The given function [tex]\(f(x) = \frac{5}{5} \cdot x\)[/tex] is indeed linear, and it can be expressed as f(x) = x in the standard linear form.
Let's break down the analysis of the given function[tex]\(f(x) = \frac{5}{5} \cdot x\)[/tex].
1. Initial Expression:
[tex]\[ f(x) = \frac{5}{5} \cdot x \][/tex]
2. Simplify the Fraction:
[tex]\[ \frac{5}{5} \][/tex] simplifies to 1, so the expression becomes:
[tex]\[ f(x) = 1 \cdot x \][/tex]
3. Multiplication by 1:
Multiplying any value by 1 does not change the value, so the expression further simplifies to:
f(x) = x
4. Linear Form:
The function is now in the form f(x) = ax + b with a = 1 and b = 0:
[tex]\[ f(x) = 1 \cdot x + 0 \][/tex]
Therefore, the given function [tex]\(f(x) = \frac{5}{5} \cdot x\)[/tex] is indeed linear, and it can be expressed as f(x) = x in the standard linear form.
Complete Question: Determine whether the given function is linear. if the function is linear, express the function in the form f(x) = ax + b. (if the function is not linear, enter not linear.)
f(x) = 5 / 5 x
Suppose e(x) = 3 and e[x(x − 1)] = 27.5. (a) what is e(x2)? [hint: first verify that e[x(x − 1)] = e[x2 − x] = e(x2) − e(x).]
An object's position is given by x(t) = 5 + 10 t 2. what is its acceleration after 5 s
The acceleration after 5 seconds is 20 m/s^2.
Explanation:To find the acceleration, we need to take the second derivative of the position function.
x(t) = 5 + 10t^2
Taking the derivative with respect to time, we get:
v(t) = 20t
Taking the derivative again, we get the acceleration:
a(t) = 20
Therefore, the acceleration after 5 seconds is 20 m/s^2.
A red candle is 8 inches tall and burns at a rate of 7/10 inch per hour. A blue candle is 6 inches tall and burns at a rate of 1/5 inch per hour. After how many hours will both candles be the same height?
Answer:
4 hours
Step-by-step explanation:
The height of the red candle in inches can be modeled by ...
h = 8 - (7/10)t
where t is the number of hours it burns.
Likewise, the height of the blue candle can be modeled by ...
h = 6 - (1/5)t
The heights of the two candles will be the same when one expression for height is equal to the other.
8 - (7/10)t = 6 - (1/5)t
2 = t(7/10 - 1/5) . . . . . . . . . add (7/10)t -6
2/(5/10) = t = 4 . . . . . . . . . divide by the coefficient of t
The Perez family has a rectangular fish tank how much water will the tank hold if it's length is 3 feet, its width is 2 feet and its height is 3 feet
A) NONE
B) 18 cubic feet
C) 3 cubic feet
D) 6 cubic feet
E) 9 cubic feet
the sum of two numbers is 18 . the difference of the two numbers is -2 find the numbers
Find the missing number of each unit rate
The cost of 5 cds and a $ 12 DVD
The cost of 5 CDs and a $12 DVD is $62.
Explanation:The subject of this question is Mathematics. The question asks for the cost of 5 CDs and a $12 DVD. To find the total cost, we need to know the price of each CD and the price of the DVD.
Let's say the price of each CD is $10. The total cost of 5 CDs would be 5 multiplied by $10, which is $50.Adding the cost of the DVD, which is $12, to the cost of the CDs, we get a total cost of $50 + $12 = $62.Therefore, the cost of 5 CDs and a $12 DVD is $62.
The measure of arc XZ is 28° what is the measure of XYZ
What is the common difference for the arithmetic sequence?
4.7, 6, 7.3, 8.6, 9.9,...
You've got 60 homework problems to do and it took you 10 minutes to do eight of them. At that rate, how long will it take?
there are 1,525 pages in a book. Julia and Kim round the number of pages to the nearest hundred
Julia and Kim round the number of pages to the nearest hundred as 1500.
Given that, there are 1,525 pages in a book.
What is the rounding off numbers?Rounding a number means the process of making a number simpler such that its value remains close to what it was. The result obtained after rounding off a number is less accurate, but easier to use. While rounding a number, we consider the place value of digits in a number.
In the given number, digit in the tens place is 2, so the number rounded to nearest hundred as 1500.
Therefore, Julia and Kim round the number of pages to the nearest hundred as 1500.
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6-1. let x have a poisson distribution with a mean of 4. find (a) p(2≤x≤5). (b) p(x≥3). (c) p(x≤3).
Factor out the coefficient of the variable. The expression 2.2x +4.4 factored is
Mr. and Mrs. Zeller close on a 20 year home loan for $150,000. The monthly payment with no points is $1,160, but if they buy a point it is $1,150. What might you infer if Mr.and Mrs. Zeller choose not to buy a point? a. They plan to sell the house at the end of 5 years. b. They plan to sell the house at the end of 15 years. c. They plan to sell the house at the end of 20 years. d. They plan to sell the house at the end of 25 years.
Answer:
the answer is A they plan to sell it in 5 years
Step-by-step explanation:
whats the nearest tenth to -61 square root
8 = 4x + 12 what does x equal
Given f(x) = x^2 - 10x + 22, what is the range of f?
f(x)=x2-10x+22 domain of f
Answer: all real numbers
Range of F
Answer: y> -3
Amanda can jog 18 miles in 5 hours. At this rate, how many miles can Amanda jog in 4 hours?
we know that
Amanda can jog [tex]18[/tex] miles in [tex]5[/tex] hours
so
by proportion
Find the number of miles that Amanda can jog in [tex]4[/tex] hours
[tex]\frac{18}{5} \frac{miles}{hours} =\frac{x}{4} \frac{miles}{hours} \\ \\5*x=18*4 \\ \\x=72/5 \\ \\ x=14.4\ miles[/tex]
therefore
the answer is
[tex]14.4\ miles[/tex]
A geologist have two rocks on a scale that weighs 2 1/2 lbs together rock a was 1/7 of a the total weight how much did rock a weight
By using the given fraction of rock 'a' against the total weight of two rocks, we can find that rock 'a' weighs approximately 0.357 lbs.
Explanation:The student's question involves calculating the weight of a rock, given as a fraction of a total weight. In this case, they are talking about a scenario where a geologist uses a scale to weigh two rocks together, with a total weight of 2 1/2 lbs, and rock 'a' is specified to be 1/7 of this total weight. To determine the weight of rock 'a', we simply divide the total weight by 7.
So, 2 1/2 lbs is equivalent to 2.5 lbs (since 1/2 is the same as 0.5). To find the weight of rock 'a', we take this total weight and perform the operation: 2.5 ÷ 7 = 0.357 lbs.
Therefore, rock 'a' weighs approximately 0.357 lbs. Remember, this is an estimation because the weight of the rock is being given as a fraction of the total weight, and actual weights can vary based on factors such as density and volume.
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the circle with center (3,5) and radius 2 has a equation?
Solve for the distance between (522, 1322) and (9000, -1337) to the third decimal.
Which three statements would produce the truth value F when p is true and q is false?
A. p -> q
B. ~p/\~q
C. p->~q
D. q\/~p
C. p/\~q
please help
Answer with Step-by-step explanation:
p is true then ~p is false.
q is false then ~q is true.
A. p -> q
if p is true and q is false then this gives false truth value.
Hence, here truth value is F
B. ~p/\~q
if any one of them is false then it gives false truth value.
Hence, here truth value is F(since,~p is false)
C. p->~q
true statement implies a true statement hence, truth value will be true
Hence, here truth value is T(p true implies ~q true)
D. q\/~p
if any one of them is true then compound statement is true.
Hence, here truth value is F(since, ~p and q both are false)
E. p/\~q
if both true then compound statement is also true.
Hence, here truth value is T(since p and ~q both are true)
determine the quadratic function of f whose graph is given. The vertex is (1,-3) and the y-intercept is -2
6578 divided 34
20\5
Answer:
263.56 :)
Step-by-step explanation:
You make a large bowl of salad to share with your friends. Your brother eats 1/3 of it before they come over. What fractional portion of the original bowl of salad does each friend receive?
Answer:
[tex]\frac{2}{3x}[/tex]
Where, x = total friends
Step-by-step explanation:
Given,
The part of the salad has eaten = [tex]\frac{1}{3}[/tex]
Total part of the salad = 1,
Thus, the remaining part of the salad = original part - part has eaten
[tex]=1-\frac{1}{3}[/tex]
[tex]=\frac{3-1}{3}[/tex]
[tex]=\frac{2}{3}[/tex]
If there are x friends,
Then the portion of the original bowl of salad received by each friend
[tex]=\frac{\text{Remaining part}}{\text{Total friends}}[/tex] [tex]=\frac{2}{3x}[/tex]
The formula for the volume of a sphere is Upper V equals four thirds pi r cubedV=
4/3πr3, where r is the radius of the sphere. The steel ball to the right is in the shape of a sphere and has a diameter of 3030 millimeters.
a. Find the exact volume of the sphere.
b. Find a 2-decimal-place approximation for the volume.
After calculating, the volume of the sphere obtained will be equal to V = 1.45 × 10¹⁰ mm³.
What is Volume?Every three-dimensional item takes up space in some way. The volume of this area is what is used to describe it. The area covered within an entity's three-dimensional bounds is referred to as its volume. The object's size is another name for it.
As per the given data in the question,
The formula for the volume of the sphere is given as,
V = 4/3 π r³
Diameter = 3030 mm
r = D/2
r = 3030/2
r = 1515 mm
So, the volume will be,
V = 4/3 π (1515³)
V = 1.45 × 10¹⁰ mm³
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Nicholas volunteers at a local soup kitchen and he notices how quickly the kitchen is going through its stock of canned goods. Below is the graph representing the data Nicholas found. Find the slope and y-intercept of the line.
Answer:
m=-63 b=825
Step-by-step explanation:
The slope of the line would be - [m] = - 63 and the [y] intercept is - [c] = 835.
What is the general equation of straight line? What is a mathematical function, equation and expression?straight line : The general equation of a straight line is -[y] = mx + c
function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that Nicholas volunteers at a local soup kitchen and he notices how quickly the kitchen is going through its stock of canned goods.
It is given that a graph has number of days on the x - axis and number of canned goods on the y-axis. The line goes through points (2, 699) and (8, 321). The slope of the line can be written as -
[m] = (321 - 699)/(8 - 2)
[m] = -378/6
[m] = - 63
For the point (2, 699), we can write -
y = - 63x + c
699 = - 63 x 2 + c
699 = -126 + c
c = 699 + 126
c = 835
Therefore, the slope of the line would be - [m] = - 63 and the [y] intercept is - [c] = 835.
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{Complete question -
A graph has number of days on the x-axis and number of canned goods on the y-axis. A line goes through points (2, 699) and (8, 321).
Nicholas volunteers at a local soup kitchen and he notices how quickly the kitchen is going through its stock of canned goods. Below is the graph representing the data Nicholas found.
Find the slope and y-intercept of the line.}
if 2 pounds of strawberries cost 4.50 how much would 3 pounds cost
MARIA WALKED 4.035 KILOMETERES. WHAT IS 4.035 WRITTEN IN AS EXPANDED FORM ?
Answer:
[tex](4 \times 1)+(3 \times \frac{1}{100})+(5 \times \frac{1}{1000})[/tex]
Step-by-step explanation:
Given : MARIA WALKED 4.035 KILOMETERS.
To Find :WHAT IS 4.035 WRITTEN IN AS EXPANDED FORM ?
Solution :
Number = 4.035
The numbers after decimals when read from first to last has positions tenth , hundredth , thousandth and so ...
The number before the decimal part has positions ones , tens , hundreds and so on when read from last to first
Now 4 is at ones place
0 is at tenth place
3 is at hundredth place
5 is at thousandth place
So, Expanded form : [tex](4 \times 1)+(3 \times \frac{1}{100})+(5 \times \frac{1}{1000})[/tex]
what is r^m divided by r^m equal to.