Given f of x is equal to the quantity x plus 3 end quantity over the quantity x squared minus 4 times x minus 21 end quantity and g(x) = log4x, evaluate (g – f)(8).

Answers

Answer 1

The numeric value of the subtraction function at x = 8 is given by:

(g - f)(8) = 0.5.

How to find the numeric value of a function or of an expression?

To find the numeric value of a function or of an expression, we replace each instance of the input variable in the function by the desired value.

To find the subtraction function, we find the numeric value of each function, then subtract them, as follows:

(g - f)(8) = g(8) - f(8).

Function f(x) is defined as follows:

f(x) = (x + 3)/(x² - 4x - 21).


At x = 8, the numeric value is given as follows:

f(8) = (8 + 3)/(8² - 4(8) - 21) = 11/11 = 1.

Function g(x) is defined as follows:

g(x) = log4(x).

At x = 8, the numeric value is given as follows:

g(8) = log4(8) = 1.5, as 4^(1.5) = 8.

Hence the numeric value of the subtraction function is given by:

(g - f)(8) = g(8) - f(8) = 1.5 - 1 = 0.5.

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Related Questions

The measures of the angles of a triangle are shown in the figure below. Solve for x.
(8x-18)°
40°
110°

Answers

The value of the variable x associated to the triangle is equal to 6.

What is the variable associated to internal angles of a triangle?

Triangles are figures with three sides and three internal angles. According to Euclidean geometry, the sum of the measures of the internal angles is equal to 180° and we must solve the following equation for x:

(8 · x - 18) + 40 + 110 = 180

(8 · x - 18) + 150 = 180

(8 · x - 18) = 30

8 · x = 48

x = 6

The triangle has internal angles of 30°, 40° and 110° and the value of variable x is 6.

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Is -7. a rational number

Answers

A rational number can be represented by dividing two integers.

So, it can be represented as a ratio of 2 integers.

-7 = -7/1

-7 is a rational number

Answer: -7 is a rational number

A store generates Monday through Thursday sales of $150, $125, $75, and $180. What sales on Friday would give a weekday average of $150?

Answers

Answer:

mi cola es grande

Step-by-step explanation:

uhh

Given the replacement set: {−9, −10, −11, −12}.

Which value of x correctly solves this equation?

3.2x−5=−40.2

Enter your answer in the box.

Answers

Answer:

  x = -11

Step-by-step explanation:

You want to know the value of x that correctly solves the equation 3.2x -5 = -40.2.

Solution

This 2-step linear equation is solved in the usual way:

Step 1: isolate the variable term

  3.2x -5 +5 = -40.2 +5 . . . . . . . . . add 5 to both sides

  3.2x = -35.2 . . . . . . . . . . . . . simplify

Step 2: isolate the variable

  3.2x/3.2 = -35.2/3.2 . . . . . . . . . . divide both sides by the coefficient of x

  x = -11 . . . . . . . . . . . . . . . . . . simplify

help l need help with this

Answers

Answer:

Step-by-step explanation:

Answer:  Y = 3x + 3

Simply plug in points on graph calculator.

Answer:

Step-by-step explanation:

I think it might be y=3/1+6 ??? i might be wrong

Two standard 6-
sided dice are
rolled. How would
you describe the
following events
of having their
sum be EVEN OR
GREATER THAN 9?

Answers

The probability of having an even or a number greater than 9 is 2/3.

What is the probability?

Probability determines the odds that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0. The more likely the event is to happen, the closer the probability value would be to 1.

The sample space of two 6-sided dice would be 36

Of this 36, there would be 18 which would have an even sum.

There would be 6 with a sum greater than 9.

The probability of having an even or a number greater than 9 = (18/36) + (6/36) = 24 / 36 = 2/3

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Answer:

  5/9

Step-by-step explanation:

You want the probability that a roll of 2 dice will produce a sum that is even or greater than 9.

Even

Half the numbers on each die are even. Their sum will be even when the dice show ...

  even + even . . . . p = (1/2)(1/2) = 1/4

  odd + odd . . . . . . p = (1/2)(1/2) = 1/4

So, the 36 possible outcomes will produce an even sum (1/4) +(1/4) = 1/2 of the time. That is, there are 1/2(36) = 18 outcomes with an even sum.

Greater than 9

The sums that are greater than 9 are 10, 11, 12. Of these, 10 and 12 are outcomes that are even, so are already counted.

The sum 11 can be made two ways: 6 +5 or 5 +6.

So, "or greater than 9" adds 2 outcomes to the 18 we have already counted.

Final tally

The final tally of outcomes of interest is ...

  18 + 2 = 20 . . . . of 36 possible outcomes

That is ...

  P(even or >9) = 20/36 = 5/9

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Gabe has just moved to a new town and wants to share plates of baked goods with his neighbors. He has 16 cookies and 24 brownies to share, and wants to split them equally among the plates with no food left over. What is the greatest number of plates he can make to share?

Answers

The greatest number of plates he can make to share is 6.

What is the greatest number of plates he can make to share?

From the information, Gabe has just moved to a new town and wants to share plates of baked goods with his neighbors and he has 16 cookies and 24 brownies to share.

It should be noted that this illustrates that we have to find the highest common factor for 16 and 24.

This will be:

18 = 2, 3, 6, 9 and 18.

24 = 2, 3, 4, 6, 8, 12 and 24

The highest common factor is 6.

Therefore, the number will be 6 plates.

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find the perimeter of ABC with vertices A(-4,4), B(4,-1) and C(-4,-1)

Answers

Answer: A=-16  B=-5  C=-3

Step-by-step explanation:

help help help help help help help

Answers

-12+6=-2/3Z
-6=-2/3z

-6*3/2=-9

Z=-9

Ken exercise at a park first he run 3 miles in 30 minutes.Then he rests for 15 minutes.Then he runs 2 miles in 15 minutes.Finally he walks 1 mile in 15 minutes.Assume each running and walking segment was done at a constant rate.skecth a graph to represent ken's exercing at the park.the fisrt segment should begin at (0,0).

Answers

The horizontal axis represents the time in hours, and the vertical axis represents the number of miles ran.

So for the first part we have 3 miles in 30 minutes (0.5 hour), so we can draw a line from point (0, 0) to point (0.5, 3)

For the second part, he rests for 15 minutes (0.25 hour), so the y-value doesn't change, therefore we have a horizontal line from (0.5, 3) to (0.75, 3).

Then, we have 2 miles in 15 minutes, so we have a line from (0.75, 3) to (1, 5).

And finally, 1 mile in 15 minutes, so a line from (1, 5) to (1.25, 6).

Sketching the graph, we have:

Would you please check this answer for me? Use elimnation to solve the system of equations:2x+2y=162x+3y=14My answer: (10, - 2)

Answers

Equation

[tex]\begin{gathered} 2x+2y=16 \\ 2x+3y=14 \\ \end{gathered}[/tex]

Let's multiply -1 by Eq 1

[tex]\begin{gathered} -2x-2y=-16 \\ 2x+3y=14 \\ 2x-2x+3y-2y=-16+14 \\ y=-2 \end{gathered}[/tex]

Now for x

[tex]\begin{gathered} 2x+2y=16 \\ x=\frac{16-2y}{2} \\ x=\frac{16-2\cdot(-2)}{2} \\ x=\frac{16+4}{2} \\ x=\frac{20}{2} \\ x=10 \end{gathered}[/tex]

The answer would be (10, -2)

Suppose that the functions s and t are defined for all real numbers x as follows.
s(x)=x-3
t(x) = 3x+4
Write the expressions for (s•t) (x) and (s-t) (x) and evaluate (s+t) (-2).

Answers

7 is the value of function s and t .

What is function explain?

A relation between a set of inputs and a set of allowable outputs is called a function, and it has the property that every input is associated to exactly one output. When every element in set A has one end and only one image in set B, then the mapping from set A to set B is a function. Let A & B be any two non-empty sets.Four main categories can be used to classify the many sorts of functions. One to one function, many to one function, onto function, one to one and into function—all based on the element.

s(x)= x-3

t(x) = 3x+4

(s•t) = ( x -3 ) ( 3x + 4 )

        = ( 3x²  + 4x - 3x² - 12 )

         = 4x - 12

(s-t) (x) = ( x-3 ) - ( 3x+4 )

           =  x-3 - 3x + 4

           = -2x + 1

(s + t) (-2) =  x-3 +  3x+4

               =  4x + 1

(s + t) (-2) =  4 *  - 2 + 1

              = 8 - 1  = 7

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ANSWERS ASAPP
i got a 57 in this class

Answers

Answer:

Y=-1/4x+-6

Step-by-step explanation:

convert the line to slope intercept form

x is the slope and the last thing is the y intercept

A local hamburger shop sold a combined total of 598 hamburgers and cheeseburgers on Wednesday. There were 52 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Wednesday?

Answers

In the local hamburger shop the total number of hamburgers sold on Wednesday , based on the given data is :

325 hamburgers.

Explanation:

A General Rule for Equation Solving

Remove parentheses and combine like terms to simplify each side of the equation.To isolate the variable term on one side of the equation, use addition or subtraction.To find the variable, use multiplication or division.

here form a equation based on given data ;

let ,  Hamburgers be = x

let, Cheeseburgers be = y

here , No. of burgers (hamburgers and cheeseburgers )sold  = 598

here,

x + y = 598 =>(1)

y = x - 52  => (2)

solving 2 equations ,

x + ( x - 52 ) = 598

x + x - 52     = 598

2x = 598 + 52

x = 650 /2

x =  325

on Wednesday  325 hamburgers were sold.

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rewrite 13% into equivalent fraction

Answers

The number 13% as an equivalent fraction is 13/100

How to rewrite the percentage into equivalent fraction?

From the question, the given parameter is

13%

This above number is a percentage or percentile

So, we have

Percentage = 13%

Next, we multiply the percentage by 1

So, we have

Percentage = 13% x 1

Express 1 as 100/100

So, we have

Percentage = 13% x 100/100

Evaluate the product of 13% and 100

So, we have

Percentage = 13/100

Rewrite as

Fraction = 13/100

The fraction cannot be further simplified

Hence, the equivalent fraction of 13% is 13/100

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Hi I have tried calling but I can’t do anything

Answers

For the given functions, we will find the first derivative of each function

Note:

a, and b are constants

y, f, and g are functions

2) y = (a+bf)/g

We will use the quotient rule to find y' as follows:

[tex]y^{\prime}=\frac{g*b\frac{df}{dx}-(a+bf)\frac{dg}{dx}}{g^2}[/tex]

=============================================================

3) y = (x+f)/g

We will use the quotient rule to find y' as follows:

[tex]y^{\prime}=\frac{g(1+\frac{df}{dx})-(x+f)\frac{dg}{dx}}{g^2}[/tex]

==========================================================

4) y = (x+f)³

We will use the exponent rule to find the derivative as follows:

[tex]y^{\prime}=3(x+f)^2(1+\frac{df}{dx})[/tex]

===========================================================

5) y = ax² + bg² + f

so, y' will be as follows:

[tex]y^{\prime}=2ax+2bg\frac{dg}{dx}+\frac{df}{dx}[/tex]

==========================================================

Raffle tickets are being sold for a fundraiser. The function a(n) relates theamount of money raised to the number of tickets sold, n.It takes as input the number of tickets sold and returns as output the amountof money raisedan) = 4n - 20Which equation represents the inverse function n(a), which takes the moneyraised as input and returns the number of tickets sold as output?O A. n(e) -47,20O B. n(e) – +20OC. n() - 0-20OD. n(a) -3 -20

Answers

A

Since The equation is

[tex]a(n)\text{ = 4n-20}[/tex]

To find its inverse we have to proceed to some steps

a= 4n-20

1) Swap a for n, in this case,

n=4a-20

2) Isolate n on the left side by subtracting 4a on both sides:

n -4a =4a-4a -20

n-4a=-20

3) Subtract n on both sides

a-a-4n =-20-a

-4n=-20 -a

4) Multiply it by -1

4n = 20 + a

5) Divide by 4, there you have it. The inverse function:

[tex]n(a)=\frac{20+a}{4}[/tex]

To find its in

Mental Math Using the slope formula, find the slope of the line through the points (0,0) and (3,6).Use pencil and paper. Explain how you can use mental math to find the slope of the line.

Answers

Given the points (0,0) and (3,6)

slope = y2 - y1 / x2 -x1

x1= 0, y1 = 0 , x2= 3, and y2 = 6

slope = 6 - 0 / 3 - 0

slope = 6 / 3

slope = 2

the answer is 2

A car was valued at $41,000 in the year 1994. The value depreciated to $13,000 by the year 2004

Answers

[tex]\begin{gathered} a)\text{ 0.1085} \\ b)\text{ 10.85 \%} \\ c)\text{ \$7,300} \end{gathered}[/tex]

Firstly, we have to write the general depreciation fomula as follows;

[tex]V(t)=I(1-r)^t[/tex]

where V(t) represents the value of the commodity after a certain t years

I is the initial value of the item

r is the annual percentage change (rate of depreciation)

t is the number of years

a) Here, we want to calculate the annual rate of change

According to the data given in the question;

V(t) = $13,000

I = $41,000

r = ?

t = 2004-1994 = 10 years

Now, we proceed to substitute these values, to find the find of r as follows;

[tex]\begin{gathered} 13,000=41,000(1-r)^{10} \\ (1-r)^{10\text{ }}\text{ = }\frac{13,000}{41,000} \\ (1-r)^{10\text{ }}=\text{ }\frac{13}{41} \\ \\ (1-r)\text{ = }\sqrt[10]{\frac{13}{41}} \\ \\ 1-r\text{ = 0.8915} \\ r\text{ = 1-0.8915} \\ r\text{ = 0.1085} \end{gathered}[/tex]

b) To write r in percentage form, we have to multiply the answer in 'a' above by 100

We have this as ;

[tex]0.1085\times100\text{ = 10.85 \%}[/tex]

c) Here, we want to get the car value by year 2009

In that instance;

V(t) = ?

I = $41,000

r = 0.1085

t = 2009-1994 = 15

Substituting these values, we have;

[tex]\begin{gathered} V(15)=41,000(1-0.1085)^{15} \\ V(15)\text{ = \$7,321.56} \end{gathered}[/tex]

To the nearest 50 dollars, this is $7,300

Molly has 250 trading cards. She gives n trading cards to her friend Carol. Marcus has 430 trading cards. He gives away three times as many cards as Molly does. How many trading cards did Molly give away if Molly and Marcus have the same number of trading cards left?

Answers

Molly gave away 90 trading cards out of 250 trading cards to her friend Carol.

Initially molly had 250 cards.

She gave away n trading cards to her friend.

Now molly has (250 - n) trading cards.

Initially Marcus had 4430 trading cards.

The number of cards that Marcus gave away is is three times of molly.

Cards gave away by Marcus = 3n

Now, Marcus is left out with (430 - 3n) trading cards/

After giving away the cards,

Molly and Marcus had same number of trading cards.

So, we can write,

250-n = 430-3n

Now, we have a linear relation between the number of cards given away and the remaining cards,

Further solving,

2n = 180

n = 90.

So, Molly gave away 90 cards.

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Write an equation in slope-intercept form for the line that passes through the given point and is perpendicular to the graph of the equation.
(-2, 3); y=-3/4x+4

Answers

Answer:

y=4/3x+17/3

Step-by-step explanation:

Perpendicular lines have reciprocal negative slopes, find the slope of the new line:

-3/4 --> m = 4/3

Write line in point slope form:

y-3 = 4/3(x+2)

Distribute:

y-3=4/3x+8/3

Simplify:

y=4/3x+17/3

7 is added to 11 divided by a number r write the algebraic expression

Answers

Answer: 7+(11/r)

Step-by-step explanation:

Determine whether the triangles are similar. If so, what are the similarity statement and the postulate or theorem used? (image attached)thank you ! :)

Answers

ANSWER

ΔOMN ~ ΔOJK; SAS

EXPLANATION

As we can observe in the diagram, the triangles share angle O and we have information about the sides forming that angle, so the postulate to use, in case they are similar, is SAS.

If two triangles are similar, then the ratio between corresponding sides is constant.

Let's assume that the similar triangles are triangle OMN and triangle OJK. Then, the previous statement is,

[tex]\frac{OM}{OJ}=\frac{MN}{JK}=\frac{ON}{OK}[/tex]

Replace the side lengths for the first and last ratios - since we don't know the lengths of sides MN and JK,

[tex]\begin{gathered} \frac{30+10}{30}=\frac{3+1}{3} \\ \\ \frac{40}{30}=\frac{4}{3} \\ \\ \frac{4}{3}=\frac{4}{3} \end{gathered}[/tex]

The ratio between corresponding sides is constant, 4/3. Hence, triangles OMN and OJK are similar, by SAS.

rectangle perimeter ; 36 unitswidth; xlength ; 4x - 2solve for x

Answers

Perimeter = 36 units

width = x

length = 4x - 2

Equation of perimeter = 2width + 2length

Substitution

36 = 2(x) + 2(4x - 2)

Expanding

36 = 2x + 8x - 4

36 = 10x - 4

36 + 4 = 10x

40 = 10x

x = 40/10

x = 4

a bucket contains 15 blue pens 35 black pins and 40 Red Pins. You pick one pin at random find the theoretical probabilities below . Express your answer as a percent to the nearest whole number p(black)=???p(blue or black)=???

Answers

The number of blue pen is 15

The number of black pens is 35

The number of red pens is 40

The total number of pens in the bucket = Blue pens + black pens + red pens

The total number of pens = 15 + 35 + 40

= 90

Therefore, the total number of pens in the bucket = 90 pens

The probability that black pen is picked is

Probablity = possible outcomes/ total outcomes

P(black) = 35 / 90 x 100%

P(black) = 0.3888 x 100%

P(black) = 38.88%

P(black) = 39%

P(blue or black)

If its pick at random without replacement then

If the first pick is blue, then the total number of pen in the bucket remains 89

For the first pick will be 15/90

Since the remaining pens is 89, then the second pick is

35/89

Then we have

15/90 + 35/89

LCM is 8010

8010 x 15 / 90 + 35 x 8010 /89 / 8010

89 x 15 + 35 x 90 / 8010

P(blue / black) = 1335 + 3150 / 8010

P(blue or black) = 4485 / 8010

P(blue or black) = 0.559 x 100%

P(blue or black) = 55.9%

P(blue or black) = 56%

jsjsjjs i just came home and ate a little poop and p to be on my way to work so we will have a great time together for you all the day and enjoy the rest of the week we are together and

You volunteer at a nursing home for 3 hours a day. You volunteered 6 hours last week and 12 hours this week. How many days did you volunteer?

Answers

Since each volunteer day is 3 hours and you volunteer for a total of 18 hours. You do 18 divided by the 3 hours volunteering each day which equals 6.

Answer: 6 days
The total of hours equal up to 18, a simple way to put it is to count by three till you reach 18. The answer is 6 days.

718-119x+719 for x =0
please simplify and find the value

Answers

The answer would be 1437 due to the zero property. Therefore you only add the other two numbers.

Find the values of the variables so that the figure is aparallelogram.

Answers

Answer:

The image is given below as

From the image above, we can deduce that

[tex]\begin{gathered} \angle GEF=\angle DFE(altenate\text{ angles are equal)} \\ \angle GEF=64^0 \\ \text{hence,} \\ \angle DFE=64^0 \end{gathered}[/tex][tex]\begin{gathered} \angle GEF=\angle BGH(correspond\in g\text{ angles are equal)} \\ \angle GEF=64^0 \\ \text{Hence,} \\ \angle BGH=64^0 \end{gathered}[/tex][tex]\begin{gathered} \angle DFE+\angle HFE=180^0(\text{ linear pair sum up to give 180)} \\ \angle DFE=64^0 \\ \angle HFE=y \\ 64^0+y=180^0 \\ \text{collect similar terms, we will have} \\ y=180^0-64^0 \\ y=116^0 \end{gathered}[/tex]

From the image also, we will have that

[tex]\begin{gathered} \angle BGH=\angle FHG(alternate\text{ angles)} \\ \angle BGH=64^0 \\ \angle FHG=x \\ \text{hence,} \\ x=64^0 \end{gathered}[/tex]

Hence,

The value of x= 64°

The value of y = 116°

2. Multiply the matrices.

Answers

Result of matrix multiplication [tex]\left[\begin{array}{ccc} - 1&2&0\\3&2&4\\ - 5& - 1&6\end{array}\right] \times \left[ \begin{array}{cc} 2& - 3 \\ 7& - 1 \\ 1&2 \end{array} \right] = \left[\begin{array}{ccc} 12&1\\ - 4 &1\\ - 11&28\end{array}\right] [/tex].

What is a matrix?

A matrix is a series of numbers forming a square or rectangle arranged in rows and columns enclosed in square brackets [ ] or regular brackets ( ).

Solution:

[tex]\left[\begin{array}{ccc} - 1&2&0\\3&2&4\\ - 5& - 1&6\end{array}\right] \times \left[ \begin{array}{cc} 2& - 3 \\ 7& - 1 \\ 1&2 \end{array} \right] [/tex]

[tex] \left[ \begin{array}{cc} - 1 \times 2 + 2 \times 7 + 0 \times 1 & - 1 \times ( - 3) + 2 \times ( - 1) + 0 \times 2 \\3 \times 2 + ( - 2) \times 7 + 4 \times 1&3 \times ( - 3) + ( - 2) \times ( - 1) + 4 \times 2\\ - 5 \times 2 + ( - 1) \times 7 + 6 \times 1&( - 5) \times ( - 3) + ( - 1) \times ( - 1) + 6 \times 2 \end{array}\right ][/tex]

[tex]\left[\begin{array}{ccc} 12&1\\ - 4 &1\\ - 11&28\end{array}\right ][/tex]

An aeroplane flies between two cities that are 8100 km apart.
The aeroplane takes 9 hours to complete the journey.
Calculate the average speed of the aeroplane, in km/h.

Answers

Answer:

7,290,000.answer

Step-by-step explanation:

1 km= 100000 m

1 hour = 60 minute

8100 km = 810000 m

9 hour=540 minute

60/540.00 cancel

6/54 will be than cut 6×9=54

SO,multiply 810000×9 = 7,290,000

Answer:

The answer is 7,290,00

Step-by-step explanation:

1 km= 100000 m

1 hour = 60 min

8100 km = 810000 m

9 hour=540 min

60/540.00 cancel

6/54 will be than cut 6×9=54

so ,multiply 810000×9 = 7,290,000

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