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Answer:

y = 1/2x+5

Step-by-step explanation:

You have two points so you can find the slope

m = (y2-y1)/(x2-x1)

m = (8-3)/(6 - -4)

   (8-3)/(6+4)

    5/10

 1/2

The slope intercept form is y = mx+b where m is the slope and b is the y intercept

y = 1/2 x+b

Substitute a point into the equation

8 = 1/2(6)+b

8 = 3+b

b=8-3 = 5

y = 1/2x+5

The integral is∫ X (x² - 4x – 5)³/2 dx.To get the main answer to the question, we will use substitution. We'll let u = x² - 4x – 5. Therefore, we haveu = x² - 4x – 5du/dx = 2x - 4 du = (2x - 4) dxdx = du / (2x - 4)Therefore, we can rewrite the integral as∫ X u³/2 (1 / (2x - 4)) du= 1/2 ∫u³/2 (1 / (x - 2)) du

Now we can use a standard integration technique to solve the integral. Let t = x - 2. Therefore, we havet =

x - 2x = t + 2dt/dx = 1 dt = dx.

Now we can rewrite the integral as:

∫ 1/2 u³/2 (1 / t) dt= (1 / 2) ∫ u³/2 t^-1 dt= (1 / 2) ∫ u³/2 (t^-1) dt= (1 / 2) ∫ (x² - 4x – 5)³/2 (x - 2)^-1 dx.

Now we can use substitution to solve the integral. Let y = x - 2. Therefore, we have:

x = y + 2dy/dx = 1dy = dx.

Now we can rewrite the integral as:

(1 / 2) ∫ y³/2 (y)^-1 dy= (1 / 2) ∫ y¹/2 dy= (1 / 2) * (2 / 3) * (y)^3/2.

Now we can substitute back to the original variable x. The final result is:

(1 / 3) * (x - 2)^(3/2) + C

Where C is the integration constant.Using the above technique, we get the main answer to the question as:(1 / 3) * (x - 2)^(3/2) + C.. This is the solution to the integral:

∫ X (x² - 4x – 5)³/2 dx

by using the substitution method, standard integration technique and substitution.

The final result is:(1 / 3) * (x - 2)^(3/2) + C.Where C is the integration constant.

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The domain of the function is a semicircle with a radius of 5 and centered at the origin, where y is non-negative.

The domain of a function is the set of all possible input values for which the function is defined. In this case, the function is defined as:

\(f(x,y) = \sqrt{y} + \sqrt{[25 - x^2 - y^2} ]\)

To find the domain of this function, we need to determine the values of x and y that would result in the function producing a real-valued output.

For the square root of y to be real, y must be non-negative. That is, y ≥ 0.

For the square root of [\(25 - x^2 - y^2\)] to be real, we must have:

\(25 - x^2 - y^2 \geq 0\\x^2 + y^2 \leq 25\)

This is the equation of a circle with radius 5 centered at the origin. Therefore, the domain of the function is the set of all points (x, y) that lie inside or on this circle and have y ≥ 0.

In interval notation, we can write:

Domain: {(x, y) |\(x^2 + y^2 \leq 25, y \geq 0\)}

To sketch the domain, we can plot the circle with radius 5 centered at the origin and shade the region above the x-axis. This represents all the valid input values for the function. The boundary of the domain is the circle, and the domain includes all points inside the circle and on the circle itself, but not outside the circle.

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Answer:

A. You may set the variables in either order. But for argument sake, let's set as follows:

x = Amount of bookshelves

y = Amount of tables

B. Because of the amount of things you need to make, the following is an inequality using those variables.

x + y > 25

Plus you can determine a second inequality based on the amount of money that you have to spend.

20x + 45y < 675

Finally you may also add in that each value must be greater than or equal to zero, since they cannot have negative tables.

C. By solving the system and looking at basic constraints when graphed, you can see the feasible region has 4 vertices.

(0,0)

(18, 7)

(0, 15)

(33.75, 0) or (33, 0) if you insist on rounding.

Step-by-step explanation: Good luck and hope this helps :)

The length of the remaining piece of beam as polynomial is 6y²⁺⁷⁺¹¹

An algebraic expression with two or more algebraic terms is known as a polynomial.It has exponents, operators, coefficients, coefficients, variables, and constants.  A polynomial is a mathematical expression that solely uses the operations addition, subtraction, multiplication, and non-negative integer powers of variables. It is made up of indeterminates (also known as variables) and coefficients.

The length of the wooden beam is (7y²⁺⁷⁺¹) meters long and a piece of length (y²⁻¹⁰) meters is cut off ¹.

Therefore, the length of the remaining piece of beam can be expressed as follows:

(7y²⁺⁷⁺¹)-(y²⁻¹⁰) = 6y²⁺⁷⁺¹¹

So, the length of the remaining piece of beam is 6y²⁺⁷⁺¹¹

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The person is approximately 1233.35 feet from the monument

Let's call the distance from the person to the monument "x". We can use basic trigonometry to solve this problem.

From the person's point of view, the monument appears as a right triangle with the monument's height (400 feet) as the opposite side and "x" as the adjacent side. The angle of elevation (from the person to the top of the monument) is 18 degrees, which is the angle opposite the opposite side (the monument's height). So we can use the tangent function to find "x":

tan(18) = opposite / adjacent

tan(18) = 400 / x

x = 400 / tan(18)

x ≈ 1233.35 feet

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The coefficients of the power series are: c0= 9, c1= 0, c2= 0, c3= 135/2, c4= 3/2

To find the coefficients of the power series, we can use the formula:

c_n = (1/n!)(d^n/dx^n)[9/(1−x^3)]

where d^n/dx^n represents the nth derivative of the function with respect to x.

First, let's find the derivatives of 9/(1−x^3):

d/dx[9/(1−x^3)] = 27x^2/(1−x^3)^2

d^2/dx^2[9/(1−x^3)] = (54x(1−2x^3))/(1−x^3)^3

d^3/dx^3[9/(1−x^3)] = (216x^4−648x^2+135)/(1−x^3)^4

d^4/dx^4[9/(1−x^3)] = (216(10x^9−45x^6+47x^3−3))/(1−x^3)^5

Now, let's substitute these derivatives into the formula for the coefficients:

c0 = 9/(1-0^3) = 9

c1 = (1/1!)[d/dx(9/(1−x^3))]_(x=0) = 0

c2 = (1/2!)[d^2/dx^2(9/(1−x^3))]_(x=0) = 0

c3 = (1/3!)[d^3/dx^3(9/(1−x^3))]_(x=0) = 135/2

c4 = (1/4!)[d^4/dx^4(9/(1−x^3))]_(x=0) = 3/2

Therefore, the coefficients of the power series are:

c0= 9
c1= 0
c2= 0
c3= 135/2
c4= 3/2

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The number line for the set of jump distances to make a new record.

Option B is the correct answer.

It is the representation of numbers in real order.

The difference between the consecutive numbers in a number line is always positive.

We have,

The school record in the long jump = 518 cm

Now,

To make a new record the set of jump distances should be greater than 518 cm.

To represent the set of jump distances on a number line we can not have a black dot on 513 on the number line.

The dot should be an open dot.

Thus,

Option B is the number line for the set of jump distances to make a new record.

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The union set for the given sets X and Y are: X∪Y = {0,1,2,4,6,8,9}.

The elements shared by all of the sets are contained in the union of two (maybe three, as well as four, or more) sets.

The given sets are;

X={1,2,8,9}

Y={0,1,2,4,6,8,9}

So, union set contains all the values from both set without repeating the values.

Thus,

X∪Y = {0,1,2,4,6,8,9}.

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To find the horizontal distance between the submarine and the airplane, we can use trigonometry.

Given:

Elevation angle = 30 degrees

Altitude of the airplane = 2000 feet

Let's denote the horizontal distance between the submarine and the airplane as 'd'.

Using trigonometry, we can set up the following relationship:

tan(30 degrees) = Altitude / Horizontal distance

tan(30 degrees) = 2000 / d

We can now solve for 'd' by isolating it:

d = 2000 / tan(30 degrees)

Using a calculator, we can calculate the value of tan(30 degrees) and then find the value of 'd'.

d ≈ 3464.102 (rounded to the nearest foot)

Therefore, the horizontal distance between the submarine and the airplane is approximately 3464 feet.

The correct answer is option a. 3464 feet.

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Answer:

12

Step-by-step explanation:

Step-by-step explanation:

which angle ? all of them ?

in such a case of intersection the various angles are mirrored or have to fulfill the complementary 180 degree criteria.

when we look either on the top or the bottom of the intersected line, there is always a half circle that can be drawn with its center in the intersection point.

therefore, the sum of such 2 neighboring angles (like 1 and 43 degrees) must be 180 degrees. the same for 2 and 3.

at the same time 2 is a mirrored version of 43 degrees, and 3 is a mirrored version of 1.

so,

1 + 43 = 180

1 = 137 degrees

2 = 43 degrees

3 = 137 degrees

Answer:

 y = -1/2x + 4

Step-by-step explanation:

We have two points ( 8,0) and ( 0,4)

We can find the slope

m =(y2-y1)/(x2-x1)

    = (4-0)/(0-8)

    4/-8

   -1/2

We can use the slope intercept form

 y = mx+b where m is the slope and b is the y intercept

 y = -1/2x + 4

Answer:

Step-by-step explanation:

eq. of line with intercepts a and b is

\(\frac{x}{a} +\frac{y}{b} =1\\here ~eq. ~of ~line~ is ~ \frac{x}{8} +\frac{y}{4} =1\\or x+2y=8\\\)

The circumference of a circle is its perimeter.

We can solve for the circumference using the following formula:

We're given:

Plug the given information into the formula for circumference:

\(C=2\pi r\\C=2\pi (14)\\C=28\pi\)

Therefore, the circumference of the circle is 28π cm.

Replace π with \(\dfrac{22}{7}\):

\(C=28\pi\\\\C=28*\dfrac{22}{7}\\\\C=4*22\\C=88\)

Therefore, the circumference of the circle with \(\pi=\dfrac{22}7}\) is 88 cm.

Answer:

A im pretty sure it is

Step-by-step explanation:

Answer:

The answer is B 1200.

Step-by-step explanation:

The area of the whole mosaic is  150.06 square feet.

What is an array?

In mathematics, an array is an ordered arrangement or display of objects or numbers in rows and columns. Arrays are commonly used to represent multiplication and division in arithmetic, and they can also be used to organize data in statistics and other fields.

The mosaic has a 7 × 7 array of square tiles, so it has a total of 7 x 7 = 49 tiles.

Each tile is 1 3/4 feet long, so its area is (1 3/4) x (1 3/4) = 49/16 square feet.

Therefore, the area of the whole mosaic is:

49 tiles x (49/16 square feet per tile) = 2401/16 square feet

Simplifying this fraction gives:

Area of mosaic = 150 1/16 square feet

So the area of the whole mosaic is approximately 150.06 square feet.

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Tthe approximate value of f(1.003, 2.001) is 0.072

The partial derivative of f with respect to x, denoted as ∂f/∂x, measures the rate of change of f with respect to x while treating y as a constant. Similarly, the partial derivative of f with respect to y, denoted as ∂f/∂y, measures the rate of change of f with respect to y while treating x as a constant.

At the point (1.003, 2.001), we can calculate the partial derivatives:

∂f/∂x = 12x²y² - 2y² - 1

∂f/∂y = 8x³y - 4xy

Evaluating these derivatives at (1.003, 2.001) gives us:

∂f/∂x ≈ 12(1.003)²(2.001)² - 2(2.001)² - 1 ≈ 11.244

∂f/∂y ≈ 8(1.003)³(2.001) - 4(1.003)(2.001) ≈ 16.048

Using the linear approximation formula, we have:

Δf ≈ (∂f/∂x)Δx + (∂f/∂y)Δy

Substituting the values, where Δx = 1.003 - 1 and Δy = 2.001 - 2, we get:

Δf ≈ 11.244(0.003) + 16.048(0.001) ≈ 0.056 + 0.016 ≈ 0.072

Therefore, the approximate value of f(1.003, 2.001) is 0.072.

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Besides vertical asymptotes, the zeros of the denominator of a rational function give rise to vertical holes or removable discontinuities in the graph of the function.

When the denominator of a rational function becomes zero at a specific value of x, it results in an undefined value for that particular \(x\) value. This means that the function is not defined at that point, creating a potential discontinuity.

However, in some cases, the numerator of the rational function may also have the same zero value as the denominator, which cancels out the undefined behavior and makes the function well-defined at that point. These canceled zeros give rise to vertical holes in the graph.

A vertical hole occurs when there is a "hole" or an open circle in the graph of the rational function at the x value where the denominator is zero. This indicates that the function has a removable discontinuity at that point.

To clarify, if the zero of the denominator is not canceled out by the numerator, it results in a vertical asymptote. On the other hand, if the zero of the denominator is canceled out by the numerator, it leads to a vertical hole or a removable discontinuity in the graph of the function.

Therefore, the zeros in the denominator of a rational function result in vertical holes or detachable discontinuities on the graph of the function in addition to vertical asymptotes.

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Answer:

9 minutes

Step-by-step explanation:

As it states in the question it takes 15 minutes to paint 5 kids so you do 15/5=3

So it takes 3 minutes to paint each kid.

In the problem it asks how long does it take to paint three kids.

So now we do 3 minutes*3 kids=9 minutes

So it takes 9 minutes to paint three kids

Hope this helps,

Please give me brainliest if you think my answer is correct.

Answer:

Step-by-step explanation:

As per the question we are looking for a number which is a multiple of the greatest possible exponent of 3.

Let's see the exponents of 3 within 1-2017 interval:

As we see the greatest exponent of 3 is 729.

There are two multiples of 729 in the given interval:

So the last number is 1458

First, we need to define rational numbers

Rational numbers are numbers that can be express as a quotient or fraction

From the question given, The square root of 16 is 4, this can be express as 4/1

Hence, it is a rational number

Therefore the correct option is A

The probabilities of random survey of students are

Total number of engineering majors = 34

Total number of business majors = 24

Total number of science majors = 22

Total number of liberal arts majors = 16

Total number of students = 34 + 24 + 22 + 16

= 96 students

The probability = Number of favorable outcomes / Total number of outcomes

The probability of engineering majors = 34 / 96

= 17/48

The probability of business majors = 24 / 96

= 1/4

The probability of science majors = 22/96

= 11/48

The probability of liberal arts majors = 16/96

= 1/6

Hence, the probabilities are

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Step-by-step explanation:

$ 11.58 is your answer....

By using Euclid's first book, we can prove that the quadrilateral produced by perpendicular, unequal, bisecting diagonals is a kite. A kite is a quadrilateral with two pairs of adjacent sides that are equal in length. In this case, the two pairs of adjacent sides are formed by the diagonals bisecting the quadrilateral into four smaller triangles with equal areas.

According to Euclid's first book, when two lines intersect at a right angle (perpendicular), they form four right angles. In the case of a quadrilateral with perpendicular, unequal, bisecting diagonals, the diagonals intersect at a right angle and divide the quadrilateral into four smaller triangles with equal areas.

1. Draw a quadrilateral with perpendicular, unequal, bisecting diagonals.
2. Label the points where the diagonals intersect as A, B, C, and D.
3. Label the point where the diagonals intersect as E.
4. Use Euclid's first book to prove that the angles at E are all right angles.
5. Use Euclid's first book to prove that the four triangles formed by the diagonals are congruent (equal in area).
6. Use the definition of a kite to prove that the quadrilateral is a kite (two pairs of adjacent sides are equal in length).
7. Therefore, the quadrilateral produced by perpendicular, unequal, bisecting diagonals is a kite.

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Answer:

3.6069 × 104

Step-by-step explanation:

Answer:

1: 1 1/3 | simplified: 4/3

2: 1 1/4 | simplified: 5/4

3: 2 1/3 | simplified: 7/3

4: 1 2/3 | simplified: 5/3

5: 1 3/7 | simplified: 10/7

6: 2 2/5 | simplified: 12/5

7: 1/2

8: 1 1/2 | simplified: 3/2

9: 2 1/4 | simplified: 9/4

10: 3 8/9 | simplified: 35/9

11: 2

12: 2 2/3 | simplified: 8/3

13: 2 1/2 | simplified: 5/2

14: 4 2/7 | simplified: 30/7

i hope this helps!

The required exponential expression equivalent to \(\sqrt[9]{z}\) is \(z^{1/9}\). Option A is correct.

The exponential expression equivalent to the nth root of a number is that number raised to the power of 1/n. Therefore, the exponential expression equivalent to \(\sqrt[9]{z}\) is:

\(z^{1/9}\)

So the answer is A. \(z^{1/9}\).

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Answer:

y= -2x +8

Step-by-step explanation:

perpendicular lines have a negative reciprocal gradient so

1/2 becomes -2/1 which is the gradient

sub in the values of x and y

2= -2 (3) +C

2= -6 + C

8=C

y=-2x +8

Answer:

y = -2x + 8

Step-by-step explanation:

for me the easiest way is simply to transform the slope and then just determine the y-intersect.

the slope of the original line is 1/2.

it is always the factor of x and represents the y/x ratio of the function (how many units is y changing when x changes a certain number of units).

a perpendicular line (90 degree angle) simply reverses x and y and the sign of the original slope.

so, the slope of the perpendicular line is -2, and the equation is

y = -2x + c

and c we get by using the point coordinates :

2 = -2×3 + c

2 = -6 + c

c = 8

so, we have

y = -2x + 8

First, lets find the numbers 8 2/3 and 1 3/5, as follows:

And:

Now we can find our division, as follows: