a) Find the definite integral L (x + 1)(x - 1)dx Answer: I= b) Find the indefinite integral (x– 1)dx Answer: I =
c) Calculate the integral \2cos(t)dt Answer: I= =

If (z³⁴)(z¹⁹)⁴ is equivalent to (zᵃ), The value of a is 110.

we can solve it by the rules of exponential :

To find the value of a, we need to use the laws of exponents. Specifically, we need to use the law that states (x^(y))(x^(z)) = x^(y+z) and the law that states (x^(y))^(z) = x^(y*z).

So, let's apply these laws to the given expression:

(z³⁴)(z¹⁹))⁴ = z³⁴ * z^(19*4) = z³⁴* z⁷⁶ = z^(34+76) = z¹¹⁰

Therefore, the value of a is 110.

So, the expression If (z³⁴)(z¹⁹)⁴ is equivalent to (z¹¹⁰).

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3 cups of fruit mix is divided equally among 18 items.

Each item will contain 1/6 cup of fruit mix.

First we need to divide the total amount of fruit mix by the number of items.

The total amount of fruit mix is :

8/5 cups of blueberries + 7/5 cups of strawberries

= (8/5 + 7/5) cups

= 15/5 cups

= 3 cups

So, 3 cups of fruit mix is divided equally among 18 items.

To find the fraction of a cup used for each item, we need to divide 3 cups by 18:

Copy code

3 cups ÷ 18 = 1/6 cup

Therefore, each item will contain 1/6 cup of fruit mix.

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The value of x, given the equation, can be found to be 2 .

We are given the equation:

( 5x + 4 ) / 2 = 7

The first step is to remove the denominator using cross - multiplication :

2 x ( 5x + 4 ) / 2 = 7 x 2

5 x + 4 = 14

Solving directly for x then gives:

5 x + 4 = 14

5 x = 14 - 4

x = 10 / 5

x = 2

In conclusion, the value of x in the equation which needed to be simplified to 5 x + 4 = 14 , and then solved, is 2.

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The value of x is equal to 10.

In Mathematics, the basic proportionality theorem states that when any of the two (2) sides of a line segment is intersected by a straight line which is parallel to the third (3rd) side of the line segment, then, the two (2) sides that are intersected would be divided proportionally and in the same ratio.

By applying the basic proportionality theorem to the given triangle, we have the following:

21/(x - 3) = 27/(x - 1)

By cross-multiplying, we have the following:

21(x - 1) = 27(x - 3)

21x - 21 = 27x - 81

27x - 21x = 81 - 21

6x = 60

x = 60/6

x = 10.

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eli=e

Cecil=c

e+c=15

e=2c

2c+c=15

3c=15

c=5

e=10

The total percentage of capital contributed by Jacklyn is 30%

The total capital contributed by Sandra, Jaclyn, and Alecia is:

$400 + $600 + $1000 = $2000

To find the percentage of capital contributed by Jacklyn contributed,

Percentage contributed by Jaclyn = (Jaclyn's contribution / Total capital) x 100

= ($600 / $2000) x 100

= 30%

Therefore, Jacklyn contributed 30% of the capital.

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The quadrants that contain all the points found on the linear function -3x + 5y = 15 are given as follows:

The linear function for this problem is defined as follows:

-3x + 5y = 15.

In slope-intercept format, it is given as follows:

5y = 3x + 15

y = 0.6x + 3.

The features of the line are given as follows:

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The y-intercept of the given function is 0.

A y-intercept is the place where a line or curve crosses, or touches, the y-axis the vertical, often darkened line in the center of a graph.

Given is a function f(x) = 3(12)x, we need to find the y-intercept.

The general equation of a line is given by

y = mx+c

Where m is the slope and the c is the y-intercept,

But in our equation, the y-intercept is not available that means it is zero,

We can write the equation as ;-

f(x) = 3(12)x + 0

Hence, the y-intercept of the given function is 0.

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(a)  If the equation  Ax=0has only the trivial solution, then  A  is row equivalent to the identity matrix  is True.
(b) If the columns of  Aspan  Rn, then they are linearly independent is True.
(c) If AT  is not invertible, then neither is  A is  True.
(d) If there is a matrix  D  with  AD=I, then  DA=I  also  is True.

If the equation Ax=0 has only the trivial solution, then the matrix A has a pivot in every column and is therefore row equivalent to the identity matrix.

If the columns of A span Rn, then they are linearly independent because if they were not, there would be a nontrivial linear combination of the columns that equals the zero vector, which would contradict the fact that they span Rn.

If AT is not invertible, then it has a nontrivial null space, which means that there is a nonzero vector x such that ATx=0. This implies that xTA=0, which means that x is in the null space of A. Since A has a nontrivial null space, it is not invertible.

If there is a matrix D with AD=I, then DA=I also because the inverse of a matrix is unique and both AD and DA must be equal to the inverse of A.

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Answer:

--------------------------------

Given two points:

Find the slope of the line containing these points.

Slope equation:

Substitute coordinates and find the slope:

Answer:

-1/10

Step-by-step explanation:

To find:-

Answer:-

We are here given two points and we are interested in finding out the slope of the line passing through the points. Slope can be calculated by using;

[tex]:\implies \sf \boxed{\pink{\sf m =\dfrac{y_2-y_1}{x_2-x_1}}} \\[/tex]

where ,

Also , we can write the coordinate (-3,-7/2) as (-3,-3.5) .

So on substituting the respective values, we have;

[tex]:\implies \sf m =\dfrac{-3.5- (-4)}{-3-2} \\[/tex]

[tex]:\implies \sf m = \dfrac{-3.5+4}{-5} \\[/tex]

[tex]:\implies \sf m =\dfrac{0.5}{-5} \\[/tex]

[tex]:\implies \sf m = \dfrac{1}{2(-5)}\\[/tex]

[tex]:\implies \sf m =\dfrac{1}{-10} \\[/tex]

[tex]:\implies \sf \pink{ m =\dfrac{-1}{10}} \\[/tex]

Hence the slope of the line is -1/10 .

Answer: $170

Step-by-step explanation:

6x + 18(6) = 1128.

6x + 108 = 1128

6x = 1020

x = 170

The price of one ticket is 170

Answer:

Step-by-step explanation:

60mi/hr

Solving a quadratic equation we can see that Jason will hit the water after 6 seconds.

We know that the height of Jason is modeled by the quadratic function:

h = - 16x² + 16x + 480

The water is at h = 0, so we need to solve the quadratic equation:

0 = - 16x² + 16x + 480

If we divide all the right side by 16,we will get:

0 = (- 16x² + 16x + 480)/16

0 = -x² + x + 30

Now we can use the quadratic formula to get the solutions:

[tex]x = \frac{-1 \pm \sqrt{1^2 - 4*(-1)*30} }{2*-1} \\\\x = \frac{-1 \pm 11 }{-2}[/tex]

We only care for the positive solution, which is:

x  = (-1 - 11)/-2 = 6

Jason will hit the water after 6 seconds.

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The ground distance, given the map distance and the scale, would be 5 kilometers.

If the scale on a map is 1:25,000, it means that one unit of distance on the map represents 25,000 units of distance on the ground. If the map distance is 20 cm, we can find the ground distance as follows:

Convert the map distance from centimeters to kilometers:

20 cm = 0.2 m = 0. 0002 km

Find the ground distance using the scale:

Ground distance = Map distance / Scale

Ground distance = 0. 0002 km / ( 1 / 25,000 )

Ground distance = 0.0002 km x 25,000

Ground distance = 5 km

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The full question is:

The scale on a map is 1:25,000. Calculate the ground distance if the map distance is 20 cm write your answer in kilometers​

Answer:

181.74

Step-by-step explanation:

I hope you meant the paycheck was $1398.. if not then this is wrong.

So you take 1398 and multiply it by 0.13 and then you get 181.74. So Jim donated 181.74 this month.

Answer:14

Step-by-step explanation:

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

to get the slope of any straight line, we simply need two points off of it, let's use those above

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{2}-\stackrel{y1}{(-6)}}}{\underset{\textit{\large run}} {\underset{x_2}{-6}-\underset{x_1}{1}}} \implies \cfrac{2 +6}{-7} \implies \cfrac{ 8 }{ -7 } \implies - \cfrac{8 }{ 7 }[/tex]

The correct answer is option C. A graphic image showing a pair of similar polygons with an X-axis showing the value range from 0 to 16 and a Y-axis values from 0 to 16.

Polygons are two-dimensional shapes with straight sides that are joined together. They are closed shapes, meaning all the sides are connected. Polygons can have anywhere from three sides to an infinite number of sides. The most common types of polygons are triangles, quadrilaterals, pentagons, hexagons, and octagons.

This correct image is showing two polygons that are similar, or which have the same shape. This means that the sides of the two polygons are equal in length and each angle is the same. In other words, they are exactly the same shape, but can be different sizes. The X-axis and Y-axis values shown in the image are the coordinates of the points that make up the polygons. The X-axis values indicate the horizontal distance from the origin, while the Y-axis values indicate the vertical distance from the origin. By looking at the coordinates of the points that make up the polygons, we can see that the two polygons are similar.

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Answer:

The pattern described in the question follows the rule that each consecutive line has a number that is one less than twice the previous line. Starting with 2 as the first line, the pattern can be written as follows:

1st line: 2

2nd line: 2(2) - 1 = 3

3rd line: 2(3) - 1 = 5

4th line: 2(5) - 1 = 9

5th line: 2(9) - 1 = 17

6th line: 2(x) - 1 (unknown)

To find the number of marbles in the 6th line, we can use the rule of the pattern and solve for x:

2(x) - 1 = 2(17) - 1 (substitute 17 for the number in the 5th line)

2x - 1 = 33

2x = 34

x = 17

Therefore, the 6th line of the pattern would have 17 marbles

Step-by-step explanation:

The pattern is described as having a number in each line that is one less than twice the previous line.

Write out the first few lines of the pattern, starting with 2 as the first line:

1st line: 2

2nd line: 2(2) - 1 = 3

3rd line: 2(3) - 1 = 5

4th line: 2(5) - 1 = 9

5th line: 2(9) - 1 = 17

To find the number of marbles in the 6th line, use the pattern rule and substitute the value for the 5th line:

6th line: 2(x) - 1

Substitute 17 for x (the value in the 5th line):

2(x) - 1 = 2(17) - 1

Simplify the right-hand side:

2(x) - 1 = 33

Add 1 to both sides:

2(x) = 34

Divide both sides by 2:

x = 17

Therefore, the 6th line of the pattern would have 17 marbles.

The complete pattern in the given question is: 2, 3, 5, 9, 17, 33.

To solve this problem, we need to apply the given rule to generate the numbers in the sequence and then find the sixth number.

Starting with two, we can apply the rule to generate the next few numbers:

First line: 2

Second line: 2(2) - 1 = 3

Third line: 2(3) - 1 = 5

Fourth line: 2(5) - 1 = 9

Fifth line: 2(9) - 1 = 17

Now we can apply the rule again to find the sixth number:

Sixth line: 2(17) - 1 = 33

Therefore, the sixth line must have 33 marbles.

The pattern starts with two, which is the first line.

The second line follows the given rule: "every consecutive line has a number that is one less than twice the previous line". We can apply this rule to the first line by multiplying it by 2 and subtracting 1: 2(2) - 1 = 3. Therefore, the second line has 3 marbles.

To find the third line, we can apply the same rule to the second line: 2(3) - 1 = 5. Therefore, the third line has 5 marbles.

Similarly, we can find the fourth line by applying the rule to the third line: 2(5) - 1 = 9. Therefore, the fourth line has 9 marbles.

We can find the fifth line by applying the rule to the fourth line: 2(9) - 1 = 17. Therefore, the fifth line has 17 marbles.

Finally, to find the sixth line, we apply the rule again to the fifth line: 2(17) - 1 = 33. Therefore, the sixth line has 33 marbles.

So, the complete pattern is: 2, 3, 5, 9, 17, 33.

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A statistical method would be best to use in this situation - Hypothesis testing

We know that the hypothesis testing is nothing but a form of statistical inference that uses data from a sample to draw conclusions about a population probability distribution. Here, first we made a tentative assumption about the distribution. This assumption is called the null hypothesis , which is denoted by H₀. An alternative hypothesis is the opposite of the null hypothesis. It is denoted by [tex]H_a[/tex]

Hypothesis testing is used for confirming a business claim or idea. It is useful for investors who trying to decide what to invest in and whether the it would provide a satisfactory return.

In this case, an investment company provides strategies for improving return on your investment. It believes that it can increase a customer’s returns by 2. 3%.

Here, hypothesis testing which is one of the statistical method that would be best to use.

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Answer:

Let's represent the width of the region by "w". According to the problem, the length of the region is 10 miles longer than the width, so we can represent the length as "w + 10".

The formula for the area of a rectangle is:

Area = Length x Width

So we can write an equation for the area of this region:

299 = (w + 10) x w

Expanding the right side, we get:

299 = w^2 + 10w

Now we can rearrange this equation into standard quadratic form:

w^2 + 10w - 299 = 0

We can solve for "w" by using the quadratic formula:

w = (-b ± sqrt(b^2 - 4ac)) / 2a

Where a = 1, b = 10, and c = -299. Plugging in these values, we get:

w = (-10 ± sqrt(10^2 - 4(1)(-299))) / 2(1)

w = (-10 ± sqrt(1180)) / 2

w = (-10 ± 34.351) / 2

We can ignore the negative solution, since the width of the region cannot be negative. So the width is:

w = (-10 + 34.351) / 2

w = 12.176

We can round the width to the nearest mile, since we can't have a fractional width. So the width is approximately 12 miles.

Now we can use the equation we derived earlier to find the length:

299 = (w + 10) x w

299 = (12 + 10) x 12

299 = 22 x 12

So the length is 22 miles.

Therefore, the width of the region is approximately 12 miles and the length is 22 miles.

The polynomial that need to be added is
(2/5)a^(4) + (-15/4)a^(3) + (1/6)a^(2) + (11/6)a - 3/5 - 5a^(2)b^(2) - 3ab^(2) + 5a^(2)b + 9

To add or subtract polynomials, we need to combine like terms. Like terms are terms that have the same variable and the same exponent.

First, let's add the first two polynomials:

((2)/(5)a^(4)-6a^(3)-(5)/(6)a^(2)+(a)/(2)+1)+((9)/(4)a^(3)+(2a^(2))/(3)+(5)/(3)a-(8)/(5))

= (2/5)a^(4) + (-6 + 9/4)a^(3) + (-5/6 + 2/3)a^(2) + (1/2 + 5/3)a + 1 - 8/5

= (2/5)a^(4) + (-15/4)a^(3) + (1/6)a^(2) + (11/6)a - 3/5

Now, let's subtract the third polynomial from this result:

(2/5)a^(4) + (-15/4)a^(3) + (1/6)a^(2) + (11/6)a - 3/5 - (2a^(2)b^(2)+3ab^(2)-5a^(2)b)

= (2/5)a^(4) + (-15/4)a^(3) + (1/6)a^(2) + (11/6)a - 3/5 - 2a^(2)b^(2) - 3ab^(2) + 5a^(2)b

Finally, let's subtract the last term from this result:

(2/5)a^(4) + (-15/4)a^(3) + (1/6)a^(2) + (11/6)a - 3/5 - 2a^(2)b^(2) - 3ab^(2) + 5a^(2)b - (3a^(2)b^(2)-9)

= (2/5)a^(4) + (-15/4)a^(3) + (1/6)a^(2) + (11/6)a - 3/5 - 5a^(2)b^(2) - 3ab^(2) + 5a^(2)b + 9

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The expression for Jack's brother's age is x = 3 + w

It is important that we know algebraic expressions are defined as expressions which are composed of variables, coefficients, constants, factors and terms.

These algebraic expressions are also identified with mathematical operations, such as;

From the information given, we have that;

Jack is w years old

His brother is 3 years old than him

His brother's age is also x

This is represented as;

x = 3 + w

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The fully factored form is (m-9)(m-12)(m+2) / [2(m+8)(m-8)].

To subtract the rational expressions and find the answer in its fully factored form, we first need to find a common denominator for the two expressions.

The denominators of the two expressions are (m^(2)-64) and (2m^(2)-128). We can factor both of these to find the common denominator.

(m^(2)-64) = (m+8)(m-8)

(2m^(2)-128) = 2(m^(2)-64) = 2(m+8)(m-8)

The common denominator is 2(m+8)(m-8).

Now we can rewrite the two expressions with the common denominator and subtract them:

[(m^(2)+4m-12)(2) - (m^(2)+11m+24)(m+8)(m-8)] / [2(m+8)(m-8)]

= [(2m^(2)+8m-24) - (m^(3)+11m^(2)+24m+8m^(2)+88m+192)] / [2(m+8)(m-8)]

= [m^(3)-17m^(2)-104m-216] / [2(m+8)(m-8)]

= (m-9)(m^(2)-8m-24) / [2(m+8)(m-8)]

= (m-9)(m-12)(m+2) / [2(m+8)(m-8)]

So the answer in its fully factored form is (m-9)(m-12)(m+2) / [2(m+8)(m-8)].

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The quadratic function in standard form of f (x) = x2 - 8x + 23 is  (x) = (x - 4)2 + 7.

The quadratic function given is f (x) = x2 - 8x + 23. To rewrite this function in standard form, we need to complete the square for the x terms. Standard form for a quadratic function is f (x) = a(x - h)2 + k, where (h, k) is the vertex of the parabola.

f (x) = 1(x2 - 8x) + 23

f (x) = 1(x2 - 8x + 16) + 23 - 16

f (x) = 1(x2 - 8x + 16) + 7

f (x) = 1(x - 4)2 + 7

The final answer is f (x) = (x - 4)2 + 7, which is the standard form of the given quadratic function.

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Answer:

C) 100

Step-by-step explanation:

[tex]3.5c - 1.5d > 50[/tex]

[tex]3.5c - 1.5(200) > 50[/tex]

[tex]3.5c - 300 > 50[/tex]

[tex]3.5c > 350[/tex]

[tex]c > 100[/tex]

The answer is $21,989.34 and Yes, $10,000 invested at 6% interest will double its value in half the time as $10,000 invested at 3% interest.

Now, For the 6% investment:


$10,000 invested at 6% interest will double in 12 years:


$10,000 × (1.06)^12 = $21,989.34


For the 3% investment:


$10,000 invested at 3% interest will double in 24 years:


$10,000 × (1.03)^24 = $21,989.34


Therefore, it will take half the time (12 years) for the 6% investment to double its value compared to the 3% investment (24 years).

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We can also plot the vertical asymptote at x = -1/3 and the horizontal asymptote at y = 0.

A rational function can be represented by a polynomial that has been divided by another polynomial. The set of all numbers omitting the zeros in the denominator makes up the domain of a rational function because polynomials are defined everywhere. First example: x = f(x) (x - 3).

A) Factor the denominator and numerator together:

w(x) = 3(x - 7)/(3x + 1) = (3x - 21)/(3x2 - 20x - 7) (x - 7)

B) Locate the discontinuity point, if one exists:

With x - 7 = 0 or 3x + 1 = 0, the denominator is 0. As a result, the function exhibits discontinuity points at x = -7 and x = -1/3.

C) Identify the vertical asymptote: For x = -1/3, the function has a vertical asymptote.

D) Locate the horizontal asymptote: The numerator and denominator each have degrees of 2 and 1, respectively. As a result, the horizontal asymptote is y = 0.

E) Visualize the function

Using the value table:

x y

-5 4.5

-2 -1.4

-0.4 -4.11

0 -7

1 -2.4

5 -0.5

7 undefined

The horizontal asymptote at y = 0 and the vertical asymptote at x = -1/3 can also be plotted.

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Answer:

6 and -4

Step-by-step explanation:

Let the first number be n.

Other number= [tex]\frac{-24}{n}[/tex]

Their sum= 2

n + [tex]\frac{-24}{n}[/tex]= 2

[tex]\frac{n^{2-24} }{n}[/tex]= 2

n²-24= 2n

You can solve this problem in either of these 2 ways:

i) Square Completion method:

  n²-2n = 24

  Half of the coefficient= [tex]\frac{2}{2}[/tex] =1

  Its square= 1²= 1

  n²-2n+1= 24+1

      (n-1)²= 25

          n-1= [tex]\sqrt{25}[/tex]

          n-1= ±5

  If n-1= 5,

     n= 5+1

     n= 6

  If n-1= -5,

     n= -5+1

     n= -4

  ∴ the numbers are 6 and -4

ii) Equation Method:

   n²-24= 2n

   n²-2n-24= 0

   a= 1,

   b= -2,

  -b= 2,

   c= -24

   n= -b±[tex]\sqrt{b^{2}-4ac }[/tex]/2a

   n= 2±[tex]\sqrt{-2^{2}-4x1x-24[/tex]/2x1

   n= 2±[tex]\sqrt{4+96}[/tex]/2

   n= 2±[tex]\sqrt{100}[/tex]/2

   n= 2±10/2

   If n= [tex]\frac{2+10}{2}[/tex],

      n= [tex]\frac{12}{2}[/tex]

      n= 6

   If n= [tex]\frac{2-10}{2}[/tex],

      n= [tex]\frac{-8}{2}[/tex]

      n= -4

∴ the numbers are 6 and -4