f(x) = x²/x² 2x+3 find Vertical asymptote find horizontal asymptote ​

On solving the provided question, we can say that Principal = 21,000, interest = 0.4% and time = 4 yrs => SI = $336

Simple interest is calculated by dividing the principal by the interest rate, the passage of time, and other elements. The formula used in marketing is simple return = principal + interest + hours. Using this approach, interest may be calculated most easily. The most common way to calculate interest is as a percentage of the principal balance. If he borrows $100 from a friend and agrees to pay it back with 5% interest, for instance, he will only pay his proportion of the 100% interest. $100 (0.05) = $5. You must pay interest when you borrow money and charge interest when you lend it. The majority of the time, interest is calculated as an annual percentage of the loan balance. This proportion is referred to as the loan's interest rate.

here,

Principal = 21,000

interest = 0.4%

time = 4 yrs

SI = Principal X Interest X time / 100

SI = 21000*0.4*4/100 = $336

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Due to the fact that parallel lines produce congruent alternate interior angles, ADB = CBD by ASA.

A pair of angles is considered to be complementary if their sum equals 90 degrees. Two angles are referred to as submissive if their sums total 180 degrees. Follow-up pains involve using freshly baked sorrowful bread. Prior to, before, ahead of The angles of 30 and 60 degrees, for example, are supplementary. In contrast to a supplemental angle, which is two angles joined to create a 90 degree angle, a supplementary angle is two angles combined to create a 180 degree angle. If the sum of two angles is 90 degrees, they are said to be complementary.

given

∠CDB = ∠ABD

and

∠ADB = ∠CBD

∠RQP = ∠SQP

since perpendicular lines form congruent right angles. PQ || PQ by reflexive so ∠PQR = ∠PQS by AAS.

Due to the fact that parallel lines produce congruent alternate interior angles, ADB = CBD by ASA.

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Answer: E⁢C=B⁢C; property of isosceles triangle

Step-by-step explanation: Got it right on Edmentum/Plato

The domain is x < 2 or x ≥ 3 and the range y > - 3

The domain of a function is the interval of valid inputs to the function.

The range of a function is the interval of valid outputs to the function.

Since we have the function

To find the domain of the function, we see that the values of x are between x < 2 or x ≥ 3.

So, the domain is x < 2 or x ≥ 3.

To find the range of the function, since

f(x) = -x/2 - 2 if x < 2 and f(x) = 2x - 4 if x ≥ 3.

Using the first function f(x) = -x/2 - 2 if x < 2 and substituing x = 2, we have that

f(2) = -2/2 - 2 = - 1 - 2 = -3

Since f(x) cannot be less than f(2), then

f(x) > - 3

So, y > - 3

Also, using the second function f(x) = 2x - 4 if x ≥ 3. and substituting x = 3 into the equation since this is the minimum value of x, then

f(3) = 2(3) - 4

= 6 - 4

= 2

Since this is the minimum value of f(3) = 2

So, y > 2

Since y > -3 and y > 2, combining both expressions, we have that

y > - 3

So, the range is y < -3

So, the domain is x < 2 or x ≥ 3 and the range y > - 3

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Answer:

t=-2

Step-by-step explanation:

5t-26=18t

5t-26+26=18t+26

simplify and subtract 18t from both sides

The sum of the Polynomial as required to be used to verify the additive property is; 5x² + 5x +9.

Given polynomials p(x), q(x), and r(x), p(x) + ( q(x) + r(x) ) = ( p(x) + q(x) ) + r(x).

Hence, to justify the associative property; we must sum up the polynomials given in two ways as follows;

Method 1;

(3x + 4) + ( (5x² - 1) + (2x + 6) )

3x + 4 + ( 5x² + 2x + 5 )

3x + 4 + 5x² + 2x + 5.

Therefore, the sum is; 5x² + 5x + 9

Method 2;

(3x + 4) + ( (5x² - 1) + (2x + 6) )

= ( 3x + 4 + 5x² - 1 ) + ( ( 2x + 6 ) )

= 5x² + 3x + 3 + ( (2x + 6) )

5x² + 3x + 2x + 3 + 6

5x² + 5x +9

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Answer:

78.54in2

Step-by-step explanation:

Answer:

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

Given sequence:

If t(n) = 200, we can try to find the value of n:

There is no integer solution, since 32 < 40 < 64 or 2⁵ < 40 < 2⁶, the value of n should be between 5 and 6.

The sequence should include integer numbers, so there is no solution.

Given function:

Solve for x if f(x) is 200:

Answer:

1.  No

[tex]\textsf{2.} \quad x=\dfrac{\ln 40}{\ln 2} \approx5.32\;(\sf 2\;d.p.)[/tex]

Step-by-step explanation:

Given sequence:

[tex]t(n)=5 \cdot 2^n[/tex]

To determine if the sequence has a term with a value of 200, substitute t(n)=200 into the equation and solve for n:

[tex]\implies 5 \cdot 2^n=200[/tex]

[tex]\implies 2^n=40[/tex]

[tex]\implies \ln 2^n=\ln 40[/tex]

[tex]\implies n\ln 2=\ln 40[/tex]

[tex]\implies n=\dfrac{\ln 40}{\ln 2}[/tex]

[tex]\implies n=5.3219280...[/tex]

In a sequence, n is a positive integer.  Therefore, it is not possible for the sequence to have a term with the value of 200, as when t(n)=200, n is not a positive integer.

Given function:

[tex]f(x)=5 \cdot 2^x[/tex]

To determine if the function has an output of 200, substitute f(x)=200 into the function and solve for x:

[tex]\implies 5 \cdot 2^x=200[/tex]

[tex]\implies 2^x=40[/tex]

[tex]\implies \ln 2^x=\ln 40[/tex]

[tex]\implies x=\dfrac{\ln 40}{\ln 2}[/tex]

[tex]\implies x=5.3219280...[/tex]

Therefore, it is possible for the function to have an output of 200 when:

[tex]x=\dfrac{\ln 40}{\ln 2}[/tex]

From the equation y = 25x + 72, the initial temperature is 72°F, the rate of change in the oven temperature is 25 degrees Fahrenheit per minute

An equation is a expression that shows the relationship between numbers and variables.

The standard form of a linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept

Let y represent the temperature of the oven in degrees Fahrenheit after x minutes.

Given the equation:

y = 25x + 72

This means that the rate of change is 25 degrees Fahrenheit per minute.

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Answer:

C. 1/4 (-x + 2)

Step-by-step explanation:

-1/4x + 1/2

1/4 (-x + 2)

Continental tropical (cT) air masses can be characterized by hot and dry air. The correct answer would be option (D).

Continental tropical air masses, on the other hand, are most common in the summer and are characterized by dry and hot air. They will be most common in Mexico's southwestern and northern regions.

These air masses frequently move into the northeast, bringing more dry and hot weather to the Great Plains, but they typically have a much smaller range than other air masses.

Therefore, the correct answer would be option (D) hot and dry air.

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a<-7 is the solution of the inequality. 8a < -56

a relationship between two expressions or values that are not equal to each other is called 'inequality.

The given inequality is 8a < -56

Eight times of a less than minus fifty six

8a < -56

Divide both sides by a

a<-56/8

a less than minus fifty six divided by eight

a<-7

Hence, a<-7 is the solution of the inequality. 8a < -56

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Answer:

[tex] \sf \: a < - 7[/tex]

Step-by-step explanation:

Now we have to,

→ find the required value of a.

The inequation is,

→ 8a < -56

Then the value of a will be,

[tex] \sf \rightarrow \: 8a < - 56[/tex]

[tex] \sf \rightarrow \: a < \frac{ - 56 \: }{ \: 8} [/tex]

[tex] \sf \rightarrow \boxed{ \sf a < - 7}[/tex]

Hence, the value of a is -7.

Answer: 480 and 300

Step-by-step explanation:

240 divided by 0.50 = 480

240 divided by 0.80 = 300

The area issue with the suggested remedy is that the playing field is 118 feet by 56 yards in size.

To determine area, multiply length by width. L times B is the formula for calculating area. Area or Radius = r2(=3.14) These methods can also be used to calculate the areas of different quadrilaterals, which are polygonal shapes with four sides and an aspect lower than 90 degrees. Application. Since its inception, area has been the foundation of geometry.

Here,

Our calculation of w = 56 reveals that the parallelogram is 56 yards long.

We can simplify the calculation by altering w to 56 in order to obtain the length of the rectangle but since width is the same as 2w + 6 already.

The rectangle is depicted as having a length of 118 yards.

Accordingly, the playing field measures 118 yards by 56 yards.

Therefore, the size of the game field—118 yards x 56 yards—is the solution to the current problem.

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Therefore , the solution of the given problem of system of inequalities comes out to be option a.

This system of inequalities defines a region in the x-y plane. The first inequality represents all the points below a line with the equation y = 2 - x, and the second inequality represents all the points above a line with the equation y = x - 1. The solution to the system is the set of points that lie in the intersection of these two regions, which is a certain area of the x-y plane.

Here,

Given : This riddle can be represented by the following system of inequalities:

x + y < 2 (the sum of two numbers is less than 2)

x - y > 1 (if we subtract the second number from the first, the difference is greater than 1)

Where x and y are the two numbers.

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The net worth of the surf shop would be $572,922.

Option (B) is correct.

What is the net worth?

Net worth is a financial metric that represents the value of an individual or a company, and it is calculated by taking the total assets and subtracting the total liabilities.

To calculate this, you would add up all of the assets (property value, long term investments, cash, savings account, owned inventory, and owned equipment) and subtract all of the liabilities (building mortgage, other debt, small business loan, and long term liabilities).

In this case, the assets total:

$130,284 (property value) + $106,987 (long term investments) + $208,634 (cash) + $172,839 (savings account) + $38,671 (owned inventory) + $38,291 (owned equipment) = $731,109

And the liabilities total:

$78,280 (building mortgage) + $21,987 (other debt) + $28,950 (small business loan) + $48,970 (long term liabilities) = $178,187

So,

$731,109 (assets) - $178,187 (liabilities) = $572,922 (net worth)

hence, The net worth of the surf shop would be $572,922.

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The standard form of a linear equation is Ax + By = C where A and B are not both zero and A, B and C are integers whose GCF is 1.

To convert the equation y = 9x - 1 to standard form, we need to rearrange it as:

9x - y = 1

We can divide both sides by -1 to get

-9x + y = -1

Which is the standard form of the equation.

So the standard form of the equation is:

-9x + y = -1

Answer: D the size of small tub

Step-by-step explanation: he needs to more if he is going to get his moneys worth

Donna need to know the size of small tub in order to decide which size is the better buy. the correct option is D.

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

Given that Donna could buy a half-gallon tub of ice cream for $4.99 or a small tub for $2.39.

We can see that he needs to more if he is going to get his moneys worth.

ice cream = $4.99

small tub = $2.39.

He need to know the size of small tub

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Answer:

Below

Step-by-step explanation:

Circumference of circle = pi * d = pi * 2r

so:        circ / 2pi = r           56.52/(2 * 3.14) = r = 9 inches

AREA of a circle = pi * r^2

                           = 3.14 * 9^2 =   254.34 in^2

Answer: Morgan will arrive at Town B at 5pm - 36 minutes = 4:24pm if she cycled at an average speed of 25km/h.

Step-by-step explanation: To solve this problem, we can use the formula: distance = speed x time.

We know that at 15km/h, Morgan reaches Town B at 6pm, and at 20km/h, she reaches Town B at 5pm.

We can use this information to find the distance between Town A and Town B and the time it takes to travel this distance at 25 km/h.

First, let's find the distance between Town A and Town B:

distance = speed x time

distance = 15 km/h x time

time = distance / 15 km/h

time = (distance / 15) hours

Since we know that when Morgan travel at 15km/h to reach town B at 6pm, we can use the time to calculate the distance:

time = 6pm - 5pm = 1hour

distance = 15 km/h x 1 hour = 15 km

Next, we can use this distance and the new speed 25km/h to calculate the arrival time:

time = distance / speed

time = 15 km / 25 km/h = 0.6 hours = 36 minutes

So, she will arrive at Town B at 5pm - 36 minutes = 4:24pm if she cycled at an average speed of 25km/h.

Please note that this calculation is assuming that the distance between Town A and Town B is a constant, and assuming that the time of arrival at 15km/h and 20km/h are accurate.

Answer: x = 10

Step-by-step explanation:

triangle shows angles are 38°, (7x+1)°, (10x+9)°(outside of the triangle)

total angle of the triangle is 180°

then

        38°+ (7x+1)°+ [180-(10x+9)°] = 180°

Simplifying

38 + (7x + 1) + [180 + -1(10x + 9)] = 180

Reorder the terms:

38 + (1 + 7x) + [180 + -1(10x + 9)] = 180

Remove parenthesis around (1 + 7x)

38 + 1 + 7x + [180 + -1(10x + 9)] = 180

Reorder the terms:

38 + 1 + 7x + [180 + -1(9 + 10x)] = 180

38 + 1 + 7x + [180 + (9 * -1 + 10x * -1)] = 180

38 + 1 + 7x + [180 + (-9 + -10x)] = 180

Combine like terms: 180 + -9 = 171

38 + 1 + 7x + [171 + -10x] = 180

Remove brackets around [171 + -10x]

38 + 1 + 7x + 171 + -10x = 180

Reorder the terms:

38 + 1 + 171 + 7x + -10x = 180

Combine like terms: 38 + 1 = 39

39 + 171 + 7x + -10x = 180

Combine like terms: 39 + 171 = 210

210 + 7x + -10x = 180

Combine like terms: 7x + -10x = -3x

210 + -3x = 180

Solving

210 + -3x = 180

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-210' to each side of the equation.

210 + -210 + -3x = 180 + -210

Combine like terms: 210 + -210 = 0

0 + -3x = 180 + -210

-3x = 180 + -210

Combine like terms: 180 + -210 = -30

-3x = -30

Divide each side by '-3'.

x = 10

Simplifying

x = 10

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When you are using the plane mirror, the image is going to have to be the same in size as you are.

When using the plane mirror and trying to get a reflection from the plane mirror, it would be found that the image that we are looking at in the mirror would turn out to be the same as the object that is being reflected. That is, your image is going to be exactly the same way.

The reason for this is because, the plane mirror is known to reflect light at the same angle that it received the light. This would cause the distance and the size of the object to be replicated in that image that has been reflected.

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Answer:

(2,2)

Step-by-step explanation:

The middle point of (-4,8) and (8,-4) is (2,2)

On solving the provided question, we can say that we know that all angles of a parallelograms  are 360 => x = 23

A parallelogram is a straightforward quadrilateral in Euclidean geometry that has two sets of parallel sides. In a particular kind of quadrilateral known as a parallelogram, both sets of opposite sides are parallel and equal. There are four different kinds of parallelograms, including three unique kinds. Parallelograms, squares, rectangles, and rhombuses are the four different shapes. Having two sets of parallel sides makes a quadrilateral a parallelogram. In a parallelogram, the opposing sides and angles are both the same length. On the same side of the horizontal line, the interior angles are additional angles as well. 360 degrees is the total number of interior angles.

as we know that all angles of a parallelograms  are 360

then, 3j +6k +(k+10) + (5j-9) = 360

3x + 6x + x +10 + 5x -9 = 360

15x = 349

x = 349/15

x = 23.2666666667 = 23

x = 23

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Answer:

See below

Step-by-step explanation:

Obviously, as h ==> 0 it becomes very small

  I would pick a very small number for h   .....  say -.001

then the equation becomes

[   f (-1.001)  - f(-1)  ] / (-.001)                where f(x) = x^5

= [ (-1.001)^5  - (-1)^5  ]  / ( -.001)         For the point that has x = -1

                       = 5.01     <==== approximation for the slope at x = - 1

Now we need line with slope = 5.01    and point  (-1,-1)

   Using point slope form :

  y - -1  = 5.01 (x - -1)     re-arrange to:

y = 5.01x - 4.01  <==equation of line with slope = 5.01 and tangent at (-1,-1)

Here is a graph: (and it looks like a good approximation !)

The factors of x² - 9 is +3 , -3.

What is factors ?

A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them. Factors can be found using either division or multiplication.

A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor in mathematics.

The numbers that can divide a number exactly are called factors. There is therefore no residual after division. The numbers you multiply together to obtain another number are called factors. A factor is therefore another number's divisor.

x² - 9 = 0

x² = 9

x = √9

x = ± 3

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Answer:

10

Step-by-step explanation:

The length of the slant height will be 4 units. Then the correct option is A.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

Let 's' be the slant height. Then the length of the slant height will be given as,

5² = s² + (6/2)²

25 = s² + 9

s² = 25 - 9

s² = 16

s = 4 units

The length of the slant height will be 4 units. Then the correct option is A.

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The missing diagram is given below.

Answer:

The other leg is 19.6cm

Step-by-step explanation:

Use Pythagorean Theorem to set up an equation and solve.

The Pythagorean Thm is:

leg^2 + leg^2= hypotenuse^2

Let's fill in what we know:

4^2 + leg^2 = 20^2

(let's use a variable)

4^2 + b^2 = 20^2

simplify

16 + b^2 = 400

subtract 16

b^2 = 384

squareroot both sides.

b = sqrt384

use a calculator to find the squareroot.

b = 19.5959179

round to the nearest tenth.

b = 19.6

don't forget units!

The other leg is 19.6cm

Option A is the correct answer. An equation for a tangent to the graph of y=arcsiny/2 at the origin is x-2y = 0

The given equation is:

y=arcsiny/2---(1)

So to find the equation of the tangent line we required Fielding's first slope and we can find the slope by differentiating the equation of graft with respect to X.

The second thing we require is the point, also we have to find the slope accessible to zero

dy/dx=1/2/√1-x^/4

Also given that points meet at the origin means (0,0) the values of x, and y is 0 and substituted in the derivative equation, we get

y'(0)=1/2

y-0=1/2(x-0)

2y-0=x

x-2y=0

Therefore, An equation for a tangent to the graph of y = arcsin y/2 at the origin is x-2y=0

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The solutions to this system are (x, y) = (1, 4), (x, y) = (0.5, 2), respectively.

Herein we find the case of a nonlinear system of the form f(x) = 0, which cannot be solved analytically. This solutions to this system by graphic approach, by means of algebra properties:

f(x) = 0

g(x) - h(x) = 0

g(x) = h(x)

By transitive property:

y = g(x)

y = h(x)

The solution to this system of the point of intersection of g(x) and h(x). The procedure is summarized below:

If we know that g(x) = 4 · x and h(x) = 4ˣ, then the solution to the nonlinear equations:

Points of intersection: (x, y) = (1, 4), (x, y) = (0.5, 2).

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