II Work out question 1) Let f(x) = 2x + 1 and g(x)=-3x-4: then Determine a) (f+g) (x) b) (f-g) (x) c) (f-g) (x) d) (f/g) (x)
Answers
These are all abbreviated ways of writing a sum or product of functions.
\((f+g)(x) = f(x) + g(x)\)
\((f\times g)(x) = f(x) \times g(x)\)
Given \(f(x) = 2x+1\) and \(g(x) = -3x-4\), we have
a)
\((f+g)(x) = (2x+1) + (-3x-4) = (2x-3x) + (1-4) = \boxed{-x-3}\)
b)
\((f-g)(x) = (2x+1) - (-3x-4) = (2x + 3x) + (1 + 4) = \boxed{5x+5}\)
c) same as (b), but I bet you meant to use some other symbol. I'll just assume multiplication:
\((f\times g)(x) = (2x+1)\times(-3x-4) \\\\ = 2x\times(-3x)+1\times(-3x) +2x\times(-4) + 1\times(-4) \\\\ = -6x^2 - 3x - 8x - 4 \\\\ = \boxed{-6x^2 - 11x - 4}\)
d)
\(\left(\dfrac fg\right)(x) = \dfrac{2x+1}{-3x-4} = \boxed{-\dfrac{2x+1}{3x+4}}\)
though you could go on to simplify the quotient via long division; you would end up with the equivalent function (assuming x ≠ -4/3)
\(\left(\dfrac fg\right)(x) = -\dfrac{2x+1}{3x+4} = -\dfrac23 + \dfrac5{3(3x+4)}\)
Related Questions
how do I do ratios? please tell me by 8:30
Answers
we obtain the ratios dividing one value by another
1.
\(\frac{\text{Vowels}}{\text{consonants}}\)the number of vowels are 5 and the consonants are 21
so the ratio is
\(\frac{5}{21}\longrightarrow5\colon21\)the unit ratio is
\(\frac{\frac{5}{21}}{1}=\frac{0.238}{1}=0.238\)2.
to determine if two ratios are equivalent we must simplify the fractions
\(\frac{12}{16}=\frac{6}{8}=\frac{3}{4}\)\(\frac{72}{96}=\frac{36}{48}=\frac{18}{24}=\frac{9}{12}=\frac{3}{4}\)the ratios are equivalent because the two represent 3/4
the unit ratio of 3/4 is
\(\frac{\frac{3}{4}}{1}=\frac{0.75}{1}=0.75\)Need help with my geometry homework grade due to
Answers
The surface area of the base ball to the nearest whole number is 26 in²
What is surface area of a sphere?A sphere is defined as the set of all points in three-dimensional Euclidean space that are located at a distance.
The area occupied by a three-dimensional object by its outer surface is called the surface area.
The surface area of a sphere is expressed as;
SA = 4πr²
where r is the radius and it's calculated as;
C = 2πr
9 = 2πr
r = 4.5/π =
SA = 4 π × (4.5/π)²
SA = 81/π
SA = 26 in²( nearest whole number)
Therefore the surface area of the sphere is 26 in²
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Help please:)
Graph the equation by plotting points.
X=4
Answers
Answer:
(4,0)
Step-by-step explanation:
You basically are plotting a point on the positive number 4 on the x line. Since they're only asking for an X and not a Y, you'd leave it as (4,0). Hope this helps!
Khloe invested $160 in an account paying an interest rate of 5.7% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest ten dollars, would be in the account after 17 years?
Answers
Answer:
420
Step-by-step explanation:
After 17 years, there will be $420 in the account.
What is compound interest?The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest. A = P(1 + r/n)^nt, where P is the principal balance, r is the interest rate, n is the number of times interest is compounded annually, and t is the number of years, which is the formula for compound interest.
Given, Khloe invested $160 in an account paying an interest rate of 5.7% compounded continuously.
From the general formula of compound interest:
A = P(1 + r/n)^nt
In our case:
P = 160
n = 12 (compound continuously)
t = 17
r = 5.7%
Thus,
A = 160(1 + (0.057/12)^12*17
A = 160(1 + 0.00475)^204
A = 420.68
Therefore, in the account after 17 years the amount will be $420.
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The mean height of the students in a class is 152 cm. The mean height of boys is 158 cmwith a standard deviation of 5 cm. And the mean height of girls is 148 cm with a standarddeviation of 4 cm. Find the percentage of boys in the class and also the S.D of heights of allthe students in the class?
Answers
The percentage of boys in the class and also the standard deviation of heights of all the students in the class are 78% and 9 cm respectively
How to find the percentage of boys in the class?Percentage of the boys in the class deals with a ratio of the boys to the number of students in the class
The given parameters that will help us to get the percentage are
Mean height of the class = 152 cm
Mean height of the boys = 158 cm
The standard deviation of the boys = 5 cm
Mean height of the girls = 148 cm
Standard deviation of the girls = 4 cm
(1) The percentage of boys in the class is
Total mean height = 158 +148 = 306
Percentage = 158/306 * 100 = 51.6%
Then the percentages 51.6/100 * 152 = 78%
(2) The total standard deviation of all the students
Boys + girls = 5+4 = 9 cm
Therefore, the percentage of boys in the class and also the standard deviation of heights of all the students in the class are 78 students and 9 cm respectively
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This is for a test please answer
Answers
Answer:
25 = b
26 = c
Step-by-step explanation:
What is 8/x^2 + 6x • 2x ?
Answers
Answer:
8+12x^4/x^2
Step-by-step explanation:
i know im right!
Answer:
16/x + 6
Step-by-step explanation:
Edge 2021
what is the graph of −36≤2x+4(x−3)
Answers
Angus earns $8.80 an hour at his Saturday job and $7.50 per hour at his after school job. Last week he earned a total of $127.80. The hours he worked after school were four hours more than he worked on Saturday. How many hours did he work on Saturday?
Answers
Based on equations, Angus worked 6 hours on Saturday and 10 hours at his after-school job last week earning a total of $127.80.
How the hours are determined:The hourly rate at Angus' Saturday job = $8.80
The hourly rate at Angus' after-school job = $7.50
The total earnings last week = $127.80
Let the hours Angus worked at Saturday job = x
Let the hours Angus worked after-school = 4 + x
The total hours worked = x + x + 4
2x + 4
Equations:The total earnings last week 127.80 = 8.8x + 7.5x + 4 (7.5)
127.80 = 8.8x + 7.5x + 30
127.8 - 30 = 16.3x
Hours worked at Saturday Job:x = 6 hours
Hours worked at After-School Job:x + 4 = 10 hours
2x + 4 = 16 (12 + 4)
Check:
Earnings at Saturday job = $52.80 ($8.80 x 6)
Earnings at after-school job = $75.00 ($7.50 x 10)
Total earnings = $127.80
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The points (0,0), (3, 3), and (0,6) are three vertices of a square. What are the coordinates of the fourth vertex of the square?
O B. (2,3)
O A. (0, 3)
OD. (4,3)
O C. (3, 3)
Answers
Answer:
Step-by-step explanation:
let 4th vertex be (x,y)
midpoint of diagonal is same.
\(\frac{0+0}{2} =\frac{3+x}{2}\\\\3+x=0\\ x=-3\\\frac{0+6}{2} = \frac{3+y}{2} \\3+y=0+6\\y=6-3\\=3\)
so 4th vertex is (-3,3)
825 use each digit once. make the smallest 3digit number
Answers
Step-by-step explanation:
Given: To make smallest 3-digit number of 825.
To find: The smallest 3-digit number of 825.
Solution: We can make the smallest 3-digit number of 825 by separating the numbers and arranging it to ascending order. The given number is 825. ...
Final answer: The smallest 3-digit number of 825 is 258.
hope it helps
Answer:
258
Step-by-step explanation:
We are given 3 numbers:
8 2 5
And we are asked to find the smallest 3 digit number using those 3 digits above.
To make the smallest number, place the numbers in value from least to greatest:
2 5 8
This is your 3 digit number: 258.
Hope this helps! :)
Find the surface area of the box shown
Answers
NEED HELP WITH FUNCTIONS HW
Answers
The possible exact values of the trigonometric functions of θ are:
sin θ = -1/√3, cos θ = √3/3, sec θ = √3
What is law sines?The law of sines, also known as the sine rule, is a mathematical principle that relates the sides and angles of a triangle. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is constant for all three sides of the triangle.
Trigonometric functions are mathematical functions that relate angles to the ratios of the sides of a right triangle. The six primary trigonometric functions are sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). Each function represents a different ratio of two sides of a right triangle and can be used to solve problems in geometry, physics, engineering, and other fields that involve angles and triangles.
According to the given information,
Given that tan θ = -√(1/3) and 0 < θ < 180°, we can use the trigonometric identities to find the values of the other trigonometric functions of θ.
First, we can use the definition of the tangent function:
tan θ = opposite/adjacent
Since tan θ = -√(1/3), we can assign opposite = -1 and adjacent = √3 as their ratio equals -√(1/3). This means that the terminal side of the angle θ will lie in the fourth quadrant of the unit circle since the opposite is negative and the adjacent is positive.
Next, we can use the Pythagorean identity:
sin²θ + cos²θ = 1
to find the value of sin θ. Since we know that θ is in the fourth quadrant, we can assign sin θ = -1/√3, since sin θ is negative in the fourth quadrant and the ratio of opposite/hypotenuse of a 30-60-90 triangle is √3/2, which means the ratio of hypotenuse/opposite is 2/√3 = √3/3.
Then, we can use the definition of the cosine function:
cos θ = adjacent/hypotenuse
to find the value of cos θ. We know that adjacent = √3 and the hypotenuse is positive (since it is a length), so we can assign cos θ = √3/3.
Finally, we can use the reciprocal identity:
sec θ = 1/cos θ
to find the value of sec θ. We know that cos θ = √3/3, so we can assign sec θ = √3.
Therefore, the possible exact values of the trigonometric functions of θ are:
sin θ = -1/√3
cos θ = √3/3
tan θ = -√(1/3)
sec θ = √3
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Brianna made 9 1/4 bags of popcorn for a movie night with some friends. Together they ate 4 bags of it. How much popcorn was left?
Answers
There were 5 1/4 bags of popcorn left after eating 4 bags.
To find out how much popcorn was left after eating 4 bags, we need to subtract the amount eaten from the total amount Brianna made.
Brianna made 9 1/4 bags of popcorn, which can be represented as a mixed number. To perform calculations, let's convert it to an improper fraction:
9 1/4 = (4 * 9 + 1) / 4 = 37/4
Now, let's subtract the 4 bags eaten from the total:
37/4 - 4
To subtract fractions, we need a common denominator. The common denominator of 4 and 1 is 4. Therefore, we can rewrite the expression as:
37/4 - 4/1
Now, let's find a common denominator and subtract the fractions:
37/4 - 16/4 = (37 - 16) / 4 = 21/4
The result is 21/4, which is an improper fraction. Let's convert it back to a mixed number:
21/4 = 5 1/4
Therefore, there were 5 1/4 bags of popcorn left after eating 4 bags.
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Find the dot product of u and v.
u = (−4, 1)
v = (5,-4)
UxV =
Answers
Answer: -24
What is 24x(3 x 2) 4x + 2y + 6
Answers
Answer:
\(24x(3 \times 2) 4x + 2y + 6 = \\ 576x {}^{2} + 2y + 6\)
Step-by-step explanation:
\(if \: 24x(3 \times 2) 4x + 2y + 6 \\ = 576x {}^{2} + 2y + 6 \\ \\ \\ \\ \\ ♨Rage♨\)
Answer:
576x + 2y + 6
Step-by-step explanation:
so let's work this out
first as you can see we need to work this out in BODMAS Method, but there are also expression.
First do the brackets
3 x 2 = 6
so it is simplified to
24x X 6 X 4x + 2y + 6
We can multiply 24x to 6, even if it doesn't have the same pro numeral since, when multiplying we don't have to look for pro numeral, but if we are adding or subtracting, we can't add or subtract a number with a number that doesn't have the same pro numeral.
so
24x X 6 = 144x X 4x = 576x
Then it is simplified to
576x + 2y + 6
we can't simplify it anymore, since it doesn't have the same pro numeral.
Answer = 576x + 2y + 6
Hope you understand
:-)
A diner served twelve hamburgers during lunch and sixteen during dinner today. It *
served forty-eight of them yesterday. How many hamburgers were served today
?
Answers
The table lists the number of members at a local gym for selected years, where year 1 represents 2002. year 3 represents 2004, and so on.Yearxy = number of members200214220043602006570802008 72010 9100Use the ordered pairs (3,60) and (5.70) to find the equation of a line that approximates the data. Express your answer in slope intercept form. (If necessary, roundthe slope to the nearest hundredth and the y-intercept to the nearest whole number.)
Answers
To solve this problem we use the two points formula for the equation of a line and solving for y we get:
\(\begin{gathered} y-60=\frac{70-60}{5-3}(x-3)\text{.} \\ y-60=\frac{10}{2}(x-3), \\ y=5(x-3)+60, \\ y=5x-15+60, \\ y=5x+45. \end{gathered}\)Answer: y=5x+45.
A bookstore keeps track of books sold in one day? Approximately how many books sold were hardcover nonfiction?
Answers
Answer:
27%
Step-by-step explanation:
The total books sold were 182 and the amount of books sold that were nonfiction hardcover were 49 as represented in the frequency table.
To find the percentage we must divide the nonfiction hardcover by the total books.
49/182≈0.269 or 0.27
Multiply the decimal by a 100 to change it into a percentage, so our answer is 27%.
Answer:a 27%
Step-by-step explanation:
Multiple choice (you can choose more than one)
Answers
Answer:
A and D
Step-by-step explanation:
What is 2308208*12-12038928=
Answers
Answer:
15,659,568
Step-by-step explanation:
To calculate the expression 2308208 * 12 - 12038928, we can follow the order of operations (PEMDAS/BODMAS):
1. Multiply: 2308208 * 12 = 27698496
2. Subtract: 27698496 - 12038928 = 15659568
Therefore, 2308208 * 12 - 12038928 equals 15,659,568.
2a+c=162.97
how do you use the elimination method for this
Answers
When 'a' is 10, 'c' is approximately 142.97. You can repeat this process for different values of 'a' to find corresponding values of 'c'. Keep in mind that there are infinitely many solutions to this equation
To use the elimination method to solve the equation 2a + c = 162.97, we need another equation with the same variables. However, as there is only one equation given, we cannot apply the elimination method directly.
The elimination method typically involves adding or subtracting equations to eliminate one of the variables, resulting in a new equation with only one variable. Since we have only one equation, we don't have the opportunity to eliminate variables using another equation.
In this case, we can solve the given equation directly by isolating one variable in terms of the other. Let's solve for 'c':
2a + c = 162.97
Rearrange the equation to isolate 'c':
c = 162.97 - 2a
Now, we have an expression for 'c' in terms of 'a'. This equation represents a line in the 'a-c' coordinate plane. We can choose any value for 'a', substitute it into the equation, and calculate the corresponding 'c' value.
For example, let's say we choose 'a' = 10:
c = 162.97 - 2(10)
c = 162.97 - 20
c = 142.97
So, when 'a' is 10, 'c' is approximately 142.97.
You can repeat this process for different values of 'a' to find corresponding values of 'c'. Keep in mind that there are infinitely many solutions to this equation since we have one equation and two variables.
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Angela is able to run 8 miles in 36 minutes. How long will it take her to run 6 miles?
Answers
Apply the proportion:
Distance / time
Angela is able to run 8 miles in 36 minutes.
8 / 36
For 6 miles:
6 / x
Equal both
8/36 = 6/ x
Solve for x
8x = 6 (36)
8x = 216
x=216/8
x= 27
Answer : 27 minutes
PLEASE HELP, 35 POINTS!!
What type of automobile insurance pays for claims against you for the injuries and property damage of persons other than yourself?
A): $170.00
B): $270.60
C): $300.50
D): $332.00
Jerome uses the formula, P = 2DB, to find his approximate six-month premium when his driver risk factor, D, is 1.02 and the basic six-month premium is $500.
What will his monthly premium be?
A): $170.00
B): $270.60
C): $300.50
D): $332.00
Answers
Answer:
1.A
Step-by-step explanation:
Many types of insurance policies include liability insurance. Generally speaking, it helps pay to repair another person's property or for their medical bills if the policyholder is found responsible for causing the damage or injuries.
Answer:
1) B. liability
2) A. 170.00
just took the quickcheck
Step-by-step explanation:
pls help i need answer
Answers
Answer:
109 degrees
Step-by-step explanation:
23 + 48 = 71
180 - 71 = 109 :)
Answer:
i think the answer is 109 im not sure
Step-by-step explanation:
48+23=71 180-72=109
Question is in the Picutre attached.
Answers
Declmal answers
A student ran out of time on a multiple choice exam and randomly guessed the answers for two problems. Each problem had 4 answer choices - a, b, c, d - and
only one correct answer. What is the probability that he answered both of the problems correctly?
Answers
Answer:
We can break this down:
The student has a one out of five chance of getting a correct answer, and a four out of five chance of an incorrect answer. We can express the students odds of getting one incorrect answer as 4/5. In order to get the odds of two wrong answers, we need to multiply this answer again by the odds of choosing a wrong answer. Therefore:
The odds of one wrong answer = 4/5
The odds of two wrong answers = (4/5) * (4/5) = 16/25 chance of getting both of the questions wrong.
Step-by-step explanation:
Bank B pays 5.9% annual percentage rate compound semiannually what is the effective annual yield round to the nearest hundredth
Answers
9514 1404 393
Answer:
5.99%
Step-by-step explanation:
The relationship between the effective annual yield (e) and the nominal annual interest rate (r) compounded n times per year is ...
e = (1 +r/n)^n -1
For r = 5.9% and n = 2, the effective rate is ...
e = (1 +0.059/2)^2 -1 = 0.059870 ≈ 5.99%
Find the following values of the function
Answers
Answer:
12, 14 , - 4
Step-by-step explanation:
f(5) is in the interval x ≤ 7 , so f(x) = x + 7 , then
f(5) = 5 + 7 = 12
f(7) is in the interval x ≤ 7 , so f(x) = x + 7 , then
f(7) = 7 + 7 = 14
f(10) is in the interval x > 7 , so f(x) = 6 - x , then
f(10) = 6 - 10 = - 4
Hexagon DEFGHI is translated on the coordinate plane below to create hexagon D′E′F′G′H′I′: Hexagon DEFGHI and Hexagon D prime E prime F prime G prime H prime I prime on the coordinate plane with ordered pairs at D 2, 5, at E 5, 5, at F 6, 3, at G 5, 1, at H 2, 1, at I 1, 3, at D prime negative 6, negative 2, at E prime negative 3, negative 2, at F prime negative 2, negative 4, at G prime negative 3, negative 6, at H prime negative 6, negative 6, at I prime negative 7, negative 4
Answers
Answer: To find the image of a figure under a translation, you need to apply the same translation to every point in the figure.
In this case, the image of hexagon DEFGHI is hexagon D′E′F′G′H′I′. To find the image of each point, you can apply the translation that maps point D to point D′.
For example, to find the image of point E under the translation, you can apply the same translation that maps point D to point D′:
Point D is located at (2, 5).
Point D′ is located at (-6, -2).
The translation that maps point D to point D′ is a translation 6 units to the left and 2 units down.
To find the image of point E under this translation, you can apply the same translation to point E:
Point E is located at (5, 5).
The image of point E is located at (5 - 6, 5 - 2) = (-1, 3).
You can follow the same process to find the images of the other points under the translation.
Alternatively, you can use the coordinates of point D and point D′ to find the translation vector that describes the translation. The translation vector is a displacement that describes the change in position of a point under the translation.
In this case, the translation vector is given by the displacement from point D to point D′:
Point D is located at (2, 5).
Point D′ is located at (-6, -2).
The translation vector is given by the displacement (-6 - 2, -2 - 5) = (-8, -7).
To find the image of any point under the translation, you can add the translation vector to the coordinates of the point. For example, to find the image of point E under the translation, you can add the translation vector to the coordinates of point E:
Point E is located at (5, 5).
The translation vector is (-8, -7).
The image of point E is located at (5 - 8, 5 - 7) = (-3, -2).
You can follow the same process to find the images of the other points under the translation.
Step-by-step explanation: