Answers
Therefore in each composite function we get different domains and ranges which is given below.
Function is whose values are found from 2 given operates by applying one operate to AN variable so applying the second operate to the result and whose domain consists of these values of the variable that the result yielded by the primary function lies within the domain of the secondThe domain of a operate is that the set of values that we tend to ar allowed to plug into our operate.This set is that the x values in a very operate like f(x).The vary of a operate is that the set of values that the operate assumes. This set is that the values that the operate shoots out when we tend to plug AN x price in. they're the y values out after we plug an x value in. They are the y values.(1) f(x) = x+2 , g(x) = 3x - 1
(f + g)(x) = f(x) + g(x)
= x+2 + 3x - 1
= 4x +1
Domain = (-∞ , ∞) and range = (-∞ , ∞)
(f - g )(x) = f(x) - g(x)
= x+2 -3x +1
= -2x + 3
Domain = (-∞ , ∞) and range = (-∞ , ∞)
(f.g)(x) = f (x) g(x)
= (x+2)( 3x - 1)
= 3x²- x + 6x - 2
= 3x²+ 5x -2
Domain = (-∞ , ∞) and range = [-49/12 ,∞)
(f/g)(x) = f(x)/g(x)
= x+2/3x-1
Domain = (-∞ , 1/3) ∪ (1/3 ,∞) and range = (-∞ , 1/3) ∪ (1/3 ,∞)
(2) f(x) = x² - 5 and g(x) = -x +8
(f + g)(x) = f(x) + g(x)
= x² - 5 -x +8
= x² - x +3
Domain = (-∞ , ∞) and range = [11/4 ,∞)
(f - g )(x) = f(x) - g(x)
= x² - 5 +x -8
= x² + x - 13
Domain = (-∞ , ∞) and range = [-53/4 ,∞)
(f.g)(x) = f (x) g(x)
= ( x² - 5 )(- x +8)
= -x³ + 8x² + 5x - 40
Domain = (-∞ , ∞) and range = (-∞ , ∞)
(f/g)(x) = f(x) / g(x)
= x² - 5 / -x +8
Domain = (-∞ , 8) ∪ (8 ,∞) and range = (-∞ , -16 - 2√59 ) ∪ (-16 + 2√59 ,∞)
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Related Questions
Describe the pattern, then list the next three numbers in the sequence.
4.5, 7, 12, 22, 42 __, __, __
Answers
Answer:
82 , 162, 322
Step-by-step explanation:
So basically add the number by two and then subtract that number by 2. 4.5(2)=9 9-2=7 and 7(2)=14 14-2=12 and so on
Carla earned a total of $84 for 7 hours of babysitting. After a total of 8 hours of babysitting, how much money will Carla have earned? Assume the relationship is directly proportional.
Answers
$84 earned / 7 hours = $12 per hour
We now know Carla earns $12 per hour. Given this information, we can multiply the unit rate by 8 hours to identify how much money Carla will have earned after 8 hours:
$12 per hour • 8 hours of babysitting = $96 after 8 hours
Final answer: After a total of 8 hours of babysitting, Carla will have earned $96.
i need help on 7 and 8.
Answers
Answer:
7 is 48b-4 and 8 is mn+4m
Step-by-step explanation:
Create an equivalent expression for 1.5 cubed over 1.3 raised to the fourth power all raised to the power of negative six.
15 points to whoever can answer this pleeease help
Answers
Answer:
1.3^24 / 1.5)^18
Step-by-step explanation:
[1.5^3 / 1.3^4]^-6
= 1.5^(3*-6) / 1.3^(4*-6)
= 1.5^(-18) / 1.3^(-24)
= 1.3^24 / 1.5)^18
A piece of machinery depreciates at a fixed rate of 12% per year for 7 years. If the machinery is valued at $100,000 after 7 years, how much would the machinery have initially cost rounded to the nearest dollar?
a.
$113,636
d.
$45,235
b.
$40,868
e.
$244,692.86
c.
$244,693
Answers
The price the machinery have initially cost rounded to the nearest dollar is $244,693
Exponential equationThe formula for calculating depreciation is expressed according to the formula:
P(t) = P0e^-rt
Given the following parameters
P(t) = $100,000
rate = 12% = 0.12
time =7 years
Substitute
100,000 = P0e^-(0.12)(7)
100000 = P0e^0.84
P0 = 100000/e^0.84
P0 = $244,693
Hence the price the machinery have initially cost rounded to the nearest dollar is $244,693
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A tennis player hits the ball with an initial speed of 55 feet per second at an angle of 17°, from a height of 1.8 feet. How far away does the ball land in feet?
Answers
The range of the tennis player hitting the ball will be 172.43 meters away from the initial point.
What is the projectile motion?An item or particle that is thrown toward the planet's surface and moves somewhere along a curved route only under the influence of gravity is said to be experiencing projectile motion.
Let u be the initial speed and θ be the angle at which the ball hits. Then the range of the call is given as,
R = (u² sin 2θ) / g
Where 'g' is the acceleration due to gravity.
A tennis player strikes the ball at a height of 1.8 feet with an initial speed of 55 feet per second and an angle of 17°.
R = [55² x sin (2 x 17°) ] / 9.81
R = [3025 x sin 34° ] / 9.81
R = 172.43 meters
The range of the tennis player hitting the ball will be 172.43 meters away from the initial point.
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Answer:
61.988 feet
Step-by-step explanation:
I took the test and got it right :)
7. Health experts recommend the average female older than 50 years of age to
consume about 1,800 calories per day.
• Mrs. Keith has already consumed 950 calories today.
She plans to consume the same number of calories per hour for
the next 5 hours.
.
Which inequality represents d, the number of calories Mrs. Keith could eat each hour
for the next 5 hours without exceeding her recommended daily caloric intake?
Answers
gerber product's gerber mixed cereal for baby contains, in each serving, 60 calories and 11 grams of carbohydrates.† gerber mango tropical fruit dessert contains, in each serving, 80 calories and 21 grams of carbohydrates.† if you want to provide your child with 300 calories and 74 grams of carbohydrates, how many servings of each should you use? gerber mixed cereal for baby serving(s) gerber mango tropical fruit dessert serving(s)
Answers
Number of servings of Gerber mixed cereal for baby = 1
Number of servings of Gerber mango tropical fruit dessert for baby = 3
Given information about Gerber products are,
Gerber mixed cereal for baby contains, in each serving, 60 calories and 11 grams of carbohydrates.
Gerber mango tropical fruit dessert contains, in each serving, 80 calories and 21 grams of carbohydrates.
We have to find the number of servings of each to provide exactly 300 calories and 74 grams of Carbohydrates. So we need to find the appropriate combination of numbers 60 and 80 to make 300 and combinations of 11 and 21 to get 74.
Since 1 x 60 + 3 x 80 = 60 +240 = 300
and 1 x 11 + 3 x 21 = 11 + 63 = 74 ,
we can conclude that 1 serving of Gerber mixed cereal and 3 servings of Gerber mango tropical fruit dessert will do.
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Write a function g with the parent function f(x) = /x/ that has a vertex at (-2, 4)
Answers
The answer for the given function g(x) is |x - 4|² - 2.
Given parent function is f(x) = |x|
Given vertex (h, k) = (-2, 4)
The simplest function in a family of functions, a parent function maintains the definition of the entire family.
The parent function that has vertex must be used to create the function of g, as shown below.
vertex form can be written as
a ( x - k )² + h
Here a = 1 , k = 4, h = -2
Now the function g(x) = | x -4 |² + ( -2)
g(x) = |x - 4|² - 2
Therefore, the function g(x) is found to be |x - 4|² - 2.
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40 . a guest orders a drink that contains 4 ½ ounces of 80-proof liquor. approximately how many drinks does this beverage contain?
Answers
Number of drinks = 3
From the question we are told that:
Ordered drink 4 1/2 ounces of 80-proof liquor
Generally,
80-proof liquor contains 40\% alcohol
Giving the drink a standard 1.5 ounce of distilled spirit
Therefore,
Number of drinks = 4.5 / 1.5
So, Number of drinks = 3
What do you mean by ounces?A number of distinct units of mass, weight, or volume are derived from the uncia, an ancient Roman unit of measurement, including the ounce, which is almost unmodified. The avoirdupois ounce, or precisely 28.349523125 g, is 116 of an avoirdupois pound and is used in both the United States and the United Kingdom. Although it is frequently used outside of the Anglosphere, it is predominantly employed in the United States to measure packaged foods and food portions, postal items, the areal density of fabric and paper, boxing gloves, and other items. Although the avoirdupois ounce is the standard unit of mass for most applications.
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1.) The weight of the tea in 100 identical tea bags is 8 ounces. What is the weight, in ounces, of the tea in 3 tea bags? Show your work.
Answers
Answer:
0.24 ounces for 3 teabags.
Step-by-step explanation:
Since this is a 1 digit number, we should find out how much each teabag weighs. We can do this by dividing 8 by 100, which gives us 0.08.
Now we can multiply that by 3, which gives us 0.24, so 3 teabags are 0.24 ounces.
− 2/ 3 is a/an . (check all that applies.) \sqrt{5} 5 is a/an . (check all that applies.) natural number integer rational number real number irrational number
Answers
The -2/3 is an integer and rational number.
It is required to choose the number.
What is real number?Real numbers are numbers that include both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5) and irrational numbers such as √3, π(22/7), etc., are all real numbers.
Given:
-2/3 is an integer and rational number.
The square root of 25 is 5 is an Natural numbers, whole number, integer, and rational number.
Natural numbers are positive whole numbers (1, 2, 3, 4, 5, ...)
Whole numbers are positive numbers start with zero (0, 1, 2, 3,...)
Integers are positive and negative whole numbers or zero (..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5...)
Rational numbers include all integers as well as positive or negative numbers that have fractional parts ( -2.0, -3/4, 0.25, 2.1, 5, etc.)
Irrational numbers are numbers that can not be written as a simple fraction. Its decimal goes on forever without repeating (π = 3.14159....)
5 is a natural number, whole number, integer, and rational number.
Therefore, the -2/3 is an integer and rational number.
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This table represents function f. If function g is a quadratic function that contains the points and , which statement is true over the interval ? A. The average rates of change of f and g cannot be determined from the given information. B. The average rate of change of f is less than the average rate of change of g. C. The average rate of change of f is the same as the average rate of change of g. D. The average rate of change of f is more than the average rate of change of g.
Answers
If function g is a quadratic function that contains the points (-3, 5) and (0, 14), the statement which is true over the interval [-3, 0] is: B. The average rate of change of f is less than the average rate of change of g.
What is an average rate of change?An average rate of change is also referred to as slope and it can be defined as a type of function that describes the average rate at which a quantity changes (decreases or increases) with respect to another quantity, over a given interval.
In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this formula:
Average rate of change = [f(b) - f(a)]/(b - a)
Next, we would determine the average rate of change of function f over the interval [-3, 0]:
a = -3; f(a) = -4.5
b = 0; f(b) = 0
Substituting the given parameters into the formula, we have;
Average rate of change = (0 - (-4.5))/(0 - (-3))
Average rate of change = 4.5/3
Average rate of change = 1.5.
Also, we would determine the average rate of change of function g over the interval [-3, 0]:
a = -3; f(a) = 5
b = 0; f(b) = 14
Substituting the given parameters into the formula, we have;
Average rate of change = (14 - 5)/(0 - (-3))
Average rate of change = 9/3
Average rate of change = 3.
In conclusion, the average rate of change of function f is less than the average rate of change of function g.
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Answer:
The average rate of change of f is less than the average rate of change of g.
Step-by-step explanation:
Plato/Edmentum
5/6 x -4 1/2 x -2 1/5
Find the product. Write your answer as a fraction in simplest form.
Answers
Answer:
8 1/4 or 33/4
Step-by-step explanation:
How to muliply fractions: just multiply all the denominators together and the numerators together
However, if your mulitplying whole numbers, you have to change those into improper fractions using the formula: Whole number x denomiator + numerator
**Make sure to put the same numerator as you had before when you change to an improper fraction!!!
-4 1/2 = -9/2
-2 1/5 = -11/5
5 -9 -11 5 x -9 x -11 -45 x -11 (use a calculator) 495
-- x -- x --- = --------------- = ------------- = ------------
6 2 5 6 x 2 x 5 12 x 5 60
1 33
= 8.25 or 8 ---- = --------
4 4
Hayley wants to be a marine biologist when she grows up. Her entire room is ocean-themed, so she is painting her bed frame blue to match. She estimates that she will need 800 milliliters of paint, but the hardware store only sells paint in liters. If Hayley buys 1 liter of paint, how many milliliters will she have left?
Answers
Answer:
Hayley will have 200 milliliters of paint left.
Step-by-step explanation:
1 liter=1000 milliliter
1000-800=200
Answer:
305
Step-by-step explanation:
There are 1,000 milliliters in 1 liter.solveYou need to find how many milliliters of blue paint Annie has left. But first, you need to know how many milliliters she started with.There are 1,000 milliliters in a liter, so multiply 0.5 liters by 1,000.0.5×1,000=500Annie started with 500 milliliters of blue paint.Now, add to find how much blue paint Annie used for her beach painting. She used 75 milliliters of blue paint for the sky and 120 milliliters for the ocean.75+120=195Annie used 195 milliliters of blue paint in all.Now, find how much blue paint Annie has left. She started with 500 milliliters. Subtract the 195 milliliters she used.500–195=305Annie has 305 milliliters of blue paint left.
perform the indicated operation and simplify the result leave yuour answer in factored form 4x/x2 - 1
Answers
The simplified result is :
[tex]4x/x^{2}[/tex] - 1
= 4/x -1
4-x / x.
Factored form, the product of a constant and two linear terms: or. The parameters and are the roots of the function (the x-intercepts of the graph). Converting a quadratic function to factored form is called factoring.
An example for a quadratic function in factored form is y=½(x-6)(x+2). We can analyze this form to find the x-intercepts of the graph, as well as find the vertex.
In algebra, simplifying and factoring expressions are opposite processes. Simplifying an expression often means removing a pair of parentheses; factoring an expression often means applying them.
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What is four hundred in standard form
Answers
standard form
Answer: 4x10²
Step-by-step explanation:
someone pls help me w this. I rlly need this!! thank uu!
"write the equation of a line that is parallel to y=2x-3 and passes through the point (1, 6)"
Answers
Hope this helps :)
part a a wall is covered with 6 wood panels. each panel is a square with a side length of x feet. write an expression to represent the total area, in square feet, covered by the wood panels.
Answers
The expression that represent the total area in square feet covered by the wood panels is: 6x² feet²
The formula and procedure to solve this geometry exercise is:
A = s²
Where:
A = area of the squares = sideProblem information:
A = ?s = x feetNo. panels= 6Using the formula of the square area we get the area of 1 panel:
A(1 panel) = s²
A(1 panel) = (x feet)²
A(1 panel) = x² feet²
Calculating the total area of the 6 wood panels we get:
A(total): No. panels * A(1 panel)
A(total): 6x² feet²
What is the area?Is the measure of the space occupied by a body bounded by an environment called perimeter, the same is expressed in units of squared side. Example: ft2, m2
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x^2y(7xy^4)
helppppp
Answers
Solve the given word problem.
Ms. Enriquez asked a carpenter to construct a rectangular bulletin board for his classroom. She told the carpenter that the length of the board is 7 ft. Longer than its width and its area is 18 square feet. Find the dimensions of the given bulletin board.
Pls solve the question
Answers
The dimensions of the bulletin board is 2 ft and 9 ft.
Let the width of board = x
Then, the length of board = 7+x
Area of board = 18 ft²
Area of rectangle = L×W
so, (7+x) × x = 18 ft²
7x + x² = 18 ft²
7x + x² + 18 = 0
x² + 9x -2x -18 = 0
x(x+9) -2(x+9) = 0
(x+9) (x-2) = 0
x+9 =0, x -2 = 0
Dimension can not be in negative number, so
x = 2, Width = 2 ft
Length = 2+7 = 9 ft
Hence, the dimensions of board will be:
The width of board = 2 ft
And, the length of bard = 9 ft.
What did Raya do wrong? Use complete sentences to describe her mistake.
Answers
During evaluation, Raya was wrong in step 2. She got the cube of -3 wrong. The correct value is -27 and not -9.
How to Evaluate an Expression?Given the expression, a³ - b³ / 5, where:
a = 2
b = -3
Substitute the values into the expression
Step 1: (2)³ - (-3)³ / 5
Evaluate
Step 2: 8 - (-27) / 5 (this is where Raya made a mistake, she had -9 instead of -27)
Step 3: 8 + 27/5
Step 4: 35/5 [addition]
Simplify
Step 5: 35/5 = 5 [division]
Thus, we can state that Raya was wrong in step 2. She got the cube of -3 wrong. The correct value is -27 and not -9.
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can someone answer 2 1/8 x 1 7/9 =
Answers
Answer:
Exact Form: 34/9
Mixed-Number Form: 3 7/9
Step-by-step explanation:
Hope this helps.
Answer:
3 7/9
Step-by-step explanation:
2 1/8
convert mixed numbers to improper fractions
2x8+1/8 = 17/8
1 7/9
1x7+9/9 =16/9
17/8 x 16/9
Factor the number 16=8x2
17x8x2/8x9
cancel the common factor =8
=17x2/9
=34/9
convert improper fractions to mixed numbers
34/9 =3 remainder of 7
34/9 = 3 7/9
Find car A and car B speed in km/h
Answers
Answer:
72 km/h and 48 km/hStep-by-step explanation:
Let the speed of the cars be x and y.
When moving in opposite directions, the speeds add up and when moving in the same direction the speeds subtracted.
Convert time from minutes to hour:
4 minutes = 4*1/60 hr = 1/15 hr20 minutes = 20*1/60 hr = 1/3 hrOpposite direction(x + y)*1/15 = 8x + y = 8*15x + y = 120Same direction(x - y)*1/3 = 8x - y = 8*3x - y = 24Add up the two equations and find the value of x:
x + y + x - y = 120 + 242x = 144x = 72Find y:
72 + y = 120y = 120 - 72y = 48Maria needs to be at the airport terminal at 16:15. It will take 1 1/3
hours to drive to the airport from her home, and a further 25 minutes to park and get to the terminal.
What is the latest time she should leave home?
Give your answer as a time in the 24-hour clock.
Answers
Maria should leave home for the airport terminal at 14:30.
How to convert hour into minutes?Local time is the time of a location as determined by the apparent motion of the sun. The fixed time for locations on the same meridian set by law in a country is referred to as standard time. Changes in real time as longitude changes. The same applies to a specific country.We all know that one hour equals sixty minutes.
As a result, 6 hours = (6 × 60) minutes = 360 minutes.
For, the given question;
The time at which Maria need to be at airport terminal is 16:15.
Time taken for the driving is 1 1/3 = 4/3 hours.
convert this in minutes;
= 4×60/3
= 80 minutes.
Now, extra 25 minutes is requires to park.
Total time = 80 minutes + 25 minutes
Or we can write 60 minutes + 45 minutes.
Total time = 1 hour + 45 minutes.
The time at which Maria has to reach = 16:15 - 1:45 = 14:30
Therefore, the time at which Maria must reach the airport is 14:30 in 24-hour clock.
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Meri paid $19.24 for 10.5 gallons of
gas. What was the cost of one
gallon?
Answers
eight congruent equilateral triangles, each of a different color, are used to construct a regular octahedron. how many distinguishable ways are there to construct the octahedron? (two colored octahedrons are distinguishable if neither can be rotated to look just like the other.)
Answers
There are 1680 ways to construct the octahedrons.
Here,
Eight congruent equilateral triangles, each of a different color, are used to construct a regular octahedron.
An octahedron has 8 equilateral triangles.
We have to find number of ways to construct the octahedron.
What is Regular octahedron?
An octahedron is a polyhedron with eight faces. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex.
Now,
An octahedron has 8 equilateral triangles.
We have to fix 2 faces before applying the colors.
So, the first face that can be fixed for any of the 8 faces but each faces are similar.
Hence, there are 8/8 ways.
And, When we fix one face, three adjoining faces are similar.
So, we have 7 colors for the second face.
Hence, 7/3 ways
Now, we can place any color anywhere, it will be different arrangement.
So, 6! ways.
Hence, Total number of ways = (8/8) * (7/3) * 6! = 7 * 6 * 5 * 4 *2 = 1680
So, There are 1680 ways to construct the octahedrons.
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You want your daily sodium intake to be less than 2300 milligrams. For breakfast, you eat a cereal bar with the nutrition label shown. What are the possible amounts of sodium you can eat during the rest of the day? Nutrition Facts Serving Size Servings Per Container Amount Per Serving Calories 120 Total Fat 3g 1 Bar (37g) Calories from Fat 30 % Daily Value* 5% 3% Saturated Fat 0.5g Trans Fat Og Cholesterol Omg Sodium 125mg 0% 5% The possible amounts of sodium you can eat during the rest of the day should be less than mg
Answers
According to the information in the nutritional table, it can be inferred that the amount of milligrams of sodium that we should consume during the rest of the day must be less than 2,175mg,
How to calculate the amount of sodium we can consume?To calculate the amount of sodium that we can consume during the rest of the day after breakfast, we must subtract the value of sodium consumed to the amount of total sodium that we want to ingest as shown below:
2300mg - 125mg = 175mgAccording to the above, it can be inferred that after consuming the cereal bar at breakfast, we should consume an amount less than or equal to 2,175mg of sodium in the other meals of the day (lunch, dinner and snacks).
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Leila wants to paint the ceiling of her restaurant. The ceiling is in the shape of a square. Its side lengths are feet. Suppose each can of paint will cover square feet. How many cans will she need to paint the ceiling?
Answers
Answer: Find the square roots and the multiply that by 4
Step-by-step explanation:
hope this helped
please help
see attached picture
Answers
Answer:
See Explanation
Step-by-step explanation:
For cement block:Given is a square cement block, thus, it's width and height would be equal.-> length (l)= h, width (w)= 2x, height (h) = 2x [tex]V_{cement \: block} = lwh[/tex][tex]\implies V_{cement \: block} = h(2x)(2x)[/tex][tex]\implies V_{cement \: block} = 4x^2h.....(1)[/tex]For cylinder:Radius (r) = 2x/2 = x, height (h) = h[tex]V_{cylinder} = \pi r^2 h[/tex][tex]\implies V_{cylinder} = \pi x^2 h.....(2)[/tex]Subtract (2) from (1), we find:[tex]V_{cement \: block}-V_{cylinder} = 4x^2h- \pi x^2 h[/tex][tex] V(cement \: block\: without\: cylinder)= x^2h(4- \pi)[/tex]Thus proved To solve 6.2.1 and 6.2.2 plug the given values in [tex]x^2h(4- \pi)[/tex] and calculate.