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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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

**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**

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

[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

help help help help help help help

-12+6=-2/3Z

-6=-2/3z

-6*3/2=-9

Z=-9

-6=-2/3z

-6*3/2=-9

Z=-9

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.

**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

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

**Answer:**

mi cola es grande

**Step-by-step explanation:**

uhh

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

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 **

Two standard 6-

sided dice are

rolled. How would

you describe the

following events

of having their

sum be EVEN OR

GREATER THAN 9?

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

**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**.

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 9The 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 tallyThe 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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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?

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

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.

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i got a 57 in this class

**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

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?

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

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

**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.**

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)=???

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

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

**Answer: A=-16 B=-5 C=-3**

**Step-by-step explanation:**

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.

**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**.

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

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

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) **

718-119x+719 for x =0

please simplify and find the value

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.

**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°**

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?

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

**325 hamburgers.**

A **General Rule** for Equation Solving

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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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?

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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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).

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:

help l need help with this

**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

The measures of the angles of a triangle are shown in the figure below. Solve for x.

(8x-18)°

40°

110°

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

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

**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

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).

7 is the value of **function **s and t .

**What is function explain?**

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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Is -7. a rational number

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

2. Multiply the matrices.

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]

rewrite 13% into equivalent fraction

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

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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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.

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

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

**Answer: 7+(11/r)**

**Step-by-step explanation:**

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