Evaluate the expression.
−5 × (−8 − 6 ÷ −3)

The functions f(x) = (2x - 3) / 2 and g(x) = (2x + 3) / 2 are the inverse functions because the composite of the given functions equal to x that is fog = x and gof = x.

The conditions for two functions f and g to be inverses: f(g(x)) = x or g(f(x)) = x.

where, f(g(x)) and g(f(x)) is the composite function.

We are given:

f(x) = (2x - 3) / 2

g(x) = (2x + 3) / 2

Let us find the value of f(g(x)) and g(f(x)):

Substitute the value of x with g(x) in f(x), we will get:

f(g(x)) = (2 * g(x) - 3) /2 = (2 * ((2x + 3) / 2) - 3) /2 = (2x + 3 - 3) / 2 = 2x / 2 = x

So, f(g(x)) = x.

Substitute the value of x with f(x) in g(x), we will get:

g(f(x)) = (2 * f(x) + 3) /2 = (2 * ((2x - 3) / 2) + 3) /2 = (2x - 3 + 3) / 2 = 2x / 2 = x

So, g(f(x)) = x.

Thus, the functions f(x) = (2x - 3) / 2 and g(x) = (2x + 3) / 2 are the inverse functions because the composite of the given functions equal to x that is fog = x and gof = x.

To learn more about the composite function visit:

https://brainly.com/question/28062427

#SPJ1

Answer:

4/9

Step-by-step explanation:

Based on the given conditions, formulate: 12 division symbol(12 +15)

Calculate the sum or difference: 12/27

Cross out the common factor: 4/9

get the result:

Answer: 4/9

Answer:10,000

Step-by-step explanation:

Answer:

Step-by-step explanation:

What is the value of 3 + 5x when x=3?

3 + 5x =

3 + 5 × 3 =

3 + 15 =

18

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

Answer:

x=12 y=15

Step-by-step explanation:

15-9=6 6+6=12

18-9=9 6+9=15

Answerx=7

Step-by-step explanation:

Answer: 18

Step-by-step explanation:  All you do is subtract 26 by 8 and you get 18. 18+8=26 :)

The value of x in given triangle is 6.403

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The given triangle is a right angled triangle whose one angle is 90 degrees.

We find the value of x by using pythagoras theorem.

the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse

4²+5²=x²

16+25=x²

41=x²

Take square root on both sides

x=√41=6.403

Hence the value of x in given triangle is 6.403

To learn more on trigonometry click:

https://brainly.com/question/25122835

#SPJ1

∵∵∵∵∵∵∵∵∵∵∵∵.........................ω

The amount of money that Lena needs to put each quarter for the annuity to have a total value of $96,000 is $953.45.

An annuity is when a series of payment is made either at the beginning of a period or at the end of a period over a period of time.

An ordinary annuity is when the payment is made at the end of the period. When the interest is compounded quarterly, it means that four times in a year, the amount that is invested and the interest that has already being earned increase in value.

The formula that can be used to determine the quarterly payments is:

Payment = future value / annuity factor

Annuity factor = {[(1+r)^n] - 1} / r

Where:

Payment = $96,000 / [{(1.009^72) - 1} / 0.009]  = $953.45

To learn more about annuities, please check: https://brainly.com/question/24108530

#SPJ1

Answer:

P 717

Step-by-step explanation:

Fraction addition using algebra:

       Let the cost of bracelet =  x

          [tex]\sf Cost \ of \ pendent = \dfrac{3}{4}*Cost \ of \ bracelet[/tex]

                                   [tex]\sf = \dfrac{3}{4}x[/tex]

Cost of bracelet + cost of pendent = 413    

                      [tex]\sf x + \dfrac{3}{4}x = 413\\\\ \dfrac{4}{4}x+\dfrac{3}{4}x=413[/tex]

                                [tex]\sf \dfrac{7}{4}x=413[/tex]

Muliply both sides by 4,

                                [tex]\sf 4*\dfrac{7}{4}x = 413*4\\\\[/tex]

                                     7x  = 413 * 4

Now, divide both sides by 7

                                      [tex]\sf x = \dfrac{413*4}{7}\\\\ x = 59*4\\\\x = 236[/tex]

Cost of bracelet = P 236

Cost of pendent = 413 - 236

                            = P 177

The mean of the data set is 22.1 , and the sample proportion of numbers less than the mean is 46.67 %

The mean is the average value which can be calculated by dividing the sum of observations by the number of observations

Mean = Sum of observations/the number of observations

Mean of the data set is calculated by adding all numbers and dividing it with total number sample data.

Then Adding all the numbers;

25.5 + 26 +18.2 +15.3 + 28.5 + 27 + 20.7 +20.2 +26.1 +18.2 +21.4 +17.9 +24.3 +22.6+ 19.6 =331.5

Now Dividing by total,

331.5/15 =22.1

Mean =22.1

The sample proportion of numbers less than the mean will be;

= (7/15 ) 100

=46.67%

Learn more about mean and median;

https://brainly.com/question/17060266

#SPJ1

The complete question is;

For this question, any non-integer answers should be entered as decimals, rounded to the hundredths place.

Consider this data set. The mean of the data set is ___ , and the sample proportion of numbers less than the mean is ___%

The correct system of equations is 5x-y=2,x-5y=10

In order to find the system of equations of the graph, we have to check the solution in the graph and then check for the system of equations that gives the same value.

Looking at the graph, the values of x and y at the point of intersection is the solution. Thus:

x =  0 and y = -2

Let's check the equations now:

5x+3y=-6, 3x+5y=-10

Solve for x and y using elimination

3 (5x+3y=-6)

5 (3x+5y=-10)

15x + 9y = -18

15x + 25y = -50

-6y = 32

y = -32/6 = -16/3 (This cannot be the system)

3x-5y=10, x-5y=-10

3x-5y = 10

x-5y = -10

2x = 20

x = 20/2 = 10  (This cannot be the system)

5x-y=2,x-5y=10

1(5x-y=2)

5(x-5y=10)

5x -y =2

5x-25y = 50

24y = -48

y = -48/24 = -2

put y = -2 into 5x -y =2:

5x -(-2) =2

5x + 2 = 2

5x = 0

x = 0

Therefore, 5x-y=2,x-5y=10 is the system of equations. The 3rd option is the answer. Move it to the box

Learn more about system of equations on:

https://brainly.com/question/13729904

#SPJ1

The error in this answer is that : The sum of angle of triangle is 180°

What is Triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

Since, we know that Angle sum property of triangle is

∠A + ∠B + ∠C = 180°

Now, let ∠A = 115, ∠B = 39 and ∠C = m∠1

Substituting the value, we get

115° + 39° + m∠1 = 180°

154° + m∠1 = 180°

m∠1 = 180 - 154

m∠1 = 26°

Thus, m∠1 = 26°

Hence, The error for finding m∠1 is that angle sum of the triangle is equal to 180° and not 360°

To learn more about Triangle click on the link

https://brainly.com/question/1058720

#SPJ1

For the given equation (x/4)+3= 1/5, the value of x which will make the given equation valid is lies between the numbers of ( -10 and -15).

As given in the question,

Given equation is equal to :

(x/4)+3= 1/5

Simplify the given equation (x/4)+3= 1/5 to get the value of x we have,

(x/4)+3= 1/5

Take least common multiple of 4 and 1 we get,

( x + 12) / 4 = 1/5

⇒5( x +12 )  =  4

⇒ 5x + 60 = 4

⇒ 5x = -56

⇒ x= -11.2

-11.2 lies between (-10 and -15).

Therefore, for the given equation (x/4)+3=1/5, the value of x which will make the given equation valid is lies between the numbers of

(-10 and -15).

The complete question is:

Consider the following equation:

(x/4)+3= 1/5

The value of x that will make the equation above valid lies between

which of the following numbers?

A) 10 and 15

B) -1 and -5

C) 1 and 5

D) -10 and -15

E) -5 and -10

Learn more about equation here

brainly.com/question/10413253

#SPJ1

Answer:

3,4,5

Step-by-step explanation:

x+x+1+x+2

therefore ,

4(x+2)=17+3

4x+8=20

4x=20-8

4x=12

x=3

Answer:

w<-28

Step-by-step explanation:

multiply both sides by 2 : -6 > w +22

subtract 22 : w < -28

The probability with replacement is = 1/16

The probability without replacement is= 5/16

What do you mean by probability with replacement?

When the results must be put back into the sample space, the probability with replacement is utilized. This means that once an item is selected, it is replaced in the sample space, keeping the sample space's total number of elements constant.

Since cards should be replaced, 5 lions or 5 birds

so, the probability is

= 5/20 ÷ 5/20

=1/16

without replacement,

since cards should not be put back, for the second draw only 19 cards are left

so, the probability is

=5÷20 × 5÷19

=5/16

Hence ,

The probability with replacement is = 1/16

The probability without replacement is= 5/16

to learn more about probability from the given link,

https://brainly.com/question/24756209

#SPJ1

The percent of the decrease in the size of the sugar order is 40%.

According to the question,

We have the following information:

Sweet Treats Bakery ordered 1,090 kilograms of sugar. This time, the bakery is ordering 654 kilograms.

We know that following formula is used to find the percent decrease:

100*(original amount-final amount)/original amount

(More to know: the same formula is used to find the percent increase. It can used to find any percent increase or decrease given that the final and initial amount or price is given.)

100(1090-654)/1090

100*436/1090

40%

Hence, the percent of the decrease in the size of the sugar order is 40%.

To know more about percent of the decrease here

https://brainly.com/question/2913116

#SPJ1

The width of the rectangular Hardee County, considering it's area, is given as follows:

21.23 miles.

The area of a rectangle of length l and width w is obtained by the multiplication of these dimensions, as follows:

Area = length x width.

For the rectangular Hardee County, the parameters are given as follows:

Considering the area and the length, the width is obtained as follows:

Area = length x width

30w = 637

w = 637/30

w = 21.23 miles.

(the area is in miles squared, hence both dimensions are in miles).

The problem is shown by the image at the end of the answer.

More can be learned about the area of a rectangle at https://brainly.com/question/10489198

#SPJ1

The first derivative by implicit differentiation of 2 · x⁶ + 5 · x⁴ · y - 7 · x · y⁶ = 8 is y' = (7 · y⁶ - 20 · x³ · y - 12 · x⁵) / (5 · x⁴ - 42 · x · y⁵).

Implicit differentiation is a differentiation method for implicit functions that combines chain rule and derivative rules. First, define the original function:

2 · x⁶ + 5 · x⁴ · y - 7 · x · y⁶ = 8

Second, use chain rule and derivative rules in the expression of the previous step:

12 · x⁵ + 20 · x³ · y + 5 · x⁴ · y' - 7 · y⁶ - 42 · x · y⁵ · y' = 0

Third, clear y' within the resulting equation:

12 · x⁵ + 20 · x³ · y - 7 · y⁶ + (5 · x⁴ - 42 · x · y⁵) · y' = 0

(5 · x⁴ - 42 · x · y⁵) · y' = 7 · y⁶ - 20 · x³ · y - 12 · x⁵

y' = (7 · y⁶ - 20 · x³ · y - 12 · x⁵) / (5 · x⁴ - 42 · x · y⁵)

The first derivative is y' = (7 · y⁶ - 20 · x³ · y - 12 · x⁵) / (5 · x⁴ - 42 · x · y⁵).

To learn more on implicit differentiation: https://brainly.com/question/14027997

#SPJ1

Answer:

123

Step-by-step explanation:

2x square = 2.7 square = 98

98 + 4y = 98 + 4.9 = 98 + 36 = 134

134 - z = 134 - 11 = 123

Ur Wellcome ;)

Answer:

Domain: (neg infinity, pos infinity)

Range: (pos infinity, 3]

Step-by-step explanation:

The quantity of sodium in the salt is 10.4 ounces

information from the problem

Table salt (sodium chloride, NaCl) is 40% sodium (Na) by weight

If a box of salt weighs 26 ounces, how much Na is in the box of salt

The question is a percentage problem, percentage deals with a fraction hundred and used as follows

40%

= 40 percent

= 40 / 100

= 0.4

The factor 0.4 of the total weight of the salt is what we calculate

the total number is 26 ounces

= 0.4 * 26

= 10.4

Learn more about percent here:

https://brainly.com/question/29230566

#SPJ1

Answer:

N = 20

Step-by-step explanation:

5/3 = 1 2/3

20/12 = 1 8/20

They are equivalent

Answer:  80% received, 20% lost.

Step-by-step explanation:  [tex]\frac{60}{300}[/tex] × [tex]\frac{x}{100}[/tex] = [tex]\frac{6000}{300}[/tex]     *Make sure to cross multiply!!*

——————————————6000 ÷ 300 = 20%

——————————————100 - 20 = 80% .

Therefore, the shop received 80% of the order because the other 20% are missing.

Answer:

282 inches

Step-by-step explanation:



24*8+

The values of H(-7)=3, H(-2)=3, H(3)=5, H(9)=11 using the given equations by substituting the values.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. a formula that expresses the connection between two expressions on either side of a sign. Typically, it has a single variable and an equal sign.

Here,

H(x)= {-5x-13 for x<-7

          3 for -7<=x< 3

          x+2 for x=> 3}

when x=-7,

H(x)=3

when x=-2,

H(x)=3

when x=3,

H(x)=x+2

H(x)=5

when x=9,

H(x)=x+2

H(x)=11

H(-7)=3, H(-2)=3, H(3)=5, H(9)=11 when the values are substituted under the conditions stated for the given equation.

To know more about equation,

https://brainly.com/question/10413253?referrer=searchResults

#SPJ1

The ordered pair that is not a solution to the inequality y ≥ 2x² - 4x + 2 is:

(-1,6).

The inequality is given as follows:

y ≥ 2x² - 4x + 2.

Each ordered pair has the following format:

(x-coordinate, y-coordinate).

Then the numeric value of the inequality is going to be calculated for each ordered pair, as follows:

Then the numeric values of the inequality for each ordered pair are presented as follows:

The contradiction, that is, the statement which is false, is given at the following ordered pair:

(-1,6).

Hence it is not a solution to the given inequality.

The ordered pairs are given by the image shown at the end of the answer.

A similar exercise, also featuring inequalities, is presented at https://brainly.com/question/25275758

#SPJ1