Step-by-step explanation:
(f○g)(x) = f(g(x))
it simply means that we put the expression of g(x) into ask places of x in f(x).
(f○g)(x) = g(x)² + 3
therefore,
g(x)² + 3 = 9x² - 12x + 7
g(x)² = 9x² - 12x + 4 = (a + b)² = a² + 2ab + b²
9x² = a² tells us that a = ±3x
4 = b² tells us that b = ±2
which signs of a and b do we need ?
-12x = 2ab gives us the answer
-6x = ab
that means the signs need to be opposite and we have 2 possible solutions
g(x) = 3x - 2
or
g(x) = -3x + 2
Tammy has a rectangular rug with an area of 28 square feet. The rug is 12 feet
longer than it is wide.
The equation to determine the length and width of the rug is
28 = w² + 12w
Since, the shape of the rug is rectangle, therefore area of rectangle has been used to obtain the solution.
What is a rectangle?
Rectangle is a flat, two-dimensional shape, having four sides and vertices with opposite sides being equal and parallel. We may easily represent a rectangle in an XY plane by using its length and breadth as the arms of the x and y axes, respectively.
Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.
We are given a rectangular rug with an area of 28 square feet.
Also, the rug is 12 feet longer than it is wide.
So,
Let 'l' be the length of the rug and 'w' be the width of the rug
As given, Length is 12 feet longer than its width
Therefore, l = w + 12
We know Area of rectangle = Length * Width and area is given to be 28 square feet.
So,
⇒28 = (w + 12)w
⇒28 = w² + 12w
Hence, the equation to determine the length and width of the rug is
28 = w² + 12w.
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Question: Tammy has a rectangular rug with an area of 28 square feet. The rug is 12 feet longer than it is wide.
Create an equation to determine the length and the width of the rug.
Why is mole Avogadro's number?.
The numerical value of both the mole and Avagadro’s number is 6.022 x 10²³. That is why the mole is also called Avogadro's number.
The Avogadro constant, A, is the number of particles (such as atoms, molecules, or ions) in one mole of something. Its value is modernly defined as exactly 6.022 140 76 × 10²³. (As it is a pure number, it has no units.)
So, in 1 mol of helium, which has a mass of (very close to) 4 g, there are A
atoms; in 1 mol of sucrose, with a mass of 342 g, there are A molecules.
We can have moles of other kinds of things, including subatomic particles. The amount of charge known as the faraday is the charge of one mole of electrons (A of them; about 96 500 C).
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Suppose that y varies jointly with w and x and inversely with z and y = 150 when w = 5, x = 15 and z = 3. Write the equation that models the relationship. Then find y when w = 3, x = 2 and z = 2.
sorry for bad handwriting :)
Evaluate 0.5^3 and 0.5^-3 as fraction
Answer:
Step-by-step explanation:
0.5^3 = 0.5*0.5*0.5
= 0.125
= 125/1000
= 1/8.
0.5^-3
= 1 / 0.5^3
= 1 / 1/8
= 8.
How do you find the median of a modal class in class 10?.
In such cases, the median may give a better idea about the central part of the distribution. In case of a skewed distribution like seen in case of wage distribution ,
income distribution, wealth assessment, mean loses its representation of the data.
Moreover, in case of qualitative data or for any ordinal data where the variable under question is not directly measurable, say when you are trying to measure intelligence, honesty, color, median would be a good choice to represent that data.
We can find the median of class 10 through class frequency C.f. (CUMULATIVE FREQUENCY)
0to10. 3. 3
10 to 20. 7 10
20to 30. 10 20
30 to 40 8 28
40 to 50. 6. 34
Total. 34
N=34
N/2 = 34/2 =17
MEDIAN class=20 to 30
C =10
L lower boundary of MEDIAN class =20
f=10
m=10
MEDIAN =L +( N/2 -- m) ×c) /F
=20+ (17-10)×10. /10
= 20+ 7=27
MEDIAN=27
It is known that median is a positional average such that you consider the number of observations above and below are almost equal hence it is not damaged by extreme values unlike in the case of mean where it is damaged the most.
In brief, for any qualitative data or in case of numerical data where the distribution is skewed, Median is the most taken average.
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Answer:
Step-by-step explanation:
In such cases, the median may give a better idea about the central part of the distribution. In case of a skewed distribution like seen in case of wage distribution , income distribution, wealth assessment, mean loses its representation of the data.
Moreover, in case of qualitative data or for any ordinal data where the variable under question is not directly measurable, say when you are trying to measure intelligence, honesty, color, median would be a good choice to represent that data.
We can find the median of class 10 through class frequency C.f. (CUMULATIVE FREQUENCY)
0to10. 3. 3
10 to 20. 7 10
20to 30. 10 20
30 to 40 8 28
40 to 50. 6. 34
Total. 34
N=34
N/2 = 34/2 =17
MEDIAN class=20 to 30
C =10
L lower boundary of MEDIAN class =20
f=10
m=10
MEDIAN =L +( N/2 -- m) ×c) /F
=20+ (17-10)×10. /10
= 20+ 7=27
MEDIAN=27
It is known that median is a positional average such that you consider the number of observations above and below are almost equal hence it is not damaged by extreme values unlike in the case of mean where it is damaged the most.
In brief, for any qualitative data or in case of numerical data where the distribution is skewed, Median is the most taken average.
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Ryann ha $800 to pend on gift. She alreadt decided to ue $25 for a carf for her grandmother. She want to pend the remaining money to purchae gift for her four friend. She will pend the ame amount of money on each friend gift. What i the mot he can pend on each friend
The most are $13.75 if she wants to give all of her friends a gift.
Ryan has an $800 present budget. She had already made up her mind to use $25 to buy her granny a vehicle. The remaining funds will be used to buy gifts for her four friends. She will invest the same sum of money in each present for a buddy.
Okay, so she would have 55 dollars left over after spending 25 of her 80 dollars.
She will distribute her 55 bucks among her four buddies equally now that she has them.
55/4 = 13.75
She could only afford to offer them a maximum of $13.75
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Find the missing side length.
The missing length is 14 yards from the given figure.
What is Quadrilateral ?
A quadrilateral is a closed form and a form of polygon that has 4 sides, 4 vertices and 4 angles. it's miles formed via joining four non-collinear points. The sum of indoors angles of quadrilaterals is continually identical to 360 tiers.
The word quadrilateral is derived from the Latin phrases ‘Quadra’ which means four and ‘Latus’ means ‘sides’. It is not essential that every one the four aspects of a quadrilateral are equal in length. therefore, we are able to have distinct kinds of quadrilaterals primarily based on aspects and angles.
Given ,
from the figure,
It was mentioned to find the missing length
As when we add up two sides we get the missing length from the given figure.
missing length = 9 + 5
missing length = 14 yards.
So, missing length is 14 yards
Therefore, the missing length is 14 yards from the given figure.
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(05. 01 LC)
The following data et how the pule rate of ome cattle at a farm:
65,68,69,67,69,68,65,69,65,68,67,69,68,67,67,69
Which plot bet repreent the data?
The dot plot that represents the data for pulse rate of some cattle at a farm is shown in the image below.
A dot plot, also known as a strip plot or dot chart, is a simple form of data visualization that consists of data points plotted as dots on a graph with an x- and y-axis
How to Construct a Dot Plot?
Given the data as: 65, 68, 69, 67, 69, 68, 65, 69, 65, 68, 67, 69, 68, 67, 67, 69, find the frequency of each data point in the data set as shown below:
65 - 3
67 - 4
68 - 4
69 - 5
Use dots to represent the frequency of each data point.
Thus, the dot plot that represents the data is shown in the image below.
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How do you find the inverse of a function in standard form?.
The inverse of a function in standard form can be determined by substituting the function in the standard form
Every function does not have an inverse. A function needs to be a one-to-one function, which means there can't be repeated output for distinct inputs, in order to have an inverse. When a quadratic function is in vertex form, if the leading coefficient (a) is not zero, the function has an inverse. The various steps to find the inverse of a function in standard form can be noted as -
The function should first be written in standard form as follows: y = f(x) = a*x + b, where a and b are constants.Substituting y for x and x for y in the equation: x = f(y)(a*y + b)(y)Isolate y on one side of the equation and solve for it: y = (x-b)/aIf required, make the equation simpler.The original function f(x) = a*x + b is now the inverse function f-1(y) = (x-b)/a.Read more about standard form on:
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Which expression is equivalent the one seen in the image
Answer: option 1
Step-by-step explanation: as when you try to simplify you get the values in option 1
Answer: 1
Step-by-step explanation:
The sum of Georges's age and his father's age is 60 years. In 6 years, George's father will be twice as old as George will be. How old are gorge and his father now?
Answer:
Father:42
Son:18
Step-by-step explanation:
Present ages are father 48–6= 42
son = 24 ‘6 = 18
What is one one function also called?.
The one-to-one function is also called the injective function.
The one-to-one function is a special function that maps every element of the range to exactly one element of its domain.
we can define one to one function as:
function g: D -> F is said to be one-to-one if
g(x₁) = g(x₂)
⇒ x₁=x₂
for all elements x₁ and x₂ ∈ D., A one-to-one function is also considered an injection, a function is injective only if it is one-to-one.
There are some examples of injective functions:
The identity function X → X is always injective.If function f: R→ R, then f(x) = 2x is injective.If function f: R→ R, then f(x) = 2x+1 is injective.To know more about the Injective function:
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so like i nee help asap
Step-by-step explanation:
[tex] {h}^{2} + {r}^{2} = {l}^{2} \\ {h}^{2} = {l }^{2} - \: {r}^{2} \\ {h }^{2} = {13}^{2} - {12}^{2} \\ {h}^{2} = 169 - 144 \\ {h}^{2} = 25 \\ h = 5[/tex]
:. h = 5 in ...
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Determine if each expression is or is not equivalent to −0.5g + 2.5.??
where is the expressions?
How do you plot 3 coordinates?.
We'll begin with a three-dimensional coordinate system where the x-axis comes toward us on the left.
The y-axis moves out toward the right, and the z-axis is absolutely vertical in order to plot points in three-dimensional coordinate space. When we need to take into account negative values of x, y, or z, then we should be aware that the negative x-axis moves out to the left.
The negative y-axis moves out to the right, and the negative z-axis is absolutely vertical and extends out below the positive z-axis.
In three-dimensional space, up until we reach our coordinate point, we advance along the x-axis, then parallel to the y-axis, then parallel to the z-axis.
Similar to how we find our point by going parallel to the y-axis after moving outside along the x-axis to our x value in two-dimensional coordinate space.
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can someone please help me with this math problem it is listed in the picture!
Answer: I think that the answer for that is fh
Step-by-step explanation:
1. the solution set of an inequality ×-2 ×+3>0 is
A. (2,3) C, (-infinity,-3)U (2,infinity)
B, (-Infinity,3) U (-2,infinity) D, (- ♾, -2) U (3, ♾)
The solution set of the inequality x - 2 × + 3 > 0 is (-Infinity,3) U (-2,infinity).
What is inequality?
An inequality is a mathematical statement that represents a relationship between two values that are not equal. It uses symbols such as < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), to describe the relationship between the values.
Isolate the variable x:
x - 2 × + 3 > 0
x - 2 × + 3 - 3 > 0 - 3
x - 2 × > -3
Divide both sides by -2 and reverse the inequality sign:
(x - 2 ×)/(-2) < (-3)/(-2)
x - 2 × < 3
x > 2 × + 3
Test values of x to see which ones make the inequality true:
If x is less than -2, the inequality is false.
If x is between -2 and 3, the inequality is true.
If x is greater than 3, the inequality is false.
So the solution set of the inequality x - 2 × + 3 > 0 is (-Infinity,3) U (-2,infinity).
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unit 1 geometry basics homework 2 segment addition postulate
The geometry questions attached are: UV = 67, x = 67, BD = 88, BC = 26 and CD = 61
What is meant by line segment?In contrast to a line, which can be extended endlessly on both ends, a line segment has endpoints.
An area or portion of a line with two endpoints is known as a line segment. A line segment has a set length as opposed to a line. Both metric measurements, such as millimeters and centimeters, as well as conventional units, such as feet or inches, can be used to measure the length of a line segment.
A line segment, in geometry, is a portion of a straight line that is constrained by two clearly defined end points and contains every point on the line that is situated in between those endpoints. The Euclidean distance between two line segments' ends determines the length of the segment.
5.)
UW = 6x - 35
UW = UV + VW (total length of a line segment)
UV = 19
VW = 4x - 20
6x - 35 = 19 + 4x - 20
simplifying the above equation, we get
6x - 4x = 19 - 20 + 35
2x = 34
x = 34 / 2
x = 17
UW = 6x - 35 = 6(17) - 35 = 67
6.)
HJ = 7x - 27
HJ = HI + IJ (total length of a line segment)
Substitute the values in the above equation, we get
7x - 27 = 3x - 5 + x - 1
simplifying the above equation, we get
7x - 3x - x = - 5 - 1 + 27
3x = 21
x = 21 /3
x = 7
7.)
BD = 7x - 10, BC = 4x - 29 and CD = 5x - 9
BD = BC + CD (total length of a line segment)
7x - 10 = 4x - 29 + 5x - 9
simplifying the above equation, we get
7x - 4x - 5x = - 29 - 9 + 10
-2x = - 28
x = 14
Therefore, the geometry questions attached are:
BD = 7(14) - 10 = 88
BC = 4(14) - 29 = 27
CD = 5(14) - 9 = 61
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What is the value of K in the polynomial 3x2 2kx 3?.
A formula with just one phrase where the unknown is squared and no terms where the unknown is raised to a power greater than 2 assumed: 3x* + 2kx+ 3= when compared to the quadratic equation ax2 + bx + c = 0, a = 3 b= 2kc= 3.
Given that the equation's roots are genuine and equal D=0 Discriminant, hence D = b2 - 4ac = 0 (2k) - 4.3.3 = 0 4k -36 = 0 4k -36 = 0 4k2 = 36 k'=9 taking square root on both sides k=3 or k=-3 as a result, the roots of the quadratic equation are real and equal for the values of k of 3, and -3.
When a polynomial is evaluated at x=2, the outcome is zero if the polynomial is divisible by (x-2). Therefore, we can substitute x = 2 into the polynomial 2kx-kx-8 and solve for k to find the value of k.
2k(2)^-k(2)-8 = 0 2
k(0.25) - 8 =0\s
k(0.25) = 8\sk=32 = 4
Therefore, k must be equal to 4 for the polynomial 2kx-kx-8 to be divisible by (x-2).
Complete question:
What is the value of K in the polynomial 3x2 2kx 3 The roots of the quadratic equation 3x2 2kx 27 are real and equivalent.
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The value of k when x = (-1/2) is a solution of the quadratic polynomial 3x² + 2kx - 3 = 0 is -2.
To find the value of k, we can substitute the value of x = (-1/2) into the equation and solve for k. So, we have:
3 * (-1/2)² + 2k * (-1/2) - 3 = 0
Expanding the square and substituting the value of x gives us:
-3/4 + k * (-1/2) - 3 = 0
Simplifying the left-hand side of the equation gives us:
k * (-1/2) = 3/4 + 3
Finally, solving for k by dividing both sides by -1/2 and simplifying gives us:
k = -2
Hence, the value of k when x = (-1/2) is a solution of the quadratic equation 3x² + 2kx - 3 = 0 is -2.
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Complete Question:
If x=(− 1/2), is a solution of the quadratic equation 3x^2 +2kx−3=0, find the value of k.?
Hey i dont know leave step by step
The exponential function f (t) = e is a mathematical function that describes a relationship between a number and its power.
What is the value for b?It is also known as the exponential growth function, as it models the continuous growth of a quantity over time.The exponential function f (t) = e can be expressed in the form f (t) = b, where b is a constant. The constant b is the base of the exponential function and determines how quickly the quantity grows or decays. The value of b for the exponential function f (t) = e is 2.718281828459045. This constant can be derived using the Taylor series expansion of the exponential function. The Taylor series is an infinite sum of terms, where the terms are the derivatives of the exponential function at the origin.The value of b for the exponential function f (t) = e is important because it helps to determine the rate of growth or decay of a quantity over time. Knowing the value of b for the exponential function allows us to easily calculate the value of a quantity at a given time, given its initial value. In summary, the value of b for the exponential function f (t) = e is 2.718281828459045. This constant can be derived using the Taylor series expansion of the exponential function and is used to determine the rate of growth or decay of a quantity over time.To learn more about The exponential function refer to:
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Find the value of each variable in the parallelogram. Round your answers to the nearest tenth, if necessary.
The value of each variable in a parallelogram can be found by measuring the lengths of the sides, the angles between the sides, and the area of the shape. The measurements should be rounded to the nearest tenth, if necessary.
The value of each variable in a parallelogram can be determined by taking measurements of the various components of the shape. The first step is to measure the lengths of the sides. These are typically labeled as a, b, c, and d. The angles between the sides can then be measured, which are typically labeled as A, B, C, and D. The area of the parallelogram can be calculated using the formula A=ab sin C. All of these measurements should be rounded to the nearest tenth, if necessary. Once all of the measurements have been taken, the values of the variables can then be determined. This is done by using the values found to solve for the unknowns in the formula. For example, if the lengths of the sides are known, the angles can be calculated using the Law of Cosines. Knowing all of the measurements of the parallelogram can allow you to solve for the values of the variables.
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The complete question is
Find the value of each variable in the parallelogram. Round your answers to the nearest tenth, if necessary labeled as A,B,C and D.
What is the difference between the largest 6 digit number and smallest 4 digit number?.
The difference between the largest 6-digit and the smallest 4-digit numbers is 998999.
The aim is to find the smallest 4-digit and largest 6-digit numbers, and then we need to determine the difference between these two values.
Let's start by finding the smallest 4-digit number.
We know that 0 is the smallest digit that can not be used in the highest place value, so we will consider the next smallest digit, 1; therefore, it can be used in the highest place value.
Thus, we can create the required 4-digit smallest number with 0 and 1.
Hence, the smallest 4-digit number is 1000.
Now, we will discover the largest 6-digit number.
As we know, the largest digit is 9, which can be used anywhere. So, we will form the largest 6-digit number with the digit 9.
Thus, the largest 6-digit number is 999999.
Now, find the difference between these two values.
So, we can determine the difference between the smallest 4-digit and the largest 6-digit numbers by subtracting the smallest from the largest.
Thus, we get,
⇒999999−1000
⇒998999
Hence, 9989999 is the difference between the smallest 4-digit and the largest 6-digit numbers.
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The store charges $12.65 for a 14 oz container of watermelon sugar scrub. How many ounces of watermelon sugar scrub do you get per dollar?
The ounces of the watermelon sugar scrub per dollars is 1.1 ounces per dollars.
How to find the ounces of watermelon per dollars?The store charges $12.65 for a 14 oz container of watermelon sugar scrub. The amount in ounces of watermelon sugar scrub per dollars can be calculated as follows:
12.65 dollars = 14 ounces
1 dollars = ?
cross multiply
Hence,
amount of ounces of watermelon sugar scrub per dollars = 14 × 1 / 12.65
amount of ounces of watermelon sugar scrub per dollars = 14/ 12.65
amount of ounces of watermelon sugar scrub per dollars = 1.10671936759
amount of ounces of watermelon sugar scrub per dollars = 1.1 ounces per dollars
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If y =sin x sec (90-x) , what is value of dy/dx of the previous ?
Answer:
We can use the chain rule to find the derivative of y with respect to x.
The chain rule states that if y = f(u) and u = g(x), then dy/dx = dy/du * du/dx
y =sin x sec (90-x)
dy/dx = cos x sec (90-x) * d/dx(sec (90-x)) - sin x tan (90-x) sec (90-x) * d/dx(90-x)
let us calculate the second derivative
du/dx = -cos(90-x)
d²y/dx² = -sin x sec (90-x) * cos (90-x) - cos x tan (90-x) sec (90-x) * cos (90-x) - cos x sec (90-x) * (-sin (90-x))
= -sin x sec (90-x) * cos (90-x) - cos x tan (90-x) sec (90-x) * cos (90-x) + cos x sec (90-x) * sin (90-x)
= -sin x sec (90-x) * cos (90-x) + cos x tan (90-x) sec (90-x) * sin (90-x)
= -(sin^2 x + cos^2 x) sec (90-x) tan (90-x)
= -sec^2 (90-x) tan (90-x)
So, the value of the second derivative of y with respect to x is -sec^2 (90-x) tan (90-x)
Step-by-step explanation:
What is the formula to find the nature of the roots of a quadratic equation?.
The roots of the quadratic equation are x and if they are the values of x that fulfill the quadratic equation. The equation (-b(b2-4ac))/2a yields roots. The discriminant determines the kind of roots.
Mathematical algebra includes solving quadratic equations. The equations that have at least one term that is squared or in square form are known as quadratic equations. The equation of the second degree is another name for quadratic equations.
The standard form of the quadratic equation is ax2 + bx + c = 0, where a, b, and c are real numbers or constants that do not equal 0, and x is an unknown variable whose value can only be determined by solving the equation using a variety of methods for solving quadratic equations. The two powers of x are equal to the square on x, and the nature of the roots can be real, estimated, or assumed.
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22. Four friends, Lerato, Jarrod, Ian and Tandeka, play a computer game in which they race a car around a circuit. Lerato takes 2 minutes, Jarrod takes 3 minutes, Ian takes 4 minutes and Tandeka takes 5 minutes to complete one circuit of the game. They play for a total of 12 minutes. a) If they play continuously and at the same rates, which one of the players will be in the middle of a circuit as the time runs out? b) After how many minutes did this player begin the last circuit? c) How many more games did Lerato play than Tandeka?
Answer:
a) Tandeka will be in the middle of a circuit as the time runs out.
b) Tandeka began the last circuit after 7 minutes.
c) Lerato played 2 more games than Tandeka.
Explanation:
a) To determine which player will be in the middle of a circuit when the 12 minutes are up, we need to figure out which player completes the most circuits in 12 minutes. We can use the formula: time available / time per circuit = number of circuits completed. In this case: 12 minutes / 2 minutes per circuit = 6 circuits for Lerato, 12 minutes / 3 minutes per circuit = 4 circuits for Jarrod, 12 minutes / 4 minutes per circuit = 3 circuits for Ian, 12 minutes / 5 minutes per circuit = 2.4 circuits for Tandeka. Tandeka completes 2 full circuits, and starts the third one, hence she will be in the middle of a circuit when the time runs out.
b) To determine when Tandeka began the last circuit, we need to figure out how many minutes were left when she completed the second circuit. We know that Tandeka completes 2 full circuits in 10 minutes (2 x 5 minutes). So, the last circuit starts after 12 minutes - 10 minutes = 2 minutes
c) To determine how many more games Lerato played than Tandeka, we can subtract the number of games Tandeka played from the number of games Lerato played: 6 games - 4 games = 2 games.
Step-by-step explanation:
What is the factor of 50?.
The factors of 50 are the natural numbers that divide the original number, evenly. They are 1,2,5,10,25 and 50.
Herbal numbers are a set of fine integers, frequently used for counting and ordering. They consist of the numbers 1, 2, 3, four, 5, and so on. The set of natural numbers is denoted by way of the symbol N. they are also called counting numbers. natural numbers are used in lots of regions of arithmetic, inclusive of number concepts and combinatorics.
They play a critical function in the look at algorithms and information structures. moreover, herbal numbers are used in lots of areas of physics and engineering, inclusive of the look at vibrations and waves. They may be also used in laptop technological know-how and programming, where they are regularly used to symbolize the number of objects in a listing or array. natural numbers are an essential idea in arithmetic, and they may be used in many areas of technological know-how, technology, and normal existence.
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What is the solution of |( 2x 3 )|= 7 *?.
The solution of |( 2x-3 )|= 7 is 5.
|(2x – 3)| = 7
2x = 7+3
2x = 10
x=5
In arithmetic, an equation is a system that expresses the equality of two expressions, by connecting them with the equals signal =. The phrase equation and its cognates in different languages may additionally have subtly one-of-a-kind meanings; as an example, in French, an équation is defined as containing one or more variables, whilst in English, any well-formed method together with expressions associated with an equals signal is an equation.
solving an equation containing variables includes figuring out which values of the variables make the equality real. The variables for which the equation must be solved are also called unknowns, and the values of the unknowns that fulfill the equality are called answers to the equation. There are kinds of equations: identities and conditional equations. An identity is real for all values of the variables. A conditional equation is handiest authentic for particular values of the variables.
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Complete Question:
What is the solution of |( 2x-3 )|= 7?
what is The quotient of a number and nine is lessthan the number. In algebraic expressions
Answer:
Step-by-step explanation:
The quotient is the result you get when dividing numbers.
Let the number be n then the expression is:
n / 9 < n.
can someone help me i don't know how to do this.
Graph −1/2x+1/8y=3/4.
[tex]-\cfrac{1}{2}x+\cfrac{1}{8}y=\cfrac{3}{4}\implies -\cfrac{x}{2}+\cfrac{y}{8}=\cfrac{3}{4}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{8}}{8\left( -\cfrac{x}{2}+\cfrac{y}{8}\right)=8\left( \cfrac{3}{4} \right)} \\\\\\ -4x+y=6\implies y=4x+6[/tex]
Check the picture below.
