x-12/x-8 rational expression

The answer is:

[tex]\frac{f(x)}{g(x)}=\frac{x+3}{x+4}[/tex]

To solve the problem,  we need to factorize the quadratic functions in order to be able to simplify the expression.

We can factorize quadratic functions in the following way:

[tex]a^{2}-b^{2} =(a-b)(a+b)[/tex]

Also, we can factorize/simplify quadratic expressions in the following way, if we have the following quadratic expression:

[tex]ax^{2}+bx+c[/tex]

We can factorize it by finding two numbers which its products give as result "c" (j) and its algebraic sum gives as result "b" (k), and then, rewrite the expression in the following way:

[tex](x+j)(x+k)[/tex]

Where,

x, is the variable.

j, is the first obtained value.

k, is the second obtained value.

We are given the functions:

[tex]f(x)=x^{2} -9\\g(x)=x^{2} -7x+12[/tex]

Then, factoring we have:

First expression,

[tex]f(x)=x^{2} -9=(x+3)(x-3)[/tex]

Second expression,

[tex]\g(x)=x^{2} -7x+12[/tex]

We need to find two number which product gives as result 12 and their algebraic sum gives as result -7. Those numbers are -4 and -3.

[tex]-4*-3=12\\-4-3=-7[/tex]

Now, rewriting the expression we have:

[tex]\g(x)=x^{2} -7x+12=(x-4)(x-3)[/tex]

So, solving we have:

[tex](f/g)(x)=\frac{f(x)}{g(x)}=\frac{(x+3)(x-3)}{(x+4)(x-3)}=\frac{x+3}{x+4}[/tex]

Have a nice day!

Answer:

You can view a kite as 4 triangles

Step-by-step explanation:

A geometric kite can easily be viewed as 4 triangles.  The formula to calculate the area of a kite (width x height)/2 is very similar to the one of a triangle (base x height)/2.

According to the formula to calculate the area of a kite, we would get:

(36 x 30)/2 = 540.

If we take the approach of using 4 triangles, we could imagine a shape formed by 4 triangles measuring 18 inches wide with a height of 15.

The area of each triangle would then be: (18 x 15)/2 = 135

If we multiply this 135 by 4... we get 540.

Answer:

Draw a vertical line to break the kite into two equal triangles with a base of 36 and a height of 15. Use the formula A = 1/2bh to find the area of each. The sum of the areas is the area of the kite.

Step-by-step explanation:

Answer:

[tex]A=\$5003.2[/tex]

Step-by-step explanation:

Use the exponential growth formula

[tex]A = Pe ^ {rt}[/tex]

Where A is the final amount in the account, P is the initial amount, r is the growth rate and t is the time in years

In this problem

We know that

[tex]P=4,200\\\\r=\frac{3.5\%}{100\%}= 0.035\\\\ t=5\ years[/tex]

So

[tex]A = 4,200e^{0.035t}[/tex]

Finally after 5 years the balance of the account is:

[tex]A=\$5003.2[/tex]

Answer:

(6 x + 7) (x + 4) thus A:

Step-by-step explanation:

Factor the following:

6 x^2 + 31 x + 28

Factor the quadratic 6 x^2 + 31 x + 28. The coefficient of x^2 is 6 and the constant term is 28. The product of 6 and 28 is 168. The factors of 168 which sum to 31 are 7 and 24. So 6 x^2 + 31 x + 28 = 6 x^2 + 24 x + 7 x + 28 = 4 (6 x + 7) + x (6 x + 7):

4 (6 x + 7) + x (6 x + 7)

Factor 6 x + 7 from 4 (6 x + 7) + x (6 x + 7):

Answer: (6 x + 7) (x + 4)

The factored form of the expression '6x^2 + 31x + 28' is '(x + 4) (6x + 7)', which corresponds to option A.

In factoring the expression '6x^2 + 31x + 28', we need to find two numbers whose product equals '6x2 * 28' (the product of the first and the last term), and sum equals '31x' (the middle term). The numbers that fit these conditions are '4' and '7'.

So, this means you can factor out 'x' from the terms '6x^2' and '31x' to get '6x*(x + 4)'. Then, you will be left with '+ 28'. The number '7' fits perfectly here, because '4 * 7 = 28'. Hence, the factored form of the expression is '(x + 4) (6x + 7)'.

This corresponds to the answer choice A.) (x + 4) (6x + 7).

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Answer:

Step-by-step explanation:

A) the slope values you have put in your problem statement are correct. As you know, they are computed from ...

  (change in gallons)/(change in time)

where the reference point for changes is P. Using the first listed point Q as an example, the secant slope is ...

  (3410 -1275)/(5 -15) = 2135/-10 = -213.5 . . . . gallons per minute

__

B) The average of the secant slopes for points Q adjacent to P is ...

  (-187 +(-145))/2 = -332/2 = -166 . . . . gallons per minute

The tangent slope at point P is estimated at -166 gpm.

The secant line joins two points on the curve of a graph.

Point P is given as:

[tex]P = (15,1275)[/tex]

(a) The slopes of the secant lines PQ

The points are given as:

[tex]Q = \{(5,3410),(10, 2210),(20, 550) ,(25, 145),(30, 0) \}[/tex]

The slope (m) is calculated using:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

So, we have:

For Q = (5,3410), the slope of the secant line is:

[tex]m_1 = \frac{1275 - 3410}{15 - 5}[/tex]

[tex]m_1 = \frac{-2135}{10}[/tex]

[tex]m_1 = -213.5[/tex]

For Q = (10, 2210), the slope of the secant line is:

[tex]m_2 = \frac{1275 - 2210}{15 - 10}[/tex]

[tex]m_2 = \frac{-935}{5}[/tex]

[tex]m_2 = -187[/tex]

For Q = (20, 550), the slope of the secant line is:

[tex]m_3 = \frac{1275 - 550}{15 - 20}[/tex]

[tex]m_3 = \frac{725}{-5}[/tex]

[tex]m_3 = -145[/tex]

For Q = (25, 145), the slope of the secant line is:

[tex]m_4 = \frac{1275 - 140}{15 - 25}[/tex]

[tex]m_4 = \frac{1135}{-10}[/tex]

[tex]m_4 = -113.5[/tex]

For Q = (30, 0), the slope of the secant line is:

[tex]m_5 = \frac{1275 - 0}{15 - 30}[/tex]

[tex]m_5 = \frac{1275}{-15}[/tex]

[tex]m_5 = -85[/tex]

(b) The slope of the tangent by average

The closest secant lines to tangent P are

[tex]Q = \{(10, 2210),(20, 550)\}[/tex]

This is so, because point P (15, 1275) is between the above points.

The slopes of secant lines at [tex]Q = \{(10, 2210),(20, 550)\}[/tex] are:

[tex]m_2 = -187[/tex]

[tex]m_3 = -145[/tex]

The average slope (m) is:

[tex]m = \frac{m_2 + m_3}{2}[/tex]

[tex]m = \frac{-187 - 145}{2}[/tex]

[tex]m = \frac{-332}{2}[/tex]

[tex]m = -166[/tex]

Hence, the average slope is -166

Read more about slopes of secant and tangent lines at:

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Check the picture below.

Answer:

5t/3

Step-by-step explanation:

r^8=5 and r^7=3/t

here r^8=5

r^7×r=5

3/t×r=5

r=5t/3

The value of r in terms of t is 5t/3.

A term written aˣ is an exponential term. Its value is obtained by multiplying a with itself x number of times. The term aˣ is read as

a raised to the power of x.

Given r⁸ = 5, r⁷ = 3/t. We are asked to determine the value of r in terms of t.

We will apply the exponential rule [tex]\frac{x^{a} }{x^b} = x^{a-b}[/tex].

Let our equations be r⁸ = 5 ... (1), and r⁷ = 3/t ... (2).

Dividing (1) by (2), we get

r⁸/r⁷ = 5/(3/t)

or, r⁸-⁷ = 5t/3 (using the rule [tex]\frac{x^{a} }{x^b} = x^{a-b}[/tex] )

or, r = 5t/3.

∴ The value of r in terms of t is 5t/3.

Learn more about the exponential rules at

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Answer:

807.8 in^2

Step-by-step explanation:

The total area of the box is the sum of the areas of all faces of the box. The top, bottom, front, and back faces are rectangles 18 in long. The end faces each consist of a rectangle and a triangle. We can compute the sum of these like this:

The areas of top, bottom, front, and back add up to be 18 inches wide by the length that is the perimeter of the end: 2·5in +2·8 in + 9.6 in = 35.8 in. That lateral area is ...

(18 in)(35.6 in) = 640.8 in^2

The area of the triangle on each end is equivalent to the area of a rectangle half as high, so we can compute the area of each end as ...

(9.6 in)(8.7 in) = 83.52 in^2

Then the total area is the lateral area plus the area of the two ends:

640.8 in^2 + 2·83.52 in^2 = 807.84 in^2 ≈ 807.8 in^2

Answer:

[tex]127,000\ members[/tex]

Step-by-step explanation:

In this problem we have an exponential function of the form

[tex]f(x)=a(b)^{x}[/tex]

where

a is the initial value

b is the base

The base is equal to

b=1+r

r is the average rate

In this problem we have

a=23,000 members

r=5%=5/100=0.05

b=1+0.05=1.05

substitute

[tex]f(x)=23,000(1.05)^{x}[/tex]

x ----> is the number of years since 1985

How many members will there be in 2020?

x=2020-1985=35 years

substitute in the function

[tex]f(x)=23,000(1.05)^{35}=126,868\ members[/tex]

Round to the nearest thousand

[tex]126,868=127,000\ members[/tex]

Answer:

[tex](f-g)(x)=4x^{4}+2x^3}-2x-4[/tex]

Step-by-step explanation:

Let f and g be two functions that are defined in the same interval and have the same independent variable. Then, the Subtraction of Function is defined as:

[tex](f-g)(x)=f(x)-g(x)[/tex]

Let's solve (f-g)(x) with [tex]f(x)=5x^{4}+4x^3}+3x^{2}+2x+1[/tex] and [tex]g(x)=x^{4}+2x^{3}+3x^{2}+4x+5[/tex]

[tex](f-g)(x)=(5x^{4}+4x^3}+3x^{2}+2x+1)-(x^{4}+2x^{3}+3x^{2}+4x+5)\\(f-g)(x)=5x^{4}+4x^3}+3x^{2}+2x+1-x^{4}-2x^{3}-3x^{2}-4x-5\\(f-g)(x)=4x^{4}+2x^3}-2x-4[/tex]

.

What is the problem about? Does x equal 24 in the problem?

Normally, x is an unknown variable that needs to be evaluated, so I don’t really know what x is at the moment. Please show me the problem so that I can solve the equation.

Answer:

$77.18

Step-by-step explanation:

Fill in your equation like this:

[tex]B=70(1+.05)^2[/tex] and

[tex]B=70(1.05)^2[/tex] and

[tex]B=70(1.1025)[/tex] so

B = $77.18

Answer:

166 m^2

Step-by-step explanation:

The enclosing rectangle is 9m by 29m, so is 261 m^2. From that, the white space of 5m by 19m = 95 m^2 must be subtracted. The result is that the shaded area is ...

261 m^2 -95 m^2 = 166 m^2

Answer:

M'(2,4), P'(2,5), A'(4,5), T'(4,4)

Step-by-step explanation:

The translation 1 unit to the right and 2 units up has the rule

(x,y)→(x+1,y+2)

Rectangle MPAT has vertices at points M(1,2), P(1,3), A(3,3) and T(3,2). The image rectangle is rectangle M'P'A'T'. According to translation rule:

Answer:

That is a VERY famous math problem first published in 1637 by Pierre Fermat.  He said that in an equation of the type

x^n + y^n = z^n

you will ONLY find solutions when "n" is no greater than 2.  He said he had a proof but the margin in his note book was too small to fit it in.

(It is now believed he never had any such proof.)

Anyway, we can find an infinite number of solutions when n = 2

3^2 + 4^2 = 5^5

5^5 + 12^2 = 13^2

but you cannot find any solutions when n = 3 or higher.

https://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem

Finally in 1995, (358 YEARS after Fermat first published this theorem), the British mathematician Andrew Wiles published his own proof of this theorem.

https://en.wikipedia.org/wiki/Andrew_Wiles

Step-by-step explanation:

Final answer:

Fermat's Last Theorem is a famous mathematical conjecture proposed by Pierre de Fermat in the 17th century, stating that there are no three positive integers a, b, and c that satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2. The theorem remained unproven for over 350 years until Andrew Wiles presented a proof in 1994.

Explanation:

Fermat's Last Theorem is a famous mathematical conjecture proposed by Pierre de Fermat in the 17th century. The theorem states that there are no three positive integers a, b, and c that satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2. In other words, there are no whole number solutions to this equation when n is greater than 2.

This conjecture remained unproven for over 350 years and became one of the most elusive problems in mathematics. However, in 1994, the British mathematician Andrew Wiles presented a proof of Fermat's Last Theorem, which is considered one of the most significant achievements in the history of mathematics.

Answer:

1131.0 m^3

Step-by-step explanation:

Let h1 represent the height of the top cone, and h2 the height of the bottom cone. The volume of a cone is given by the formula ...

V = (1/3)πr^2·h

so the volumes of both cones together will be ...

V = (1/3)πr^2·h1 + (1/3)πr^2·h2 = (1/3)πr^2·(h1 +h2)

= (1/3)π(6 m)^2(12 m + 18 m) = 360π m^3

≈ 1131.0 m^3

ANSWER

[tex]g(x) = {x}^{2} + 4x + 4[/tex]

EXPLANATION

The given function is

[tex]f(x) = {x}^{2} - 6x + 9[/tex]

This can be rewritten as:

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

If this function is shifted 5 units to the left to create g(x), the

[tex]g(x) = f(x + 5)[/tex]

We substitute x+5 into f(x) to get:

[tex]g(x) = {(x + 5 - 3)}^{2} [/tex]

[tex]g(x) = {(x + 2)}^{2} [/tex]

We expand to get:

[tex]g(x) = {x}^{2} + 4x + 4[/tex]

Answer:

g(x) = x^2 + 4x + 4

Step-by-step explanation:

In translation of functions, adding a constant to the domain values (x) of a function will move the graph to the left, while subtracting from the input of the function will move the graph to the right.

Given the function;

f(x) = x2 - 6x + 9

a shift 5 units to the left implies that we shall be adding the constant 5 to the x values of the function;

g(x) = f(x+5)

g(x) = (x+5)^2 - 6(x+5) + 9

g(x) = x^2 + 10x + 25 - 6x -30 + 9

g(x) = x^2 + 4x + 4

Answer:

30 mm

Step-by-step explanation:

The volume of a rectangular prism is the product of its three dimensions. To find the missing dimension, divide the volume by the product of the two that are given:

(165000 mm^3)/((100 mm)(55 mm)) = 165000/5500 mm^3/mm^2 = 30 mm

Answer:

30mm

Step-by-step explanation:

30mm

Answer with explanation:

[tex]\text{Average}=\frac{\text{Sum of all the observation}}{\text{Total number of Observation}}[/tex]

Average Height of tallest Building in San Francisco

                    [tex]=\frac{260+237+212+197+184+183+183+175+174+173}{10}\\\\=\frac{1978}{10}\\\\=197.8[/tex]

Average Height of tallest Building in Los Angeles

                    [tex]=\frac{310+262+229+228+224+221+220+219+213+213}{10}\\\\=\frac{2339}{10}\\\\=233.9[/tex]

→→Difference between Height of tallest Building in Los Angeles and  Height of tallest Building in San Francisco

               =233.9-197.8

               =36.1

⇒The average height of the 10 tallest buildings in Los Angeles is 36.1 more than the average height of the tallest buildings in San Francisco.

⇒Part B

Mean absolute deviation for the 10 tallest buildings in San Francisco

 |260-197.8|=62.2

 |237-197.8|=39.2

 |212-197.8|=14.2

 |197 -197.8|= 0.8

 |184 -197.8|=13.8

 |183-197.8|=14.8

 |183-197.8|= 14.8

 |175-197.8|=22.8

 |174-197.8|=23.8

 |173 -197.8|=24.8

Average of these numbers

     [tex]=\frac{62.2+39.2+14.2+0.8+13.8+14.8+14.8+22.8+23.8+24.8}{10}\\\\=\frac{231.2}{10}\\\\=23.12[/tex]

Mean absolute deviation=23.12

Answer:

1st -36.1 meters or more

2nd -23.12

Step-by-step explanation:

Answer:

Step-by-step explanation:

Google is your friend for such conversions. It will generally give answers correct to 6 significant figures.

___

Normal atmospheric pressure is defined as 1 atmosphere.

  1 atm = 101,325 Pa = 760 torr (mmHg) ≈ 14.695 948 775 514 2 psi

To convert 745 mmHg into psi, divide the value by 51.71. 745 mmHg is approximately equal to 14.41 psi. To convert 727 mmHg into kPa, divide the value by 7.5. 727 mmHg is approximately equal to 96.93 kPa. To convert 55.5 kPa into atm, divide the value by 101.325. 55.5 kPa is approximately equal to 0.55 atm.

To convert 745 mmHg into psi, divide the value by 51.71. Therefore, 745 mmHg is approximately equal to 14.41 psi.

To convert 727 mmHg into kPa, divide the value by 7.5. Therefore, 727 mmHg is approximately equal to 96.93 kPa.

To convert 55.5 kPa into atm, divide the value by 101.325. Therefore, 55.5 kPa is approximately equal to 0.55 atm.

Answer:

D

Step-by-step explanation:

The larger standard deviation, the greater the variability.  So even before looking at the data, we can eliminate a) and c).

The standard deviations of men's preference of shortest and tallest acceptable height (3.7 and 2.7, respectively) were more than the standard deviations of women's preference of shortest and tallest acceptable height (2.6 and 2.2, respectively).

So men showed greater variability overall because the standard deviations for men were larger than for women.  Answer D.

Final answer:

Men showed greater variability in their height preferences for dating partners than women, as indicated by the larger standard deviations in men's responses.

Explanation:

The question asks whether men or women showed greater variability in their height preferences among dating partners based on a study by Salska and colleagues (2008). In the given study, variability is indicated by the standard deviation (SD) values. A larger standard deviation signifies greater variability in the responses. For the shortest acceptable height, men had an SD of 3.7 inches, while women had an SD of 2.6 inches. Likewise, for the tallest acceptable height, men had an SD of 2.7 inches versus women's 2.2 inches. These SD values clearly show that men displayed greater variability in their height preferences compared to women.

Answer:

• ΔCFB ~ ΔEDB by the AA similarity

• mCE = 46°

Step-by-step explanation:

No lengths are marked equal on the diagram, so we cannot assume any of the chords is the same length as any other. Then there is no evidence that the conditions for SAS congruence are met for the given triangles. Likewise, there is no evidence that arcs DE and CF are the same length, which they would have to be to have measure 108°.

The angles with vertices C and E subtend the same arc, so have equal measures. Likewise for the angles with vertices D and F. The angles CBF and EBD are vertical angles, so also congruent. Hence the two triangles are AA similar.

The angle labeled 72° is half the sum of the measures of arcs CE and DF, so we have ...

(CE + 98°)/2 = 72°

CE = 144° -98° = 46° . . . . . multiply by 2 and subtract 98°

Answer:

Answer:

• ΔCFB ~ ΔEDB by the AA similarity

• mCE = 46°

Step-by-step explanation:

Answer:

The measure of DE is 12

Step-by-step explanation:

* Lets study the figure to solve the problem

- There are two intersected circles B and C

- BA is a radius of circle B and CE is a radius of circle C

- AD is a tangent to the two circles touch circle B in A and touch

 circle C in E

- The line center BC intersects the tangent AD at D

- There are two triangles in the figure Δ BAD and Δ CED

* Now lets solve the problem

∵ AD is a tangent to circles B and C

∵ BA and CE are radii

∴ BA ⊥ AD at A

∴ CE ⊥ AD at E

- Two lines perpendicular to the same line, then the two lines are

 parallel to each other

∴ BA // CE

- From the parallelism

∴ m∠ABD = m∠ECD ⇒ corresponding angles

∴ m∠BAD = m∠CED ⇒ corresponding angles

- In any two triangles if their angles are equal then the two triangles

 are similar

- In the two triangles BAD and CED

∴ m∠ABD = m∠ECD ⇒ proved

∴ m∠BAD = m∠CED ⇒ proved

∵ ∠D is a common angle of the two triangle

∴ The two triangle are similar

- There are equal ratios between their sides

∴ BA/CE =AD/ED = BD/CD

∵ BD = 50 , AD = 40 , CD = 15

∴ 40/ED = 50/15 ⇒ using cross multiplication

∴ ED(50) = 15(40)

∴ 50 ED = 600 ⇒ divide both sides by 50

∴ ED = 12

The answer is D. Have a nice day.

Your answer should be d!

Answer: 4) 0.8/(1/6)=4.8 miles per hour

6) 100%-16%=84%

500*0.84=420 mL

Step-by-step explanation:

4) rate=miles/hour

30.8% ≅ 31%. The probability in percent that a given graduate student is on financial aid is 31%.

The key to solve this problem is using the conditional probablity equation P(A|B) = P(A∩B)/P(B). Conditional probability is the probability of one event occurring with some relationship to one or more other events.

From the table we can see P(A∩B) which is the intersections of event A and event B, in this case the intersection is the amount of graduates students receiving financial aid 1879. Then P(A∩B) = 1879/10730.

From the table we can see P(B) which is the probability of the total of students  undergraduate and graduate and the total of the students of the university data. Then P(B) = 6101/10730

P(A|B) = (1879/10730)/(6101/10730) = 0.307982

Round to nearest thousandth 0.308

Multiplying by 100%, we obtain 30.8% or ≅ 31%

Period of a function is [tex]2\pi[/tex]. You can see on graph, the distance between two points lying on intersection with x axis and function is [tex]2\pi[/tex] so A would be an answer.

Answer:

528 cm^3

Step-by-step explanation:

The volume of a pyramid is given by the formula ...

V = 1/3·Bh

where B is the area of the base and h is the height.

The area of a square of side length s is given by ...

A = s^2

Then the area of the base of the pyramid is ...

A = (12 cm)^2 = 144 cm^2

So, the volume of the pyramid is ...

V = 1/3·(144 cm^2)(11 cm) = 528 cm^3

Answer:

2.29%

Step-by-step explanation:

1. Chance of landing on black for one spin:

There are 38 spaces, and 18 lead to the wanted result. That means the chance is ¹⁸/₃₈, or about 0.47.

2. Chance for 5 spins.

We need to find (0.47)⁵, which is about 0.0229, which is 2.29%

That is none of the choices, but from every way I did this problem, that is the only solution I got.

Collin

22 years = 55,000 USD

+15 years

37 years = 2 x 55,000 = 110,000 USD

+15 years

52 years = 2 x 110,000 = 220,000 USD

Cameron

22 years = 35,000 USD

+10 years

32 years = 2 x 35,000 = 70,000 USD

+10 years

42 years = 2 x 70,000 = 140,000 USD

+10 years

52 years = 2 x 140,000 = 280,000 USD

+10 years

62 years = 2 x 280,000 = 560,000 USD

Retirement Salaries

Collin = 220,000 USD

Cameron = 560,000 USD