The results of the operation of multiplication between two functions are, respectively:
2 · x³ + 12 · x² + 24 · x + 16 x⁴ + 4 · x³ - 16 · x - 16 - 32 2 · x³ + 12 · x² + 24 · x + 16 x⁴ + 4 · x³ - 16 · x - 16 2 · x³ - 4 · x² - 8 · x - 16 - 27How to find the product of two functions
According to function theory, there are five operations between two functions to create resulting functions:
Addition - f(x) + g(x) = (f + g) (x).Subtraction - f(x) - g(x) = (f - g) (x).Multiplication - f(x) · g(x) = (f · g) (x).Division - f(x) / g(x) = (f / g) (x).In this problem we must use the operation of multiplication between two functions.
Case 1
(f · g)(x) = (2 · x + 4) · (x² + 4 · x + 4)
(f · g)(x) = (2 · x + 4) · x² + 4 · (2 · x + 4) · x + 4 · (2 · x + 4)
(f · g)(x) = 2 · x³ + 4 · x² + 8 · x² + 16 · x + 8 · x + 16
(f · g)(x) = 2 · x³ + 12 · x² + 24 · x + 16
Case 2
(h · g)(x) = (x² - 4) · (x² + 4 · x + 4)
(h · g)(x) = (x² - 4) · x² + (x² - 4) · (4 · x) + (x² - 4) · 4
(h · g)(x) = x⁴ - 4 · x² + 4 · x³ - 16 · x + 4 · x² - 16
(h · g)(x) = x⁴ + 4 · x³ - 16 · x - 16
Case 3
(f · h)(x) = (2 · x + 4) · (x² - 4)
(f · h)(x) = 2 · x³ - 8 · x + 4 · x² - 16
(f · h)(x) = 2 · x³ - 4 · x² - 8 · x - 16
(f · h)(2) = 2 · 2³ - 4 · 2² - 8 · 2 - 16
(f · h)(2) = - 32
Case 4
(g · f)(x) = (x² + 4 · x + 4) · (2 · x + 4)
(g · f)(x) = 2 · x³ + 12 · x² + 24 · x + 16
Case 5
(g · h)(x) = (x² + 4 · x + 4) · (x² - 4)
(g · h)(x) = x⁴ + 4 · x³ - 16 · x - 16
Case 6
(f · h)(x) = (2 · x + 4) · (x² - 4)
(f · h)(x) = 2 · x³ - 4 · x² - 8 · x - 16
Case 7
(h · g)(x) = (x² - 4) · (x² + 4 · x + 4)
(h · g)(x) = x⁴ + 4 · x³ - 16 · x - 16
(h · g)(1) = 1⁴ + 4 · 1³ - 16 · 1 - 16
(h · g)(1) = - 27
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Rewrite 4^-3 x 4 using a single positive exponent.
The term 4^-3 x 4 can be rewritten using a single positive exponent as 1/4^2.
What is positive exponent?The positive exponent serves as the exponents that contain a positive number, it should be noted that the exponent is the degree at the top[ of the given number which is a negative exponents and the question expect us to turn it to a positive exponents after simplification of the given terms which will be simplified below to the simplest expression.
To rewrite the given term so that it can have a positive exponents then it can be expressed as :
=4^-3 x 4
= 4^-2
1/4^2
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does anyone know how to solve and find out the answer? Thank you so much if you help!
Answer:
perpendicular
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - [tex]\frac{2}{3}[/tex] x + 5 ← is in slope- intercept form
with slope m = - [tex]\frac{2}{3}[/tex]
3x - 2y = 4 ( subtract 3x from both sides )
- 2y = - 3x + 4 ( divide through by - 2 )
y = [tex]\frac{3}{2}[/tex] x - 2 ← in slope- intercept form
with slope m = [tex]\frac{3}{2}[/tex]
• Parallel lines have equal slopes.
clearly the slopes are not equal, so not parallel.
• the product of the slopes of perpendicular lines = - 1
- [tex]\frac{2}{3}[/tex] × [tex]\frac{3}{2}[/tex] = - 1
then the lines are perpendicular to each other.
Answer:
The lines are perpendicular.
Step-by-step explanation:
[tex]3x -2y=4[/tex]
Step 1: Add -3x to both sides.
[tex]3x-2y+-3x=4+-3x[/tex]
[tex]-2y=-3x+4[/tex]
Step 2: Divide both sides by -2.
[tex]\frac{-2y}{-2} =\frac{-3x+4}{-2}[/tex]
[tex]y=\frac{3}{2} x-2[/tex]
Finally...
[tex]y=\frac{3}{2} x-2\neq y=-\frac{2}{3} x+5[/tex] so the lines are not parallel.
However, [tex]\frac{3}{2}[/tex] is the opposite reciprocal of [tex]-\frac{2}{3}[/tex], so, the lines are perpendicular.
(You can also try drawing the lines.)
The following figure shows the entire graph of a relationship.
Does the graph represent a function?
Yes or no
Answer:
No
Step-by-step explanation:
The graph fails the vertical line test. More than one y-value is on one x-value.
what is the highest in order from least to greatest
Answer:
Least to greatest: 1. International finance center
2. Petronas towers
3. Zifeng towers
4. Burj Khalifa
Write an equation point-slope form of the line that passes through the point (3,3) with slope 5/3
We solve as follows:
[tex]y-3=\frac{5}{3}(x-3)[/tex][tex]\Rightarrow y-3=\frac{5}{3}x-5\Rightarrow y=[/tex]with show work. trigonometry
10. (2, -4); slope = -3
The equation (-4 = -3x + 2) is formed and plotted on the graph (Refer to the graph attached below).
What is a graph?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph. Charts and graphs come in a variety of styles. Line graphs, bar graphs and histograms, pie charts, and Cartesian graphs are likely the four most popular types.So, the equation can be:
The slope is -3 and the coordinates are (2, -4):Formula: y = MX + bWhere m is the slope.From the equation:
y = MX + b-4 = -3x + 2Now, plot the equation on the graph as follows:
(Refer to the graph attached below)Therefore, the equation (-4 = -3x + 2) is formed and plotted on the graph (Refer to the graph attached below).
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The correct question is given below:
From the equation and plot it on a graph when, (2, -4) and slope = -3.
Model with Mathematics
The owner of a frozen yogurt stand considers different pricing options for a serving of yogurt plus toppings. For what number of toppings do the two options give the same price?
A. Define the variables.
B. Write a system of equations that models this situation.
C. Graph the system. What is the intersection point?
D. What is the solution of the problem?
E. Is the solution reasonable for this situation? Explain.
Answer:
Step-by-step explanation:
A, B: Define the Variables and Write Equations
Let T be the number of toppings.
Option 1: $3 + $0.75*T
Option 2: $4 + $0.50*T
C. Graph the System
See the attached graph. The intersection point is (4,6). This means that 4 toppings will result in a cost of $6 for both yogurt options.
D. Solution to the Problem
The solution is given above, but we can also solve using equations, instead of graphing. We want the value of T that will make these expressions equal:
$3 + $0.75*T = $4 + $0.50*T
$0.25*T = $1
T = 4 toppings
=============
CHECK:
For 4 toppings:
Option 1: $3 + $0.75*T
$3 + $0.75*(4)
$3 + $3 = $6
Option 2: $4 + $0.50*T
$4 + $0.50*(4)
$4 + $2 = $6
Four toppings will make both options equal in cost.
E: Is the solution reasonable?
Yes. The cheaper option ($3) has a more expensive topping, so at some point (at 4 toppings) it will be the same price as the second option, with a higher initial price, but with cheaper toppings.
Ayuda es para mañana son similar figures
Answer:
2. x = 2
3. x = 43.2
4. x = 3.6
Step-by-step explanation:
Determine the y-value of each ordered pair based on the given x-value
y= -x + 9; (-9, ), (1, ), (5, )
Brainfiy to correct person
The value of y in each case are 18,8 and 4 respectively.
Given equation:-
y = -x + 9
Values of x = {-9, 1, 5}
We have to find the corresponding values of y for each value of x.
Putting x = -9 in the given equation, we get,
y = -(-9) + 9 = 9 + 9 = 18
Putting x = 1 in the given equation, we get,
y = -1 + 9 = 8
Putting x = 5 in the given equation, we get,
y = -5 + 9 = 4
Hence, the values of y are {18, 8,4}
The complete ordered pair of (x,y) is given by:-
(-9,18)
(1,8)
(5,4)
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A particular bacterium population is found to double the in 20 minutes. If a laboratory culture
begins with a population of P=340 of this bacteria and there is no change in the growth rate, how
many bacteria will be present in t=37 minutes?
Hint: Use equation P = Poekt, where k is the relative growth. Round to two decimal places.
The bacteria present at t=37 minutes is found to be 8.40, with no change in growth rate.
What does population growth exponentially mean?When a population's per capita growth rate remains constant, regardless of population size, exponential growth occurs, causing the population to grow exponentially as the population increases.
Given:
P = 340
It has been discovered that a specific bacterial population doubles in 20 minutes.
k = 2/20 = 0.1
t = 37 minutes
We know that,
P = P₀[tex]e^{kt}[/tex]
340 = P₀([tex]e^{0.1*37}[/tex])
340 =P₀(40.44)
P₀ = 8.40
As a result, the bacteria that will be present in t=37 minutes is found to be 8.40 with no change in growth rate.
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If you partition a line segment in a ratio of 4:1, what is the fraction?
Answer:
Your answer would be 4 over 1
Three consecutive intergers are such that four times the least integer is three times the greatest . What is the greatest of this integers? A-16, B-8, C-10, D-12, E-14
If we call the middle number in the sequence [tex]x[/tex], the numerical values of the other terms will be [tex]x-1[/tex] and [tex]x+1[/tex], respectively, since they are consecutive.
We are told that [tex]4[/tex] times the smallest number is equal to [tex]3[/tex] times the largest number. Let us write our equality.
[tex]4(x-1)=3(x+1)[/tex][tex]4x-4=3x+3[/tex][tex]4x-3x=4+3[/tex][tex]x=7[/tex]We found our number in the middle. Since it wants the value of our largest number, let's add 1 to the middle number.
[tex]x+1=7+1=8[/tex]The answer is B.
Richey bought a 35-pound bag of dog food on Monday. His dog eats an
average of 3.5 pounds a day. How many pounds will remain in the bag after 8
days? 7 pounds
Answer:
Step-by-step explanation:
//////////////////////////////
PLS HELP 9th Grade MAth
The equation of the given linear function passing through two points is
y = 6 -2x.
What is equation of a linear function passing through given two points?Let (x₁, y₁) and (x₂, y₂) be two points on the given linear function whose equation in variables x and y is given by formula below.
(y - y₁) = {(y₂ -y₁)/(x₂-x₁)} (x -x₁)
Given that f is a linear function ,
f(-3) = 12
f(6) = -6
⇒(x₁, y₁) = ( -3,12)
(x₂, y₂) = ( 6,-6)
Thus the equation of the linear function is :
⇒ y - 12 = { ( -6-12)/(6-(-3))} ( x - (-3))
⇒ y - 12 = { -18/ 9} ( x +3)
⇒ y - 12 = -2 ( x+3)
⇒ y = 12 -2x - 6
⇒ y = 6 -2x
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A group of 40 children attended a baseball game on a field trip. Each child received either a hot dog or a bag of popcorn. Hot dogs were $2.25 and popcorn was $1.75. If the total bill was $83.50, how many hotdogs and bags of popcorn were purchased?
Write the equations for the situation above. (Use the variable x for hotdogs and y for popcorn)
Answer:
See Explanation
Step-by-step explanation:
[tex]x+y=40\\2.25x+1.75y=83.5\\[/tex]
from the first you have
[tex]h=40-p[/tex] substitute into the second:
[tex]2.25(40-p)+ 1.75x= 83.5\\90-2.25y+1.75x= 83.5[/tex]remaining
[tex]0.5y=6.5\\p= \frac{6.5}{0.5} =13\\[/tex]
substitute back into [tex]h= 40 - y\\h = 40 - 13 = 27[/tex]
Hope this helped :)
FRUIT Ronald buys fresh fruit from a fruit stand. Apples cost $5 per pound and peaches cost $6 per pound. He has $60 to spend. The table
shows the function relating the number of pounds of apples, x, and the number of pounds of peaches, y, Ronald could purchase.
Apples (lb) Peaches (lb)
X
y
0
1.2
3
6
7.2
12
The ?
y
10
9
7.5
5
4
0
Hintercept shows that if Ronald buys only apples, he can buy ?
intercept shows that if Ronald buys only peaches, he can buy ?
pounds. The
pounds
Answer:
a
Step-by-step explanation:
your a could be the same.
Why do visit the zoo on cold days
Answer:
How is this math?
Step-by-step explanation:
Answer:
Visiting the zoo on cold days limits the number of people there and it isn't too hot so you don't stand in the sweltering heat. Besides, on cold days, the animals may be in a better mood, but be cautioned, remember to bring a jacket just in case.
Step-by-step explanation:
Sixty and sixty eight thousandths
Answer: 60 and 68/1000
Step-by-step explanation:
Not sure if you wanted it in fraction, decimal, or percentage form.
Answer:
60 and 68.000
Step-by-step explanation:
i not sure if that was what u were looking for
What is -3 times 4??
Answer:
-12
Step-by-step explanation:
hope it helps
have a nice evening
Four students are sharing 1/3 carton of yogurt
equally. How much yogurt will each student
get
Answer: 1/12
Step-by-step explanation:
1) Set up the equation
1/3 / 4
2) Change 4 into a fraction
1/3 / 4/1
3) Change the divide into a multiply by flipping the 2nd fraction
1/3 * 1/4
4) Solve
1/12
express y in terms of x: 6(x-y) = 19
Expressing y in terms of x gives y = x - 19/ 6
What is subject of formulaSubject of formula can be defined as the variable that is being expressed in terms of other variables in an equation, function or expression.
It is also described as the variable that is being worked out in an expression or equation.
It is made to stand alone on on side of the equality sign.
We have the equation;
6(x-y) = 19
To make 'y' the subject of formula, let's take the following steps;
Divide both sides by 6, we have;
x - y = 19/ 6
now, take the variable 'x' over the equality sign
-y = 19/ 6 - x
Divide both sides by -1
y = x - 19/ 6
Hence, the equation is y = x - 19/ 6
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Which relation represents a function?
3×(9-4)³ - 46×3
A) 1
B) 237
C) 711
D) 987
Answer:
237
Step-by-step explanation:
3×(9-4)³ - 46×3
subtract 4 from 9 to get 5
3x5³-46x3
calculate 5 to the power of 3 and get 125
3x125-46x3
multiply 3 and 125 to get 375.
375-46x3
Multiply 46 and 3 to get 138
375-138
subtract 138 from 375 to get 237.
And there's your answer
You can follow the rule of BODMAS.
BODMAS stands for Bracket, Of, Division, Multiplication, Addition, Subtraction
By following the rule of BODMAS, the solution will be like this:
3×(5)³ - 46×3
= 3×125 - 46×3
= 375 - 138
= 237
I hope my explanation has helped you.
You can do well to declare this answer as the Brainiest Answer.
Thanks so much
PLEASE SOMEONE HELP ME
question 6
The exponential function in the graph shows the value, in dollars, of an investment over time. What real-world information is given by each feature of the graph?
THE TWO PICTURES GOES WITH QUESTION 6
Question 12
Evan runs a website that has gotten quite popular. However, its popularity seems to be decreasing and the site is now getting 7% fewer hits each week. If Evan's site got 34,000 hits this week, how many weekly hits can he expect it to get 3 weeks from now?
Round to the nearest whole number.
A. 134,360 hits
B. 27,348 hits
C. 41,651 hits
D. 714,000 hits
Considering exponential functions, it is found that:
6.
(1.7.5): The value after one year.y-intercept of 10: starting value.12. The number of hits 3 weeks from now will be of 27,348, hence option B is correct.
What is an exponential function?An exponential function is modeled according to the rule given next:
[tex]y = ab^x[/tex]
The parameters of the exponential function are defined as follows:
a is the y-intercept, which is the numeric value of the function when x = 0.b is the rate of change of the function.For item 6, considering the points (0,10) and (1,7.5), the parameters are given as follows:
y-intercept of 10, which is the starting value.When x = 1, y = 7.5, given the value after one year.For item 12, the initial amount and the rate of change are given as follows:
a = 34,000, b = 1 - 0.07 = 0.93.
Hence the number of hits x weeks from now is modeled according to the following function:
[tex]h(x) = 34000(0.93)^x[/tex]
After 3 weeks, x = 3, hence the number of hits will be of:
[tex]h(3) = 34000(0.93)^3 = 27348[/tex]
Meaning that option B is correct.
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←
For the given function, find (a) f(1) (b) f(-2).
(a) f(1) =
(b) f(-2) =
For the given functions , f(1) = -3 and f(-2) = -6 .
In the question
a graph is given
we have to find the value of the functions f(1) and f(-2)
the value of f(1) means the value of y, when x=1 .
we see that ,
on the graph when x = 1 , the value of y = -3 .
so the value of [tex]f(1)[/tex] = -3 .
the value of f(-2) means the value of y, when x = -2 .
we see that ,
on the graph when x = -2 , the value of y = -6 .
so the value of [tex]f(-2)[/tex] = -6 .
Therefore , For the given functions , f(1) = -3 and f(-2) = -6 .
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You have a $25 calling card. calls made using the card within the united states costs $10 per minute. while calls made from the us to france cost $25 per minute. write an inequality that relates the number of minutes x you can use for calls within the us and the number of minutes y you can use from de us and france
Answer:
10× + 25y ≤ 25
Answer:
0.1x + 0.25y ≤ 25
Step-by-step explanation:
A call within the US is $0.10, a call to France is $0.25, and you have $25.00. Your total amount of money spent depends on how many calls you make. Now, turn this information into an inequality.
The perimeter of AMUD is 38cm.
m/D=
MD=
14cm
360
Blank 1:
Blank 2:
cm
M
D
The side MD measures 10 cm and ∠D=72° for the given triangle.
What is triangle?
A shape with corners and three vertices is called a triangle. It is one of the most fundamental geometric shapes. Triangle ABC is the designation for a triangle containing vertices A, B, & C. In Euclidean geometry, all three points that are not collinear produce a singular triangle and a singular plane.The perimeter of ΔMUD= 38cm
MU=DU=14cm
∠U=36°
⇒∠M=∠D=x
Applying Angle sum property,
36°+x+x=180°
2x=180°-36°
x=72°
∴∠D=72°
Perimeter of triangle=14+14+MD
38=28+MD
⇒MD=10cm.
The side MD measures 10 cm and ∠D=72° for the given triangle.
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If pH = -log [H+], find the pH of a substance that has a hydrogen concentration [H+] = 5.7 X 10-4.Round your answer to the nearest ten thousandth (4 decimals).
[H+] = -1.7243
Explanation:
Since [H+] = 5.7 * 10 - 4, in the function -log[H+] representing pH, replace H+
pH = -log [5.7 *10 - 4]
pH = -log[53]
pH = -1.7243
NB:
This number is rounded up from -1.72427.....
what is −2x+y=15? i cant undestand
Step-by-step explanation:
it is a linear equation
Normally two if them are given together to solve
hope it helps