Write an equation for a rational function with the given characteristics.
Vertical asymptotes at
x = −3
and
x = 6,
x-intercepts at
(−4, 0)
and
(1, 0),
horizontal asymptote at
y = −3

The direction of the point (-3, 2) is 3 units to the left and 2 units up from the origin (0, 0). Obtained by applying the translation rules.

The translation rules are:

(x, y) → (x + a, y); translated by 'a' units to the right

(x, y) → (x - a, y); translated by 'a' units to the left

(x, y) → (x, y + a); translated by 'a' unit up

(x, y) → (x, y - a); translated by 'a' units down

The given points are (-3, 2) and (0, 0).

The point (-3, 2) is 3 units to the left and 2 units up from the origin (0, 0).

This is obtained by the rules:

(x, y) → (x - a, y); translated by 'a' units to the left

(x, y) → (x, y + a); translated by 'a' unit up

Thus, option C is correct.

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Answer: 0

Step-by-step explanation:

A horizontal line always has a slope of 0

(2, 11) is the vertex of f(x) = 4(x - 2)² +11.

A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .

The given equation is f(x) = 4(x - 2)² +11.

The vertex form is y=a(x-h)²+k

y=a(x-h)²+k of a parabola is said to be in vertex form because the vertex can be determined by examining the equation: (h, k) is the vertex.

(h, k) are the vertices of the given equation.

a=4,

h=2 and

k=11

so the (2,11) is the vertex of the function.

Hence, the vertex of f(x) = 4(x - 2)² +11 is (2, 11).

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The correct answers are:

1) 1/2

2) 1/10

3) 3/4

Step-by-step explanation:

[tex]\boxed{50=0.5\\}\\\boxed{10=0.1\\\\\\} \boxed{75=0.75}[/tex]

50% means 0.5. This 0.5 was (multiplied before by 100) to get this percentage.

Therefore, the answer is true

(a)  The corresponding angles are congruent.

So, m ∠ TLC = 66°

(b)  m ∠KGX = m ∠DNK = 120°

"Information available from the question"

In the question:

A graphic artist created a design for a flower using four congruent hexagons as shown:

B P⊥M K, m ∠ M Y F=m ∠ F H B, m° W M C=m ∠ W P T, m ∠G X R=66°, m ∠ D N K=(3 x+18)°, and m ∠ W B R=(5 x-8)°.

The sum of the angles in WKNDSP is 720°.

Now, According to the question:

Part(a) Since the four hexagons are congruent

So, the corresponding angles are congruent.

Thus, m ∠ T L C=  m ∠ 6 x R

Since, m ∠ 6 x R = 66°

So, m ∠ TLC = 66°

Part(b) In WKNDSP

m  ∠KWP + m ∠ WPS + m ∠ PSD + m ∠ SDN + m ∠ DNK + m ∠ NKW = 720°

Since, 1)  B P⊥M K => m ∠KWP = 90°

2) m ∠WPS =m ∠NKW =m ∠WBR = (5x - 8)°

3) m ∠PSD = m ∠DNK = (3x + 18)°

4) m ∠SDN = m ∠GXR = 66°

So, 90 + (5x + 8) + (3x + 18) + 66 + (3x + 18) + (5x - 8) = 720°

90 + 5x + 8 + 3x + 18 + 66 + 3x + 18 + 5x - 8 = 720

176 + 16x = 720

16x = 720 - 176

16x = 544

x = 34

=> m ∠DNK = (3x + 18)° = (3 × 34 + 18)° = 120°

So, m ∠KGX = m ∠DNK = 120°

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Answer: 27/16

Step-by-step explanation: evaluate

Answer:(22.5/3)-1.75=e

Step-by-step explanation:

3x/3=22.5/3

x=7.5 per book

7.5-1.75=5.75 per book after coupon

Answer:

p(x) = (x+7)(x+5)(-x+1)(x-35).

Step-by-step explanation:

To factor p(x), we can use the following steps:

Find the factors of 35 that add up to 4, which is the coefficient of the quadratic term (x^2). In this case, the factors of 35 that add up to 4 are 7 and 5.

Use these factors to rewrite the quadratic term as the product of two binomials. In this case, we can write the quadratic term as (x+7)(x+5).

Substitute this expression into the original polynomial to get p(x) = (x+7)(x+5) + 2x + 35.

To complete the factorization, we need to find two numbers that multiply to 35 and add up to 2. These numbers are -1 and -35.

Use these numbers to rewrite the remaining linear term as the product of two binomials. In this case, we can write the linear term as (-x+1)(x-35).

Substitute this expression into the polynomial to get p(x) = (x+7)(x+5) + (-x+1)(x-35).

Finally, we can factor p(x) as the product of two quadratics: p(x) = (x+7)(x+5)(-x+1)(x-35).

The solution of the given inequalities will be the common region between the two (refer to the graph).

What is an inequality ?

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance.

Nachelle has x dimes and y nickels.

We know that, A nickel is worth 5 cent, A dime is worth 10 cent and have maximum of $0.8 combined.

So, 5% x + 10% y ≤ 0.8

     5x + 10y ≤ 80

She has at least 11 coins.

So, x + y ≥ 11

Hence, We have two inequalities as:

5x + 10y ≤ 80 and x + y ≥ 11

Similarly, x≥ 0 and y≥ 0.

Now, We'll find the points that lie on the given lines and draw the lines ( refer the given figure )

After drawing the graph, we'll check the inequalities where the portion is true.

If take point (0,0),

5x + 10y ≤ 80

5(0) + 10(0) ≤ 80

0 ≤ 80 which is true, hence we will shade the region which is down because the point (0,0 ) lies in downward region.

Similarly,

x + y ≥ 11

0 + 0 ≥ 11

 0 ≥ 11 which is false hence, we will shade the region which is up because the point (0,0 ) lies in downward region.

In result, We get the common region which is the solution.

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The adjusting journal entries for the following unrelated transactions are as follows:

a) Dec. 31, 2020: Debit Interest Expense Php. 6,667

Credit Interest Payable Php. 6,667

(To record the adjusting entry.)

b) Dec. 31, 2020: Debit Insurance Expense Php. 12,500

Credit Prepaid Insurance Php. 12,500

(To record the adjusting entry under the asset method.)

Debit Prepaid Insurance Php. 17,500

Credit Insurance Expense Php. 17,500

(To record the adjusting entry under the expense method.)

c) Dec. 31, 2020: Debit Interest Revenue Php. 12,000

Credit Interest Receivable Php. 12,000

(To record the adjusting entry.)

d) Dec. 31, 2020: Debit Unearned Rent Revenue Php. 133,333

Credit Rent Revenue Php. 133,333

(To record the adjusting entry under the Liability method.)

Debit Rent Revenue Php. 66,667

Credit Unearned Rent Revenue Php. 66,667

(To record the adjusting entry under the income or revenue method.)

One of the methods is the asset method (similar to the liability method) that records the asset when cash is received.

Another is the expense method (similar to the revenue or income method) that records the amount as expense until adjusted.

a) Dec. 31, 2020: Interest Expense Php. 6,667 Interest Payable Php. 6,667

b) Dec. 31, 2020: Insurance Expense Php. 12,500 Prepaid Insurance Php. 12,500

Prepaid Insurance Php. 17,500 Insurance Expense Php. 17,500

c) Dec. 31, 2020: Interest Revenue Php. 12,000 Interest Receivable Php. 12,000

d) Dec. 31, 2020: Unearned Rent Revenue Php. 133,333 Rent Revenue Php. 133,333

Rent Revenue Php. 66,667 Unearned Rent Revenue Php. 66,667

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Answer:

see explanation

Step-by-step explanation:

N(t)=4|t+5|+3, evaluate N(2).

Evaluate: Plug in a number for each variable.

4(|t+5|)+3

t=2

Evaluate for t=2

4(|2+5|)+3

4(|2+5|)+3

=31

(Hope this answer does you some good )

Answer:

  1.8 cans of paint are needed

Step-by-step explanation:

A large statue has a volume of 135 m³ and an area of 81 m², while a small statue has a volume of 5 m³. You want to know the number of cans of paint required to paint the small statue, if each can covers 5 m².

The ratio of linear dimensions on the small statue to those on the large statue is the cube root of their volume ratio:

  sf = ∛(5/135) = ∛(1/27) = 1/3

The area of the small statue is the larger statue's area multiplied by the square of the scale factor:

  smaller area = larger area × (sf)²

  smaller area = (81 m²)(1/3)² = 9 m²

Each can of paint covers 5 m², so the number of cans required is ...

  (9 m²)/(5 m²/can) = 1.8 cans

You will need 1.8 cans of paint to paint the small statue.

__

Additional comment

If you must pay for whole cans of paint, you must buy 2 cans of paint.

Trigonometry is the application of certain functions to determine the value of a quantity. The tree stands 10.77 meters tall.

Some trigonometric functions can be used to solve the given problem. Let s represent the distance from the tip of the tree's shadow to where Aria stands, so that;

s = 27.75 - 23.5

= 4.25 m

s = 4.25 m

Also, let the angle formed by the line connecting the tree's tip and the shadow's tip be, so that;

Tan θ = opposite / adjacent

Here given,

Opposite side = 1.65

Adjacent side = 4.25

          = 1.65 / 4.25

          = 0.3882

θ = Tan⁻¹ 0.3882

  = 21.216

θ = 21.216°

We get θ = 21.216°

The tree's height, h, can be calculated as follows:

Tan 21.216° = h/27.75

h = Tan 21.216° x 27.75

  = 0.3882 x 27.75

h = 10.77m

As a result, the tree's height is 10.77m.

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The amount that Tom’s most recent book earn is 10^7.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

Since Tom’s most recent book earned 10*4 times as much money as his first book which was 10³.

The total amount of the recent book will be:

= 10⁴ × 10³

= 10^(4 + 3)

= 10^7

The amount is 10^7.

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Answer:

2x - y - 2 = 0

Step-by-step explanation:

A (1,0)

B (0,-2)

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

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

-y/2 = -x + 1

-y = 2(-x+1)

-y = -2x + 2

2x - y - 2 = 0

Answer:

To factor out the GCF from the given expression, we can use the distributive property. This property states that we can distribute a common factor to all of the terms in an expression by multiplying the common factor by each term separately. In this case, the common factor is n, so we can distribute it to each term by multiplying it by -26, 7, and 13:

(-26n * n) + (7n * n) + (13n * n)

This gives us:

-26n^2 + 7n^2 + 13n^2

We can then combine like terms by adding the coefficients of n^2:

(-26 + 7 + 13) * n^2

This gives us the final result:

-6 * n^2

Therefore, we can factor out the GCF of -6n^2 from the given expression.

Step-by-step explanation:

The surface area of the prism is 84 square centimeters.

What is a prism?

A prism is a polyhedron in geometry that has n parallelogram faces that connect the n-sided polygon basis, the second base, which is a translated duplicate of the first base, and the n faces. The bases are translated into all cross-sections that are parallel to them.

In the figure,

The surface area of the figure consists of 2 triangles, 3 rectangles.

The area of the triangle and rectangle is the surface area of the triangle.

The area of the triangle is (1/2) × base × height

The base of the triangle  ABC is BC and the height is AB.

The area of triangle ABC is (1/2) × 4 × 3 = 6 square centimeters.

The area of triangle DEF is (1/2) × 4 × 3 = 6 square centimeters.

The area of the rectangle ACDE  is 5 × 6 = 30 square centimeters.

The area of the rectangle ABEF  is 4 × 6 = 24 square centimeters.

The area of the rectangle BCDF  is 3 × 6 = 18 square centimeters.

The total surface area of the figure is ( 6 + 6 + 30 + 24 + 18) square centimeters = 84 square centimeters

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Answer:

1/82.

Step-by-step explanation:

In a cross country race with 40 athletes, 10 of them are on the same team. The probability that the top four finishers are all from that same team is given by the expression 10P4/40P4.

The expression 10P4 represents the number of ways that the top four finishers can be chosen from the team of 10 athletes. Since the order in which the athletes finish does not matter, this is equivalent to choosing 4 athletes from a group of 10 without regard for order, which can be done in 10!/(4!6!) = 210 ways.

The expression 40P4 represents the number of ways that the top four finishers can be chosen from the entire group of 40 athletes. Since the order in which the athletes finish does not matter, this is equivalent to choosing 4 athletes from a group of 40 without regard for order, which can be done in 40!/(4!36!) = 34,650 ways.

Therefore, the probability that the top four finishers are all from the same team is given by the expression 10P4/40P4 = 210/34,650 = 1/164. This can be simplified to 1/82 by dividing the numerator and denominator by 2, so the final answer is 1/82.

Answer: 2 is equal to or less than 5

Step-by-step explanation:

When the dot is colored in that means it’s equal to or _, while when it’s hollowed out it’s equal to a simple greater or less than symbol.

Answer:

4(x-2 +y) = 4x-8+4y

Step-by-step explanation:

You have to apply the distributive law

4(x-2+y) = 4x + 4 (-2) + 4y

Then solve it which equals

4 x +4 (-2) + 4y

Then multiply the numbers

4 (-2) = -8

Which gets you 4x-8+4y

Answer:

630 people could ride the Ferris wheel in 6 hours.

Step-by-step explanation:

First, let's find the people-per-hour amount:

Since there are 3 "20 minutes" in an hour, we multiply the amount it can accommodate by 3 as well:

35 * 3 = 105

Next, since we have 6 hours, we multiply our people-per-hour by 6:

105 * 6 = 630 people in 6 hours, final answer.

Answer:

  $11,127.75

Step-by-step explanation:

You want to use the compound interest formula A=Pe^rt to find the value of an $8000 investment compounded continuously at 11% for 3 years.

Put the values of the variables into the formula and do the arithmetic.

  A = $8000·e^(0.11·3) ≈ $11127.75

The accumulated value after 3 years will be $11,127.75.

Answer:

Step-by-step explanation:

r2=x2+y2,tanθ=yx,x=rcosθ,y=rsinθ

The required equations can be used to model the situation is x = 1/2y - 3 and y = 10(x-1)

What is equation ?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."

Equations can be classified as either conditional equations or identities. Any value of the variables results in an identity being true. Only certain values of the variables in a conditional equation result in truth. When two expressions are joined together by the equals sign ("="), the result is an equation.

If the smaller number is 3 less than half a larger number, this is expressed as:

x = 1/2y - 3 ⇒(1)

If the larger number is 10 times 1 less than the smaller number, this is expressed as;

y = 10(x-1) ⇒ (2)

Substitute equation 2 into 1 as shown;

x = 1/2y - 3

x = 1/2(10x-10)- 3

x = 5x - 5 - 3

-4x = -8

x = 2

The required equations can be used to model the situation is x = 1/2y - 3 and y = 10(x-1)

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Answer:

a d

Step-by-step explanation:

The equation of the exponential function represented in this table is;

y = 6(1.8)ˣ

We are given the table of values of the exponential function and we can write the coordinates as;

(3, 34.99)

(4, 62.99)

(5, 113.37)

(6, 204.07)

(7, 367.33)

The general formula for an exponential function is;

y = a(b)ˣ

where;

a is the initial value

b is the constant multiplier

For the third coordinate, we have;

a(b)³ = 34.99    ------(1)

For the fourth coordinate, we have;

a(b)⁴ = 62.99    ------(2)

Divide eq 1 by eq 2 to get;

b = 1.8

Put 1.8 for b in eq 1 to get;

a(1.8)³ = 34.99

a = 6

This gives the exponential equation as; y = 6(1.8)ˣ

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Answer:

A=Right, B=Acute, C=Obtuse, D=Obtuse

Step-by-step explanation:

A.right

B.acute

C.obtuse

D.obtuse

Answer:

slope is 7/4

y intercept (0,2)

Step-by-step explanation:

m= 7/4 y=mx + b to find slope.

Answer:

The value of x is equal to tan^-1(0.5961538461538461). This is the angle opposite to the side with length 3.1 in the given right triangle.

Step-by-step explanation:

To find the value of x, you can use the inverse tangent function, which is denoted as tan^-1. To use the inverse tangent function, you need to know the length of the adjacent side and the length of the opposite side of the right triangle. In this case, the length of the adjacent side is 3.1 and the length of the opposite side is 5.2. So, the value of x is equal to tan^-1(3.1/5.2) or tan^-1(0.5961538461538461).

Answer: d

Step-by-step explanation:

edge 2023

The equations for parallel lines:

y = -1/2 x - 2  ----- y = -1/2 x + 6

y = 1/2 x + 4   ----- y = 1/2 x - 4

y = 2x -4       -----  y =2/1x + 2

y = 5x + 2     -----  y = 5x - 1

y = 1/5 x + 10 ----   y = 1/5 x + 3

What is slope of line?

A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).

If an equation in the form y = mx + c then m is the slope of the line.

Equation of line               slope          Slope parallel line

y = -1/2 x - 2                        -1/2                        -1/2

y = 1/2 x + 4                          1/2                           1/2

y = 2x -4                                2                            2

y = 5x + 2                               5                           5

y = 1/5 x + 10                          1/5                         1/5

Now identify the lines from the option whose slope are  -1/2,  1/2, 2, 5,  1/5.

The slope of the line y = -1/2 x + 6 is  -1/2.

The slope of the line y = 1/2 x - 4 is  1/2.

The slope of the line y = 2x -4 is 2.

The slope of the line y = 5x + 2  is 5.

The slope of the line y = 1/5 x + 10 is 1/5.

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