find the indefinite integral. (use c for the constant of integration.) 16 − 4x2 dx

(x+1) & (x-5) are the factors of given equation.

The given Equation is,

x3- \(3x^{3}\) - 9

Here, If we substitute x =5, in the given equation, then we find

     (5)3 - 3(5)3 - 9*5 -5 = 0

x-5 is factor of given equation to find another factor dividing given equation by x-5

    we will get =(x2+2x+1) after dividing the equation by x - 5

Hence x3- \(3x^{3}\) - 9 =(x2+2x+1) (x-5)

                            =(x+2)2 (x-5)

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Answer:

0.0045045045

Step-by-step explanation:

Have a good day I hope this helps! :)

\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{-7}~,~\stackrel{y_1}{5})\qquad B(\stackrel{x_2}{4}~,~\stackrel{y_2}{-9})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AB=\sqrt{[4 - (-7)]^2 + [-9 - 5]^2}\implies AB=\sqrt{(4+7)^2+(-14)^2} \\\\\\ AB=\sqrt{121+196}\implies AB=\sqrt{317}\)

SOLUTION

By definition, adjacent angles are (of a pair of angles) formed on the same side of a straight line when intersected by another line.

Vertical Angles are the angles opposite each other when two lines cross.

Going by this above definition, a pair of adjacent angles in the figure in Q1 are:

4 and 2.

Going by this above definition, a pair of vertical angles in the figure in Q1 are:

3 and 2.

Answer: The answer is 1x

Step-by-step explanation: Because It has (10x-9) Just Subtracted

Solution,

2x-56=8

or,2x=8+56

or,2x=64

or,X=64/2

X=32

Hope it helps

Good luck on your assignment

Answer:

x=32

Step-by-step explanation:

First I put the 56 on the other side by doing the opposite to it, so adding 56 to both sides.

2x - 56 = 8

   +56      +56

2x=64

Then divide both sides by two to single out the x and know it's value

2x=64

/2     /2

x=32

Answer:

Answer

3.0/5

78

Brainly User

There are 128 ounces in 1 gallon

1,5gallons= 192 ounces

Scott = 3 oz per lid

192 divided by 3 = 64 lids of detergent

Nikki = 4oz per lid

192 divided by 4 = 48 1/2 lids

64 - 48.5 = 15.5 lids more

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

5% of 820= 41    would be one possible

As per the addition formula, the value of the trigonometric function is -0.809.

In statistics, function is defined as a relationship between inputs where each input is related to exactly one output.

Here we have to find the value of the trigonometric function cos(13/15)cos(-/5)-sin(13/15)sin(-/5)  by using the addition and subtraction formula.

Here we have the following trigonometric function:

=> cos(13/15)cos(-/5)-sin(13/15)sin(-/5)

Now, we have to use the trigonometric addition formula,

=> Cos (A+B) = Cos A Cos B - Sin A Sin B

To solve the given function,

Here let us rewrite the given function based on the addition formula, then we get,

=> Cos ( 13π/15 + (-π/5) )

=> Cos( 12π/5)

=> Cos(144°)

=> -0.809

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Answer:

  7

Step-by-step explanation:

We want to find the number 4-digit of positive integers n such that removing the thousands digit divides the number by 9.

__

Let the thousands digit be 'd'. Then we want to find the integer solutions to ...

  n -1000d = n/9

  n -n/9 = 1000d . . . . . . add 1000d -n/9

  8n = 9000d . . . . . . . . multiply by 9

  n = 1125d . . . . . . . . . divide by 8

The values of d that will give a suitable 4-digit value of n are 1 through 7.

When d=8, n is 9000. Removing the 9 gives 0, not 1000.

When d=9, n is 10125, not a 4-digit number.

There are 7 4-digit numbers such that removing the thousands digit gives 1/9 of the number.

Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, the statement which is most likely true for g is that: A. g(-13) = 20.

In Mathematics, a range can be defined as the set of all real numbers that connects with the elements of a domain.

Based on the information provided in this scenario, the domain and range of this function g(x) in interval notation are as follows:

Function g(0) = 2 is false because it was stated that g(0) = -2. Also, g(-4) = -11 is outside the scope of the given range for this function.

Furthermore, function g(7) = -1 is not within the domain for the given function. However, we can logically deduce that g(-13) = 20 is within the domain for the given function and it would produce an output that is within the scope of the given range for this function.

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There is only one rectangle that satisfies the conditions of having the given nonadjacent vertices (4, 3) and (-4, -3) with integer coordinates for the other two vertices.

Let's consider the given vertices (4, 3) and (-4, -3) as the diagonal endpoints of the rectangle.

The other two vertices will lie on the perpendicular bisectors of this diagonal. Since we want the other two vertices to have integer coordinates, the midpoint of the diagonal must also have integer coordinates.

The midpoint of the diagonal can be found by taking the average of the x-coordinates and the average of the y-coordinates:

Midpoint: \($\left(\frac{4 + (-4)}{2}, \frac{3 + (-3)}{2}\right) = (0, 0)$\)

So, the midpoint of the diagonal is (0, 0).

Now we need to find the other two vertices that lie on the perpendicular bisectors passing through this midpoint.

The slope of the diagonal line is given by:

\($m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-3 - 3}{-4 - 4} = \frac{-6}{-8} = \frac{3}{4}$\)

The slope of the perpendicular bisector is the negative reciprocal of the diagonal slope:

\($m_{\text{perpendicular}} = -\frac{1}{m} = -\frac{4}{3}$\)

Now we can use the midpoint (0, 0) and the slope

\($m_{\text{perpendicular}} = -\frac{4}{3}$\)  to find the equations of the two perpendicular bisectors.

Equation of the first bisector:

\($y - 0 = -\frac{4}{3}(x - 0)$\)

\($y = -\frac{4}{3}x$\)

For the first bisector, let's assume one vertex lies on the line \($y = -\frac{4}{3}x$\) with integer coordinates (a, b).

Now, since (a, b) lies on the bisector, the distance between (a, b) and the midpoint (0, 0) is equal to the distance between (a, b) and (4, 3).

Distance formula:

\($\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$\)

\($\sqrt{(0 - a)^2 + (0 - b)^2} = \sqrt{(4 - a)^2 + (3 - b)^2}$\)

Simplifying the equation, we get:

\($a^2 + b^2 = (4 - a)^2 + (3 - b)^2$\)

Expanding and simplifying further:

\($a^2 + b^2 = a^2 - 8a + 16 + b^2 - 6b + 9$\)

Simplifying again:

\($8a + 6b = 25$\)

Since a and b must be integers, we can analyze the possible values for a and b.

To have integer solutions for a and b, 8a + 6b must be a multiple of 25.

The possible values for 8a + 6b are:

\($0, 25, 50, 75, 100, \dots$\)

To satisfy the condition 8a + 6b = 25, there is only one solution: a = 2 and b = 3.

Therefore, there is only one rectangle that satisfies the given conditions.

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The conditional expectation of Y given X = x is x/2 + 1.

Here, we have

Given: If the joint density of the random variables X and Y is f(x,y) = 0 [emin(x,y) - 1] e-(x+y) if 0 < x, y < [infinity].

A variable having an unknown value or a function that assigns values to each of an experiment's results is referred to as a random variable. A variable having an unknown value or a function that assigns values to each of an experiment's results is referred to as a random variable. A random variable may be continuous or discrete, with defined values or any value falling within a continuous range.

The conditional expectation of Y given X = x is x/2 + 1.

Hence, the statement "x/2 + 1" is the answer to the question.

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Answer:

4/8 - 2/8 = 2/8 = 1/4

Step-by-step explanation:

Answer:

on the first part the answer is 1/4

as for the blanks here it is 4/8 - 2/8 = 2/8

Answer:

the correct answer is B

Step-by-step explanation:

Answer:

the second choise is the answer

To find the largest number of passengers in the tram, we need to calculate the maximum number of passengers who can go without a ticket.

Given that 12% of passengers go without a ticket, we can set up the following equation:

12% of x = 60

To solve for x, we can divide both sides of the equation by 0.12:

x = 60 / 0.12

x = 500

Therefore, the largest number of passengers in the tram, if it is not greater than 60, would be 500.

To find the largest number of passengers in the tram, we use the percentage given and set it equal to the number of passengers. By solving for x, we determine that the largest number of passengers in the tram is 500.

The largest number of passengers in the tram, if it is not greater than 60, is 500.

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The winner received 570 votes.

Let the winner candidate be c1

Let the  second-place candidate be c2

Let the  third-place candidate be c3

\(c2=c1-155\\\).........equation 1

\(c2=c3+200\\\)

\(c3=c2-200 \\\)

\(c3=c1-155-200\\\).........by equation 1

\(c3=c1-355\)........equation 2

Now we know,

\(c1+c2+c3=1200\)

\(c1+(c1-155)+(c1-355)=1200\) .....by equations 1 and 2

\(3c1-510=1200\)

\(3c1=1200+510\\3c1=170\\c1=570\)

Hence, The winner received 570 votes.

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Answer:

Step-by-step explanation:

When solving for a variable you need to math operations to isolate the vaiable by itself on one side of the equation.

\(-4+x\le 9\text{ adding 4 to both sides isolates x by itself}\\ \\ x-4+4\le 9+4\\ \\ x\le 13\)

Answer:

A

Step-by-step explanation:

the parrallel lines are not intersecting look up what congruent means and it will help you out

Answer: a

Step-by-step explanation:

The total amount of money earned by Nora salary over the 21 years is approximately $1,848,000.

To find the total amount of money earned by Nora over 21 years, we need to calculate the salary for each year and then sum them up.

In the first year, Nora's salary is $40,000.

In the second year, her salary will be increased by 3%, so it will be:

$40,000 + 3% of $40,000 = $40,000 + $1,200 = $41,200.

In the third year, her salary will again increase by 3%, so it will be:

$41,200 + 3% of $41,200 = $41,200 + $1,236 = $42,436.

We can continue this process for each year, adding 3% of the previous year's salary to calculate the next year's salary.

To calculate the total amount of money earned over the 21 years, we need to sum up the salaries for each year. Here's the calculation:

Total = $40,000 + $41,200 + $42,436 + ... (21 terms)

To simplify the calculation, we can use the formula for the sum of an arithmetic series:

Total = (n/2) * (2a + (n - 1)d)

where:

n = number of terms (21 in this case)

a = first term ($40,000)

d = common difference (3% of the previous year's salary)

Plugging in the values:

Total = (21/2) * [2(40,000) + (21 - 1)(0.03)(40,000)]

Simplifying further:

Total = (21/2) * [80,000 + 20(0.03)(40,000)]

= (21/2) * [80,000 + 2,400(40,000)]

= (21/2) * [80,000 + 96,000]

= (21/2) * 176,000

= 21 * 88,000

= 1,848,000

Therefore, the total amount of money earned by Nora salary over the 21 years is approximately $1,848,000.

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The length of the rectangle is 7 cm and the width is 5 cm.

The whole distance covered by the rectangle's borders or its sides is known as its perimeter. As we know the rectangle will have 4 sides then the perimeter of the rectangle will be equal to the total of its four sides. And the unit will be in meters, centimeters, inches, feet, etc.        

The formula for the Perimeter of the rectangle is given by

Here we have

The length of a rectangle is 2cm greater than the width of the rectangle

And perimeter of the rectangle = 24 cm

Let x be the width of the rectangle

From the given data,

Length of the rectangle = (x + 2) cm  

As we know Perimeter of rectangle = 2(Length+width)

=> Perimeter of rectangle = 2(x+2 + x) = 2(2x +2)

From the given data,

Perimeter of rectangle =  24cm

=> 2(2x +2) = 24 cm

=> (2x +2) = 12     [ Divided by 2 into both sides ]

=>  2x = 12 - 2

=>  2x = 10

=>   x = 5         [ divided by 2 into both sides ]  

Length of rectangle, (x+2) = 5 + 2 = 7 cm

Therefore,

The length of the rectangle is 7 cm and the width is 5 cm.

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A world without engines is certainly an appealing idea. Although engines are a vital transportation source that allow us to move around and travel much faster and efficiently, passenger vehicles are a major pollution contributor. they produce large amounts of carbon monoxide, nitrogen oxides, and other forms of pollution. Removing all engines would definitely have downsides, but the significant amount of help it would provide towards lowering pollution rates would be extremely impactful towards our environment and earth. Engines are important parts of human life, and getting things done faster is much more efficient, without engines humans would have to do many things by hand and it would slow production of many things that are necessities. There are also many situations regarding human lives that require the fastest transportation possible, and without engines many things wouldn't get done fast enough. In conclusion, a world without engines would have many benefits towards the environment, however, we've grown to be too dependent on these machines and without them production of many things would start to slow and many trips around the world would be near impossible or extremely delayed.

sorry about it being one big block, wasnt sure how u wanted it to be spaced. hope this helps atleast a little, gl

Profit per kilogram = R1.90

The profit per kilogram is the difference between the selling price and the cost price per kilogram.

a) To find the profit per kilogram, we can use the following formula:

Profit per kilogram = Selling price per kilogram - Cost price per kilogram

Therefore,

Profit per kilogram = R2.80 - R0.90

Profit per kilogram = R1.90

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Answer:

They are in reverse order

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

When \(0<a<1\), the parabola horizontally expands, so \(a=0.25\) matches with the rightmost graph.

When \(a>1\), the parabola horizontally shrinks, so \(a=4\) matches with the leftmost graph

Last, but not least, \(a=1\) matches with the middlemost graph since the parabola is not affected.

The price of the first pastry and the filled donuts are 0.72 and 1.1 dollars respectively.

Bill and Mary Ann went to the viola bakery. Bill bough 3 pastry and 8 filled donuts for 10.96 dollars.  Mary Ann bought 4 of each for 7.28 dollars.

Therefore, the price of each type of pastry can be calculated as follows:

using equation,

let

cost of each pastry = x

cost of each filled donuts = y

Therefore,

3x + 8y = 10.96

4x + 4y = 7.28

Multiply equation(ii) by 2

3x + 8y = 10.96

8x + 8y = 14.56

subtract the equation

5x = 3.6

divide both sides by 5

x = 3.6 / 5

x = 0.72

Let's find y

4y = 7.28  - 4(0.72)

4y = 7.28 - 2.88

4y = 4.4

y = 4.4 / 4

y = 1.1

Therefore,

price of the first pastry = 0.72 dollars

price of filled donuts = 1.1 dollars

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L = k/f, where k is the variational constant, is the formula for the inverse variation.

A mathematical relationship between two variables in which they vary in opposing directions is referred to as an inverse proportion, also known as an inverse relationship. When one variable increases while the other decreases, this is known as having inverse proportions.

Using the variables length of violin 'l' and frequency of vibration 'f'

If the length of violin 'l' is inversely proportional to the frequency of vibration 'f', this is expressed as:

l α 1/f

l = k/f

Hence the formula for the inverse variation is l = k/f where k is the constant of variation.

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The value of side a and b for the given triangle is 46.68 units and 17.92 units.

A triangle's angles and side lengths are related by the law of sines, a trigonometric identity. It asserts that the ratio of the sine of one angle to the length of the side opposite that angle is constant for all three angles for any triangle with sides a, b, and c and opposing angles a, b, and c:

If a/sin(A) = b/sin(B) = c/sin(C), then

As long as at least one angle and its matching side length are known, this can be used to solve for unknown angles or side lengths in a triangle.

For the given triangle we have:

cos B = a / c

Thus, substituting the values we have:

cos 21 = a / 50

a = 46.68 units.

Now, sin B = b/50

Sin 21 = b / 50

b = 17.92 units.

Hence, the value of side a and b for the given triangles is 46.68 units and 17.92 units.

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The complete question is:

Answer:

Y' = (0, -8)

Z' = (7, -2)

Step-by-step explanation:

The pattern is (+5, -5).

For Y,

(-5+5, -3-5)

(0, -8)

For Z,

(2+5, 3-5)

(7, -2)

The length of the arc will be 22 cm.

Length of the radius 'r'= 28 cm

central angle 'a' in degrees = 45

The formula for length of arc is 2πra÷360

The standard value of pie that we take is 22÷7

so after putting all the given values, we get,

2×22/7×28×45 = 22cm.

Radius is any line that we draw from the centre of the circle to its outside edge.

Arc is the part of the circle's circumference.

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