What is the value of 8.3x10^4
Which is the completely factored form of 12x³-60x² + 4x - 20? 4(3x² - 1)(x - 5) 4x(3x² + 1)(x - 5) 4x(3x² - 1)(x + 5) 4(3x² + 1)(x - 5)
The completely factored form of 12x³-60x² + 4x - 20 can be expreesed as 4(3x² - 1)(x - 5).
How can the completely factored form be gotten?The concept that will be used here is factorization. The process of breaking or decomposing an entity (like a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number or matrix is known as factorization or factoring.
To solve this problem then we need to take out all the common ratios :
12x³ - 60x² + 4x - 20
The we can factor 4 out as;
=[ 4(3x³ - 15x² + x - 5)]
The we can factorize the inner brackets as:
[3x³ - 15x² + x - 5]
The we will have this
= [3x²(x - 5) + (x - 5)]
Then we can now express as
= (3x² + 1)(x - 5)
Therefore, option A is correct.
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state if the two triangles are congruent and how
Correct option is B, the given triangles are congruent by LL.
Theorem LLAccording to the leg-leg theorem (LL theorem), if the legs of two right triangles are the same length, then the complete triangle must be congruent.
Keep in mind that in this instance, the shorter (non-hypotenuse) sides of the triangle are referred to as the "legs." Right triangle sides all adhere to a particular pattern known as the Pythagorean theorem, which is why this theorem holds true.
According to the Pythagorean theorem, the length of the hypotenuse, squared, equals the length of each of the two legs, squared. Congruence states that two triangles must have equal hypotenuses and equal legs in order to be congruent.
Thus, the side-side-side (SSS) theorem, which was previously mentioned, is simply condensed into the leg-leg theorem.
In the given triangles,
the base of the triangles is same
the height of the triangles is common,
So, by Leg - Leg theorem, triangles are congruent.
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What is the volume of this pyramid?
Answer: 5040
Step-by-step explanation: The equation for the volume of a pyramid is v=lhw/3
Answer:
Answer: 5040
Step-by-step explanation:
The volume of a triangular pyramid can be found using the formula V = 1/3AH where A = area of the triangle base, and H = height of the pyramid or the distance from the pyramid's base to the apex.
fill in the table using this function rule.
y=-10x-1
The table using this function rule is:
x y
-1 -9
0 1
1 11
5 51
How might a function rule be demonstrated?When the specified input values are applied, the function rule y = 2x+4 produces the output values displayed in the table. As of right now, the output numbers are denoted by and the input values are denoted by and. The function rule y = 3 x + 1 can therefore alternatively be represented as f (x) = 3 x + 1.
The connection between the input or domain and the output or range is called a function rule. When there is exactly one value in the range for each domain value, a relation is a function.
y = 10x+1
x = -1→y=10(-1)+1=-10+1→y=-9
x = 0→y=10(0)+1=0+1→y=1
x = 1→y=10(1)+1=10+1→y=11
x = 5→y=10(5)+1=50+1→y=51
x y
-1 -9
0 1
1 11
5 51
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The complete question is,
Use this function rule to complete the table's fields.
y = 10x + 1.
⎩
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎧
d(1)=
12
1
d(n)=d(n−1)⋅(−6)
What is the 4^{\text{th}}4
th
4, start superscript, start text, t, h, end text, end superscript term in the sequence?
The 4-th term in the sequence d(n) = d(n - 1) × (-6) is -2592
Consider the mentioned recursive function of a sequence :
d(n) = d(n - 1) × (-6) and d(1) = 12
To find the fourth term of the sequence i.e., when n = 4,
Since the sequence is a recursive sequence, in order to find d(4) first we need to find d(2) and d(3)
For n = 2,
⇒ d(2) = d(2 - 1) × (-6)
⇒ d(2) = d(1) × (-6)
⇒ d(2) = 12 × (-6)
⇒ d(2) = -72
For n = 3,
⇒ d(3) = d(3 - 1) × (-6)
⇒ d(3) = d(2) × (-6)
⇒ d(3) = (-72) × (-6)
⇒ d(3) = 432
For n = 4,
⇒ d(4) = d(4 - 1) × (-6)
⇒ d(4) = d(3) × (-6)
⇒ d(4) = 432 × (-6)
⇒ d(4) = -2592
Thus, the fourth term is -2592.
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The complete question is:
d(1) = 12,
d(n) = d(n - 1) . (-6)
What is the 4-th term in the sequence?
Amy deposits $100 into an account that earns simple Interest at an annual rate of 6.5%. How much interest will she earn after 4 years
Amy will earn $26 in interest after 4 years.
How to Calculate Simple Interest?Simple interest is a type of interest calculation where interest is only earned on the original principal (initial deposit) amount. It does not take into account any interest that has already been earned and is not compounded.
To calculate the simple interest earned on a deposit, you can use the formula: I = P * r * t, where I is the interest earned, P is the principal (initial deposit), r is the annual interest rate as a decimal, and t is the time in years.
In this case:
I = (100)(0.065)(4)
I = 26
The interest is: $26.
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an accounting professor wants to know the average gpa of the students enrolled in her class. she looks up information on blackboard about the students enrolled in her class and computes the average gpa as 3.29. a. determine whether the following statement is true or false. the population is all students enrolled in the accounting class. multiple choice 1 true false b. does the value 3.29 represent the population parameter or the sample statistic?
The population is all students in accounting class. 3.29 is sample statistic, not population parameter.
What is average ?
An average, also known as a mean, is a measure of central tendency that represents the typical value of a set of data. To calculate the average of a set of numbers, you add them up and then divide by the number of items in the set.
a. The statement "the population is all students enrolled in the accounting class" is true.
The population in this case refers to all the students who are currently enrolled in the accounting class and from which the sample is taken from.
b. The value 3.29 represents the sample statistic.
The sample statistic is a value that is calculated from a sample of data taken from the population. In this case, the average GPA of 3.29 is calculated using a sample of students enrolled in the accounting class, which is a subset of the population of all students enrolled in the accounting class. This value is used to make inferences about the population parameter, which is the true mean GPA of all students enrolled in the accounting class.
The population is all students in accounting class. 3.29 is sample statistic, not population parameter.
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514
4
Which expression is equivalent to
O 16 45
O√√25
02
04
4
4
112
14
712
?
The expression is equivalent to 2, and option C is correct.
What is simplification?To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. By eliminating all common factors from the numerator and denominator and putting the fraction in its simplest/lowest form, we can simplify fractions.
Given expression
[tex](\frac{4^{5/4} 4^{1/4} }{4^{1/2} } )^{1/2}[/tex]
using properties,
aⁿ/aˣ = aⁿ⁻ˣ
aⁿaˣ = aⁿ⁺ˣ
(aⁿ)ˣ = aⁿˣ
so expression is
[tex]({4^{5/4} 4^{1/4} }{4^{-1/2} } )^{1/2}[/tex]
adding powers
5/4 + 1/4 - 1/2 = 6/4 -1/2
5/4 + 1/4 - 1/2 = 1
substitute the values,
expression is, √4 = 2
Hence option C is correct.
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Written as a product of its prime factors, 540 = 2² x 3³ x 5.
Find the smallest positive integer k such that 540k is a perfect cube.
The smallest positive integer k such that 540k is a perfect cube is 8.
What is perfect cube? How to find smallest positive integer in perfect cube?A perfect cube is an integer (whole number) that is the result of cubing another integer. Cubing an integer is the same as multiplying it by itself three times. For example, 8 is a perfect cube because it is the result of cubing 2 (2 x 2 x 2 = 8). The smallest positive integer in a perfect cube is 1, because it can be achieved by cubing the integer 1 (1 x 1 x 1 = 1). To find the smallest positive integer in a perfect cube, you must first determine what the cube is. To do this, you can use the formula c^3 = a, where c is the cube root of a. This formula can be solved to find c, which is the cube root of a, or the number that was cubed to get a. Once c is determined, the smallest positive integer in the cube is c^3, or c cubed. For example, let's say you want to find the smallest positive integer in the cube of 27. You would first use the formula c^3 = 27 to find c, which is 3. Then, you would use the formula c^3 = a to calculate the smallest positive integer in the cube, whichTo learn more about perfect cube refer to:
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Diane deposits $400 into an account that pays simple interest at a rate of 5% per year. How much interest will she be paid in the first 2 years
(7th grade math)
Answer:
Simple interest is calculated by multiplying the principal (the initial amount of money deposited), the interest rate, and the number of years the money is on deposit.
To find out how much interest Diane will be paid in the first 2 years, we need to calculate the total interest earned over that time period.
First, we find the interest rate by multiplying the annual interest rate of 5% by .01 (to convert the percentage to decimal form)
0.05 * .01 = 0.05
Next, we find the total interest earned by multiplying the principal (400), the interest rate (0.05), and the number of years (2)
400 x 0.05 x 2 = 40
So, in the first 2 years, Diane will be paid $40 in interest on her deposit of $400.
Answer:
in total, Diane will be paid $20 + $40 = $60 in interest over the first 2 years.
Step-by-step explanation:
Simple interest is calculated as:
I = Prt
where:
I = Interest
P = Principal (initial amount deposited)
r = Interest rate (expressed as a decimal)
t = Time (in years)
So in this case, with a principal of $400 and an interest rate of 5% (or 0.05 as a decimal), the interest paid in the first year would be:
I = $400 * 0.05 * 1 = $20
And in the second year, it would be:
I = $400 * 0.05 * 2 = $40
So in total, Diane will be paid $20 + $40 = $60 in interest over the first 2 years.
what is (8/9)^2 pls help i need it right now
Answer:
0.7901
Step-by-step explanation:
the equation 2(c^2+d^2)x^2+(c-d)x+9=0 has imaginary roots if
(a)c>d (b)c -d
The equation has an imaginary root when (b) c = d
How to determine when the equation has an imaginary rootFrom the question, we have the following parameters that can be used in our computation:
2(c^2+d^2)x^2+(c-d)x+9=0
At the point of imaginary root, we have
b^2 < 4ac
This means that
(c - d)^2 < 4 * 2(c^2+d^2) * 9
So, we have
c^2 + d^2 - 2cd < 72c^2 + 72d^2
Evaluate the like terms
71c^2 + 71d^2 + 2cd > 0
Using a graphing calculator, we have
c = d
Hence, the solution is (b) c = d
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ii. (2 points) you put the coin back, take another, and flip it 4 times. it lands t, h, h, h. how likely is the coin to be type h50?
If the coin is tossed four times , then the probability of getting exactly two heads and two tails is 3/8 .
the number of outcomes in tossing a coin is = 2 = {H , T} ;
the number of outcomes in tossing the coin four times is = 2⁴ = 16 ;
we have to find the probability of getting exactly 2 heads and 2 tails :
So , the required outcomes will be = {HHTT, HTHT, HTTH, THHT, THTH , TTHH} ;
the number of favorable outcomes is = 6 ;
the probability is = 6/16 = 3/8 .
Therefore , the required probability is 3/8 .
The given question is incomplete , the complete question is
If a coin is tossed 4 times, what is the probability of getting exactly two heads and two tails ?
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A line is perpendicular to y = −1/3x + 7
and intersects the point (4,2).
What is the equation of this
perpendicular line?
y = [?]x + [ ]
Hint: Use the Point-Slope Form: y - y₁ = m(x - X1)
Then write the equation in slope-intercept form.
A line that is perpendicular to the line y = -1/3x + 7 has a slope that is the negative reciprocal of -1/3 which is 3.
We know that the line intersects the point (4,2), so we can use this point and the slope to write the equation of the line in point-slope form:
y - y1 = m(x - x1)
where (x1, y1) is the point the line passes through, m is the slope, and y and x are the coordinates of any point on the line.
So the equation of the line that is perpendicular to y = −1/3x + 7 and intersects the point (4,2) is:
y - 2 = 3(x - 4)
Simplifying this, we get
y = 3x - 2
To convert this to the slope-intercept form we can rewrite it as
y = 3x + b
Therefore, the equation of the line that is perpendicular to y = −1/3x + 7 and intersects the point (4,2) is y = 3x - 2
A parabola has vertex (2,3) and contains the point (0,0). Write and equation for this parabola
The equation of the parabola with a vertex (2,3) and contains the point (0,0) is: y = -3/4(x - 2)² + 3
How to write the equation of parabolaParabolic equitation or Quadratic equation with a vertex (2,3) and contains the point (0,0) is written using the vertex form of the equation which is:
(x - h)² = 4P (y - k)
OR
standard vertex form, y = a(x - h)² + k where a = 1/4p
The vertex
v (h, k) = (2, 3)
h = 2
k = 3
substitution of the values into the equation gives
y = a(x - 2)² + 3
considering the parabola passed the point (0, 0)
y = a(x - 2)² + 3
0 = a(0 - 2)² + 3
-3 = a(4)
a = -3/4
substituting for a
y = -3/4(x - 2)² + 3
hence the required equation is y = -3/4(x - 2)² + 3
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75 km= Every car in the USA is fitted with a milometer. The milometer shows the total distance a car has travelled. Evan is a salesman. miles 120 This is the reading on his car's milometer at the start of one week. 125465 miles This is the reading on his car's milometer at the end of the week. 126335 miles How many kilometres has Evan travelled in this week? a b Evan is paid 20 cents for each kilometre he travels. This is to pay for the fuel he uses. Evan works out that, in this week, he will be paid more than $250 for the fuel he uses. Is Evan correct? Explain your answer. Sim-
Evan's earnings for the fuel he uses in the week are $1515.07597, which is more than $250. So Evan is correct that he will be paid more than $250 for the fuel he uses.
How to convert miles to kilometers?To convert miles to kilometers, we can use the conversion factor 1 mile = 1.609344 kilometers. Therefore, to convert the milometer readings to kilometers, we can multiply them by 1.609344:
Start of the week reading in kilometers: 120 miles * 1.609344 km/mile = 193.12128 km
End of the week reading in kilometers: 125465 miles * 1.609344 km/mile = 201788.50112 km
The distance Evan has traveled in the week can be calculated by subtracting the start of the week reading from the end of week reading:
Distance traveled in the week: 201788.50112 km - 193.12128 km = 7575.37984 km
Therefore, Evan has traveled 7575.37984 km in the week.
To calculate Evan's earnings for the fuel he uses, we can multiply the distance traveled in the week by the payment rate of 20 cents per kilometer:
Earnings for the week: 7575.37984 km * $0.20/km = $1515.07597
Therefore, Evan's earnings for the fuel he uses in the week are $1515.07597, which is more than $250. So Evan is correct that he will be paid more than $250 for the fuel he uses.
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For each equation, write a story problem that could be represented by the equation. Then find the value of x and explain what it represents in your story. 3/4 + x = 2
The story: John requires 2 liters of oil for a trip. they have 3/4 liters of oil at home, how many liters of oil will he get from his father to make the trip?
x in the equation is the liters of oil required from the father. It was solved to be 1 1/4
How to solve for xIn the problem, the equation made available is 3/4 + x = 2
The solution of the equation is as follows
3/4 + x = 2
collecting like terms
x = 2 - 3/4
x = 5/4
x = 1 1/4
The value of x = 1 1/4
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What is the scale factor from Figure A to Figure B?
The scale factor of figure A to fig B is 1 : 4
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
Figure A is the small triangle and figure B is the small triangle.
The ratio of the corresponding lengths of the triangles must give thesame value.
scale factor = original length/ new length
scale factor = 14/56 = 1/4 = 1 : 4
also , 16/64 = 1/4 = 1:4
7/28 = 1/4 = 1:4
therefore since the ratio of all the sides are equal, the scale factor of figure A to fig B is 1:4
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what is the sum in the simpelest form
4 1/2 + 1 3/5
Find the sum of -3x+9 and 7x2-2x+1
The sum of the given expressions -3x + 9 and 7x^2 - 2x + 1 is
= 7x^2 - 5x +10
What is Algebraic expression ?
Algebraic expression can be defined as the combination of variables and constants.
Given expressions are ,
-3x + 9 and 7x^2 - 2x + 1
So,
The sum of the expressions could be
= -3x+9 + 7x^2 - 2x + 1
= 7x^2 -3x-2x + 9+1
=7x^2 - 5x +9+ 1
= 7x^2 - 5x +10
Hence, The sum of the given expressions -3x + 9 and 7x^2 - 2x + 1 is
= 7x^2 - 5x +10
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Select all inequalities that include 7 in the solution set
The inequalities that include 7 in the solution set are;
D) -3 - x < -9
E) ¹/₂(x + 3) ≥ 2
How to solve Inequality expressions?A) -6 + x ≤ 5
Add 6 to both sides using addition property of equality to get;
x ≤ 11
B) 11 - x ≥ 7
Add x - 7 to both sides to get;
4 ≥ x
C) 3(2x - 9) > 15
Expand the bracket to get;
6x - 27 > 15
Add 27 to both sides to get;
6x > 42
Divide both sides by 6 to get;
x > 7
D) -3 - x < -9
Add 9 + x to both sides to get;
6 < x
E) ¹/₂(x + 3) ≥ 2
Multiply both sides by 2 to get;
x + 3 ≥ 4
Subtract 3 from both sides to get;
x ≥ 1
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Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
=====================================
Work Shown:
[tex](\text{x}-7)^2 = 36\\\\\sqrt{(\text{x}-7)^2} = \sqrt{36}\\\\\text{x}-7 = \pm\sqrt{36}\\\\\text{x}-7 = \pm6\\\\\text{x}-7 = 6 \ \text{ or } \ \text{x}-7 = -6\\\\\text{x} = 6+7 \ \text{ or } \ \text{x} = -6+7\\\\\text{x} = 13 \ \text{ or } \ \text{x} = 1\\\\[/tex]
-------------
Check:
Plug in x = 13
[tex](\text{x}-7)^2 = 36\\\\(13-7)^2 = 36\\\\(6)^2 = 36\\\\36 = 36 \ \ \checkmark\\\\[/tex]
This confirms x = 13
Now check x = 1
[tex](\text{x}-7)^2 = 36\\\\(1-7)^2 = 36\\\\(-6)^2 = 36\\\\36 = 36 \ \ \checkmark\\\\[/tex]
The value x = 1 is confirmed as well.
Both solutions are confirmed.
Calculate the amount of the child and dependent care credit allowed before any tax liability limitations or other credits for 2019 in each of the following cases, assuming the taxpayers had no income other than the stated amounts. William and Carla file a joint tax return. Carla earned $27,500 during the year, while William attended law school full-time for 9 months and earned no income. They paid $3,500 for the care of their 3-year-old child, Carl
Carla earned $27,500 during the year, while William attended law school full-time for 9 months and earned no income. They would not get dependent child care credit.
Credit for dependent care:
A married couple or single person who cares for his or her own or dependent child can earn this dependent care credit.
'The dependent tax credit is non-refundable.
* General credit qualifications.
- Employment-related care cost is required for a
= dependent under the age of 13 or
A dependent or spouse who lives with the taxpayer for more than half the year and is physically or mentally incapacited.
* amount of credit.
* applicable percentage - eligible care cost
- the appropriate percentage ranging from 20% to 35% depending on AGI
If your income is less than $15,000, the rate will be 35%. Income above $15,000 will decrease by 1% for every 2000.
* To get credit, married taxpayers must file a joint return.
*the cost of eligible care has been defined.
- costs for qualified individual care within the taxpayer's homr or outsider's home.
= if outside the home, the dependent or spouse must spend at least 8 hours per day within the taxpayer's home.
= unless the relative is a child under the age of 19, child care payments to a relative are eligible for the credit.
- The amount of costs that qualify is the lower of the actual cost or 3000 for one qualified individual and 6000 for two or more qualified individuals.
* Limitation on earned income.
- The amount of eligible care costs may not exceed the lower of the taxpayer's or spouse's earned income.
- Full-time students, disabled taxpayers, and spouses are deemed to have earned income up to the monthly limits of $250 for one child and $500 for two.
William and carla submit a combined tax return.
Carla earned $27,500 last year.
William attended law school full time for 9 months without earning any money.
They paid $3,500 for carl, their 3 year old child.
William and Carla are ineligible for dependent care credit. Because they should both have employment income.
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The length of the rectangle i 5 more than the ide of a quare and the width of the rectangle i 5 le than the ide of the quare . If the area of the quare i 45 what i the area of the rectangle
The area of the rectangle is 20 square unit.
Let the length and width of the rectangle are respectively l and w.
Let another side of square is a.
Given that length of the rectangle is 5 more than the side of square.
l = a + 5
The width of the rectangle is 5 less than the side of the square.
w = a – 5
Given that the area of square is 45 square unit.
So, a² = 45
Now calculate the area of rectangle:
Area of rectangle = l * w
= (a + 5)(a - 5)
= a² - 25
= 45 – 25
= 20
Therefore, the area of rectangle is 20 square unit.
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Suppose the radius of a circle is 2 units. What is its circumference?
Use 3.14 for and enter your answer as a decimal
Answer:
Step-by-step explanation:
Solve the system of equations by multiplying first. Enter the solution as an ordered pair.
2x + 8y = 36
5x − 4y = 18
the ordered pair solution
(?,?)
The value of x will be 6, while the value of y will be 3 in the given pair of the ordered equation.
As we have,
The pair of equations as:
2x + 8y = 36 -----------------(i)
5x − 4y = 18 -----------------(ii)
From above,
We can see that in the first equation the coefficient of x is 2 while in the second one, the coefficient of x is 5.
So, for solving the given sets of equation we need to first equalise the co-efficient of x in both the equations.
So, to make the coefficient equal we will multiply the first equation by 5 and the second equation by 2.
Thus we will get the set of equations as:
10x+40y=180--------(iii)
10x-8y=36------------(iv)
From (iii) and (iv), Now subtracting the (iv) from (iii),
We will get it as:
48y = 144
y = (144/48) = 3
Now for getting the value of x, we will put the value of y in the first equation.
Thus, we will get it as:
2x+24=36
=>2x=12
=>x = (12/2)=6
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PLEASE HELP!! 100 POINTS!
A line has a slope of –2/5 and a y-intercept of –2/5. Write its equation in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Step-by-step explanation:
The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept.
Given that the slope of the line is -2/5 and the y-intercept is -2/5. We can substitute these values into the equation:
y = -2/5x + -2/5
y = -2/5x - 2/5
The equation in slope-intercept form is y = -2/5x - 2/5.
cam signed up to run a 15-kilometer running race. what distance in miles will she have ran when she finishes?
Cam can run 9.3205 miles when she finishes.
mile, any of several distance measurements, such as the statute mile of 5,280 feet (1.609 km). It was derived from the Roman mille passus, or "thousand paces," which was equivalent to 5,000 Roman feet.
The term "mile" is derived from the Latin "mille passus," which means "one thousand paces," and a mile was 1,000 Roman strides, with a stride equaling two steps. In 1592, the English Parliament standardised the Mile measurement at eight furlongs (660 feet).
Cam signed up to run a 15-kilometre running race.
So, here, we will convert kilometers to miles-
I kilometer is =0.621371 miles
And, I mile =1.609344 kilometres.
Thus, converting kilometres to miles.
Simply multiply the Number of kilometres by 0.62137.
Therefore, 1 kilometre =0.621371 miles
1.5 kilometer=15*0.621371 miles =9.32057 miles
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I’ll give brainliest
Which function is NOT linear
f(x) = -1/x is not a linear function.
Option (B) is correct,
What is a function?
A function is a mathematical relationship between two sets of quantities, called the domain and the range. In other words, a function is a rule that assigns to each element of a set (called the domain) exactly one element of another set (called the range). The most common way to represent a function is using an equation of form f(x) = y, where x is the input variable (or independent variable) and y is the output variable (or dependent variable).
A linear function is a function whose graph is a straight line. A linear function can be represented by an equation of the form f(x) = mx + b, where m and b are constants.
Out of the given options, the function which is not linear is B) f(x) = -1/x
This function is not linear because it's graph is not a straight line.
All the other options are linear functions, option A) f(x) = x/4 is a function with a slope of 1/4, option C) f(x) = 2x + 1 is a function with a slope of 2, and option D) f(x) = -3 is a constant function with a slope of 0.
Hence, f(x) = -1/x is not a linear function.
Option (B) is correct.
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