For the following exercises, find the domain, vertical asymptotes, and horizontal asymptotes of the functions. 10. f(x)=x−14​ 11. f(x)=5x+22​ 12. f(x)=x2−9x​ 13. f(x)=x2+5x−36x​ 14. f(x)=x3−273+x​ 15. f(x)=x3−16x3x−4​ 16. f(x)=x3+9x2+14xx2−1​ 17. f(x)=x2−25x+5​ 18. f(x)=x−6x−4​ 19. f(x)=3x−14−2x​ For the following exercises, find the x - and y-intercepts for the functions. 20. f(x)=x2+4x+5​ 21. f(x)=x2−xx​ 22. f(x)=x2+11x+30x2+8x+7​ 23. f(x)=x2−10x+24x2+x+6​ 24. f(x)=3x2−1294−2x2​

The radius οf the dilated lοgο will be apprοximately 8.66 feet.

The scale factοr is a number that represents the ratiο οf the cοrrespοnding side lengths οf twο similar figures. It can be used tο enlarge οr reduce the size οf a figure by a certain percentage οr factοr.

The area οf the lοgο is given as 5 square feet, and the radius οf the lοgο is 1.25 feet.

Therefοre, we can find the scale factοr as fοllοws:

k = √(A/5) = √(240/5) = √48 ≈ 6.93

Sο the scale factοr is apprοximately 6.93. Tο find the radius οf the dilated lοgο, we multiply the οriginal radius by the scale factοr:

r' = kr = 6.93(1.25) = 8.66

Hence, the radius οf the dilated lοgο will be apprοximately 8.66 feet.

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Answer:

Step-by-step explanation:

last one since if you plug in zero for the x in the denominator you get 0 and if you have 0 in the denominator it's always undefined

The trigonometric ratios can find the missing side of a right triangle given an angle, such as by using the tangent ratio to calculate the adjacent side length when given the length of the opposite side.

The trigonometric ratios are used to calculate specific values of a triangle. The three main ratios are sine, cosine, and tangent. The sine ratio is the ratio of the side length opposite the angle to the hypotenuse of the triangle. The cosine ratio is the ratio of the side length adjacent to the angle to the hypotenuse of the triangle. The tangent ratio is the ratio of the side length opposite the angle to the side length adjacent to the angle.

To find the missing side of a right triangle, given an angle, we use the trigonometric ratios. For example, if we have an angle of 45 degrees and a side length of 8, we can use the tangent ratio to calculate the missing side length. To do this we use the formula tan(45) = opposite/adjacent. We know the opposite side is 8, so to calculate the adjacent side we solve for x in the equation 8/x = tan(45). We get x = 8/tan(45), and x = 8/1 = 8. Therefore, the adjacent side length is 8.

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The density of the granite is 2690 kg/m³ and the mass of 1.3 m³ of granite is ​3497 kg.

Density is expressed mathematically as;

p = m / v

Where m is mass and v is volume.

Given that;

Plug the given values into the above formula and solve for density of the granite.

p = m / v

p = 6725 kg / 2.5 m³

p = 2690 kg/m³

b) The mass of 1.3 m³ of granite in kg will be;

p = m / v

m = p × v

m = 2690 kg/m³ × 1.3 m³

m = 3497 kg

Therefore, the mass of  1.3 m³ of granite is 3497 kg.

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Answer: 1.07x107 but the seven goes on top of the 10

Step-by-step explanation:

Answer:

1.07 × 10⁷

Step-by-step explanation:

To express 10,700,000 in scientific notation, we have to rewrite it as a decimal number that is between 1 and 10 multiplied by a power of 10.

As a decimal, the number is:

1.07.

We have to move the decimal point 7 places to get this number (see the attached image). Therefore 1.07 is multiplied by 10⁷ to get 10,700,000.

The value of D is 49.1º to the nearest degree using the law of sines.

To solve for angle D, we can use the law of sines, which states that for any triangle with sides a, b, and c opposite angles A, B, and C respectively:

a/sin(A) = b/sin(B) = c/sin(C)

Using this formula, we can solve for angle D:

sin(D)/d = sin(F)/f

sin(D) = (d/f) × sin(F)

sin(D) = (76/20) × sin(17º)

sin(D) = 0.7588

Taking the inverse sine of both sides, we get:

D = [tex]sin^{-1}[/tex] × (0.7588)

D = 49.1º (rounded to the nearest tenth of a degree)

The law of sines can have two possible solutions for an angle, depending on the triangle. However, in this case, since angle D is opposite the longer side (d), there is only one possible solution.

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Answer:

(x-15)(x-1) x²

Step-by-step explanation:

x² (x²-16x+15)

a+b=-16

ab=15

a=-15

b=-1

x(x²-15)- (x-15)

(x-15)(x-1)

(x-15)(x-1) x²

The acceleration of the system is 0.83 m/s² and the tension in the string is 8.3 N.

The acceleration of the system can be calculated using Newton's second law of motion. The equation is F = ma, where F is the net force on the system, m is the total mass, and a is the acceleration. Since the two masses are connected by a light inextensible string, the net force acting on the system is equal to the tension in the string. Therefore, the equation becomes T = (5 kg + 2 kg)a, where T is the tension and a is the acceleration. Solving for a, the acceleration is found to be 0.83 m/s². The tension in the string can also be calculated using the equation above. Plugging in the acceleration, the tension is found to be 8.3 N.

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The volume of the rectangular prism can be calculated by using the formula V = lwh, where l is the length, w is the width, and h is the height.

The volume of a rectangular prism can be calculated by the formula V = lwh, where l is the length, w is the width, and h is the height. To calculate the volume of a rectangular prism, first measure the length, width, and height of the prism. Then, plug these measurements into the formula V = lwh and solve for V.

For example, if the length of the prism is 6 cm, the width is 5 cm, and the height is 4 cm, the volume can be calculated by plugging these values into the formula. V = 6 x 5 x 4 = 120 cm3. This means that the volume of this rectangular prism is 120 cm3.

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Complete question:

What are the labels for the highlighted parts of a rectangular prism: A, B, and C?

Answer:

A. is an edge

B. a vertex

C. a face

Step-by-step explanation:

I have this same question now and got this. If you need more proof then look at attachment.

Option C, MN/LK||MN, is the additional piece of information required to demonstrate that ΔLKN ~ΔKNM by the SAS similarity theorem.

The SAS (Side-Angle-Side) similarity theorem: what is it?

According to the SAS (Side-Angle-Side) similarity theorem, two triangles are similar if they have two pairs of corresponding sides that are in proportion and the included angles are congruent.

In this example, we know that ΔLKN and ΔKNM share the angle at vertex K, and we also know that LN/MN and LK/KN are in proportion.

To clarify that MN is parallel to LK and forms a transversal with LN, we must first prove that MN/LK||MN.

To prove that the included angles between the matching sides are congruent, which is necessary for the triangles to be similar, this information is required.

Consequently, in order to demonstrate that ΔLKN~ΔKNM according to the SAS similarity theorem, option C is the correct additional piece of information.

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Therefore , the solution of the given problem of volume comes out to be false we must first know the cylinder's radius and height.

A three-dimensional object's volume, which is expressed in cubic units, indicates how much space it takes up. The symbols cm3 and in3 stand for cubic dimensions. However, you can use an object's bulk to estimate its dimensions. Usually, the weight of the item is converted into mass measures like kilograms and kilos.

Here,

The capacity of a cylinder and a cone that are the same height and radius are not the same.

The formula V = πr²h,

where r is the radius of the base and h is the height, determines the volume of a cylindrical. Contrarily, the equation

=> V = (1/3)r²h gives the volume of a cone.

To calculate the volume of a cone with the same measurements if the cylinder's volume is 99 cubic cm,

False we must first know the cylinder's radius and height.

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The function with the greatest rate of change are:

1. C = 3

2. A = 5

3. A = 1

4. B = 3

The rate of change of a linear function, also known as the slope of the line, represents the amount by which the output (y) changes for a given change in the input (x). In other words, it is the measure of how steep the line is.

The formula for the rate of change, or slope, of a linear function is:

slope = (change in y) / (change in x)

1. Rate of change for function A = change in y / change in x = 4/3

For B = 1/2

For C = 3/1 = 3

The function with the greatest rate of change is C = 3

2. Rate of change for function A = change in y / change in x = (10 - 5)/(1 - 0) = 5

For B = (12 - 8) / (3 - 1) = 2

For C = (6 - 3)/(1 - 0) = 3

The function with the greatest rate of change is A = 5

3. Rate of change for function A = change in y / change in x = 2/2 = 1

For B = (3 - 2)/(2 - 0) = 1/2

For C = 1/3

The function with the greatest rate of change is A = 1

4. Rate of change for function A = change in y / change in x = -1/3

For B = (10 - 1)/(4 - 1) = 3

For C = 2

The function with the greatest rate of change is B = 3

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5 times the sum of x squared and y squared. This can be expressed as 5(x^2 + y^2).

Express is a web application framework for Node.js, released as free and open-source software under the MIT License. It is designed for building web applications and APIs and is the de facto standard server framework for Node.js. It provides a host of features to facilitate the development of web and mobile applications, including routing, templating, and a middleware system to handle requests and responses. Express is the backend component of the MEAN stack and enables the rapid development of dynamic web applications.

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The number line model begins at 2.5 and then adds 4.5 to it, resulting in the number 7 being plotted at the end of the line.

The number line model for the expression 2.5 + 4.5 is shown below. The equation for this expression is 2.5 + 4.5 = 7. This number line model illustrates this expression by starting at the number 2.5 and then adding 4.5 to it, which results in the number 7 being plotted at the end of the line. This is represented by the arrow extending from 2.5 to 7. Starting at 2.5, the arrow first passes through 3, then 4, then 5, then 6, before finally reaching 7. This is the result of adding 4.5 to 2.5, which is shown on the number line model.The expression 2.5 + 4.5 can also be written mathematically as 2.5 + 4.5 = 7. This equation is read as "2.5 plus 4.5 equals 7," and it is a statement that the sum of 2.5 and 4.5 is equal to 7. The number line model of this expression illustrates this mathematical equation by showing how 2.5 plus 4.5 equals 7. The number line model begins at 2.5 and then adds 4.5 to it, resulting in the number 7 being plotted at the end of the line.

|-----|-----|-----|-----|-----|-----|

0    1     2     3     4     5     6

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Which number line model represents the expression 2.5 + 4.5?

Answer:

-6, -3, -2, 0, 2, 3, 6

Step-by-step explanation:

Normally the biggest number has the bigger value but in negative integers the smaller number has the bigger value.

Eg- If you have 2 dollars it is bigger that -2 dollars as then you will be going in dept.

-5 is smaller than -1

-1 is the greatest negative integer.

The expression that represents the perimeter of the rectangle in centimeters is 45.2g - 30.6h.

Let's start by finding the length of the top and bottom sides, which are equal to the width. The width is given by (9.8g - 4.5h) centimeters, so the length of the top and bottom sides is:

2(width) = 2(9.8g - 4.5h) = 19.6g - 9h

Next, we need to find the length of the left and right sides, which are equal to the length. The length is given by (1.5g - 3.4h) centimeters, so the length of the left and right sides is:

2(length) = 2(1.5g - 3.4h) = 3g - 6.8h

Now that we have the lengths of all four sides, we can find the perimeter of the rectangle by adding them together:

Perimeter = length + width + length + width

Perimeter = (3g - 6.8h) + (19.6g - 9h) + (3g - 6.8h) + (19.6g - 9h)

Perimeter = 45.2g - 30.6h

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Answer:

Step-by-step explanation:

[tex]m=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]

    [tex]=(\frac{-12+(-8)}{2}, \frac{-7+(-4)}{2})[/tex]

    [tex]=(-10,-5.5)[/tex]    

The diameter οr radius οf the circular οbject is 120mm, and the circumference οf the οbject 1 frοm the centre tο the edge οf a DVD is 380mm.

A circle's οr an ellipse's circumference is its perimeter. In οther wοrds, if the circle were tο be straightened οut alοng a line segment, the length οf the arc wοuld be the circumference. The perimeter is mοre frequently used tο refer tο the length οf the curve surrοunding any defined figure.

The given infοrmatiοn is that a DVD's edge is 60 mm lοng.

The diameter, radius, and circumference οf the circular οbject must be determined in οrder tο determine the measurement.

We cοncluded that

Radius = 60mm

Diameter = 120mm

Circumference = 380mm

Hence, Diameter = 120mm

Circumference = 380mm

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so, since we know that the derivative is simply the equation we use to get the slope at any point on the curve, thus df/dx will be that.

now, we know that g(x) is already in slope-intercept form, so it has a slope of "4", hmmm what's "x" at that instance?

[tex]f(x)=-x^2+8x+20\implies \cfrac{df}{dx}=-2x+8 \\\\[-0.35em] ~\dotfill\\\\ g(x)=\stackrel{\stackrel{m}{\downarrow }}{4}x+k\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\\\ 4~~ = ~~-2x+8\implies 2=x[/tex]

well, now we know that x = 2, hmmm what's "y" at that instance? well, our "y" will be simply f(2) = g(x), because g(x) is touching f(x) at that point on the curve.

[tex]f(2)=-(2)^2+8(2)+20\implies f(2)=32 \\\\[-0.35em] ~\dotfill\\\\ g(x)=4x+k\implies 32=4(2)+k\implies 32=8+k\implies \boxed{24=k}[/tex]

Check the picture below.

In this scenario, the dependent variable is the cost of the boxes of cookies and the independent variable is the number of boxes of cookies being purchased.

The cost of the boxes of cookies depends on the number of boxes being purchased. The more boxes of cookies that are purchased, the higher the cost will be. Therefore, the cost of the boxes of cookies is the dependent variable, as it depends on the independent variable of the number of boxes being purchased.

Conversely, the number of boxes of cookies being purchased is the independent variable, as it is the variable that is being manipulated or changed. The cost of the boxes of cookies is not being changed, but rather is dependent on the number of boxes being purchased.

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Answer: infinity technically the answer is infinity

nothing less nothing more

Step-by-step explanation:

There will be 8980 illiterate people in Sylvania 4 years from now if the country continues to reduce the number of illiterate citizens by 5 each year.

We can write a function P(t) to represent the number of illiterate people in Sylvania t years from today, where t is the number of years after the current year.

Given that the country has decided to reduce the number of illiterate citizens by 5 each year, we can subtract 5 from the number of illiterate people each year.

The initial number of illiterate people in the country is 9000. So, the function can be written as:

P(t) = 9000 - 5t

where t is the number of years after the current year.

For example, if we want to find out how many illiterate people will be in Sylvania in 4 years from now, we can substitute t with 4:

P(4) = 9000 - 5(4) = 9000 - 20 = 8980

Therefore, there will be 8980 illiterate people in Sylvania 4 years from now if the country continues to reduce the number of illiterate citizens by 5 each year.

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To know whether people can bargain the price down when purchasing a house at a 5% level of significance, we need to put a hypothesis test. The null hypothesis would be that people cannot bargain the price down

To determine whether 3-bedroom houses are cheaper than 4-bedroom houses, we would again give out a hypothesis test. The null hypothesis would be that there is no difference in price between 3-bedroom and 4-bedroom houses.

but the other hypothesis would be that 3-bedroom houses are cheaper than 4-bedroom houses.  If the p-value is less than 0.05, we can reject the null hypothesis and say that 3-bedroom houses are more cheaper than 4-bedroom houses.

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Lesley gets 10/18 or 5/9 of the counters.Adam has 18 counters, so we can express the total number of counters as 18/18. If he gave 10 of those counters to Lesley, we can express that as 10/18.

Adam has 18 counters, so we can express the total number of counters as 18/18, which is equivalent to 1. If he gave 10 of those counters to Lesley, we can express that as 10/18. To find out what fraction of the 18 counters Lesley gets, we need to simplify 10/18. Since both the numerator and denominator are divisible by two, we can divide both the numerator and denominator by two, which gives us 5/9. This means that Lesley gets 5/9 of the 18 counters, which is equivalent to 10/18 or half of the total number of counters.

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tan t = -4/3

The equation for the unit circle is

x2 + y2 = 1


For the point (-3/4, y) we have

(-3/4)2 + y2 = 1


Rearranging this gives us

y2 = 1 - (3/4)2

Solving for y gives us

y = √ (1 - (3/4)2)


Now we can find tan t by using the equation

tan t = y / -3/4


Substituting in the value of y we found earlier gives us

tan t = √ (1 - (3/4)2) / -3/4


Finally, simplifying the equation gives us the answer

tan t = -4/3

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In the context of economics, the term “break-even point” is used to indicate the number necessary to make enough money to keep going, and it is expressed in both units and dollars.

Break-even point is a term used in cost accounting to describe the point at which total cost and total revenue are equal. At this point, there is no profit or loss; it is a neutral zone. At this point, a firm's revenue from the sale of products and services is just sufficient to cover the total costs of producing those products and services.

The break-even point can be expressed in terms of units sold or in terms of total revenue. The point at which the total revenue equals total cost is the break-even point in terms of dollars. The point at which the number of units sold equals the fixed costs divided by the contribution margin per unit is the break-even point in terms of units sold. Therefore, the break-even point is expressed in both units and dollars to show the number necessary to make enough money to keep going.

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Answer:

13 for 5 bags.

Step-by-step explanation:

Dani spends 5.20 in total for 2 bags. You would do 5.20/2 to get 2.60 which tells us that 2.60 is the cost per bag. Then you would do 2.60 x 5 to get 13.

The 6.02 line of best fit is a straight line that best represents the trend or pattern of association between two variables on a scatter plot. It is also known as the regression line.

What is regression line?

In the context of MS Pre-Algebra S2 V16.2, the line of best fit is used to analyze patterns of association between two sets of data. For example, if we have data on the height and weight of a group of individuals, we can use a scatter plot to visualize the relationship between these two variables.

By drawing a line of best fit through the data points, we can see the general trend or pattern of association between height and weight. This line can then be used to make predictions about the weight of an individual based on their height, or vice versa. The line of best fit is a useful tool for analyzing patterns of association in a variety of fields, including statistics, economics, and social sciences.

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Complete question is: The 6.02 line of best fit is a straight line that best represents the trend or pattern of association between two variables on a scatter plot.

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]x+2y=2\implies 2y=-x+2 \\\\\\ x=\cfrac{-x+2}{2}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{1}{2}}x+1\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{-1}{2}} ~\hfill \stackrel{reciprocal}{\cfrac{2}{-1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{2}{-1} \implies 2}}[/tex]

so we're really looking for the equation of a line whose slope is 2 and it passes through (5 , 6)

[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{ 2}(x-\stackrel{x_1}{5}) \\\\\\ y-6=2x-10\implies {\Large \begin{array}{llll} y=2x-4 \end{array}}[/tex]

The equation of a line perpendicular to line QR in slope-intercept form that contains point (5, 6) is y = 2x-4.

y = mx + b is the slope intercept form of writing the equation of a straight line. In the equation 'y = mx + b', 'b' is the point, where the line intersects the 'y axis' and 'm' denotes the slope of the line.

Given that a line QR has an equation is x+2y = 2, we need to find the equation of a line passing through (5, 6) and is perpendicular to the given line,

Converting the equation into slop-intercepts form,

y = -0.5x+1

Here, slope m = -0.5

We know that the slopes of the perpendicular lines are negative reciprocal of each other,

Therefore, the slope of the asked line is 2.

So, its equation =

y = 2x+c

To find c, put x = 5 and y = 6

6 = 2(5) + c

c = -4

Therefore, the final equation will be =

y = 2x-4

Hence, the equation of a line perpendicular to line QR in slope-intercept form that contains point (5, 6) is y = 2x-4.

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To have a higher salary than 99% of her male counterparts, a woman would have to make more than $5229.48 per month, or $62753.76 per year

To find out how much a woman would have to make in a year to have a higher salary than 99% of her male counterparts, we need to find the salary level that corresponds to the 99th percentile of the male salary distribution.

First, we need to calculate the standard deviation of the annual salaries for both men and women. Since the standard deviation of the monthly salaries is $300, the standard deviation of the annual salaries can be calculated as:

σ_annual = σ_monthly * √12 = 300 * √12 = $1039.23

Next, we can calculate the salary level that corresponds to the 99th percentile of the male salary distribution using the standard normal distribution table.

z-score for the 99th percentile = 2.33

salary level for the 99th percentile of male salary distribution = mean + z-score * σ_annual

= $2750 + 2.33 * $1039.23 = $5229.48 (rounded to the nearest cent)

Therefore, to have a higher salary than 99% of her male counterparts, a woman would have to make more than $5229.48 per month, or $62753.76 per year (rounded to the nearest cent).

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