What are the restrictions on the domain for the following rational expression?

Step-by-step explanation:

1. 0.9862

2. 2.3

3. 7

4. 45.1

5. 18.735

The point (-√2,1) can also be represented as (√3, 5.18) in polar coordinates.

To find the polar coordinates of the rectangular coordinates (-√2,1), we can use the following formulas:

r = √(x² + y²)

θ = tan^⁻1(y/x)

Plugging in the given values of (-√2,1), we get:

r = √((-√2)² + 1²) = √(2 + 1) = √3

θ = tan^⁻1(1/(-√2)) ≈ 2.0344 radians

Note that since the point (-√2,1) is in the second quadrant, we need to add π to the value of θ obtained from the inverse tangent in order to obtain an angle in the interval [0,2π). Thus, we have:

θ ≈ 2.0344 + π ≈ 5.1779 radians

Rounding to 2 decimal places as needed, we get the polar coordinates of (-√2,1) as (r,θ) ≈ (√3, 5.18).

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Answer:

B

Step-by-step explanation:

use quadratic formula:  (-b ±√b²-4ac) ÷ 2a

a = 10,  b = -9,  c = -6

The component form of the following vectors is Option A. V = (38.3, 32.1).

To find the component form of a vector given its magnitude and direction angle, we can use trigonometry.

The component form of a vector in two dimensions is represented as (x, y), where x is the horizontal component and y is the vertical component.

In this case, the magnitude of the vector is given as 50, and the direction angle θ is 50°. We can use this information to calculate the horizontal and vertical components.

The horizontal component (x) can be found using the formula x = magnitude * cos(θ), and the vertical component (y) can be found using y = magnitude * sin(θ).

Let's calculate the components:

x = 50 * cos(50°) ≈ 38.3

y = 50 * sin(50°) ≈ 32.1

Rounding the answers to the nearest tenth, we get the component form of the vector V as (38.3, 32.1).

Therefore, the correct answer is A. V = (38.3, 32.1).

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The question is incomplete. Find the full content below:

Find the component form of the following vectors. Round your answers to the tenth.

Magnitude of v = 50, direction angle θ = 50°

A. V = (38.3, 32.1)

B. V = (33.8, 31.2)

C. V = (32.1, 38.3)

D. V = (31.2, 33.8)

The term formula for a geometric progression where the second term is 54, the fourth term is 6, and the common ratio is 0.5 is Un = 108 * (0.5)n-1.

In a Geometric Progression (G.P.), each term is the product of the previous term and a constant multiplier (known as the common ratio). To begin, identify the common ratio (r) by using the formula r = Un / Un-1. If the second term is 54 and the fourth term is 6, then the common ratio (r) is √(6/54) = 0.5.

Once we have established the common ratio, we can find an arbitrary term of the progression using the formula Un = U1 * r(n-1). However, since we don't know the first term, we can derive it from U1 = U2 / r, substituting our given values, we find U1 = 54 / 0.5 = 108.

Now, we can substitute U1 and r into our term formula to find any term (n) in the series: Un = 108 * (0.5)n-1.

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The Present value is $6,139.132.

We have,

FV=100000, pmt = 4000, I =5%, n=10

So, The present value formula is

PV=FV / (1 + \(i)^n\)

So, PV =  100, 000 / (1+ 5/100\()^{10\\\)

PV = 100,000 / (1+ 0.05\()^{10\\\)

PV = 100, 000/ (1.05\()^{10\\\)

PV = 100,000 / 1.6288946

PV= $6,139.132

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y = 3x + 25

Choose two points from the table, say

x1 = 2, x2 = 6

y1 = 31, y2 = 43

The slope here is:

(y2 - y1)/(x2 - x1)

(43 - 31)/(6 - 2)

= 12/4

= 3

The equation of the line if given as:

y = mx + b

where m is the slope and b is the y-intercept.

31 = 3(2) + b

31 - 6 = b

b = 25

Therefore, the equation is:

y = 3x + 25

The required amount of the space available is 0.045 cubic meter.

We need to determine Space inside the steps.

The Volume is defined as the mass of object per unit density.

The required space = 0.3*0.4*0.5 - 0.15*0.5*0.2

                                 =  0.06 - 0.015

                                 =    0.045 cubic meter

Hence, the required amount of the space available will be 0.045 cubic meter.

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The distance between the two points is

d = √( -2-x)² + (3 -y)² OR d = √ (x+2)² + (y-3)².

Distance between two points is the length of the line segment that connects the two points in a plane.

The distance between two points is expressed as;

d = √ (X-x )² + (Y-y)²

X = -2

x = x

Y = 3

y = y

Therefore the distance between the two points is

d = √( -2-x)² + (3 -y)²

or it can also be written in this form

d = √ x-(-2)² + (y-3)²

d = √ x+2)² + (y-3)²

therefore the model of the distance between the two points can be

d = √( -2-x)² + (3 -y)² OR d = √ (x+2)² + (y-3)².

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Answer:

P ($)=70-5(t)

Where p = price at t days

t = number of days

Step-by-step explanation:

The product price initially = $70

Now, every day , it reduces $5

The rate=$5 per day reduction

The price in the days will be determined by the formula below

P ($)=70-5(t)

Where p = price at t days

t = number of days

So let's assume it's on the second day

The price after the second day

P($) = 70-5(2)

P($) = 70-10

P($)= $60

The price after two days will be reduced to $60

Answer:

(40+ 19) – 38

Step-by-step explanation:

We need to find the expression for "thirty-eight less than the sum of forty and nineteen".

Sum of forty and nineteen = 40 + 19

38 less than the above is 40 + 19 - 38

Overall expression is :

(40 + 19) - 38

Hence, the correct option is (d) "(40+ 19) – 38".

Answer: -5 + 14 - 20 = -11

Answer:

-1

Step-by-step explanation:

x = -5, y = 4, and t = 7

|-5| + 2(7) - 5(4) =

|-5| + 14 - 20

|-5| = 5 absolute rule

5 + 14 - 20 =

-1

Answer:

215

Step-by-step explanation:

7*(6+2)4-9

7*8*4-9

56*4-9

224-9=215

Answer:

7.12.2= 168

Step-by-step explanation:

168 x 168 =28224

28224-3= 28221

28221 x 28221 = 796424841

( 1 + sinx / cosx ) + ( cosx / 1 + sinx ) =

_________________________________

(1 + sinx)(1 + sinx)/cosx(1 + sinx)

+

(cosx)(cosx)/(1 + sinx)(cosx) =

_________________________________

(1 + sinx)^2 /cosx(1 + sinx)

+

(cosx)^2/cosx(1 + sinx) =

_________________________________

1 + 2sinx + sin^2 x/cosx(1 + sinx)

+

cos^2 x/cosx(1 + sinx) =

_________________________________

1 + sin^2 x + cos^2 x + 2sinx / cosx(1 + sinx) =

1 + 1 + 2sinx / cosx(1 + sinx) =

2 + 2sinx / cosx(1 + sinx) =

2(1 + sinx)/cosx(1 + sinx) =

( 1 + sinx) simplifies from the face and the denominator of the fraction

2/cosx

Answer:

Option C, neither.

Step-by-step explanation:

Here we have the table:

x: -10    -3    4    11

y:   1      6    30   120

This means that if our function is f(x), then:

f(-10) = 1

f(-3) = 6

f(4) = 30

f(11) = 120

We want to know if this represents a linear equation or an exponential equation or neither.

First, let's try with a linear equation.

We know that a linear equation can be written as:

f(x) = a*x + b

Then let's input the known values and let's see if this equation works.

We can use two of the known points to get:

f(-10) = 1 = a*-10 + b

f(4) = 30 = a*4 + b

With these equations, we can find the value of a and b, once we find these values, we can see if the equation also works for the other two points.

1 = a*-10 + b

30 = a*4 + b

First, we need to isolate one of the variables in one of the equations.

I will isolate b in the first one:

b = 1 + a*10

Now we can replace this in the other one to get:

30 = a*4 + 1 + a*10

30 = 1 + a*14

30 - 1 = a*14

29 = a*14

29/14 = a = 2.07

and using the equation b = 1 + a*10 we can find the value of b:

b = 1 + 2.07*10 = 1 + 20.7 = 21.7

Then the equation we get is:

f(x) = 2.07*x +  21.7

Now we need to see if this works for the other two points:

for x = -3, we need to get: f(-3) = 6

f(-3) = 2.07*-3 + 21.7 = 15.49

We did not get the value we expected, then we already know that the relationship is not linear.

Now let's see if the relationship can be exponential.

An exponential function is written as:

f(x) = A*(r)^x

Let's do the same as above, let's use two of the known points to find the values of A and r

f(-3) = 6 = A*(r)^(-3)

f(4) = 30 = A*(r)^4

Now we have the system of equations:

30 = A*(r)^4

6 = A*(r)^(-3)

If we take the quotient of these two equations, we get:

(30/6) = (A*(r)^4)/( A*(r)^(-3))

5 = (r^4)*r^3 = r^(4 + 3) = r^7

(5)^(1/7) = r = 1.258

And the value of A is given by:

30 = A*(1.258)^4

30/( (1.258)^4 ) = 11.98

Then the exponential equation is something like:

f(x) = 11.98*(1.258)^x

Now let's see if this equation also works for the other two points:

for x = -10, we should get f(-10) = 1

Let's see that:

f(-10) = 11.98*(1.258)^(-10) = 1.2

And for x = 11 we should get f(11) = 120

f(11) =  11.98*(1.258)^(11) = 149.6

So we get values closer to the ones we should get, but not the exact ones, so this is not an exponential relation.

Then the correct option is C, neither.

The statement that accurately describes the internet is that it was created by the US Department of Defense for military purposes.

It is a complex massive network that connects devices all around the world, this includes cellphones, computers, tablets. etc.

The first official project that developed this network was the ARPA project or Advanced Research Project Agency. This project was developed by the Department of Defense in the United States and the purpose was to create a network that could be used as part of military strategies.

Based on this, the true statement is that the internet was created for military purposes by the Defense Department.

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Answer:

Sorry I'm late to answer, but the answer is C.

Hope this helps!

Answer:

Plot B

Step-by-step explanation:

Plot B has a negative slope.

The domain is x is all real numbers where x does not equal negative 4 comma range is y is all real numbers where y does not equal negative 11. Option C

The domain of a function refers to the entire area for which the function returns a value. The function in this case is; f(x) = x^2 - 3x - 28/x + 4. The domain of the function will be real numbers except -4.

Hence, we can say that domain is x is all real numbers where x does not equal negative 4 comma range is y is all real numbers where y does not equal negative 11.

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Answer:

The answer is C.

Answer:

9 7/8

Step-by-step explanation:

1. 4 3/8 can be converted into the improper fraction 35/8, and 5 1/2 can be converted into 11/2.

2. Now that we have 35/8 + 11/2, we have to find a common denominator. Since 2 goes into 8 four times, we can turn 11/2 into 44/8 by multiplying the numerator and denominator (the top and the bottom numbers) by 4.

3. Now we have 35/8 + 44/8. At this point, the all we have to do is add the numerators (the top numbers). 35+44=79, so our answer is 79/8, which we can simplify to 9 7/8.

The total interest that he would pay on this loan is given as follows:

$2,160.

The balance of an account after t years, using simple interest, that is, a single compounding per year, is given by the equation shown as follows:

A(t) = P(1 + rt).

In which the parameters of the equation are explained as follows:

Considering this equation, the interest accrued is given as follows:

I(t) = Prt.

In the context of this problem, the values of these parameters are given as follows:

P = 7500, r = 0.064, t = 4.5.

Hence the interest accrued on the payment is obtained as follows;

I(4.5) = 7500 x 0.064 x 4.5 = $2,160.

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Here are the correct matches to the expressions to their solutions.

The GCF of 28 and 60 is 4.

(-3/8)+(-5/8) = -4/4 = -1.

-1/6 DIVIDED BY 1/2 = -1/6 X 2 = -1/3.

The solution of 0.5 x = -1 is x = -2.

The solution of 1/2 m = 0 is m = 0.

-4 + 5/3 = -11/3.

-2 1/3 - 4 2/3 = -10/3.

4 is not a solution of -4 < x.

1. The GCF of 28 and 60 is 4.

The greatest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. To find the GCF of 28 and 60, we can factor each number completely:

28 = 2 x 2 x 7

60 = 2 x 2 x 3 x 5

The factors that are common to both numbers are 2 and 2. The GCF of 28 and 60 is 2 x 2 = 4.

2. (-3/8)+(-5/8) = -1.

To add two fractions, we need to have a common denominator. The common denominator of 8/8 and 5/8 is 8. So, (-3/8)+(-5/8) = (-3 + (-5))/8 = -8/8 = -1.

3. -1/6 DIVIDED BY 1/2 = -1/3.

To divide by a fraction, we can multiply by the reciprocal of the fraction. The reciprocal of 1/2 is 2/1. So, -1/6 DIVIDED BY 1/2 = -1/6 x 2/1 = -2/6 = -1/3.

4. The solution of 0.5 x = -1 is x = -2.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate x by dividing both sides of the equation by 0.5. This gives us x = -1 / 0.5 = -2.

5. The solution of 1 m = 0 is m = 0.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate m by dividing both sides of the equation by 1. This gives us m = 0 / 1 = 0.

6. -4 + 5/3 = -11/3.

To add a fraction and a whole number, we can convert the whole number to a fraction with the same denominator as the fraction. In this case, we can convert -4 to -4/3. So, -4 + 5/3 = -4/3 + 5/3 = -11/3.

7. -2 1/3 - 4 2/3 = -10/3.

To subtract two fractions, we need to have a common denominator. The common denominator of 1/3 and 2/3 is 3. So, -2 1/3 - 4 2/3 = (-2 + (-4))/3 = -6/3 = -10/3.

8. 4 is not a solution of -4 < x.

The inequality -4 < x means that x must be greater than -4. The number 4 is not greater than -4, so it is not a solution of the inequality.

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For the given triangle the value of z = 1, y = 6, and x = 4.75.

One of the earliest areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects.

The value of x,y, and z will be calculated by the property states that the ratio of the median line passing from the centroid of the triangle is divided into the ratio of 1: 2.

The value of x,

( 2x - 6 ) / 7 = 1 / 2

2 ( 2x - 6 ) = 7

4x - 12 = 7

4x = 19

x = 19 / 4

The value of y,

3 / y = 1 / 2

y = 3 x 2

y = 6

The value of z,

2z / 4 = 1 / 2

4z = 4

z = 1

Therefore, the values are z = 1, y = 6, and x = 4.75.

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1. Relation 1 is a function

2. Relation 2 is a function

3. Relation 3 is not a function

4. Relation 4 is a function

From the question, we have the following parameters that can be used in our computation:

The relations (1) to (4)

Relation (1)

This relation is a function

This is because each range value point to unique domain values

Relation (2)

This relation is a function

This is because each range value point to unique domain values

Relation (3)

This relation is not a function

This is because domain values w have different range values.

Relation (4)

This relation is a function

This is because each range value point to unique domain values

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The measure of side length EF in the right triangle is 24.

The Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

It is expressed as;

c²  = a² + b²

From the diagram:

Hypotenuse DE = c = 26

Leg DF = a = 10

Leg EF = b = ?

Plug in the values and solve for b:

c²  = a² + b²

26²  = 10² + b²

676  = 100 + b²

b² = 676  - 100

b² = 576

b = +√576 ( we take the positive value since we are dealing with dimensions)

b = 24

Therefore, the length EF is 24.

Option C)24 is the correct answer.

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The ratio of the volume of water in Jug B to the volume of water in Jug C is 35:18.

Let's assume the volume of water in Jug B is x.

According to the given information, Jug A contains 6/7 as much water as Jug B. Therefore, the volume of water in Jug A can be calculated as (6/7) * x.

Similarly, Jug C contains 3/5 as much water as Jug A. Hence, the volume of water in Jug C can be expressed as (3/5) * [(6/7) * x].

To find the ratio of the volume of water in Jug B to the volume of water in Jug C, we divide the volume of water in Jug B by the volume of water in Jug C:

(x) / [(3/5) * (6/7) * x]

Simplifying the expression, we get:

x / (18/35 * x)

The x values cancel out, leaving us with:

1 / (18/35)

To simplify further, we multiply the numerator and denominator by the reciprocal of the denominator:

1 * (35/18)

The final ratio is:

35/18

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Answer:

option b decreasing is your answer

Two triangles are congruent if they meet one of the following criteria. : All three pairs of corresponding sides are equal. : Two pairs of corresponding sides and the corresponding angles between them are equal. : Two pairs of corresponding angles and the corresponding sides between them are equal.