep the cost to less than $35. Write a system of inequalities where x is the number of grams of To’ak Chocolate and y is the number of grams of Saffron in each gift bag.

The total number that can be formed by the numbers 1,2,3,4,5 (without repeating digits) is 120.

Now, half of the unit's digit will be bigger than the ten's digit and in half of them it will be smaller.

Example: Let's say we have three digits 1,2,3. Total number of numbers without repeating digits = 3*2*1=6

Numbers with the Unit's digit greater than the ten's digit

123, 213, 312

Numbers with Ten's digits greater than the unit's digit

321, 132, 231

So total Number of cases = 120/2 = 60

Thus, the Total Number which can be formed by numbers 1,2,3,4,5 (without repeating digits) = 5*4*3*2*! = 5! = 120.

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As per the combination method, the number for formation from the digits 12345 is 120 without repetition.

The term combination method in math is defined as  a way of selecting items from a collection where the order of selection does not matter.

Here we have given the digits as 12345.

Here we have calculated the total Number of Numbers which can be formed by numbers 1,2,3,4,5 without repeating digits is written as

=> 5 x 4 x 3 x 2 x 1

Which is also equal to,

=> 5! = 120.

While we looking into the set we have identified that in half them unit's digit will be bigger than the ten's digit and in half of them it will be smaller.

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The speed of yellow car has a higher speed. Then the yellow car has more momentum.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The equation of the momentum is written as,

P = mv

Where 'm' is the mass and 'v' be the velocity.

On the motorway, two similar vehicles of various colors may be seen. The yellow automobile is traveling at 70 mph while the green vehicle is moving at 50 mph.

Let the mass of the bodies be the same.

The speed of yellow car has a higher speed. Then the yellow car has more momentum.

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There are 28 numbers in total that are odd numbers greater than 500 with no digit being repeated.

First, there are 18 odd numbers with four digits, and all of them are greater than 500. To see that, starting from the end of the number, there are 3 options for the last digit, 3 for the second last, 2 for the second digit, and 1 for the first digit. Multiplying one gets 3*3*2*1=18.

Second, for numbers with 3 digits, in order to be greater than 500, it must start either with 5 or with 6. If it starts with 5, there are 2 options for the last digit and 2 options for the second digit.

Thus, there are 4 different numbers in this case. Finally, if it starts with 6, then there are 3 options for the last digit and 2 options for the second digit. Thus, there are 6 different numbers in this case.

Complete question: How many different odd numbers greater than 500 can be made using some or all of the digits 1,3,5 and 6 with no digit being repeated?

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As per the permutations, there as 36 three digit numbers that are greater than 500 and which are odd one also.

The term permutation in math is defined as the way of arranging objects or numbers in order.

Here we have given that we have to identify the 3 digit numbers greater than 500 are odd

Let us make three digit numbers 1st

Here we know that if we want odd number at end then one number from three numbers can come there so

=> 3P1

Then the rest of the two numbers don't matter so

Then it can be written as

=> 3P2

Then the overall combination is written as

=> 3P1 * 3P2=18

Here now let us make four digit numbers

Then the digit odd again and it can be written as

=> 3P1

Here also the rest of the order Doesn't matter so

then it can be written as

=> 3P3 =6

Then the four digit value is

=> 3p1 * 3p3= 18

Therefore, the overall count is written as

=> Overall = 18+18= 36

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All the measures of central tendency are, The median, The mode, and The mean.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

There are some measures,

A. The median

B. A sample statistic

C. The mode

D. The lowest value

E. The mean

We know that;

The four measures of central tendency are mean, median, mode and the midrange.

Here, mid-range or mid-extreme of a set of statistical data values is the arithmetic mean of the maximum and minimum values in a data set.

Hence, All the measures of central tendency are, The median, The mode, and The mean.

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For f'(a) is given by f'(a) = 6a + 2 and equation of the line tangent to the graph is y = -10x - 12.

f(x) = 3x² + 2x

f'(x) = 6x + 2

So f'(a) = f'(-2) = -12+2 = -10

In order to find tangent line , we need a slope and a point. We have the x-co-ordinate for our point, so we can plug that in to find Y-coordinate.

F(-2) = 8

The slope of tangent line is the derivative at this point  , f'(-2) = -10

Equation of line tangent,

y - 8 = -10(x - (-2))

y = -10x - 12.

The limit of a function in mathematics is a key idea in calculus and analysis regarding the behavior of that function close to a specific input.

Informally, a function f gives each input x an output f(x). If f(x) approaches L as x approaches input p, we say that the function has a limit L at that location. More specifically, any input that is sufficiently close to p when f is applied forces the output value arbitrarily close to L.

The concept of limit is specifically used in the various definitions of continuity. Roughly speaking, a function is continuous if all of its limits agree with the values of the function. The term "limit" is also used in the definition of the mathematical term "derivative," which in one-variable calculus refers to the maximum value of the slope of secant lines on a function's graph.

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Answer:

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by 2 gives the next term.

Step-by-step explanation:

The maximum possible outcome for the situation is 36.

The number of favorable events to all the events in an experiment is the ratio that makes up the probability formula. Theoretical probability, Experimental probability, and Axiomatic probability are the three categories into which probability can be divided.

We have been Given that Ruby is designing a new board game and is trying to figure out all the possible outcomes.

Ruby flips a coin, rolls a fair die in the shape of a cube that has six sides labeled 1 to 6, and spins a spinner with three equal-sized sections labeled Walk, Run, Stop.

we know that there are 3 things happening simultaneously and favorable moments will be chosen by all three.

Thus, Maximum possible outcome are;

2 x 6 x 3 = 36

Therefore, For the given, 36 outcomes are available in total.

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Answer: B. 128a⁶b¹³

Step-by-step explanation:

The area of the rectangle with the dimensions shown below represents :

[tex](2a^2b)^3*(4b^5)^2=\\\\2^3a^{2*3}b^3*4^2b^{5*2}=\\\\8a^6b^3*16b^{10}=\\\\(8*16)a^6b^{3+10}=\\\\128a^6b^{13}[/tex]

Answer: nomial  data

Step-by-step explanation:

Answer:

1/2x - 2 = Graph D, with the x intercept as 4, and the y intercept at

Answer:

D

Step-by-step explanation:

f(x) = mx + b

f(x) = 1/2 x - 2

m is the slope (1/2) and b is the y-intercept (b) -2.

Only graphs C and D cross the y axis at -2 .  That is the point (0, -2)

The slope is 1/2.  That means a rise of 1  space up and a run of 2 spaces left.

If you start at the point (0,-2) and go up 1 space and 2 spaces right, you end up back on the line at the point (4,0).

On solving the provided question, we can say that the value of the ellipse from give data will be = 4/9 + 9/36 = OD. (-2,4±3√3)

In mathematics, an ellipse is a planar curve that encompasses two focus points and ensures that the sum of the two distances from any point on the curve to the focal points is constant. In doing so, the circle—a particular variety of ellipse with two equal focus points—is generalized. The ellipse, whose eccentricity is less than 1, indicates the area containing the points whose distances from its two foci add up to a certain amount. Running tracks in sporting arenas and 2D egg forms are two straightforward examples of ellipses in daily life.

[tex](x+2)^2/9 + (y-4)^2/ 36 = 1[/tex]

x = 0 and y = 1

4/9 + 9/36

OD. (-2,4±3√3)

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Answer:

6.45 kg

Step-by-step explanation:

250 g is equal to 0.25 kg, so the pumpkin weighs [tex]2+0.25=2.25[/tex] kg.

Thus, the combined weight is [tex]2.25+4.2=6.45[/tex] kg.

Answer:

sinθ = -3/5, Quadrant IV (Option B)

Step-by-step explanation:

Let's first find the sine

cosθ = adj./hyp.

Pythagorean theorem (in terms of right triangle trig) = (opp)^2 + (adj)^2 = (hyp)^2

Plug in the adjacent and hypotenuse

(opp.)^2 + 16 = 25

solve for the opposite side

opp. = 3

To find the quadrant, recall the sin <0, so the sin has to be negative.

So, your sine value is -3/5.

Sine is negative at Quadrants III and IV, so eliminate C and D.

Since your cosine value is positive, it is at Quadrant IV (Cosine is positive at the first and fourth quadrants.)

Therefore, Option B is correct.

If a man has a collection of stamps made up of 5 cent stamps and 8 cent stamps and there are three times as many 8 cent stamps as 5 cent stamps. The number of each stamp he have is: 5 cent stamp is 12, 8 cent stamp is 36.

Let x represent 5 cent =  0.05x + 0.08 = 3.48

Let y  represent 8 cent = 3x

Hence,

0.05x + 0.08(3x)= 3.48

0.05x + 0.24x = 3.58

Combine like terms

0.29x = 3.58

Divide both side by 0.29x

x = 3.58/0.29

x =12 (5 cent stamps)

Now let solve for y

y =3x

y =3(12)

y = 36 (8 cent stamps)

Therefore the number of each stamp he have is: 5 cent stamp is 12, 8 cent stamp is 36.

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C is the most accurate one i guess

Answer:

Below

Step-by-step explanation:

x = third part

5/9 x    + 5/9 x  + x   = 114    <=======given

19/9  x = 114

x = 114 * 9/19 = 54 cm      then the other two are 30 cm each

Answer:

The two equal parts are 30 cm, the third part is 54 cm

Step-by-step explanation:

x =  third part

(5/9)x + (5/9)x + x = 114

10/9(x) + x = 114

(19/9)x = 114

x = 114(9/19) = 54

(5/9)54 = 30