The table below gives selected values for the differentiable and increasing function ff and its derivative. If g(x) = f^-1(x), what is the value of g'(-2)?

The cost of each ream of paper is $4.5 and that of DVD is $5.

A system of linear equations is a group of  equations having same number of variables and degree.

For the n number of variables n number of equations are required.

On the basis of number of solutions a system of equations can be classified as consistent and inconsistent.

Given that,

The price for 17 reams of paper and 12 DVDs is $136.50.

And, the price for 8 reams of paper and 21 DVDs is $141.

Suppose the cost of each ream of paper be x.

And, the cost of each DVD be y.

THen, the following equations can be made for the two cases,

17x + 12y = 136.50      (1)

8x +  21y = 141            (2)

Solve these equations by multiplying equation (1) by 7 and (2) by 4 and then subtracting them as,

7(17x + 12y) - 4(8x +  21y) = 7 × 136.50 - 4 × 141            

=> 87x = 391.5

=> x = 4.5

Substitute x = 4.5 in equation (1) to get,

17 × 4.5 + 12y = 136.50

=> 12y = 136.50 - 76.50

=> 12y = 60

=> y = 5

Hence, the cost of each ream of paper and each DVD are $4.5 and $5 respectively.

To know more about system of equations click on,

brainly.com/question/24065247

#SPJ1

In dollars and cents, the total projected insurance for three years would be $555.00.

In this exercise, you are required to calculate the total projected insurance for a V-8 sedan that was driven 15,000 miles each year, from the first through the third year (three years). Therefore, we would determine the projected insurance for each year in dollars and cents as follows:

For the first year, we have:

The projected insurance for first year = Insurance cents per miles × miles driven

The projected insurance for first year = 1.1/100 × 15,000

The projected insurance for first year = 0.011 × 15,000

The projected insurance for first year = $165.00.

For the second year, we have:

The projected insurance for second year = Insurance cents per miles × miles driven

The projected insurance for second year = 1.2/100 × 15,000

The projected insurance for second year = 0.012 × 15,000

The projected insurance for second year = $180.00.

For the third year, we have:

The projected insurance for third year = Insurance cents per miles × miles driven

The projected insurance for third year = 1.4/100 × 15,000

The projected insurance for third year = 0.014 × 15,000

The projected insurance for third year = $210.00.

Therefore, the total projected insurance for three years is given by:

Total projected insurance = $165.00 + $180.00 + $210.00

Total projected insurance = $555.00

Read more on insurance here: https://brainly.com/question/22713486

#SPJ1

The complete square of the given expression is x² + x + 1/4 = (x + 1/2)².

An expression is a combination of some mathematical symbol such that an arithmetic operator and variable such that all are constrained and create an equation.

In other meaning, expression is very useful to determine the end or root value of constraint.

As per the given

x² + x + (__) = (____)²

Let's say the square is (x + a)²

Then, (x + a)² = x² + 2xa + a²

Compare x² + x + (__) with  x² + 2xa + a²

2xa = x → a = 1/2

So, (x + 1/2)² = x² + 2x(1/2) + (1/2)²

⇒ x² + x + (1/4)

Hence "The complete square of the given expression is x² + x + 1/4 = (x + 1/2)²".

To learn more about expression,

https://brainly.com/question/14083225

#SPJ1

Given question is incomplete and incorrect, correct question is attached below;

The complete square of the given expression is x² + x + 1/4 = (x + 1/2)².

An expression has been defined as the combination of some mathematical symbol such that an arithmetic operator and variable such that all are constrained and create an equation.

In other meaning, expression is very useful to determine the end or root value of constraint.

As per the given

x² + x + (__) = (____)²

Let's say the square is (x + a)²

Then, (x + a)² = x² + 2xa + a²

Compare x² + x + (__) with  x² + 2xa + a²

2xa = x → a = 1/2

So, (x + 1/2)² = x² + 2x(1/2) + (1/2)²

⇒ x² + x + (1/4)

Hence "The complete square of the given expression is x² + x + 1/4 = (x + 1/2)²".

Therefore, An expression has been defined as the combination of some mathematical symbol such that an arithmetic operator and variable such that all are constrained and create an equation. "The complete square of the given expression is x² + x + 1/4 = (x + 1/2)²".

Learn more about expression on:

https://brainly.com/question/14083225

#SPJ1

The true statement about the domain and the range is that the domain is discrete, and the range is continuous

From the question, the given parameters are:

Amount to download = $2.50

Amount to add each player = $1.50

Represent the number of players with x

So, we have the following representations

Total amount = Amount to download + Amount to add each player * Number of players

So, we have

y = 2.50 + 1.50 * x

Evaluate

y = 2.50 + 1.5x

The above function is a linear function and the input is the number of players

This means that the domain is discrete

However, the amount can take decimal points

This means that the range is continuous

Read more about domain and range at

https://brainly.com/question/2264373

#SPJ1

Answer: $89.91

Step-by-step explanation:

$99.90-10% of it would be $99.90-$9.99= $89.91.

The value of x for the given equation is 3,11.

What is equation?

In arithmetic, an equation may be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.

Main Body:

According to given equation:

√2x+3 = -x+6

2x+3 = (-x+6)²

2x + 3 = x²+ 36 -12x

x²-14x +33 = 0

Now splitting the middle term t find the factor.

x² -11x -3x +33 = 0

x(x-11) -3(x -11) = 0

(x-3)(x-11) = 0

so either x- 3 = 0   or x -11 = 0

hence value for x = 3,11.

To know more about equation click on the link below

https://brainly.com/question/22688504

#SPJ1

By using the concept of dilation factor, length of BC obtained is 3 units

What is dilation factor?

Dilation is a transformation which changes the size of a figure by a certain factor.

That factor is called the scale factor

In the figure, A'B'C'D' is the image of ABCD under dilation with a scale factor of 3

A'B'C'D' is the dilated figure

Length of B'C' = 9 units

Length of BC = [tex]9 \div 3[/tex] = 3 units

To learn more about dilation factor, refer to the link-

https://brainly.com/question/3457976

#SPJ9

Complete Question

The figure has been attached here

The linear equation which represents this situation would be 0.05A - 0.03B = 375.

What is a linear function?

A linear function has a positive relationship, so increasing one variable (input variable) causes an increase in the other variable (output variable), implying that the variables are directly proportional. As a result, the graph of a linear function is a straight line with a constant slope.

Similarly, a linear equation is a first-order algebraic equation with two variables and terms with exponents of one.

In general, a system of two linear equations must have at least two solutions.

Given Elisa earned a total of $375 profit at the end of the first year.

Also, she suffered a profit of 5% in fund A and a loss of 3% in fund B

So we can write the equation as

                   Total profit = Profit - Loss

                       375 = 0.05A - 0.03B

Hence, the linear equation which represents this situation would be

   0.05A - 0.03B = 375.

To learn more about linear equations, visit:

https://brainly.com/question/24085666

#SPJ1

Therefore:

[tex](30+5x)^o+(15+10x)^o=180^o\\\\45^o+(15x)^o=180^o\\\\(15x)^o=135^o\\\\15x=135\\\\\large\text{$\bold{x=9}$}[/tex]

Answer:

Answer B is correct

Step-by-step explanation:

In a parallelogram opposite sides are parallel to each other.

AB // CD

Therefore, Co interior angles are added up to 180°.

<BAD + <CDA = 180

That is,

30 + 5x + 15 + 10x = 180

And now, solve the expression and find the value of x.

First, combine like terms.

45 + 15x = 180

Subtract 45 from both sides.

15x = 180 - 45

15x = 135

Divide both sides by 15.

x = 9

The water level is falling at the rate of -2/9π m³/min when the water's level is 12 meters high.

Given, water is draining from a conical tank at the rate of 2 m³/min.

Also, the height of the tank is 16 meters and the radius of the tank is 4 meters.

Using the concept of similarity in triangles, we get

r/4 = h/16

r = h/4

Now, the volume of the cone is

V = (1/3)πr²h

V = (1/3)π(h/4)²h

V = (1/3)π(h³/16)

On differentiating both the sides with respect to t, we get

dV/dt = π(h²/16)(dh/dt)

Now, as dV/dt = -2m³/min

-2 = π(144/16)(dh/dt)

dh/dt = (-2/9π)

Hence, the water level is falling at the rate of -2/9π m³/min when the water's level is 12 meters high.

Learn more about Applications of Derivatives here https://brainly.com/question/2912519

#SPJ1

The function of f and g is  (−3x − 8) ² is  (f× g)(x)

A function is composed in mathematics when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Therefore, a function is essentially applied to the output of another function.

A composite function typically refers to a function that is contained within another function. The process of creating a function involves substituting one function for another. For instance, the composite function of f (x) and g is called f [g (x)]. You can read the composite function f [g (x)] as "f of g of x."

Given ,

h(x) = (−3x − 8) ²

h(x)=(f× g)(x).

(−3x − 8) ² = (f× g)(x)

Therefore  the function of f and g is  (−3x − 8) ² is  (f× g)(x)

To learn more about composite function refer to:

https://brainly.com/question/10687170

#SPJ1

[tex]\sqrt{18}\implies \sqrt{9\cdot 2}\implies \sqrt{3^2\cdot 2}\implies 3\sqrt{2}[/tex]

The total number of tacos sold was 66, and the total number of burritos sold was 53.

What is an equation?

An expression that depicts the relationship between two or more numbers and variables is called an equation.

Dependent variables are used to describe function outputs that depend on other values, whereas independent variables are used to describe function inputs that are independent of other values.

Here, we have

Let x be the number of tacos sold and y be the number of burritos sold daily.

It is given that Enola sells each taco for $3 and each burrito for $7.5. She made a total of $529.25 in revenue.

The equation that represents this is

3 x + 7.5 y > 570

x + y ≤ 120

After further simplified, we get

y = 120 - x

Now put the value of y in equation 3 x + 7.5 y > 570, we get

3x + 7.5(120-x) = 570

3x + 900 - 7.5x = 570

4.5x = 300

x = 66

now put the value of x in equation x+y = 120, we get

y = 53

Hence, the number of tacos sold were 66, and the number of burritos sold were 53.

To learn more about the equation from the given link

https://brainly.com/question/25645169

#SPJ1

b. P(sum of 8) = 5/36

c. P(odd sum or sum greater than 9) = 2/3

d. P(odd sum and sum greater than 9) =  1/12

e. P(A) = 1/3

f. P(B) =

g. P(A and B) = 1/18

h. A and B are not mutually exclusive because both events can occur at the same time.

i. A and B are not independent because the occurrence of A and lead to the occurrence of B.

P(sum of 8) = number of sample spaces that sum up to 8 / total number of sample spaces

P(sum of 8) = 5/36

P(odd sum or sum greater than 9) = (sample spaces that have an odd sum / total number of sample spaces) + (sample spaces that have a sum greater than 9 / total number of sample spaces)

P(odd sum or sum greater than 9) =(18 / 36) + (6/36) = 24/36 = 2/3

d. P(odd sum and sum greater than 9) = (sample spaces that have an odd sum / total number of sample spaces)  x (sample spaces that have a sum greater than 9 / total number of sample spaces)

P(odd sum and sum greater than 9) = 18/36 x 6/36 = 1/12

P(A) = (sample spaces that have a 3 first / total number of sample spaces) +  (sample spaces that have a 3 first / total number of sample spaces)

P(A) = 6/36 + 6/36 = 1/3

P(B) = (sample spaces that adds up to 7 / total number of sample spaces)

= 6/36 = 1/6

P(A and B) = 1/3 x 1/6 = 1/18

To learn more about probability, please check: https://brainly.com/question/13234031

#SPJ1

By using exponent properties we will see that:

1) The expression is equal to 16.

2) The expression is equal to 4^6, so the correct option is B.

Here we want to solve the expression:

(2^0*4^(-2)*2^3*4^3)/2

Remember the exponent property:

a^x*a^y = a^{x + y}

let's rewrite the numerator:

2^0*4^(-2)*2^3*4^3

= (2^0*2^3)*(4^(-2)*4^3)

= 2^(0 + 3)*(4^(-2 + 3))

= 2^3*4 = 2^3*2*2 = 2^(3 + 1 + 1) = 2^5

Then we can rewrite the expression as:

2^5/2 = 2^4 = 16

b)

(1/4^-3)^2

The negative exponent means that we need to take the inverse:

(1/4^-3)^2 = (4^3)^2 = (4^3)*(4^3) = 4^(3 + 3) = 4^6

So the correct option is B.

Learn more about exponents:

https://brainly.com/question/847241

#SPJ1

Equation: [tex]\boxed{\pi}(8^2)[/tex]

Area: [tex]64\pi \approx 201.06[/tex]

The amount of flour that is needed if the recipe is tripled is 11 ¹ / ₄ cups of flour

To find the flour needed for the recipe, first convert the mixed  fraction to an improper fraction for easier calculation.

= 3 ³ / ₄

= (4 x 3 + 3) / 4

= 15 / 4 cups of flour

If the recipe was tripled, then the number of cups of flour would also need to be tripled.

The amount of flour needed becomes:
= 15 / 4 x 3

= 45 / 4

= 11 .25

= 11 ²⁵ / ₁₀₀

= 11 ¹ / ₄ cups of flour

Find out more on cups of flour at https://brainly.com/question/608093

#SPJ1

Answer: x = 66

Step-by-step explanation:

All angles of a triangle equal 180 degrees.

This means we need to find out how many degrees we need.

48 + 63 = 111

180 - 111 = 69 (nice)

Now we need to subtract 3 from 69.

69 - 3 = 66.

This means x = 66

Answer:

x = 66°

Step-by-step explanation:

Formula we use,

→ A + B + C = 180°

Now the value of x will be,

→ 63° + 48° + (x + 3°) = 180°

→ 114° + x = 180°

→ x = 180° - 114°

→ [ x = 66° ]

Hence, the value of x is 66°.

Answer:

1/2

Step-by-step explanation:

m = (Y2 - Y1) / (X2 - X1)                  Slope formula

m = (1 - 0) / (2 - 0)                           Plug in any two points, I chose (2,1) & (0,0)

m = 1 / 2

P.S. You could also count rise/run

Basically count the amount of units going up or down then counts the units going left or right that get you to the next point of the line

The perimeter of triangle is 55.

What is perimeter of triangle?

The sum of the lengths of the sides is the perimeter of any polygon. In the case of a triangle,

Perimeter = Sum of the three sides

Given, QA=5, AP=12, RB= 9.5

We know tangent drawn from external point are equal.

therefore, PA=PB

PB=12

Similarly, RB=RC, RC =9.5

QC=QA, QC =6

Perimeter of triangle = PQ+PR+QR

=6+12+9.5+12+6+9.5

=55

To know more about the perimeter of triangle, visit:

https://brainly.com/question/17394545

#SPJ1

If the above trend continues, the total number of tickets that will be sold by Cher for the Sixth Decade Still Touring" tour is: 871 tickets.

In mathematics, a trend is often a pattern of occurrence often depicted with the use of a graph. In this case, the pattern is an arithmetic sequence.

Note that the lowest number of tickets we can get to before we can no sell again is 1.

We get this by dividing 133 tickets by 11 (rate of decline).

133/11 = 12 (remaining 1)

Spread out, the sequence will appear as follows:

1, 12, 23, 34, 45, 56, 67, 78, 89, 100, 111, 122, 133.

Recall that the task is to determine the total number of tickets sold. We can either do this directly or use the Sum of an Arithmetic Sequence.

That is 1 + 12 +23 +34 +45 +56 +67 +78 +89 +100 +111 +122 +133 = 871; or

The formula for the sum of an Arithmetic Sequence:

Sn = n ((a₁ + aₙ)/2) Where

n is the number of terms and

a1 is the value of the first term and

aₙ is the value of the last term in the sequence.

that is:

n = 13
a₁ = 1
aₙ= 133

Hence
Sn = (13)((1 + 133) / 2) = (13)(134 / 2) = (13)(67)

= 871

Learn more about trends:
https://brainly.com/question/12588988?
#SPJ1

The pentagon has the following type of symmetry:

This refers to a type of symmetry where one-half part of an object shows the other half of the object. It is also be called mirror symmetry.

Point symmetry refers to the shape of a figure or graph after begin turned about 180° and it still looks the same as its initial shape. eg Star, heart -shape, etc.

Note that When something is identical on all sides, it is said to be symmetrical. If a center dividing line (also known as a mirror line) can be drawn on a shape to demonstrate that both of its sides are identical, then the shape is said to be symmetrical.

Learn more about symmetry from

https://brainly.com/question/20168388
#SPJ1

Answer:

x=25

Step-by-step explanation:

(3x+10)+(5x-30)=180

8x-20=180

8x=200

x=25

Hopes this helps please mark brainliest

The bill usage summary that could belong to a resident of that city are:

$14.40 per 3000 gallons

$19.20 by 4,500 gallons

$28.80 per 6000 gallons

The bill usage summary that could belong to a resident of that city have to be equivalent to $4.80 per 1000 gallons.

A -In order to determine if $2.20 per 500 gallons is equivalent, convert the quantity to 1000 gallons. To do this, multiply by 2.

t ($2.20 per 500 gallons) x 2 = $4.40 per 1000 gallons

B - In order to determine if $12.60 per 2,500 gallons is equivalent, divide 12.60 by 2500 and then multiply by 1000

(12.60 per 2500 gallons) x (1000 / 2500) = $5.04

C-  In order to determine if $14.40 per 3000 gallons is equivalent, divide $14.40 by 3

($14.40 per 3000 gallons ) / 3 =  $4.80 per 1,000 gallons

D-  In order to determine if $16 per 4000 gallons is equivalent, divide by 4.

($16 per 4000 gallons) / 4 = $4 per 1000 gallons

E- In order to determine if $19.20 by 4,500 is equivalent, multiply $19.20 by 1000 / 4,500.

($19.20 by 4,500) x (1000 / 4500) = $4.27 per 1000 gallons

F - In order to determine if $26.40 per 5,500 gallons is equivalent, multiply $26.40 by 1000 / 5500.

( $26.40 per 5,500) x 1000 / 5500 = $4.8 per 1000 gallons

G- In order to determine if $28.80 per 6000 gallons, divide by 6.

($28.80 per 6000) / 6 = $4.8 per 1000 gallons

Please find attached the complete question. To learn more about cost, please check: https://brainly.com/question/7886884

#SPJ1

Answer:

0

Step-by-step explanation:

7 + (-8) + 2 + (-1)

is the same as:

7 - 8 + 2 - 1

Simplify these:

-1 + 1

Solve:

0

you can do it first + each other and than × each them

Answer:

-1/2

Step-by-step explanation:

[tex]\frac{10}{6}[/tex] + [tex]\frac{-7}{6}[/tex] = [tex]\frac{-3}{6}[/tex] = [tex]\frac{-1}{2}[/tex]

The ratio of tan is equal to opp/adj or sin/cos so Option H and Option I are correct.

we know that,

Tan = sin/cos

sin = opp/hyp

cos = adj/hyp

Tan = opp/hyp / adj/hyp

= opp*hyp / adj*hyp

= opp/adj.

Therefore The ratio of tan is equal to opp/adj or sin/cos so Option H and Option I are correct.

Learn more about the tan here:

https://brainly.com/question/14347166

#SPJ9