A cone has a volume of $12288\pi$ cubic inches and the vertex angle of the vertical cross section is 60 degrees. what is the height of the cone? express your answer as a decimal to the nearest tenth.

The inscribed angle theorem tells you that both angles must have the same measure, so

[tex]2(3m+2)=4m+20[/tex]

[tex]6m+4=4m+20[/tex]

[tex]2m=16[/tex]

[tex]m=8[/tex]

But this isn't the final answer! You're supposed to find the angles' measures, which are [tex]2(3m+2)^\circ[/tex] and [tex](4m+20)^\circ[/tex] where [tex]m=8[/tex]. So the answer is [tex]2(3\cdot8+2)^\circ=\boxed{52^\circ}[/tex].

The inscribed angle is half that of the arc it comprises. The measure of both the angle is 52°.

we know that the inscribed angle is half that of the arc it comprises.

Here, the arc that the inscribed angles comprise is the same.

2(3m+2)° = (4m+20)°

by solving for m

6m + 4 = 4m + 20

6m - 4m = 20 - 4

2m = 16

m = 8

To find the measure of the angle

(4m+20)°= 4(8) + 20 = 52°

2(3m+2)° = 2(26) = 52

Learn more about angles here:

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Answer:

$20

Step-by-step explanation:

Since we are talking about the unknown cost of a shirt AND a sweater, we are dealing with 2 unknowns.  However, we can only have one unknown in a single equation or we cannot solve it.  The cost of the sweater is based on the cost of the shirt, so the shirt will be our "main" unknown.

Cost of the shirt:  x

Since the sweater is $5 more than (this is addition) twice (that is 2 times) the cost of the shirt, the expression for the sweater is 2x + 5

The cost of both is (equals) 65.

x + 2x + 5 = 65 and

3x + 5 = 65 and

3x = 60 so

x = 20

The shirt cost $20 so the sweater had to cost 65 - 20 = 45

Answer:

Third answer choice is correct: 8/17

Step-by-step explanation:

You have to know the "parts" of the triangle: three angles, A B & C + three sides, labelled with measures 8, 15 & 17

Also, this is a right triangle (90 degree angle in the bottom left corner)

Also, since you're asked about angle A in the question (it asks What is the ratio of cosA), you have to know that the "8" side is adjacent to angle A and the "17" side is the hypotenuse (hypotenuse is always opposite the 90 degree angle)

Finally, with the mnemonic SOH-CAH-TOA (to help you remember how to find sin, cos & tan), you know the ratio of the cosine of angle A (cosA) is Adjacent over Hypotenuse or 8 over 17 (the fraction 8/17)

Answer:

38.2 miles

Step-by-step explanation:

343.8 miles divided by 9 gallons equals 32.2 miles per gallon.

[tex]\bf 7~~,~~\stackrel{7+6}{13}~~,~~\stackrel{13+6}{19}~~,~~\stackrel{19+6}{25}\qquad \impliedby \qquad \textit{common difference "d" is 6}[/tex]

we know all it's doing is adding 6 over again to each term to get the next one, so then

[tex]\bf \stackrel{\textit{Recursive Formula}}{\stackrel{\textit{nth term}}{f(n)}~~=~~\stackrel{\textit{the term before it}}{f(n-1)}~~~~\stackrel{\textit{plus 6}}{+~~~~6}}[/tex]

now for the explicit one

[tex]\bf n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ a_1=7\\ d=6 \end{cases} \\\\\\ a_n=7+(n-1)6\implies a_n=7+6n-6\implies \stackrel{\textit{Explicit Formula}}{\stackrel{f(n)}{a_n}=6n+1} \\\\\\ therefore\qquad \qquad f(10)=6(10)+1\implies f(10)=61[/tex]

The exact value for the equation is true but I don't really think that's the question so anyways...

- 15.) The exact form for this equation is -13pi/3 and the decimal form -13.613...

- 16.) The exact form for this equation is 23pi/4 and the decimal form 18/064...

- 17.) The exact form is -7pi/2 as the decimal is -10.995...

- 18.) The exact is -29pi/6 and the decimal is -15.184...

We know any trig problem that asks for exact values probably has something to do with 30° or 45° and their multiples.  That's [tex]\pi/6[/tex] and [tex]\pi/4[/tex]; we're apparently doing radians in this one.

General rules off the top of my head: Coterminal angles (gotten by adding or subtracting multiples of 2π) have the same values for their trig functions , cosine is even, sine is odd, cosine negate supplementary angles, sine of supplementary angles is unchanged, and the cosine of an angle is the sine of the complementary angle.

15

[tex]\cos (- \frac{13\pi}{3}) = \cos( 13\pi/3-6(2\pi)) =\cos(\pi/3) = \frac 1 2[/tex]

16

[tex] \csc(\frac{23 \pi}{4}) = \dfrac{1}{\sin (23\pi/4 - 3(8\pi/4))} = \dfrac{1}{\sin(-\pi/4)}= \dfrac{1}{- 1 /\sqrt{2}} = - \sqrt{2}[/tex]

17

[tex]\sec(-\frac {7 \pi}{2}) = \dfrac{1}{\cos(-7\pi/2+ (4/2)(2\pi) )}= \dfrac{1}{\cos(\pi/2)} = \dfrac 1 0[/tex]

That one is undefined

18

[tex]\cot(-\frac{29\pi}{6}) = \cot(-29\pi/6 + (18/6) (2 \pi)) = \cot(7\pi/6) \\= \tan(\pi/2 - 7\pi/6) = \tan(-4\pi/6)= \tan(-2\pi/3 + \pi) = \tan(\pi/3)= \sqrt{3}[/tex]

Whoever created this math homework problem needs a lesson in writing and typesetting math.  Let's list the errors:

Exact -- capitalized

each equation -- there are no equations

0 to 2 pi for theta -- do they want us to find the values or find the thetas but not evaluate the trig function?

theta is spelled out, not typeset

trig functions shouldn't be typeset in italics

sec -(7 pi/2)  is a typo

Sometimes there's a space after the problem number sometimes there isn't

This is awful.  Demand more of your teachers and online exercises!

Final answer:

The expression for the number of miles traveled by the airplane is 150h.

Explanation:

The expression for the number of miles traveled by the airplane is 150h. This expression represents the distance covered by the airplane based on the number of hours, h, it has been traveling at a speed of 150 miles per hour.

The expression for the number of miles traveled is [tex]\[ \text{Distance} = 150h \][/tex].

To determine the number of miles an airplane travels given its speed and the duration of travel, we can use a basic formula from physics that relates distance, speed, and time. The formula is:

[tex]\[ \text{Distance} = \text{Speed} \times \text{Time} \][/tex]

Here, the speed of the airplane is given as 150 miles per hour, and the time is represented by ( h ) hours.

Step 1.Identify the given values:

Speed ( v ) = 150 miles per hour

Time ( h ) = number of hours

Step 2. Apply the formula for distance:

Distance ( d ) = [tex]Speed (\( v \)) \(\times\) Time (\( h \))[/tex]

Step 3. Substitute the given values into the formula:

[tex]\( d = 150 \text{ miles per hour} \times h \text{ hours} \)[/tex]

[tex]\( d = 150h \)[/tex]

Thus, the expression for the number of miles traveled by the airplane, when it travels at 150 miles per hour for ( h ) hours, is:

[tex]\[ \text{Distance} = 150h \][/tex]

Answer:

  (n+2)(n+1)

Step-by-step explanation:

Write out the numerator and cancel common factors:

  (n+2)!/n! = (n+2)(n+1)n!/n! = (n+2)(n+1)

_____

You might be expected to multiply it out:

  = n·n +2·n +n·1 +2·1

  = n² +3n +2

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{1}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{2})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[-5-1]^2+[2-(-6)]^2}\implies d=\sqrt{(-5-1)^2+(2+6)^2} \\\\\\ d=\sqrt{(-6)^2+8^2}\implies d=\sqrt{36+64}\implies d=\sqrt{100}\implies d=10 \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{-3}~,~\stackrel{y_1}{9})\qquad B(\stackrel{x_2}{-1}~,~\stackrel{y_2}{6})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AB=\sqrt{[-1-(-3)]^2+[6-9]^2}\implies AB=\sqrt{(-1+3)^2+(6-9)^2} \\\\\\ AB=\sqrt{2^2+(-3)^2}\implies AB=\sqrt{13}\implies AB\approx 3.6[/tex]

5. Slope intercept form is written as y = mx +b, where m is the slope and b is the y-intercept.

Using two of the points on the graph find the slope:

(0,-3) and (6,1)

Slope = change in Y over the change in X:

Slope =  (1-(-3) / (6-0) = 4/6 = 2/3

The y-intercept is the Y value when x = 0, which is -3.

The formula is y = 2/3x - 3

6. Point slope form is written as y - y1 = m(x- x1) where m is the slope, y1 and x1 are a known point on the line.

Slope = (1-0) / (1-3) = 1/-3 = -1/3

You can use either point shown for x1 and y1, so I am using the point (1,1)

The equation becomes y -1 = -1/3(x-1)

Answer: x^3+30x+75

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

                       15x

Step-by-step explanation:

5x/x^2+2x÷30x^2/x+2

1/15x^5+2x^3+5x^2

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

x^3

x^3+30x+75

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

15x

[tex]\bf \cfrac{5x}{x^2+2x}\div \cfrac{30x^2}{x+2}\implies \cfrac{5x}{x^2+2x}\cdot \cfrac{x+2}{30x^2}\implies \cfrac{\begin{matrix} 5x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}{x~~\begin{matrix} (x+2) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}\cdot \cfrac{\begin{matrix} x+2\\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} }{\begin{matrix} 5x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}\cdot 6x} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \cfrac{1}{6x^2}~\hfill[/tex]

Answer:

x=0 , y=0

Step-by-step explanation:

3x+4y=0 , 4y=-3x , y = -3x/4 by substitution in tho other equation

14x+5( -3x/4)=0 , 14x - 15x/4 =0

41x/4=0 , so x = 0 and y = 0

Answer:

x=0 , y=0

Step-by-step explanation:

Answer:

Step-by-step explanation:

Easy way to do this is step by step.  Your quadratic, from your entry, must be

[tex]5x^2-3x-1[/tex].

Step by step looks like this, one thing at a time:

[tex]x=\frac{3+\sqrt{(-3)^2-4(5)(-1)} }{2(5)}[/tex] becomes

[tex]x=\frac{3+\sqrt{9-(-20)} }{10}[/tex] becomes

[tex]x=\frac{3+\sqrt{9+20} }{10}[/tex]

and this of course is

[tex]x=\frac{3+\sqrt{29} }{10}[/tex]

Do the same with the subtraction sign to get the other solution.

If you're unsure of how to enter it into your calculator, do it step by step so you don't mess up the sign.  If you enter it incorrectly, you could end up with an imaginary number when it should be real, or a real one that should be imaginary.

Just my advice as a high school math teacher.

Answer:

13.74

Step-by-step explanation:

the top right angle is 90 (opposite angles in a quadrilateral add up to 180). use the sine rule. x = 47/sin 90 × sin 17

= 13.74

Answer:

x = 13.7

Step-by-step explanation:

The angle at the top of the triangle = 90° - 17° = 73°

The left side of the triangle is x ( opposite sides of a rectangle )

Using the cosine ratio in the right triangle

cos73° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{47}[/tex]

Multiply both sides by 47

47 × cos73° = x, hence

x ≈ 13.7

Answer:

C(1,3) and D(1,4).

Step-by-step explanation:

The given quadrilateral ABCD has vertices at A (3,7) and B (3,6). The diagonals of  this quadrilateral ABCD intersect at E (2,5).

Recall that, the diagonals of a parallelogram bisects each other.

This means that; E(2,5) is the midpoint of each diagonal.

Let C and D have coordinates C(m,n) and D(s,t)

Using the midpoint rule:

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

The midpoint of AC is [tex](\frac{m+3}{2}, \frac{n+7}{2})=(2,5)[/tex]

This implies that;

[tex](\frac{m+3}{2}=2, \frac{n+7}{2}=5)[/tex]

[tex](m+3=4, n+7=10)[/tex]

[tex](m=4-3, n=10-7)[/tex]

[tex](m=1, n=3)[/tex]

The midpoint of BD is [tex](\frac{m+3}{2}, \frac{n+7}{2})=(2,5)[/tex]

This implies that;

[tex](\frac{s+3}{2}=2, \frac{t+6}{2}=5)[/tex]

[tex](s+3=4, t+6=10)[/tex]

[tex](s=4-3, t=10-6)[/tex]

[tex](s=1, t=4)[/tex]

Therefore the coordinates of C are (1,3) and D(1,4).

Final answer:

To ensure ABCD is a parallelogram with given vertices A (3,7) and B (3,6), and diagonals intersecting at E (2,5), the coordinates of C and D must be C (1,3) and D (1,4), derived using the midpoint formula.

Explanation:

To ensure that quadrilateral ABCD is a parallelogram, the diagonals AC and BD must bisect each other at the point E (2,5). Given vertices A (3,7) and B (3,6), and knowing that E is the midpoint of the diagonals, we can find the coordinates of C and D. Since E is the midpoint, for diagonal AC we have E's x-coordinate as the average of A and C's x-coordinates, and the same for the y-coordinate.

The coordinates of C can be found using the midpoint formula:

2 = (3 + xC)/2

5 = (7 + yC)/2

Solving these equations gives us C's coordinates:

xC = 2*2 - 3 = 1

yC = 2*5 - 7 = 3

Thus, point C is (1,3). For diagonal BD, we repeat the process:

2 = (3 + xD)/2

5 = (6 + yD)/2

Solving these equations gives us D's coordinates:

xD = 2*2 - 3 = 1

yD = 2*5 - 6 = 4

Point D is then (1,4). With vertices at A (3,7), B (3,6), C (1,3), and D (1,4), ABCD is a parallelogram because both pairs of opposite sides are parallel and equal in length, as indicated by their coordinates.

Answer:

Step-by-step explanation:

The cross section will have the same shape as the base of the pentagonal prism; the dimensions will be proportionally smaller.

Answer:

every point will be 4 tons lower than it was

Step-by-step explanation:

26 is 4 less than 30, so the new function g(x) is ...

g(x) = f(x) -4

It is shifted down 4 units (tons) from the original function.

Answer:

Choose the correct answer from your choices.

Step-by-step explanation:

First, we find the price of the turkey by multiplying the weight of turkey by the price per pound.

2.1 pounds of turkey at the deli. The price of the turkey was 2.87 per pound.

2.1 lb * 2.87 $/lb = $6.03

Then, we find the price of the ham by multiplying the weight of ham by the price per pound.

She also bought 4.8 pounds of ham. The price of the ham was 2.11 per pound.

4.8 lb * 2.11 $/lb = $10.13

Now we add the two prices together.

$6.03 + $10.13 = $16.16

The total price was $16.16

We have similar triangles so

[tex]\dfrac{4'6"}{18"} = \dfrac{x}{11'9"}[/tex]

[tex] x= \dfrac{ (12(11)+9 )(12(4)+6) }{18 } = 423 \textrm{ inches}[/tex]

Answer: 35' 3"

To find the height of a light pole given the shadow lengths of the pole and a woman of known height, we use a proportion. The height of the light pole is calculated to be 35.25 feet based on the given information.

The question asks how tall a light pole is if the pole's shadow is 11 feet 9 inches, and a woman who is 4 feet 6 inches tall casts a shadow that is 18 inches long. This is a problem of proportional relationships between the heights of objects and the lengths of their shadows. Using the fact that the ratio of the height of an object to the length of its shadow is the same for all objects at a given time, we can set up a proportion:

Height of woman / Length of woman's shadow = Height of light pole / Length of light pole's shadow

(4.5 feet) / (1.5 feet) = Height of light pole / (11.75 feet)

Now, we can solve for the height of the light pole:

Height of light pole = (11.75 feet) * (4.5 feet) / (1.5 feet)

Height of light pole = (11.75 * 4.5) / 1.5 = (52.875) / 1.5 = 35.25 feet

So, the height of the light pole is 35.25 feet.

Answer:

19

Step-by-step explanation:

to find the range, you have to subtract the smaller number from the biggest number

In this case it would be 45-26

45-26=19

range=19

A newspaper asking readers to complete a survey on their webpage is not conclusively biased or unbiased without knowing more about the survey's design and intention. Surveys can be a method to engage with and understand the readership better, but the potential for selection bias and the phrasing of questions could introduce bias. Whether the survey is biased or not depends on its execution and underlying methodological rigor.

The question "Is a newspaper asking readers to complete a brief survey on their webpage biased or unbiased" revolves around evaluating the intentions and methodology behind collecting reader satisfaction feedback. Given the nature of the survey is to collect feedback directly from readers on the newspaper webpage this can initially seem like a genuine effort to improve their service.

For evaluating the unbiased information based on research, it is crucial to consider the intent behind the survey and the potential for selection bias. It might inadvertently capture only the opinions of those willing to participate, or primarily those with strong opinions, positive or negative. Despite these considerations, the effort to engage with the readership directly can also be seen as a step towards transparency and improvement, indicating a potential to balance partiality with constructive feedback.

However, to ensure the process is unbiased, the newspaper would need to follow rigorous methodological standards, like random sampling, to ensure that the survey findings reflect the actual population of readers accurately. It's also essential to ensure that questions are phrased neutrally to avoid leading respondents towards a particular answer.

Experimental studies compare B. Two or more treatments are compared in the study (possibly including "no treatment" and C. One or more treatment groups and a control group are included in the study.

Regarding the characteristics that experiments have but surveys do not, the options that apply are that two or more treatments are compared in the study (possibly including "no treatment and one or more treatment groups and a control group are included in the study. These characteristics are specific to experimental design. In an experiment, there is a deliberate manipulation of variables to test a hypothesis, often involving a treatment and a control group to establish causality.

Surveys, on the other hand, typically gather data at one point in time or over time without manipulating variables, as seen in longitudinal or cross-sectional surveys. The two methodologies are distinct in that experiments can provide causal conclusions due to their internal validity, while surveys, although helpful in understanding correlations and trends, cannot as readily establish causation.

Final answer:

To find the probability of drawing a four and then a five from a standard deck with replacement, multiply the probabilities of the independent events: (1/13) × (1/13) = 1/169.

Explanation:

The question involves calculating the probability of two independent events when drawing cards from a standard deck. The first event (A) is drawing a card that is a four, and the second event (B) is drawing a card that is a five. The probability of each of these events is calculated separately since the card is replaced after each draw, making the draws independent of each other.

The probability of drawing a four (P(A)) from a standard deck is 1/13, as there are four fours in a 52-card deck. Similarly, the probability of drawing a five (P(B)) is also 1/13. Since the events are independent, the combined probability is the product of the two probabilities: P(A) × P(B) = (1/13) × (1/13) = 1/169.

Answer:

$1236.25

Step-by-step explanation:

We can convert the percentage to 0.075 to make it easier. Then, multiply 1150 by 1.075 to get 1236.25. We add the one because we need to include the initial $1150.

Answer:-9+2I

Step-by-step explanation: MUTIPLYING THE SECOND BRACKET BY THE NEGATIVE SIGN.

(-3-3I)(-6+5I)

COLLECTING LIKE TERMS

(-3-6)(-3I+5I)

=-9+2I

Answer:

The difference is:

[tex]-9+2i[/tex]

Step-by-step explanation:

We have the subtraction of two complex numbers.

[tex](-3-3i)-(6-5i)[/tex]

To solve the operation, the product of:

[tex]-(6-5i)[/tex]

[tex]-6 +5i[/tex]

Now add the two expressions. Add real numbers with real numbers and complexes with complex numbers

[tex]-3-3i-6 +5i[/tex]

[tex]-3-6 +5i-3i[/tex]

[tex]-9+2i[/tex]

The difference is:

[tex]-9+2i[/tex]

Answer:

It will take about 27.7 years

Step-by-step explanation:

* Lets talk about the compound continuous interest

- Compound continuous interest can be calculated using the formula:  

 A = P e^rt  

• A = the future value of the investment, including interest

• P = the principal investment amount (the initial amount)

• r = the interest rate  

• t = the time the money is invested for

- The formula gives you the future value of an investment,  

  which is compound continuous interest plus the  principal.  

- If you want to calculate the compound interest only, you need

 to deduct the principal from the result.  

- So, your formula is:

 Compounded interest only = Pe^(rt)  - P

* Now lets solve the problem

∵ The invest is $ 1000

∴ P = 1000

∵ The interest rate is 2.5%

∴ r = 2.5/100 = 0.025

- They ask about how long will it take to make double the investment

∴ A = 2 × 1000 = 2000

∵ A = P e^(rt)

∴ 2000 = 1000 (e)^(0.025t) ⇒ divide both sides by 1000

∴ 2000/1000 = e^(0.025t)

∴ 2 = e^(0.025) ⇒ take ln for both sides

∴ ln(2) = ln[e^(0.025t)]

∵ ln(e)^n = n

∴ ln(2) = 0.025t ⇒ divide both sides by 0.025

∴ t = ln(2)/0.025 = 27.7 years

* It will take about 27.7 years

Answer:

D. <F = 65 degrees

Step-by-step explanation:

First off, we know that the measures of <F and the angle adjacent to it add to 90 degrees, as indicated by the right angle. They are complementary angles.

The complementary angle of <F has an intercepted arc of 50 degrees. Because the angle is on the opposite end of the circle, it is half of the measure of the arc. Therefore, it is 25 degrees.

Because this angle and <F sum to 90, just subtract 90-25 to find <F.

<F = 65 degrees

Answer:

F is equal to 65 (option D)

For this case we have that by definition, the distance between two points is given by:

[tex]d = \sqrt {(x_ {2} -x_ {1}) ^ 2+ (y_ {2} -y_ {1}) ^ 2}[/tex]

We have to:

[tex](x_ {1}, y_ {1}) = (- 4,4)\\(x_ {2}, y_ {2}) = (2,4)[/tex]

Substituting:

[tex]d = \sqrt {(2 - (- 4)) ^ 2+ (4-4) ^ 2}\\d = \sqrt {(2 + 4) ^ 2 + (4-4) ^ 2}\\d = \sqrt {(6) ^ 2 + (0) ^ 2}[/tex]

[tex]d = \sqrt {36}\\d = 6[/tex]

ANswer:

[tex]d = 6[/tex]

Answer:

6

Step-by-step explanation:

ANSWER

2nd and 3rd quadrant.

EXPLANATION

The given trigonometric equation is:

[tex] \sec(x) = - 2[/tex]

The secant ratio is negative in the second and third quadrant.

But it is positive in the first and fourth quadrants.

The given secant ratio is negative.

This implies that , the solution to given equation lies in the second and third quadrant.

Given the conditions: f(x) approaches 300 and g(x) approaches 0 (and is less than zero as x approaches 5), the limit as x approaches 5 of the quotient f(x)/g(x) is negative infinity.

Based on the given conditions: f(x) approaches 300 and g(x) approaches 0 as x approaches 5. Moreover, g(x) is less than zero, and therefore negative, as x approaches 5. When you divide f(x) by g(x), the sign of the outcome is determined by the signs of the numerator (f(x)) and the denominator (g(x)).

As f(x) is positive and g(x) is negative, the quotient will be negative. Since f(x) is approaching a finite value and g(x) is approaching 0, the quotient f(x)/g(x) tends toward negative infinity as per the properties of limits.

Therefore, the value of lim x→5 f(x)/g(x) is negative infinity.

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