Answer:
So the answer would be 20 for 50-[20+[50-40]]
Step-by-step explanation:
50 - 40 =10 and 20 +10 = 30 so we 50 minus 30 which is 20
If its the other one it is 9 because 3 times 2 is 6 and 8 minus 6 is 2 and 7 plus 2 equals 9
f(a)= a +1
g(a)=-2a²-3
Find (f x g)(-4)
In the given expressions (f x g)(-4) is -8a³ - 8a² + 12a + 12.
What exactly are expressions?A mathematical expression is a sentence that has at least two variables or numbers and one or more mathematical operations.Mathematicians can multiply, divide, add, or subtract.An expression is structured as follows: Number/variable, mathematical operator, and expressionSo, (a+1)(2a²-3)(-4):
(a+1)(2a²-3)(-4)a(2a²-3) +1(2a²-3)(-4)(2a³-3a +2a²-3)-4-8a³ - 8a² + 12a + 12Therefore, in the given expressions (f x g)(-4) is -8a³ - 8a² + 12a + 12.
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Round your answer to the nearest hundredth B C 7 A 65°
The value of BC the nearest hundredth is 15.01 .
Trigonometric Ratios area unit outlined because the values of all the pure mathematics functions supported the worth of the quantitative relation of sides in an exceedingly trilateral. The ratios of sides of a trilateral with relation to any of its acute angles area unit referred to as the pure mathematics ratios of that exact angle.The 3 sides of the correct triangle are:Hypotenuse (the longest side)Perpendicular (opposite aspect to the angle)Base (Adjacent aspect to the angle)From the image , we are able to see that CA = seven and angle A = 65°
Using ,Trigonometric Ratios , we get
Tan A = Perpendicular / Base
Tan 65° = BC / CA
2.144 =BC / 7
2.144 ×7 = BC
15.011 = BC
On rounding off to the closest hundredth , we have a tendency to get BC = 15.01
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Simplify each expression.
ln 1
ln (1) = 0, by properties of logarithms.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Now,
ln (1) = [tex]log_e(1)[/tex]
By properties of logarithms, we get that: [tex]log_b(1) = 0[/tex], for any value of b.
Hence, ln (1) = 0, by properties of logarithms.
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Multiply. (3+√2)(4+√2)
The multiplication of the expression ( 3 + √2)( 4 +√2 ) is 14 + 7√2.
Multiplication in elementary algebra is the process of figuring out the outcome of multiplying a number by a number b. The product of a and b is the outcome of multiplication, and each of the integers a and b is referred to as a factor of the product ab.
Consider the expression,
y = ( 3 + √2)( 4 +√2 )
Using the distributive property,
a( b + c ) = ab + ac
y = ( 3 + √2)( 4 +√2 )
y = 3( 4 + √2 ) + √2( 4 + √2 )
y = 3 × 4 + 3 × √2 + √2 × 4 + ( √2 )²
y = 12 + 3√2 + 4√2 + 2
y = 14 + √2( 3 + 4 )
y = 14 + 7√2
The value of the expression ( 3 + √2)( 4 +√2 ) when simplified is 14 + 7√2.
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Amari and ethan planned an end-of-season soccer party. they purchased 45 hot dogs and 30 individual bags of chips.
15 is the greatest number of people they can be without having any leftovers
Given data
45 hotdogs in 30 individual bags of chips
How to solve for the greatest number of people they can be without having any leftoversGiven data
45 hotdogs in 30 individual bags of chips
The greatest common factor of 45 and 30 is 15
using ratio
45 : 30
3 : 2
This means that one person will receive 3 hotdogs in 2 bags. Also 15 people will get the equal amount without left overs
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complete question
Amari and Ethan planned an end of season soccer party to purchase 45 hotdogs in 30 individual bags of chips which person will receive the same amount of food what is the greatest number of people they can be without having any leftovers
describe fully the single transformation that takes shape a to shape b
The single transformation from shape A to B is: dilate A by 1/2, then rotate by 180 degrees
What is transformation?Transformation involves changing the position and size of a shape.
How to determine the transformation of the shapes?The single transformation from shape A to B is: dilate A by 1/2, then rotate by 180 degrees
From the figure, we have:
The side lengths of shape A are twice as large as the side lengths of shape BShape A can be rotated 180 degrees to map onto shape B, after dilation.So, the scale of dilation from shape A to B is:
Scale = 1/2
Hence, the single transformation from shape A to B is: dilate A by 1/2, then rotate by 180 degrees
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15. Given the following relation {(2, 1), (-4,5), (1,7), (2, -3), (-1,2)), determine if it is a function.
We get that the relation { ( 2 , 1) , ( - 4 , 5 ) , ( 1 , 7 ) , ( 2 , - 3 ) , ( - 1, 2 ) } is a function.
We are given a relation as:
{ ( 2 , 1 ) , ( - 4 , 5 ) , ( 1 , 7 ) , ( 2 , - 3 ) , ( - 1, 2 ) }
We need to find that whether it is a function or not.
A relation is a set that shows a relationship between two values. A function is from a set X to a set Y assigns to each element of X exactly one element of Y.
Here, we can see that it is a function as one value of x only has one image in the set y.
Therefore, we get that the relation { ( 2 , 1) , ( - 4 , 5 ) , ( 1 , 7 ) , ( 2 , - 3 ) , ( - 1, 2 ) } is a function.
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help please 3 2/5 ⋅ 2 1/3
Answer:
7 14/15
Step-by-step explanation:
Banana Boat sunscreen sells for $12 for a 20 fluid ounce bottle. What is the cost per ounce for the sunscreen?
Answer: 20/12
Step-by-step explanation:
What is the average rate of change of 2|x| on the interval [-3, 5].
The average rate of change of 2|x| on the interval [-3, 5] is 0.5
How to determine the average rate of change of 2|x| on the interval [-3, 5]?The function is given as
2|x|
Rewrite as
f(x) = 2|x|
The interval is given as
[-3, 5]
So, we have
f(-3) = 2|-3| = 6
f(5) = 2|5| = 10
The average rate of change of 2|x| on the interval [-3, 5] is then calculated as
Rate = (f(5) - f(-3))/(5 --3)
This gives
Rate = (10 - 6)/(5 --3)
Evaluate
Rate = 0.5
Hence, the average rate of change of 2|x| on the interval [-3, 5] is 0.5
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Find each composition of functions. Simplify your answer.
Let f(x)=2 x-3 . Find f(1+h)-f(1) / h, h≠0
A composite function exists as a function that depends on another function. The value for (f(1+h)-f(1)) / h = 2
What is meant by composition function?In mathematics, function composition exists as an operation ∘ that takes two functions f and g, and has a function h = g ∘ f such that h(x) = g. In this operation, the function g exists used to the result of applying the function f to x.
Function composition is a mathematical procedure where two functions, f, and g, are taken and a function, h = g ∘ f, is produced such that h(x) = g(f(x)). The function g exists used in this operation on the outcome of applying the function f to x.
Let the function be f(x) = 2x - 3
f(1+h) = 2 (1+h) -3 = 2h - 1
f(1) = 2(1) - 3 = -1
(f(1+h)-f(1)) = (2h - 1 ) + ( -1) = 2h
simplifying the equation, we get
(f(1+h)-f(1)) / h = 2h/ h
(f(1+h)-f(1))/h = 2
Therefore, the value of (f(1+h)-f(1))/h = 2.
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Ranger wants to verify that the expression
8x - 20 is the correct simplified expression for 4(2x - 5) Explain how to verify the simplified expression.
Answer: It is correct.
The first step here is to distribute the numbers
4 times 2x is 8x
4 times -5 is -20
Therefore, you're left with 8x-20
I hope this helps!
A bee flies at 20 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 19 minutes, and then flies directly back to the hive at 16 feet per second. It is away from the hive for a total of 21 minutes?
The distance is mathematically given as
D=1066.66667
What is the time function?The TIME function is included as part of Excel's Date and Time features. With the assistance of TIME, we are able to create a time by employing various components for the hours, minutes, and seconds.
While conducting financial analysis, it's possible that we'll need to date a report. Under these conditions, the TIME function may be used to convert a text string into a format that presents the time as a decimal representation of the seconds, minutes, and hours. Additionally, the function's capabilities include the ability to merge several values into a single time value.
formula= TIME (hour, minute, second)
distance = rate X time
D = RT
T = D/R
20 feet per second = 1200 feet per minute
16 feet per second = 960 feet per minute
(D/R) + 19 + (D/R) = 21
(D/R) + 19 + (D/R) = 21
(D/1200) + 19 + (D/960) = 21,
This is the equation we can use to find the distance from the flowerbed to the hive.
(D/1200) + (D/960) = 2
(D(1200)(960))/1200 + (D(1200)(960))/960 = 2(1200)960
960D + 1200D = 5(1200)960
2,160D = 2304000
D=1066.66667
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2+2 (free easy answer)
Answer:
5-1, known colloquially as four, 4, or 1+3.
Step-by-step explanation:
Find the approximate length (in Earth years) of each planet's year.
b. A Jovian year if Jupiter is 5.46 AU from the sun.
The approximate length is 12.755 year or 4653.75 days.
A year is the time it takes for a planet, moon, or other celestial body to make one orbit around the Sun. ( when we take our solar system as an example). In the case of other exoplanets, the celestial bodies, moon and other planets orbit around the main star. The period of the moon's orbit around the earth is related to the moon.
The reference point is very important in determining the exact length of a year. The length is dependent upon the reference point used for the orbital movement.
Jupiter completes a Single orbit once every 4333 days, due to which one Jupiter year is equivalent to 11.86 earth years.
The complete calculation is done below. (Image Attached)
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Complete the following angle identities. tan (A+B)=
Answer:
tan A +tanb
Step-by-step explanation:
1-tan a tan b
i think so
400 students were surveyed about their favorite school lunch. Exactly how many students chose pizza as their favorite school lunch based upon the data in the circle graph above?
The students chose pizza as their favorite school lunch based upon the data will be 130 students.
How to illustrate the information?Let the assumed fraction for those who choose pizza be 3/10.
From the information, 400 students were surveyed about their favorite school lunch.
Therefore, the students chose pizza as their favorite school lunch based upon the data will be:
= Fraction for pizza × Total students
= 3/10 × 400
= 120 students
Note that an overview was given as the graph wasn't found.
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PLS HELP
Look at the picture I attached, please help!
The expression which models the maximum number of days in which she can rent the car is 20x + 10 ≤ 80
How to illustrate the information?The maximum amount to spend = 80
Fixed charge per day $20
Charge per mile = $0.10
The inequality which represents the number of days Can be expressed thus :
(Charge per day × number of days) + (charge per mile × number of miles) ≤ 80
20x + 0.10 × 100 ≤ 300
20x + 10 ≤ 300
Hence, the required inequality expression is 20x + 10 ≤ 80.
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For any function, we call x the ____ value and y is the ____ value.
For any function, we call x the numerator value and y is the denominator value.
What is a function?A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable to an output variable.
The parts of a fraction.In Mathematics, a fraction comprises two (2) main parts and these include the following:
NumeratorDenominatorFor any function in Mathematics, we call x the numerator value while y is the denominator value.
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1-(r+2)=9 (pls help, I'm not the smartest person)
Answer:
r = -10
Step-by-step explanation:
1. Distribute
1-(r+2)=9
1-r-2=9
2. Subtract the numbers
1-r-2=9
-1-r=9
3. Rearrange the terms
-1-r=9
-r-1=9
Solution: r = -10
The sum of two consecutive numbers is 85, find the numbers
Answer:
85
Step-by-step explanation:
Consecutive numbers are numbers that follow each other in order. The two consecutive numbers are 42 and 43.
42+43=85
Answer:
42 & 43
Step-by-step explanation:
Let the two consecutive numbers be x and x+1 .
Here it is given that the sum of two consecutive numbers is 85.
So we get the equation,
x + (x+1) = 85
We get,
x + x + 1 = 85
2x + 1 = 85
Transposing +1 to RHS,
2x = 85 - 1
2x = 84
Transposing 2 to RHS,
x = 84 ÷ 2
Therefore, we get x = 42
Therefore, the two numbers are x and x+1, so they are: 42 and 43.
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Sam will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $65 and costs an additional $0.30 per mile driven. The
second plan has no initial fee but costs $0.80 per mile driven. How many miles would Sam need to drive for the two plans to cost the same?
Sam would need to drive for the two plans to cost the same is 130 miles.
Let, x = Number of miles driven
y = Total cost
The first plan:
Initial fee = $65
Cost of 1 mile = $0.3
Cost of drive x mile = $0.3x
In total, you will pay
y = 0.3x + 65 for the first plan.
The second plan:
There are no initial costs, but
Cost of 1 mile = $0.80
y = 0.80x
Now we have two equations
y = 0.3x + 65
y = 0.80x
As we know that y is equal to both 0.3x + 65 and 0.80x, this means we can equate the right hand sides and solve for x.
0.3x + 65 = 0.80x
0.80x - 0.3x = 65
0.5x = 65
x = 65÷0.5
x = 130
The cost of two plans will be same when Sam drive 130 miles.
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Please answer!!!!!!!!
Rectangle EFGH has vertices E(−3, 4), F(−2, 4), G(−2, −2), and H(−3, −2).
A dilation with a scale factor of 3 and centered at the origin is applied to the rectangle.
Which vertex in the dilated image has coordinates of (−6, 12)?
E′
F′
G′
H′
The vertex F(−2, 4) in the dilated image has coordinates of (−6, 12) option (B) F' is correct.
What is dilation?The transformation dilation is used to resize an item. Dilation is a technique for making items appear larger or smaller. The image created by this transformation is identical to the original shape.
It is given that:
The coordinates are:
Rectangle EFGH has vertices E(−3, 4), F(−2, 4), G(−2, −2), and H(−3, −2).
After applying dilation with a scale factor of 3:
E(−3, 4) → E'(-3x3, 4x3) = E'(-9, 12)
Similarly,
F(−2, 4) → F'(-6, 12)
G(−2, −2) → G'(-6, -6)
H(−3, −2) → H'(-9, -6)
Thus, the vertex F(−2, 4) in the dilated image has coordinates of (−6, 12) option (B) F' is correct.
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Simplify the expression where possible
Is the answer 6^-9 or -54
The given expression can be rewritten as [tex]6 ^{-9}=\frac{1}{6^9}[/tex].
Power RulesThere are different power rules, as presented below:
Multiplication with the same base: you should repeat the base and add the exponents.Division with the same base: you should repeat the base and subtract the exponents.Power. For this rule, you should repeat the base and multiply the exponents.Zero Exponent. When you have an exponent equals to zero, the result must be 1.For solving this exercise, you should identify the power rules you will apply. For this question, you can apply the following rule:
"Power - repeat the base and multiply the exponents."
Lilke the base is 6 and the exponents are 3 and -3, then you can rewrite the expression as:
[tex](6^3) ^{-3}=6 ^{-9}=\frac{1}{6^9}[/tex]
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how many quarts of soil are used to fill 2 flower pots
Answer: 20 quarts for two "standard" sized pots.
Step-by-step explanation:
A water tank holds 18,000. How long will it take for the water level to reach 6000 gallons if the water used at an average rate of 450 gallons per day?
Answer:
You start with 18.000 gallons and want to know when you reach 6.000 gallons, with a daily use of 450 gallons. This means you need to know how many days it take to use 18.000 - 6.000 = 12.000 gallons. This can simply be calculated with 12.000/450, which gives 26 2/3 day
Step-by-step explanation:
hi, can anyone help me with this problem?
Find the distance between each pair of points.
Simplify each expression. x³/₅ / x³/₁₀
The result of simplifying the expression x³/₅ / x³/₁₀ using the exponent rules is [tex]\sqrt[10]{}[/tex](x³)
To solve this exercise we have to resolve algebraic operations following the exponent rules.
[(x)³/₅ ] / [(x)³/₁₀]
Using the quotient rule that indicates that: the exponent result will be the subtraction of these exponents, we have:
x⁽³/⁵ ⁻³/¹⁰⁾
(x)⁽⁶⁻³⁾/¹⁰
(x)³/¹⁰
As we have a fractional exponent, you must convert the exponent to root:
[tex]\sqrt[10]{}[/tex](x³)
What is an exponent?In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.
Example: 3² = 3*3 = 9
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By measuring the amount of carbon-14 in an object, a palaeontologist can determine its approximate age. The amount of carbon- 14 in an object is given by y=a e⁻⁰.⁰⁰⁰¹²t, where a is the amount of carbon- 14 originally in the object, and t is the age of the object in years. In 2003, a bone believed to be from a dire wolf was found at the La Brea Tar Pits. The bone contains 14 % of its original carbon-14. How old is the bone?
b. What properties of logarithms and exponents can you use to solve the equation?
The bone is approximately 16384 years old, as solved by basic algebra and logarithm.
The properties of logarithms and exponents so used are: [tex]log_b(a)^m=m(log_b(a))[/tex], [tex]log_e(e) = 1[/tex]
What is basic algebra and logarithm?Numbers, variables, constants, expressions, equations, linear equations, and quadratic equations are all part of the basics of algebra. Additionally, the algebraic expressions contain the basic arithmetic operations of addition, subtraction, multiplication, and division.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Let 'a' be the original amount of the object.
Then, according to question, for y = amount of carbon in the object, y = 0.14(a) (as the bone contains 14% of its original carbon-14).
We are also given that: y = a [tex]e^{-0.00012t}[/tex]
On substituting the value of y, we get: 0.14a = a [tex]e^{-0.00012t}[/tex]
By basic algebra, we can solve it as:
=> 0.14 = [tex]e^{-0.00012t}[/tex]
=> ln (0.14) = ln ([tex]e^{-0.00012t}[/tex]) (taking natural logarithm on both sides)
=> ln (0.14) = - 0.00012t (as [tex]log_b(a)^m=m(log_b(a))[/tex]; further [tex]log_e(e) = 1[/tex])
=> [tex]\frac{ln(0.14)}{-0.00012}[/tex] = t
=> t = 16384 years (approx.)
Hence, the bone is approximately 16384 years old, as solved by basic algebra and logarithm; The properties of logarithms and exponents so used are: [tex]log_b(a)^m=m(log_b(a))[/tex], [tex]log_e(e) = 1[/tex].
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