can the graph of intersect a vertical asymptote? can it intersect a horizontal asymptote? illustrate by sketching graphs.

The common binomial factor for the given expression is[tex]$x+3$[/tex].

We are given the expression[tex]$x^2+3 x+5 x+15$.[/tex]

We wish to find the common binomial factor for the given expression. So, we have:

Solution:

Factoring by grouping, we have:

[tex]x^2+3 x+5 x+15 & =x(x+3)+5(x+3) \\[/tex]

[tex]& =(x+3)(x+5)[/tex]

Therefore, we can see that the common binomial factor for the given expression is[tex]$x+3$[/tex].

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The linear regression model is expressed as y = -25.31x + 1017.075.

The best-fit line is given by:

y = bx + a

The slope is as follows:

b = Σ(x - X) ( y - Y)/Σ(x - X)²

After determining the slope using the means for x and y, the coefficient an is calculated.

The means are provided by:

X = (0 + 1 + 2 + 3 + 4 + 5)/ 6 = 2.5

Y= (904 + 924 + 938 + 957 + 977 + 1023)/6

= 953.83

The figures are as follows:

Σ(x - X) = (0 - 2.5) +(1 - 2.5) + ---------+ (5 - 2.5)

Σ( y - Y) = ( 904 - 953.83) + (924 - 953.83) + ---------- + ( 1023 - 953.83)

Making use of a calculator:

Σ(x - X) ( y - Y) = -443

Σ(x - X)² = 17.5

As a result, the slope is:

b = -443/17.5

= -25.31

y = -25.31x + a

Using the means to locate a:

953.83 = -25.31 x 2.5 + a

a = 1017.075

As a result, the linear regression model is:

y = -25.31x + 1017.075

After 2012, the number of cases would reach 1171 in x years, and x is found when y = 1171. Thus:

1171 = -25.31x + 1017.075

1171 - 1017.075 = -25.31x

x = 6

2012 + 6 = 2018

The number of reported cases is expected to reach 1171 by 2018.

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Therefore , the solution of the given problem of equation comes out to be cost of one pair of pants is $40.

The similar symbol (=) is used in mathematical equations to variables denote equality between two propositions. Mathematical formulae, which are abstractions of reality, are used to demonstrate how different numerical factors can be compared. For instance, the equal sign splits the integer 12 or perhaps the equation y + 6 = 12 to two separate halves. One can compute how so many characters each side of the a character has. Contradictory meanings are common in symbols.

Here,

Given :

Mathew bought 5 shirts and 2 pairs of pairs is $165.

Toby bought 3 shirts and 5 pairs of pants for $251.

x is the shirt of price ,

y is the pants of price .

Thus,

=> 5x + 2y = 165

=> 3x + 5y = 251

So,

=> x = 165 -2y/5

=> 3(165 - 2y/5) + 5y = 251

=> 3(165 - 2y /5) + 5y = 251

=>  495 - 6y  + 25y = 251 *5

=>  495 + 19y = 1255

=> 19y = 1255 - 495

=> 19 y =  760

=> y =760/19

=> y = 40

and

=> x = 165 - 2*40 /5

=> x = 165-80/5

=> x = 85/5

=> x =17

Thus , cost of one pair of pants is $40.

Therefore , the solution of the given problem of equation comes out to be cost of one pair of pants is $40.

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When the figure is rotated around the line, a cylinder is created.

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Answer:

[tex]y=(x-3)^{2}[/tex]

Step-by-step explanation:

First, it should be noted that the parabola shown is just the parent parabola translated over 3 units to the right. To shift the parent parabola over to the right 3 units, we need to square x-3. So, the equation for the parabola shown is [tex]y=(x-3)^{2}[/tex].

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The interest earned and the balance of the account 200 at 3 % for 5 years is 30.

percentage, a relative value indicating hundredth parts of any quantity.

Given that an account earns simple intrest

We have to find the interest earned

the balance of the account 200 at 3 % for 5 years

I=PRT

P is the principal amount

t is the time

r is the rate of interest

I=200×0.03×5

I=30

Hence, the interest earned and the balance of the account 200 at 3 % for 5 years is 30.

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Answer:

Step-by-step explanation:

600.15/ 7.5 = 80.02

Answer:

the answer is a. -2

Step-by-step explanation:

i hope that helps you

thanku

0.96×10⁴ is the quotient of 7.584×10⁶ and 7.9×10²

A division is a process of splitting a specific amount into equal parts.

We need to find the quotient of

7.584×10⁶ and 7.9×10²

Dividend is the number that is to be divided by the divisor.

Divisor is the number by which the dividend is to be divided is called the divisor.

The resultant of the division is called the quotient.

7.584×10⁶/7.9×10²

0.96×10⁶⁻²

0.96×10⁴

Hence, 0.96×10⁴ is the quotient of 7.584×10⁶ and 7.9×10²

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The required  mark-up percentage of the manager is 60%.

The gross profit of a unit, which is its sales price less its cost to produce or acquire for resale, is divided by the unit's cost to determine the markup %. The markup percentage, which is computed as (12 - 8) / 8, is 50% for an item that costs the business $8 to produce but is priced at $12.

We have,

Cost price of the Unit = $350

Selling price of the unit = $560

Then,

Mark-up percentage = ($560 - $350)/$350 × 100

Mark-up percentage = $210/$350 × 100

Mark-up percentage = 0.6 × 100

Mark-up percentage = 60%

Thus, required mark-up percent is 60%.

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Divide the principal by the time, interest rate, and time period to calculate simple interest.Annual interest rate is 0.02.

Divide the principal by the time, interest rate, and time period to calculate simple interest.The equation is expressed as "Simple Interest = Principal x Interest Rate x Time."It is easiest to calculate interest using this equation.

I, or the interest earned or charged on a loan, can be calculated using the straightforward interest formula.

I = Prt, where P is the principal, r is the yearly interest rate stated in decimal form, and t is the loan term expressed in years, gives the amount of interest.

It is necessary to transform the rate r from percentage to decimal form.

Then, 2,000 = 1,000 * r * 10 ;

Finally, r = 2 ÷ 10 = 20 ÷ 100 = 0.02

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The slope of the red line is -1/2

What is a slope?

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

Here, we have

Two lines are parallel. Two lines are shown by the color green and red line.

As we know if lines are parallel then their slope is equal.

W are given a green line parallel to the red line.

The slope of the green line is -1/2

But The slope of the red line = slope of the green line.

The slope of the red line = -1/2

Hence, The slope of the red line is -1/2.

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The glass can hold up to 9 ounces of water.

Given that the glass is [tex]$\dfrac{3}{7}$[/tex]  full, there must be [tex]$\dfrac{4}{7}$[/tex] a glass that is empty. If the glass has 6 ounces of water in it, then we can able to find the total volume of the glass by dividing the amount of water in the glass by the fraction that is full.

Here is the calculation of the total volume of the glass:

[tex]$\text{Volume of glass}[/tex] =[tex]\dfrac{\text{Amount of water}}{\text{Fraction full}}[/tex] =[tex]\dfrac{6}{\dfrac{3}{7}}[/tex] = [tex]9$[/tex] ounces

By calculating the volume of the glass we came to know that the glass can hold 9 ounces of water in total.

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Following APA criteria, statistical power should be stated along with effect magnitude, sample size, and alpha level.

Following the recommendations of the American Psychological Association (APA), statistical power should be stated. This includes stating the sample size that was utilised, the estimated effect size, and the alpha level that was chosen for the analysis. The degree of the difference between two groups is measured by the effect size, which should be stated together with the accompanying confidence interval. The sample size, which represents the number of observations used in the study, is also crucial. The degree of significance, commonly known as the alpha level, should also be given. This shows the likelihood of a false-positive finding and can be used to assess the accuracy of the findings. Researchers are able to accurately assess the trustworthiness of the results when statistical power is reported in accordance with APA recommendations.

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The inequality to represent the instances when a vehicle other than a cargo van is used, where x is the distance of a location from the warehouse is given as follows:

x ≤ 8.

The four inequality symbols, along with their meaning, are presented as follows:

Distances of 8 miles or less are of at most 8 miles, hence the inequality is defined as follows:

x ≤ 8.

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The value of the trigonometric relation tan θ = 0.25819889

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin (-θ) = -sin (θ)

csc (-θ) = -csc (θ)

cos (-θ) = cos (θ)

sec (-θ) = sec (θ)

tan (-θ) = -tan (θ)

cot (-θ) = -cot (θ)

In the first quadrant, sin, cos and tan are all positive.

In the second quadrant going anti-clockwise, only sin is positive.

In the third quadrant going anti-clockwise, only tan is positive.

In the fourth quadrant going anti-clockwise, only cos is positive

Given data ,

Let the angle be represented as θ

Now , the measure of sin θ = - ( 1/4 )

So , the value of θ lies in the 3rd quadrant

Taking inverse on both sides of the equation , we get

θ = sin⁻¹ ( - ( 1/4 ) )

θ = 194.47751218° + 2πn

Now , In the third quadrant going anti-clockwise, only tan is positive.

So , tan θ = tan ( 194.47751218 )

On simplifying the equation , we get

tan ( 194.47751218 ) = 0.25819889

Hence , the value of tan ( 194.47751218 ) is 0.25819889

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The percentage of his income he saved is 44.4%.

Percentage is a way of expressing a number as a fraction of 100. It is commonly used to represent a proportion or share of a whole, such as a percentage of a total amount, a percentage of a target or goal, a percentage of a population, etc.

In mathematical terms, a percentage can be represented as a decimal or a fraction, and is expressed as a symbol, such as "%".

If Ravindra's monthly income is rupee 90000 and saves rupee 40000 per month, then the percentage can be calculated as:

percentage = (40,000/90,000) x 100% = 44.4%

Hence, she saves 44.4% of his income per month.

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Answer:

Step-by-step explanation:

Step-by-step explanation:

it says it in the headline : the cube root function.

1.

it goes through (0, 0) and (1, 1) and (-1, -1).

so,

f(x) = cubic root(x)

domain = (-infinity, +infinity)

range = (-infinity, +infinity)

x-intercept = 0

y-intercept = 0

2.

the function is y = cubic root(x + 2)

compared to

y = cubic root(x)

the domain is x >= -2

wrong !

this is not a square root. for the square root that domain would be correct (there are no real number square roots for negative values). but cubic roots are possible also for negative values. this function has the same domain and range as the basic y = cubic root(x) : (-infinity, +infinity).

the function is a vertical translation of g(x) = cubic root(x).

wrong !

vertical means up/down.

but it is a horizontal (left/right) translation of that g(x). by 2 units to the left, actually.

3.

for 1 <= x <= 4 we have already the average rate of change :

about 0.197

for 4 <= x <= 7 we get

(f(7) - f(4))/(7 - 4) ≈ (1.91 - 1.59)/3 ≈ 0.109

so, the interval [1, 4] has a greater average of change.

which is also clear when looking at the graph : the function increases stronger for the lower x-values than for the larger x-values.

Answer: 4/D

Step-by-step explanation: going through the options one by one.

for the first point, the first statement is true since both lines intersect at (4,5)

for the second point, this is also true because since (4,5) is on both functions, x=4 and y=5 will be a solution for both

for the third point, this is also true since the point of intersection is (4,5), this is the solution for the system

for the fourth point, this is untrue. since we don't know what f and g are and the only solution to the system is (4,5), what works for f may not necessarily work for g. so 4/d is the answer.

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The characteristic equation has 2 distinct real solutions if α > 16, 2 complex solutions if α < 16, and 1 repeated real solution if α = 16.

The characteristic equation of the differential equation y'' - 8y + αy = 0 is given by:

r^2 - 8r + α = 0

For 2 distinct real solutions, the discriminant of the characteristic equation must be positive, which leads to the condition:

(8)^2 - 4α > 0

64 - 4α > 0

-4α < -64

α > 16

For 2 complex solutions, the discriminant must be negative, which leads to the condition:

(8)^2 - 4α < 0

64 - 4α < 0

-4α > -64

α < 16

For 1 repeated real solution, the discriminant must be zero, which leads to the condition:

(8)^2 - 4α = 0

64 - 4α = 0

α = 16

For 2 distinct real solutions α > 16, For 2 complex solutions α < 16 and For 1 repeated real solution α = 16.

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Answer:

0.125 miles

Explanation:

1/4 of a mile is 440 yards and 1/8 of a mile is 220. 440-220=220.

The slope of the line that passes through the points (9,8) and (2,3) is 5/7.

The slope of a line in a graph is a measure of its steepness or slant. It is defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. In mathematical terms, the slope of a line can be represented as the difference in the y-coordinates of two points on the line divided by the difference in the x-coordinates of the same two points.

The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula:

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

Plugging in the given points, we get:

slope = (3 - 8) / (2 - 9) = -5 / -7 = 5/7

So, the slope of the line that passes through the points (9,8) and (2,3) is 5/7.

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Ms. Lee would save $40.19 per month by buying Brand B. To calculate this, we must first find out how much each brand costs to operate each month.

Brand cost is the amount of money invested in a brand or product in order to create, maintain, and grow its value. This includes the costs associated with advertising and promotion, research and development, marketing, and product design. Brand cost also includes activities such as creating and maintaining a good corporate image, creating brand loyalty, and expanding the customer base.

For Brand A, this would be $75.54 (442 kW x $0.17/kW).
For Brand B, this would be $67.35 (397 kW x $0.17/kW).
We can then subtract the cost for Brand B from the cost for Brand A to get the amount of money Ms. Lee would save each month.
This would be $40.19 ($75.54 - $67.35).

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y = 3 + 2[tex](3\sqrt{x} -1)[/tex] is a quadratic function.This function represents a real-valued function that maps a real number x to the real number y.

The graph of a quadratic function is called a parabola and has a curved shape. One of the main points of a parabola is its vertex. It is the highest or the lowest point on its graph

A quadratic function is one of the form f(x) = ax² + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola. Parabolas may open upward or downward and vary in "width" or "steepness", but they all have the same basic "U" shape.

The function y = 3 + 2[tex](3\sqrt{x} -1)[/tex] can be explained as follows:

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Francisco uses the method of similar triangles to find the distance across the river, and the distance across the river is 372 feet.

A triangle is a polygon with three sides and three vertices. The triangle's total number of angles comes to 180°. The distances between the formed the sight-lines are;

RB = 210 feet

OC = 275 feet

The distance between the point close to the river and the next point further from the river = is 115 feet

In triangles ΔPRB and ΔPOC,

we have;

∠PRE = ∠POC = 90°

Given;

∠PER ≅ ∠PCO

By the corresponding angle formed between two parallel lines and a common transversal.

Using angle-angle similarity theorem;

ΔPRE is similar to ΔPOC Which gives;

PR / PO = RE / OC

Let x represent the distance across the river,

we have;

PR = x

PO = 115 + x

Which gives;

x / (115+x) = 210 / 275

275x = 210 × (115 + x)

275x = 24150 + 210x

275x - 210x = 24150

65x = 24150

x = 371. 54

Therefore, the distance across the river is 372 feet.

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The number you think is 5.5

An algebraic expression is an expression that is made up of variables and constants, along with algebraic operations like addition, subtraction, square root, etc.

Let x represent the number you think. Thus, we can write:

(x - 10)² =  x²-10

x² - 20x + 100 = x²-10

-20x + 100 = -10

20x = 100 + 10

20x = 110

x = 110/20

x = 5.5

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The given graph represents a quadratic function with negative leading coefficient, hence it opens down.

c) Its vertex is its maximum and the function is increasing before reaching vertex and decreasing after it.

The vertex is at (-2, 8) so the domain on which the function is increasing is:

d) The x-intercepts of the graph are x = - 6 and x = 2. The function is positive between the x-intercepts and negative outside, so: