Algebra 2 volume 2 question 60

Answers

Answer 1

The value of function fg(x) is -x^4-4x^3.

What is a function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).

There are several types of functions in math. Some important types are:

Injective function or One to one function: When there is mapping for a range for each domain between two sets.

Surjective functions or Onto function: When there is more than one element mapped from domain to range.

Polynomial function: The function which consists of polynomials.

Inverse Functions: The function which can invert another function.

Now,

given functions are f(x)=-x^3 and g(x)=x+4

so, fg(x)=f(x)*g(x)=-x^3(x+4)

Therefore, the value of

fg(x) = -x^4-4x^3

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Answer 2

The value of function fg(x) is -x^4-4x^3.

What is a function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).

There are several types of functions in math. Some important types are:

Injective function or One to one function: When there is mapping for a range for each domain between two sets.

Surjective functions or Onto function: When there is more than one element mapped from domain to range.

Polynomial function: The function which consists of polynomials.

Inverse Functions: The function which can invert another function.

Now,

given functions are f(x)=-x^3 and g(x)=x+4

so, fg(x)=f(x)*g(x)=-x^3(x+4)

Therefore, the value of

fg(x) = -x^4-4x^3

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Related Questions

a company invests $91,000 for equipment to produce a new product. each unit of the product costs $11.40 and is sold for $17.98. let x be the number of units produced and sold. (a) write the total cost c as a function of x.

Answers

Total cost c as a function of x is $94000 + 11.2x.

A company invests $94,000 for equipment to produce a new product. each unit of the product costs $11.40 and is sold for $17.98.

let x be the number of units produced and sold.

now,

Number of units = x

so,

c(x)= $94000 + 11.2x

Equation

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Function

A function relates an input to an output. It is like a machine that has an input and an output. And the output is related somehow to the input.

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Please help
TEACHING TEXTBOOKS GEOMETRY

Answers

Answer:

x=125 y=130

Step-by-step explanation:

I believe if you add 50+75 you get x

50+75=125

And if you subtract 180 from 50 you get y

180-50= 130

The reason being is because the two numbers inside the triangle add up to the number outside of the triangle "x". Then you would subtract 180 from 50 because that is a supplementary angle meaning it adds up to 180 to get the number on the outside of the triangle "y".

Hope this helped!

Find the Area of the figure below.

Answers

Answer:

Your answer is 9x^6*y^2π

Step-by-step explanation:

The formula for a circle is πr^2, with r as the radius.

Since 3x^3*y is the radius, you put that value in to get the equation:

(3x^3*y)^2*π

Once simplified, you get 9x^6*y^2π.

You can simplify further using the value of π, but it depends if the questions wants you to or not, mostly it doesn't.

I hope this was helpful.

Has the marrying age of a man changed over the years? The United States Bureau of the Census takes a formal count of everyone in the U.S. every 10 years and has provided the following data that gives the median age of an American man at the time of his first marriage.

Year
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
Median Age
25.1
24.6
24.3
24.3
22.8
22.8
23.2
24.7
26.1
26.8

Determine the average rate of change in median age per year from 1930 to 1960.
a.
-0.5 years of age per year
b.
20 years of age per year
c.
-0.05 years of age per year
d.
+0.05 years of age per year

Answers

-0.05 is the average rate of change in median age per year from 1930 to 1960.

What is ratio?

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given, a data set that gives the median age of an American man at the time of his first marriage.

Year Median age

1910 25.1

1920 24.6

1930 24.3

1940 24.3

1950 22.8

1960 22.8

1970 23.2

1980 24.7

1990 26.1

2000 26.8

The average rate of change from 1930 to 1960 = (-24.3 + 22.8) / (1960-1930)

The average rate of change from 1930 to 1960 = -0.05

Therefore, the average rate of change in median age per year from 1930 to 1960 is -0.05.

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15. Death Valley's Badwater Basin has an elevation of 284 feet below sea level, the lowest
elevation in the United States. Mount McKinley has an elevation of 2,500 feet above sea
level, the highest elevation in the United States. What is the difference between the
elevation of Badwater Basin and Mount McKinley?

Answers

Answer:2216 feet

Step-by-step explanation:

Badwater Basin is below sea level, so already we know that the 284 should be a negative number since it is below sea level. Mount McKinley is above sea level, so that number stays as a positive number. Now we can put these two number into an equation to solve, which would be 2,500 + (-284).

Note that the parenthesis are only there so you know that the number is negative, you don't need to solve anything.

Since adding a negative to a positive number is the same as subtraction, we can simplify it to look a little less confusing. You only need to solve 2,500 - 284 , which then equals 2216 ft.

Hope this helps you!

Trina is buying favors for a birthday party. All of the party favors cost more than $13. What is the least expensive the party favors could be?

Answers

The least expensive will be the lowest cost among the cost greater than $13.

i.e $13.5

If the cost of the favors is:

$13.5 < $14 < $15 < $20

What is inequality?

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

All of the party favors cost more than $13.

This means,

Cost = x

x > 13

Now,

If the following are the cost of the favors:

$13.5, $14, $15, and $20

The least expensive will be the lowest cost among the cost greater than $13.

i.e $13.5

13.5 < 14 < 15 < 20

Thus,

The least expensive will be the lowest cost among the cost greater than $13.

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Use the graph of the parabola to fill in the table.

PLEASE HURRY

Answers

a) The graph of the parabola opens downwards.

b) The point for axis of symmetry is x = -3.

c) The points of vertex for the parabola is (-3,-3).

d) There is no x-intercept and only one y-intercept, y = - 7.

What is a parabola?

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves.

The graph of a parabola is given.

a) The parabola is starting from -∞ and is rising and then it is falling downwards towards the +∞.

Therefore, the parabola opens downwards.

b) The vertical line that passes through a parabola's vertex is the axis of symmetry, making the parabola's left and right sides symmetric. This line divides the graph of a quadratic equation into two mirror representations in order to make things simpler.

The parabola is symmetrical about x = -3.

Therefore, the axis of symmetry is x = -3.

c) There is a pivotal point in every parabola. To put it another way, it has a turning point where it either goes from "growing" to "decreasing" or vice versa. The vertex of the parabola is the name given to that pivotal point.

Here, the parabola turns at point (-3,-3).

Therefore, the points of vertex is (-3,-3).

d) The x-intercept is when the graph of parabola crosses the x-axis. In this case the parabola is drawn below the x-axis so there is no x-intercept.

The y-intercept is when the graph of parabola crosses the y-axis. In this case the parabola crosses the y-axis once at y = -7.

Therefore, the y-intercept is y = -7.

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what is the equation of a line that passes through the point (6,-8) and has a slope of -5/6

Answers

Answer:

y = (-5/6)x - (5/3)

Step-by-step explanation:

The equation of a line in point-slope form is y - y1 = m(x - x1) where (x1,y1) is a point on the line, and m is the slope of the line.

Given that the line passes through the point (6,-8) and has a slope of -5/6, the equation of the line is:

y - (-8) = (-5/6)(x - 6)

y + 8 = (-5/6)x + (-5/6) * 6

y = (-5/6)x - (5/3)

Answer:

(6,-5)

Step-by-step explanation:

(y-y1)=m(x-x1)

(y--8)=-5/6(x-6)

6y=-5x+2

Please answer I’m giving 16 points to the right answer please be quick

Answers

The expression for the area of a rectangle is A = L * W, where L is the length and W is the width.

Find an expression in simplest form for the Permiter of the rectangle in terms of X?(a) The expression for the area of a rectangle is A = L * W, where L is the length and W is the width.Substituting the given values into this expression yields 12x + 24 = 4 * W.Solving for W yields W = 12x + 24 / 4.Thus, the expression for the width of the rectangle in terms of the variable X is W = 3x + 6.(b) The expression for the perimeter of a rectangle is P = 2(L + W). Substituting the expressions for L and W from part (a) yields P = 2(4 + 3x + 6).Simplifying this expression yields P = 8 + 6x.Thus, the expression for the perimeter of the rectangle in terms of X is P = 8 + 6x.(c) Using the expression for the perimeter of the rectangle in terms of X, the perimeter when x = 8 is 8 + 6(8) = 64.Thus, the perimeter when x = 8 is 64.

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Suppose you spend $500. 00 on an oven to bake bread. Each loaf of bread costs 0. 20 to bake. You sell the loaves for 1. 00 each. How many loaves of bread must you sell for you to break even? (Use a system of equations to model each situation. Solve by any method. ) (PLEASE SHOW ANSWER AND WORK. SERIOUS APPLICANTS ONLY, THIS IS A MATH TEST, I FAILED THE LAST ONE. )

Answers

We must sell 625 loaves of bread to break even.

If it is a solution of equations, fill all the information of your solution into the equations you are working on to ensure that all equations are satisfied by your solution. And then, solve these equations to find the answer to your problem.

Let N be the number of loaves you sell.

Your cost would be,

C = 500 + 0.2N

Your revenue would be,

R = 1. N

Now, find out when is C = R

⇒500 + 0.2N = N

⇒500 = 0. 8 N

⇒N = 500/0. 8

⇒N = 625

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Matthew and David have $689.45. If David has $346.90, how much does Matthew have? Write and solve an additional equation to find how much money belongs to Matthew.

Answers

Answer: 342.55

Step-by-step explanation:

689.45 - 346.90 = 342.55

346.90 + 342.55 = 689.45

A 2-column table with 3 rows. The first column is labeled time (t) with entries negative 2, 3.5, 30. The second column is labeled Elevation(e) with entries a, b, c.
Rory is staying in a cabin on a hill 300 feet above sea level. She walks down the hill to the water’s edge. The equation of her average change in elevation over time is e = 300 – 10t, where t is the time in minutes since she left the cabin, and e is her elevation with regard to sea level. Which values are viable points, and what are their values in the table relating t and e?

a =

b =

c =

Answers

Answer:

a = not viable

b = 265

c = 0

good?

Answer: a = not viable b= 265 c = 0

Step-by-step explanation:

if anyone had this question on their quiz can u pls show me the answer i’m stuck on this question

x 1 2 3 5
y 2 3 4 6

x 2 4 6 8
y 0 2 3 4

x 0 2 4 6
y 1 3 5 7

x −2 1 2 3
y −6 3 6 9

Answers

The proportional relationship is option D. The graph of the relationship is given below.

What is Proportion?

Proportions are defined as the concept where two or more ratios are set to be equal to each other.

A relationship is proportional if y = kx, for some constant k.

Consider the last table.

x −2 1 2 3

y −6 3 6 9

When x = -2, y = -2 × 3 = -6

When x = 1, y = 1 × 3 = 3

When x = 2, y = 2 × 3 = 6

When x = 3, y = 3 × 3 = 9

So this is a proportional relationship with constant of proportionality k = 3.

Hence the table shown in the last option is the proportional relationship.

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Trina must spend at least 45 minutes, m, studying for her test

Answers

The inequality that describes that Trina must spend at least 45 minutes studying for her test at x ≥ 45 min.

How to write the inequality ?

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance. In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions.

Trina is to spend at least 45 minutes studying for her test which means that she can either spend 45 minutes studying, or more than 45 minutes.

The inequality for this is therefore:

x ≥ 45

Assuming that the minutes she spends studying is x.

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Full question is:

Trina must spend at least 45 minutes studying for her math test. (find the inequality)

the nine horizontal and nine vertical lines on an $8 \times 8$ checkerboard form $r$ rectangles, of which $s$ are squares. the number $s/r$ can be written in the form $m/n$, where $m$ and $n$ are relatively prime positive integers. find $m n$.

Answers

By using the combination theorem, it can be concluded that the value of m + n = 125

Combination is the number of ways to choose a sample of r elements from a set of n distinct objects where order does not matter and replacements are not allowed.

nCr = n! / (n - r)! r!

Let's denote the number of rectangles as r, and the number of squares as s:

r = ⁹C₂ x ⁹C₂

= (9! / (9 - 2)! 2!) x (9! / (9 - 2)! 2!)

= (9! / 7! 2!) x (9! / 7! 2!)

= 36 x 36

= 1296 rectangles

s = 1² + 2² + 3² + 4² + 5² + 6² + 7² + 8²

= 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64

= 204 squares

Then we get the ratio of s : r as follows:

s / r = 204 / 1296

= 17 / 108

Since m represents the horizontal lines and n represents the vertical lines, then m + n = 17 + 108 = 125.

Thus, it can be concluded that the value of m + n = 125

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Two cars leave the same parking lot, with one heading north and the other heading east. After several minutes, the northbound car has traveled 4 kilometers, and the eastbound car has traveled 4 kilometers. Measured in a straight line, how far apart are the two cars? If necessary, round to the nearest tenth

Answers

The straight line distance between the northbound and eastbound cars is 5.7 kilometres.

The movement of cars and straight line connecting them forms a right angled triangle. The straight line will be hypotenuse will the eastbound and northbound distance will be perpendicular and base of the triangle. Thus, using Pythagoras theorem to find the distance between the two cars.

Distance between the two cars = ✓4² + 4²

Taking square of the numbers

Distance between the two cars = ✓16 + 16

Performing addition

Distance between the two cars = ✓32

Taking square root

Distance between the two cars = 5.66

Round to nearest tenth = 5.7

Thus, the distance is 5.7 kilometres.

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Evin is modeling the temperture of water heating on the stove. She find the fahrenheit temperture can be modeling by the linear function F(m)= 15. 2m + 58, where m is the number of minutes the water has been heating. Give a physical interpretation of the parameters 15. 2 and 58 in the linear model. Use appropiate units in your explaination

Answers

The last temperature will be 73.2 degrees Fahrenheit.

The parameter f(m) 15.2m+58 in the straight capability addresses the rate at which the water temperature increments over the long haul. In particular, it addresses the number of degrees Fahrenheit that the water temperature increments for each 1 moment of warming. So assuming the water has been warming for 2 minutes, its temperature will have expanded by 2 * 15.2 = 30.4 degrees Fahrenheit.

Parameter 58 in the linear function addresses the underlying temperature of the water when it begins warming. It is estimated in degrees Fahrenheit. So on the off chance that the water begins at a temperature of 58 degrees Fahrenheit and is warmed for 1 moment, its last temperature will be 15.2 + 58 = 73.2 degrees Fahrenheit.

Subsequently, The last temperature will be 73.2 degrees Fahrenheit.

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Market researchers were interested in the relationship between the price of bobbleheads and the demand of bobbleheads. Information was collected from a survey and used to obtain the regression equation ŷ = –0. 227x + 50. 455, where x represents the price of bobbleheads (measured in dollars) and ŷ is the predicted demand of bobbleheads (in units). What is the predicted demand of a bobblehead that has price of $6. 00?

–1. 362 units

49. 093 units

51. 817 units

195. 837 units

Answers

The predicted demand of a bobblehead that has price of $6.00 is given as follows:

49.093 units.

What is the function?

The function in the context of this problem is defined as follows:

y = -0.227x + 50.445.

In which:

x is the price of the bobblehead.y is the predicted demand.

For a price of $6.00, the predicted demand is obtained with the numeric value at x = 6, replacing the lone instance of x by 6, hence:

y = -0.227(6) + 50.445

y = 49.093 units.

Meaning that the second option is the correct option.

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Solve the equation
1
4
(4x − 24) + x = 14.

Answers

Answer:

To solve the equation (4x - 24) + x = 14, we can start by combining like terms on the left side of the equation:

4x - 24 + x = 14

Next we'll add the x terms together and the constants together:

5x - 24 = 14

Then we'll add 24 to both sides to get all the x terms on one side:

5x = 38

Finally we'll divide both sides by 5 to find the value of x:

x = 7.6

So the solution to the equation is x = 7.6

Help I need the answer

Answers

Answer:

Step-by-step explanation:

make them equal to each other

15x = 14x + 9

x = 9

Louis bought 8 2/5 oranges for the soccer team. The team ate 4 5/8 pounds of the oranges. How many are left?

Answers

0.3 pounds of oranges are left and this can be calculated by following steps :

Convert the 8 2/5 oranges to pounds.

8 2/5 oranges = 8.4 oranges

1 orange = 0.5 pounds

8.4 oranges x 0.5 pounds = 4.2 pounds

Subtract the amount of oranges eaten (4 5/8 pounds) from the total amount of oranges (4.2 pounds).

4.2 pounds - 4 5/8 pounds = 0.3 pounds

Answer: 0.3 pounds of oranges are left.

One of the four operations used in mathematics, along with addition, multiplication, and division, is subtraction. Removal of items from a collection is represented by the operation of subtraction.

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I drive 378 miles in 3.5 hours. How many miles per hour am I driving

Answers

Answer: 108 mph

Step-by-step explanation: 378 divided by 3.5= 108mph

Answer: 108mph

Step-by-step explanation: 378 divided by 3.5= 108mph

Calcula la fuerza resultante de un avión que viaja 24 km al sur y 17 km al oeste.

Answers

La ecuación de la fuerza resultante es el vector R = F · cos 234.689° i + F · sin 234.689° j.

¿Cómo determinar la fuerza resultante de un avión?

Los vectores se caracterizan por tener magnitud y dirección, sea F la magnitud de la fuerza resultante del avión (nótese que la magnitud es un valor no negativo por regla general), cuya fórmula es la siguiente:

R = F · cos θ i + F · sin θ j

Donde:

F - Magnitud de la fuerza, en newtons. θ - Dirección del vector con respecto a la dirección este, en grados.

La dirección del vector se determina mediante la siguiente función trigonométrica inversa:

θ = tan⁻¹ (Fy / Fx)

Donde:

Fx - Componente horizontal, en kilómetros. Fy - Componente vertical, en kilómetros.

Si sabemos que Fx = - 17 km y Fy = - 24 km, entonces la ecuación de la fuerza resultante es:

θ ≈ 234.689°

R = F · cos 234.689° i + F · sin 234.689° j

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Gary used to make bottles of glitter glue.

Bottles Glue Glitter
1 3.8 1.9
4

How much glue and glitter would he need to make 4 bottles?
Gary would need 15.2 oz glue and 3.8 oz of glitter to make 4 bottles.
Gary would need 6.8 oz glue and 4.9 oz of glitter to make 4 bottles.
Gary would need 7.8 oz glue and 5.9 oz of glitter to make 4 bottles.
Gary would need 15.2 oz glue and 7.6 oz of glitter to make 4 bottles.

Answers

The answer is the fourth one: Gary would need 15.2 oz glue and 7.6 oz of glitter to make 4 bottles.

What are the zeros of f(x)=x²-8x+15?
A. x=3 and x = 5
B. x= -5 and x = -3
C. x = -5 and x = 3
D. x = -3 and x = 5

Answers

The zeros of the function f(x)=x²-8x+15 are x = 3 and x = 5. Option A

How to determine the values

From the information given, we have that the quadratic equation is given by the function;

f(x)=x²-8x+15

Using the factorization method, we have to multiply the coefficient of x² by the constant 15

Then move further to find the pair factors of 15 that add up to -8

Substitute the value, we get;

x² - 5x - 3x + 15

Pair the expression

(x² -5x) - (3x + 15)

factorize

x(x -5) - 3(x-5)

Then,

x - 3

x = 3

And

x = 5

Hence, the values are 3 and 5

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Given the measure of arc(ABC) = 7x + 20 and arc(AC) = 4x + 10, find x.

Answers

Answer:

Step-by-step explanation:

Ahh hell nah

At Sneaky Pete’ chool, the teacher-tudent ratio i 1:30. If the chool ha 900 tudent,
how many additional teacher need to be hired to have a 1:18 ratio?

Answers

The school need to hire additional teacher to get 1:18 ratio is 20.

The teacher and student ratio in a school is 1:30,

let the number of teachers in a school=x,

then the number of students in school=30x,

total number of students in school=900

So, the number of teachers in school x=900÷30

x=30.

We want to take ratio of students and teachers =1:18

So, according to this ratio number of students=18x

and the number of required teachers x= 900 ÷ 18

x=50,

the school required 50 teachers,

Hence, the school need to hired teachers = 50-30=20

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What is the slope of the line that passes through the points (0,-10) and (-4,-11)

Answers

Answer:

To find the slope of a line, we can use the formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of two points on the line.

Given the points (0,-10) and (-4,-11), we can plug these coordinates into the formula:

slope = (-11 - (-10)) / (-4 - 0) = -1 / -4 = 1/4

So, the slope of the line that passes through the points (0,-10) and (-4,-11) is 1/4.

Step-by-step explanation:

Kaitlin's fish tank has 15 liters of water in it. She plans to add 6 liters per minute until the tank has at least 63 liters. What are the possible numbers of minutes
Kaitlin could add water?
User for the number of minutes.
Write your answer as an inequality solved for t.

Answers

15 + 6t >= 63

t >= (63 - 15) / 6

t >= 4.5

t >= 5 (since t must be a whole number of minutes)

So the possible numbers of minutes Kaitlin could add water are 5, 6, 7, 8, ... (any whole number greater than or equal to 5). This can be written as t >= 5.

pharmacist needs of a solution with a concentration of medicine. They have one solution with a concentration and another solution with concentration. How many cc of each should be mixed? Setup an equation and solve. Label your answers.

Answers

The cc of each that should be mixed are 73.33 and 146.67

How many cc of each should be mixed

From the question, we have the following parameters that can be used in our computation:

Needs 220cc of a solution with a 10% concentration of medicine. They have one solution with 14% concentration and another solution with 8% concentration

Using x and y as the variables, we have the following equations:

x + y = 220

0.14x + 0.08y = 220 * 10% = 22

So, we have

x + y = 220

0.14x + 0.08y = 22

Make y the subject

y = 220 - x

So, the second equation becomes

0.14x + 0.08(220 - x) = 22

This gives

0.14x - 0.08x + 17.6 = 22

Evaluate the like terms

0.06x = 4.4

This gives

x = 73.33

Recall that

y = 220 - x

So, we have

y = 220 - 73.33

y = 146.67