The relationship between the number of years that Simon's money is invested and the account balance can be described as 4:The relationship is linear. His account increases each year by a constant value of $28.
How to find the relationship between variables?The simple interest due to Simon's account every year is:
= Simple interest rate x Amount invested
= 0.4% x 7, 000
= $28
This means that every year, Simon's account would increase by a value of $28.
This represents a linear relationship because in linear relationships, the value of the variables increases by a constant amount each year or period.
Find out more on linear relationships at https://brainly.com/question/2030026
#SPJ1
If f(x) = 4x² and g(x)=3x, what is (fg)(x)?
(fg)(x)=
(Simplify your answer.)
The multiplication of the given function is (fg)(x) = 12[tex]x^3[/tex]
What is operations of the function ?
Similar to how a function's constituent terms can be added, subtracted, multiplied, and divided, so can functions. These are to be noted as follows:
Addition f( x ) + g ( x ) means to combine two functions, and it may alternatively be expressed as ( f + g ) ( x )
It is possible to write ( f g ) ( x ) to represent the operation of subtracting the g(x) function from the f(x) function.
The two functions are multiplied together when you multiply f (x ) g (x), which can also be represented as (f g ) (x).
Division f (x)/g (x) means to split the two functions in half, and it can alternatively be expressed as (f/g)(x).
Here the given function ,
=> f(x) = 4[tex]x^2[/tex]
=> g(x)= 3x
Now (fg)(x) = f(x)*g(x)
=> (fg)(x)= 4[tex]x^2[/tex]*3x
=> (fg)(x) = 12[tex]x^3[/tex]
Hence the (fg)(x) = 12[tex]x^3[/tex].
To learn more about operations of the function
https://brainly.com/question/28726030
#SPJ13
On what intervals is the function increasing?
Indicate intervals on the x-axis using the Ray tool for intervals that extend to infinity and the Segment tool for bounded intervals.
Graph a ray by selecting the endpoint followed by a point on the ray. Graph a segment by selecting an endpoint followed by the other endpoint.
Answer:
[-7, - 2] and [3, 7]--------------------------------------
The graph has two local maximums and two local minimums.
The intervals between those points are the increasing intervals.
Refer to the attached, where the intervals are marked.
The intervals are
x = [-7, - 2] and [3, 7]Previ
Question 3 Multiple Choice Worth 2 points)
(Pythagorean Theorem and the Coordinate Plane MC)
Determine the length of the line segment shown
-8 -7 -6
O 100 units
025 units
O 10 units
4
08 units
31
2
1
--5433/-2 -10
-1
O
N ?
&
2
3
4
D
5
x↑
The length of the line segment with endpoints at (0, 3) and (-6, -5) is 10 units
What is an equation?An equation shows the relationship between two or more numbers and variables.
The distance between two points A(x₁, y₁) and B(x₂, y₂) on the coordinate plane is:
[tex]AB=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
The line segment have endpoints at (0, 3) and (-6, -5). Hence:
Length = √[(-5-3)² + (-6 - 0)²] = √(8² + 6²) = √100 = 10
The length of the line segment is 10 units
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
Fill in the table using the function rule y=5x-2
The table has been shown using the function rule y = 5x - 2. (Refer to the table attached below).
What is the function rule?The relationship between the input or domain and the output or range is known as the function rule. If and only if there is a single value in the range for each domain value, a relation is a function.When the provided input values are applied, the function rule y = 2 x + 4 produces the output values displayed in the table. Now, the output numbers " are represented by and the input values are represented by. Consequently, the expression f (x) = 3 x + 1 can be used to represent the function rule y = 3 x + 1.So, the rule is y = 5x - 2:
Now calculate values as follows:
(A) When x = 0:
y = 0 - 2y = - 2(B) When x = 1:
y = 5 - 2y = 3(C) When x = 2:
y = 10 - 2y = 8(D) When x = 3:
y = 15 - 2y = 13Therefore, the table has been shown using the function rule y = 5x - 2. (Refer to the table attached below)
Know more about the function rule here:
https://brainly.com/question/28503724
#SPJ13
What is the solution to (x + 2)(x - 3)² > 0?
The solution is x > -2 and x > 3
x is greater than -2 and x is greater than 3.
This can be represented by the number line Option D.
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,
(x + 2) (x - 3)² > 0
This can be written as,
x + 2 > 0 and (x - 3)² > 0
x + 2 > 0
x > -2 _____(1)
(x - 3)² > 0
Squaring both sides.
x - 3 > 0
x > 3 _____(2)
From (1) and (2) we get,
x > -2 and x > 3
Thus,
The solution is x > -2 and x > 3
x is greater than -2 and x is greater than 3.
This can be represented by the number line Option D.
Learn more about inequalities here:
https://brainly.com/question/20383699
#SPJ1
Is there a proportional relationship between the area and radius of a circle? Explain.
The area of any circle is directly proportional to the square of the radius thus there are proportional relationships between the area of a circle and to the radius of the circle.
What are the ratio and proportion?The ratio is the division of the two numbers.
Proportion is the relation of a variable with another. It could be direct or inverse.
The area of a circle with radius "r" is given as,
A = πr²
Since,π = constant.
Removing constant by proportionality.
A ∝ r²
Hence "The area of any circle is directly proportional to the square of the radius thus there are proportional relationships between the area of a circle and to the radius of the circle".
For more information about ratios and proportions,
brainly.com/question/26974513
#SPJ1
Using the declining-balance method, complete the table as shown (twice the straight-line rate): (Enter your answers as a whole dollar amount.) Auto: $30,000 Estimated life: 5 years Residual value: $800 Year Cost Accumulated Depreciation B.O.Y Book Value B.O.Y Depreciation Expense Accumulated Depreciation E.O.Y Book Value E.O.Y 1 $30,000 A B C D E 2 $30,000 F G H I J 3 $30,000 K L M N O
Using the double-declining-balance method of depreciation, the completion of the table as shown is as follows:
Year Cost Accumulated Book Value Depreciation Accumulated Book
Depreciation B.O.Y Expense Depreciation Value
B.O.Y E.O.Y E.O.Y
1 $30,000 $0 $30,000 $12,000 $12,000 $18,000
2 $30,000 $12,000 $18,000 $7,200 $19,200 $10,800
3 $30,000 $19,200 $10,800 $4,320 $23,520 $6,480
What is the double-declining-balance method?The double-declining-balance method is a depreciation method that allocates more cost to the earlier years of the asset's life.
The double-declining-balance method uses twice the straight-line rate and is computed as the product of 100/estimated useful life multiplied by 2.
The double rate is applied at the end of the year's balance for each year's depreciation expense.
The difference between the previous year's ending balance and the residual value is taken as the depreciation expense for the last year.
Auto = $30,000
Estimated life = 5 years
Residual value = $800
Depreciable amount = $29,200 ($30,000 - $800)
Straight-line depreciation rate = 20% (100/5)
Double-declining depreciation rate = 40% (20% x 2)
Depreciation Expense:1st year = $12,000 ($30,000 x 40%)
2nd year = $7,200 ($18,000 x 40%)
3rd year = $4,320 ($10,800 x 40%)
4th year = $2,592 ($6,480 x 40%)
5th year = $3,088 ($3,888 - $800)
Year Cost Accumulated Book Value Depreciation Accumulated Book
Depreciation B.O.Y Expense Depreciation Value
B.O.Y E.O.Y E.O.Y
1 $30,000 $0 $30,000 $12,000 $12,000 $18,000
2 $30,000 $12,000 $18,000 $7,200 $19,200 $10,800
3 $30,000 $19,200 $10,800 $4,320 $23,520 $6,480
4 $30,000 $23,520 $6,480 $2,592 $26,112 $3,888
5 $30,000 $26,112 $3,888 $3,088 $29,200 $800
Learn more about the double-declining-balance depreciation method at ttps://brainly.com/question/15263644
#SPJ1
Mr. Dunston and Mr. Dolland spent $45 all
together. Mr. Dunston and Ms. Campbell
spent $65 all together. If Ms. Campbell spent
3 times as much as Mr. Dolland, how much
did Mr. Dunston spend?
The money spent by Mr. Dunston is $ 35.
Given that:-
Money spent by Mr. Dunston and Mr. Dolland = $ 45
Money spent by Mr. Dunston and Ms. Campbell = $ 65
Ms. Campbell spent 3 times as much as Mr. Dolland.
We have to find the money spent by Mr. Dunston.
Let the money spent by Mr. Dunston be $ x,
Let the money spent by Mr. Dolland be $ y and,
Let the money spent by Ms. Campbell be $ 3y
Hence, from the data given in the question, we can write,
x + y = 45 ...(1)
x + 3y = 65 ... (2)
By elimination method, we can write,
(2) - (1)
2y = 20
y = 10
x + 10 = 45
x = 45 - 10 = 35
x = 35
Hence, the money spent by Mr. Dunston is $ 35.
To learn more about elimination method, here:-
https://brainly.com/question/12090959
#SPJ1
Please help me to solve this simple question.
I will mark your answer brainliest!
Answer:
4/3
Step-by-step explanation:
You want the limit as t→1 of (t³+t²-5t+3)/(t³-3t+2).
Simplified formThe fact that each polynomial evaluates to 0 at t=1 tells you that (t-1) is a factor of each. Factoring that out gives ...
[tex]\dfrac{t^3+t^2-5t+3}{t^3-3t+2}=\dfrac{(t-1)(t^2+2t-3)}{(t-1)(t^2+t-2)}=\dfrac{(t-1)(t-1)(t+3)}{(t-1)(t-1)(t+2)}\\\\=\dfrac{t+3}{t+2}[/tex]
The limit at t = 1 is found by direct substitution:
lim = (1 +3)/(1 +2) = 4/3
Cassidy has $425 in her savings account, and she has to pay $5 each month to her parents for her cell phone. Calvin has $95 and he saves $25 each month from his job walking dogs for his neighbor. At this rate, when will Cassidy and Calvin have the same amount of money? How much will they each have?
Cassidy and Calvin have the same amount of money in 11 months.
The amount is $370.
How to illustrate the equation?Cassidy has $425 in her savings account, and she has to pay $5 each month to her parents for her cell phone. This will be:
= 425 - 5m
Calvin has $95 and he saves $25 each month from his job walking dogs for his neighbor. This will be:
= 95 + 25m
where m = number of months
The equation will be:
425 - 5m = 95 + 25m
Collect like terms
425 - 95 = 25m + 5m
330 = 30m
Divide
m= 330/30
m = 11
The number of months is 11.
The amount will be:
= 425 - 5m
= 425 - 5(11)
= 425 - 55.
= 370
Learn more about equations on:
brainly.com/question/2972832
#SPJ1
5 miles is 8km Convert 22.3miles to km
Answer:
13.9375
Step-by-step explanation:
this is your answer 1234
Please help I need the answer
The range of function f(x) = 4x + 5 for given input values is {-3, 1, 5, 9, 13}
The correct answer is an option (C)
In this question, we have been given a function f(x) = 4x + 5
We need to find the range of given function for input {-2, -1, 0, 1 , 2}
We know that the range of a function is the set of all output values for given input.
for x = -2,
f(-2) = 4(-2) + 5
f(-2) = -3
for x = -1,
f(-1) = 4(-1) + 5
f(-1) = 1
for x = 0,
f(0) = 4(0) + 5
f(0) = 5
for x = 1,
f(1) = 4(1) + 5
f(1) = 9
for x = 2,
f(2) = 4(2) + 5
f(2) = 13
Therefore, the range of function f(x) = 4x + 5 for given input values is {-3, 1, 5, 9, 13}
The correct answer is an option (C)
Learn more about function here:
https://brainly.com/question/28193995
#SPJ1
Current Attempt in Progress
Monty Corp. purchased a new machine on October 1, 2022, at a cost of $124,000. The company estimated that the machine will have
a salvage value of $15,000. The machine is expected to be used for 10,000 working hours during its 5-year life.
(a)
Compute the depreciation expense under straight-line method for 2022.
Depreciation expense $
2022
The depreciation expense under the straight-line method for 2022, for Monty Corp., is $5,450.
What is the straight-line depreciation method?Under the straight-line depreciation method, one of the cost-recovery methods, the depreciable amount of an asset is divided by its estimated useful life.
The quotient is the depreciation expense for each year. However, if the asset is not used for a full year, the depreciation expense is prorated according to the number of months or days that the asset is in use.
Note that the depreciable amount is the difference between the cost of the asset and its salvage value.
Cost of new machine = $124,000
Purchase date = October 1, 2022
Estimated salvage value = $15,000
Depreciable amount = $109,000 ($124,000 - $15,000)
Estimated useful life = 5 years
Estimated working hours = 10,000 hours
Depreciation method = Straight-line
Annual Depreciation Expense = $21,800 ($109,000/5)
October 1, 2022, to December 31, 2022, = 3 months
Depreciation expense for 2022 = $5,450 ($21,800 x 3/12)
Thus, using the straight-line method, Monty Corp. will record a depreciation expense of $5,450 for the new machine it purchased on October 1, 2022.
Learn more about the straight-line depreciation method at https://brainly.com/question/27258396
#SPJ1
Use the given equivalents, along with dimensional analysis, to convert the given unit to the unit indicated.
580 Ib to kg. (Round to the nearest hundredth as needed.)
By using the dimensional analysis 580 lb = 263.084 kg.
What is dimensional analysis?
Dimensional analysis, which is used in both engineering and science, examines the links between various physical quantities by determining their foundational quantities and units of measurement and then following these dimensions while computations or comparisons are made.
A technique for analysis that, in the absence of sufficient data to establish accurate equations, expresses physical quantities in terms of their fundamental dimensions.
We have to convert 580 lb into kg along with the dimensional analysis.
Since, 1 pound (lb) is equal to 0.45359237 kilograms (kg).
So,
580 lb = (0.4535927) x 580
580 lb = 263.0835746
580 lb = 263.084 kg
Hence, along with the dimensional analysis 580 lb = 263.084 kg.
To know more about the dimensional analysis, click on the link
https://brainly.com/question/28571069
#SPJ1
Find the equation of a line perpendicular to -5x + y = 9 that passes through the
point (0, -9)
The equation of a line perpendicular to -5x + y = 9 that passes through the point (0, -9) is [tex]y = -\frac{1}{5}x -9[/tex]
How to find the equation of a line?The equation of the line in slope intercept form can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptPerpendicular lines follows the following rules as follows:
m₁ m₂ = -1
Let's find the slope of -5x + y = 9 .
y = 5x + 9
Hence,
slope = 5
Let's find the slope of the equation of the line that passes through (0, -9) and perpendicular to -5x + y = 9 .
5m₂ = -1
m₂ = -1 / 5
m₂ = - 1 / 5
Therefore, let's find the y-intercept of the line using (0, -9)
-9 = - 1 / 5(0) + b
b = -9
Therefore, the equation of the line is y = - 1 / 5 x - 9
learn more on equation of a line here: brainly.com/question/11546551
#SPJ1
the difference of ten times a number and six is fourteen as a equation and solve it
The equation for the word problem the difference of ten times a number and six is fourteen is (10x-6 = 14) and the value of x is 2.
According to the question,
We have the following information:
The difference of ten times a number and six is fourteen.
Now, let's take the number to be x.
So, we have the following expression:
10x-6 = 14
Now, moving 6 from the left hand side to the right hand side will result in the change of the sign from minus to plus:
10x = 14+6
10x = 20
x = 20/10
x = 2
Hence, the equation for the word problem the difference of ten times a number and six is fourteen is (10x-6 = 14) and the value of x is 2.
To know more about equation here
https://brainly.com/question/3162971
#SPJ1
Use the product-to-sum identities to rewrite the following expression as a sum or difference.
2sin(2x)sin(2x)
The sum form of the trigonometric function 2 · sin 2x · sin 2x by product-to-sum formula is 1 - cos 4x.
How to transform a product of trigonometric functions into a sum of trigonometric functions
Herein we find the definition of a trigonometric function defined as a product of trigonometric function, this can be transformed into a sum of trigonometric functions by means of the following product-to-sum formula:
sin α · sin β = [cos (α - β) - cos (α + β)] / 2
First, write the trigonometric function defined in the statement:
2 · sin 2x · sin 2x
Second, use the product-to-sum formula by considering α = β = 2 · x:
2 · [[cos (2x - 2x) - cos (2x + 2x)] / 2]
cos 0 - cos 4x
1 - cos 4x
Third, write the resulting expression:
2 · sin 2x · sin 2x = 1 - cos 4x
To learn more on trigonometric formulas: https://brainly.com/question/19560372
#SPJ1
If x = 2 and t = 4, what is the value of 1/8(x^3− 4)(t² + 8)?
Answer:
64
Step-by-step explanation:
you need to plug the number in subtract and add then multiply the number from the first pair of parenthesis into the main number and after multiply the second pair into it.
Solve 2x2 + 20x + 8 = 0 by completing the square.
Answer:
x=−5+ 21 ,−5− 21
Step-by-step explanation:
x= 4−20+4= 214−20−4 =21
Eugene has a collection of 140 pet rocks. Of these rocks, 35% are sedimentary, 40% are igneous, and the rest are metamorphic. How many are metamorphic?
Answer:
25% or 35 rocks.
Step-by-step explanation:
To find this answer, simply add up 40% and 35% to get 75%. Now, 100% is the most we can have. So, 100 - 75 = 25%.
To find even more in depth of exactly how much 25% of 140 is, we can simply move the decimal point from 25 over twice to get 0.25. The term "of" means multiply:
0.25 x 140 = 35 rocks.
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
The graph shows Derek’s pay compared to the hours he has worked.
What is Derek’s hourly rate of pay?
Charlie earns $52.25 in 5 hours of work. What is Charlie’s hourly rate of pay?
Who gets paid more per hour? How much more?
Answer:
Charlie gets paid more then Derek. Charlie gets paid per hour $52.25
Some students were playing tag on a playground. The number of girls was less than twice the number of boys. If there were 7 girls, how many boys were playing tag? Write an equation and solve.
The number of boys were playing tag are 5.
What is equation?
Two expressions joined by an equal sign form a mathematical statement known as an equation. An equation is, for instance, 3x - 5 = 16. We can solve this equation and determine that the value of the variable x is 7.
Given: Some students were playing tag on a playground. The number of girls was three less than twice the number of boys. If there were 7 girls.
Suppose the number of boys are x,
So, the number of girls are, 2x - 3.
There are 7 girls.
So, 2x - 3 = 7
2x = 10
x = 10/2
x = 5
Therefore, the number of boys were playing tag are 5.
To know more about an equation, click on the link
https://brainly.com/question/2972832
#SPJ13
help pleas now...............math
The value of q after solving the expression, q/3+2/3 = 8q/3-5/3, is 1.
According to the question,
We have the following expression:
q/3+2/3 = 8q/3-5/3
Now, taking 3 as the denominator on both the sides:
(q+2)/3 = (8q-5)/3
Now, 3 in the denominator on the left hand side can be divided by 3 in the denominator on the right hand side:
q+2 = 8q-5
Now, changing the sides of this expression:
8q-5 = q+2
Moving q from the right hand side to the left hand side:
8q-q-5 = 2
7q -5 = 2
Moving 5 from the left hand side to the right hand side:
7q = 2+5
7q = 7
q = 7/7
q = 1
Hence, the value of q after solving the given expression is 1.
To know more about value of q here
https://brainly.com/question/19634511
#SPJ1
Which expression is equivalent to 5x - 5x + 3x - 3x?
Answer:
0
Step-by-step explanation:
subtracting same numbers give you zero
I've spent 1 hour on two separate days trying to understand this problem. Calc professor isn't being helpful at all either. Any help is appreciated!
Answer:
[tex]f(x)=-log_{3}(-x)[/tex]
Step-by-step explanation:
Based on the points given on the graph, I would say this is a Log function, reflected across both x- and y-axes.
And given the point (-3, -1), it must be [tex]-log_{3}(-x)[/tex]
Use technology to obtain approximate solutions graphically. All solutions should be accurate to one decimal place. (Zoom in for improved accuracy.)
Find the intersection of the line through (0, 1) and (4.3, 2) and the line through (2.1, 3) and (5.4, 0).
(x, y) =
Answer:
(x, y) ≈ (3.4, 1.8)
Step-by-step explanation:
You want the point of intersection of the lines through (0, 1), (4.3, 2) and (2.1, 3), (5.4, 0).
GraphThe first attachment shows a graph of the lines and the coordinates of the point of intersection. The solution is ...
(x, y) ≈ (3.42, 1.8)
(x, y) = (3.4, 1.8) . . . . accurate to 1 decimal place
__
Additional comment
For each pair of points, the equation of the line can be written as ...
(y2 -y1)(x -x1) -(x2 -x1)(y -y1) = 0
(2 -1)(x -0) -(4.3 -0)(y -1) = 0 ⇒ x -4.3y +4.3 = 0
and
(0 -3)(x -2.1) -(5.4 -2.1)(y -3) = 0 ⇒ -3x -3.3y +16.2 = 0
The calculator result in the second attachment shows the exact solution to be ...
(x, y) = (3 229/540, 1 43/54) ≈ (3.42407, 1.79630)
For each chart below, identify the output rule and classify the function as exponential, linear or neither.
The classification and the output rule for each function in this problem is given as follows:
1. Output rule: y = 5x + 11. Classification: Linear.
2. Output rule: y = 2^x. Classification: Exponential.
3. Output rule: y = 3 if |x| is even, y = 1 if |x| is odd. Classification: Neither.
What defines a linear function?A linear function is defined when the increase of 1 in x result in the addition of a constant to y, hence the rule is:
y = mx + b.
In which:
m is the addition to y when x increases by one.b is the value of y when x = 0.Hence, for the first table, as 5 is added to x when x increases by one, the rule is:
y = f(x) = 5x + 16.
What defines an exponential function?An exponential function is defined when the increase of 1 in x result in the multiplication of a constant to y, hence the rule is:
y = a(b)^x.
In which:
b is the addition to y when x increases by one.a is the value of y when x = 0.Hence, for the second table, the rule is:
y = 2^x.
For the third table, none of the definitions for linear and for exponential functions are true, hence the function is neither, as it is a piece-wise function that assumes one value for odd numbers and another for even numbers.
More can be learned about functions at https://brainly.com/question/24808124
#SPJ1
What is the area of a circle with a diameter of 5 feet? Round to the nearest thousandth.
What do this mean on this work
Answer:
The answer should be 13.928
Step-by-step explanation:
You do A square + B square = C square
caliper assessment Choose the answer that best completes the visual analogy #64
The answer that best completes the visual analogy of caliper is the first option (picture attached)
How to get the next movement of the caliperInformation given in the question
A polygon of 5 sides
Visual analogy refers to using the power of sight to detect of feel things
A polygon of 5 sides is called pentagon is used to describe the caliper
The movement is forecasted by:
Firstly, the question mark symbol "?" the line mark will go the spot the symbol ? appearedSecondly, the dot at the center will not be dark but remain a hollow spotconsidering these the first option become the best option
The line mark will align where the ? was positioned and the center will not be a dark spot
Learn more about Visual analogy here:
https://brainly.com/question/28427170
#SPJ1
