Which binomial is a factor of f/x )= x³ 6x² +3x 10?
Factor (x+1) is the binomial factor for x³ - 6x²+ 3x + 10 using the rational roots test.
If a polynomial function has integer coefficients, then every rational zero will have the form p/q where p is a factor of the constant and q is a factor of the leading coefficient.
p = ±1, ±10, ±2, ±5
q = ±1
Find every combination of ± p/q . These are the possible roots of the polynomial function.
±1, ±10, ±2, ±5
Substitute −1 and simplify the expression. In this case, the expression is equal to 0 so −1 is a root of the polynomial.
Substitute: −1 into the polynomial.
(−1)3−6(−1)2+3⋅(−1)+10
Raise −1 to the power of 3.−1−6(−1)2+3⋅−1+10
Raise −1 to the power of 2.−1 −6⋅1 + 3⋅−1+ 10
Multiply −6 by 1.−1−6+3⋅−1+10
Subtract 6 from −1.−7+3⋅−1+10
Multiply 3 by −1.−7−310
Subtract 3 from −7.−10+10
Add −10 and 10.0Since −1 is a known root, divide the polynomial by x+1 to find the quotient polynomial. This polynomial can then be used to find the remaining roots.
x³− 6x²+ 3x+ 10x+ 1
Divide
x³−6x²+ 3x+ 10 by x + 1.
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What is the slope if it is perpendicular?
The slope if it is perpendicular is [tex]-\frac{1}{m}[/tex].
What is slope ?
The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
What is perpendicular ?
The word perpendicular means at right angles and this is because when two lines meet, they form right angles. Perpendicular lines can face in any direction such as up and down, crossways, and side-to-side.
Let y = 3x + 1 is perpendicular ,
differentiate respect of x
[tex]\frac{dy}{dx} = 3[/tex] , m = 3
Thus , [tex]-\frac{1}{m}[/tex]
then [tex]-\frac{1}{3}[/tex]
The slope if it is perpendicular is [tex]-\frac{1}{m}[/tex].
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How do you identify a quadrilateral?
We can identify quadrilateral because a regular polygon must have four equal sides in order to be called a quadrilateral.
Describe the quadrilateral.
Having four sides, four vertices, and four angles, a closed quadrilateral is a type of polygon. It consists of four connected non-collinear points. Quadrilaterals' internal angles always add up to 360 degrees.
According to the given question:
In a quadrilateral -
Four vertices make up each of them.Four sides comprise each side.All interior angles add up to 360 degrees.There are 2 diagonals.Both regular and irregular quadrilaterals exist.In order to be considered a quadrilateral, it must have four sides, four angles.
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If quadrilateral ABCD is rotated 90° clockwise about point A and then reflected across the y-axis to create quadrilateral A’B’C’D’, what will be the coordinate of D’?
According to the 90° clockwise rotation, the new coordinate of the quadrilateral D' is (3, -2)
Quadrilateral
Quadrilateral refers a closed shape and a type of polygon that has four sides, four vertices and four angles.
If quadrilateral ABCD is rotated 90° clockwise about point A and then reflected across the y-axis to create quadrilateral A’B’C’D’.
Here we need to find the coordinate of D'.
In order to find the new coordinates, first we have to identify the current coordinates of the quadrilateral.
While we looking into the graph, we have identify the point of
A (0,0), B(-4, 3), C(1,5) and D(2,3)
Now, we have to use the rule of clockwise 90° rotation, states that to rotate the figure 90 degrees clockwise about a point, every point(x , y) will rotate to (y, -x).
According to this rule, the new coordinates are written as,
A(0,0) = A'(0,0)
B'(-4,3) = B'(-3,-4)
C(1,5) = C'(5, -1)
D(2,3) = D' (3, -2)
Therefore, the new coordinate of D' is (3, -2).
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what is the equation of a line perpendicular to y = 2x - 6 that passes through (5, 4)
(use y = m x + b)
(must solve for y to get slope)
The equation of the perpendicular line is y = -0.5x + 6.5
How to determine the perpendicular line equation?From the question, we have the following parameters that can be used in our computation:
y = 2x - 6
Also, from the question;
We have the following points
Point = (5, 4) i.e. (x, y) = (5, 4)
The equation of a line can be represented as
y = mx + c
Where
Slope = m
By comparing the equations, we have the following
m = 2
This means that the slope is 2
The slopes of perpendicular lines are opposite reciprocals
This means that the slope of the other line is -1/2
The equation of the line is then calculated as
y = m(x - x₁) +y₁
Where
m = -1/2
(x₁, y₁) = (5, 4)
So, we have
y = -1/2(x - 5) + 4
Evaluate
y = -0.5x + 6.5
Hence, the line has an equation of y = -0.5x + 6.5
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Is rigid motion congruent?
Yes, rigid motion is congruent?
What is rigid motion congruency?A stiff motion occurs when an object is transported from one place to another while maintaining its original size and shape.
If and only if there is a stiff motion that establishes a correspondence of one figure as the likeness of the other, then two figures are said to be congruent. Interior angles are unchanged, as well as side lengths.
An object is rigidly moved from its initial place to the exact same location in a motion known as an identity motion. It appears as though the thing hasn't changed at all.
According to the Common Core, the "principle of superposition" states that two figures are congruent if there is a rigid motion projecting one onto the other.
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A woman put $580 into a savings account for one year. The rate of interest on the account was 6.5%. How much was the interest for the vear in dollars and cents? (Round to the nearest cent)
Answer:
580-80=500×6.5=3250 its ans iit
The mass of one methane (natural gas) molecule is 2.7x10^-23 grams. Find the mass of
60,000 methane molecures in grams.
The mass of 60,000 molecules of methane is 1.62 × 10⁻¹⁸ g
what is mass of molecule ?
Watch your pronunciation. pronounced "muh-LEH-kyoo-ler mas" the total atomic mass of every atom in a molecule, calculated using a scale with hydrogen, carbon, nitrogen, and oxygen having atomic masses of 1, 12, 14, and 16, respectively.
solution:
The mass of one methane molecule should be "2.7 × 10⁻²³ gram" instead of "27 × 10⁻³ grams".
Mass of 60,000 molecules of methane
= (2.7 × 10⁻²³ g) × 60,000
= 1.62 × 10⁻¹⁸ g
Therefore,The mass of 60,000 molecules of methane is 1.62 × 10⁻¹⁸ g
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What will be the nature of roots of quadratic equation 2x2 4x 7?
The roots of the quadratic equation 2x2 4x 7 will be two complex conjugate roots.
To determine the nature of roots of a quadratic equation, we can use the formula of the discriminant. The discriminant of a quadratic equation ax2 + bx + c = 0 is given by D = b2 - 4ac.
For the equation 2x2 4x 7, the discriminant is D = (-4)2 - 4(2)(7) = 16 - 56 = -40.
Since the discriminant is negative, the roots will be two complex conjugate roots.
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Select all the expressions which are equivalent to –4/3p – 2/5.
–4/3p + 2/5
–2/5 – 4/3p
4/3p – 2/5
–4/3p + (−2/5)
2/5 + 4/3p
A collection of numbers, variables, and mathematical operations is referred to as an expression. The expression is -2/5- 4/3P and 2/5+4/3P
What is meant by expression ?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation .A collection of numbers, variables, and mathematical operations is referred to as an expression.
Given,
-4/3p - 2/5
= -20p - 6/15
= 2(10 p +3)/15
A mathematical expression is a sentence that includes numbers, variables, or both. The equal symbol is never used in expressions. Here are a few phrases as examples. A mathematical statement stating the equality of two expressions is known as an equation.
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Sandra et the cruie control in her car to 69 mile per hour when he goe on road trip. Which equation can be ued to find how many hour, h, it will take her to drive m mile at her contant peed?
A. B. C. D
Sandra sets the speed to 69 miles per hour. The equation that express how many hours it will take her to drive m miles is: h = m/69.
Speed or velocity 69 miles per hour means: in 1 hour she will travel 69 miles
69 miles need 1 hour
1 miles need 1/69 hours
m miles need m x 1/69 hours.
If h is the amount of time need to take her to drive m miles, then:
h = m x 1/69 = m/69 hours
We can also solve the problem, using formula:
s = vt
Where:
s = distance
v = speed = 69 mph
t = time
In the given problem, the distance is m, hence s = m, and t = h
Hence,
t = s/v
h = m/69
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Please help and give a great answer get u brainlist
Answer:
7.62
Step-by-step explanation:
Simplify the following:
7 + 6/10 + 2/100
Express 6/10 in its lowest form by cancelling out gcd(6, 10) = 2 from the numerator and denominator. 6/10 = (2×3)/(2×5) = 3/5:
7 + 3/5 + 2/100
Express 2/100 in its lowest form by cancelling out gcd(2, 100) = 2 from the numerator and denominator. 2/100 = (2×1)/(2×50) = 1/50:
7 + 3/5 + 1/50
Put 7 + 3/5 + 1/50 over the common denominator 50. 7 + 3/5 + 1/50 = (50×7)/50 + (10×3)/50 + 1/50:
(50×7)/50 + (10×3)/50 + 1/50
50×7 = 350:
350/50 + (10×3)/50 + 1/50
10×3 = 30:
350/50 + 30/50 + 1/50
350/50 + 30/50 + 1/50 = (350 + 30 + 1)/50:
(350 + 30 + 1)/50
| 3 | 5 | 0
| | 3 | 0
+ | | | 1
| 3 | 8 | 1:
Answer: |
| 381/50
Why binomial theorem is used?
Binomial theorem is used to calculate the roots of the equations with highest degree in advance mathematical calculation in any subject.
Binomial theorem is represented by :
( a + b )ⁿ = ⁿC₀aⁿb⁰ + ⁿC₁aⁿ⁻¹b¹ + ⁿC₂aⁿ⁻²b² +..............+ ⁿCₙa⁰bⁿ
When the value of n is higher it helps us to calculate the value of the given expression easily and accurately.I t helps us to calculate the roots of the equation with higher degree in advance mathematics.It also help us to prove many mathematical and Physics equations.It help us to determine the Weather forecast , in architecture calculations , and cost estimation in many engineering projects.Therefore, the binomial theorem help us to calculate the roots of the equations with highest degree in advance mathematical calculations in many subjects.
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the ratio 800g:1kg can be written in a form 1:n find out the value of n
If 800g:1kg is equal to 1:n then the value of n is 1/8.
What is a ratio?The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
We have,
800g : 1kg = 1 : n
This can be written as,
800g/1kg = 1/n
Cross multiply.
n = 1kg/800g
[ 1 kg = 1000g ]
n = 1000g/8000g
n = 1/8
Thus,
The value of n is 1/8.
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If sally has 29 apples but then bob takes 1 apple how many apples does sally have left?
Answer:
28 apples
Step-by-step explanation:
29 - 1 = 28 apples
Answer:
28apples
Step-by-step explanation:
simple:29-1
hope this helps
plot the distance and time data for distance the train traveled on the grid below. plot the distance on the vertical axis and time on horizontal axis. label the axes and add a title to your plot.
Distance Traveled by Train
Time (h) Distance (km)
0 0
1 110
2 220
3 330
4 400
5 500
A graph of the distance and time data for distance traveled by this train is shown in the image attached below.
What is a scatter plot?In Mathematics, a scatter plot is sometimes referred to as scatter chart and it can be defined as a type of graph which is used for the graphical representation of the values of two (2) variables, with the resulting data points showing any association or correlation between the data set.
In this scenario, the time (in hours) would be plotted on the vertical axis (x-axis) of the scatter plot while the distance (in kilometers) would be plotted on the horizontal axis (y-axis) of the scatter plot by using an Excel worksheet.
From the scatter plot (see attachment) which models the relationship between the distance (in kilometers) and time (in hours), a linear equation for the line of best fit or trend line is y = 99.43x + 11.43.
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How many terms are there in the expression x³ 4x² 7x − 2 *?
There are totally 4 terms in the given polynomial
We have a polynomial given by -x³+4x² +7x − 2
Algebraic expressions with coefficients and variables make up polynomials. Occasionally, variables are referred to as indeterminates. For polynomial expressions, addition, subtraction, multiplication, and positive integer exponents are all possible; however, division by variable is not. x2+x-12 is an illustration of a single-variable polynomial. Three terms are involved in this example: x2, x, and -12.
Since there are 4 terms with either an addition or a subtraction performed between them, the total number of terms is given by 4.
Those 4 terms are -x³ ,4x²,7x,−2
Therefore, there are totally 4 terms in the given polynomial.
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Find the total surface area of the cone in the figure. (Use π = 3.14.)
A) 282.6 cm^2
B) 219.8 cm^2
C) 266.9 cm^2
D) 314.0 cm^2
The total surface area of the cone is calculated to be
A) 282.6 cm²How to find the total surface area of the coneInformation given in the problem
the total surface area of the cone in the figure. (Use π = 3.14.)
A cone is a three-dimensional geometric structure with a smooth transition from a flat, usually circular base to the apex or vertex, a point that creates an axis to the base's center.
The formula of the total surface are of a cone is given by
T = πr(r + l) square units.
calculating for l
l = √(12² + 5²) = 13
= 3.14 * 5 (5 + 13)
= 3.14 * 5 *(18)
= 282.6 cm^2
282.6 cm^2 is the total surface area of the cone
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What is a linear graph formula?
Linear graph equations are one-degree equations. It is a straight-line equation. A linear equation with parameters a and b equal to zero has the conventional form ax + by + c = 0.
How do one express the standard form of a linear equation?
A linear equation has the following standard form: ax + by + c = 0.
Here, variables x and y and constants a, b, and c are used.
Also, a ≠ 0, and b ≠ 0.
For linear equations, the slope-intercept formula is: y=mx+b
Where m stands for the line's slope and b represents the y-intercept.
The three types of linear equations are point-slope, slope-intercept, and standard form.
When an algebraic equation is graphed, it always produces a straight line since each term has an exponent of 1 or 0. This type of equation is known as a linear equation.
Steps of drawing linear graphs are described below:
Step 1: Using the provided linear equation, determine the value of y with respect to x.
Step 2: Arrange these data in a table format.
Step 3: Create a graph using the points from the database.
Step 4: Connect the points to form a straight line.
So, ax + by + c = 0 is a linear graph formula.
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What does discontinuity mean?
In mathematics, a discontinuity is a point or set of points at which a function or curve is not defined, or is not "well-behaved," meaning it exhibits some kind of sudden or unexpected change in behavior.
What does discontinuity mean?Discontinuities can occur in functions or curves of all types, including functions of one variable, functions of several variables, and geometric curves.
There are several types of discontinuities that can occur in a function. For example, a function may have a jump discontinuity, which occurs when the function has a finite limit from one side but a different finite limit from the other side at a given point.
In all, the presence of discontinuities in a function can make it more difficult to analyze or work with, as the behavior of the function may not be predictable at these points.
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Is longitude equidistant?
Latitude lines always have an equal distance between them, however longitude lines are separated from one another at the equator and come together at the poles. Longitude and latitude lines near the equator are equal in distance, with one degree covering 111 kilometers (69 miles).
Latitude lines are always equally spaced apart because they are always parallel to one another. Never do latitude lines converge or intersect. Distances north or south of the equator are measured by lines of latitude.
How do longitudes work?
Distance east or west of the prime meridian is measured by longitude. Meridians, which are also known as lines of longitude, are fictitious lines that divide the globe. They measure the distance either east or west, running from pole to pole from north to south. The units of longitude are degrees, minutes, and seconds.
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What is postulate and theorem?
A postulate is an unsupported assertion that is taken to be true. A provable true assertion is referred to as a theorem.
What is meant by postulate ?A claim that is accepted as true without evidence, also referred to as an axiom. For instance, Euclid's postulates, a set of five postulates, provide the foundation of all of Euclidean geometry. An unsupported assertion is referred to as a postulate. A postulate is also referred to as an axiom. For instance, you would believe Pam if she claimed that all of her siblings are at least five foot one tall if you knew that she is five feet tall and that all of her siblings are taller than her. A postulate is an unsupported assertion that is taken to be true. A provable true assertion is referred to as a theorem.To learn more about postulate refer to:
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Multiply pls
a
1. (a + b)(a + b) =
2. (3a-2b) (3a - 2b) =
3. (x - 4y)(-3x - 2y) =
4.(-y-2z)(y-2z) =
Answer: FOIL method
1. (a + b)(a + b) =
= a² + ab + b² + ab
= a² + 2ab + b²
2. (3a-2b) (3a - 2b) =
= 9a² - 6ab - 6ab + 4b²
= 9a² -12ab + 4b²
3. (x - 4y)(-3x - 2y) =
= -3x² -2xy +12xy +8y²
= -3x² + 10xy + 8y²
4.(-y-2z)(y-2z) =
= -y² + 2yz -2yz + 4z²
= -y² + 4z²
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-The base of a triangular prism is a right triangle with a base of 20 feet and a height of 120 inches. The height of the prism is 5 feet. What is the volume of the prism, in cubic feet? Enter your answer as a number, like this: 42 Do not enter units.
750 cubic feet is the volume of the prism and Therefore, the volume of Jake's box is 8 times larger than Havana's box.
What are a right triangle's three sides?A right right triangle hypotenuse is its longest side, its "across" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question. To describe both sides of right triangles, we utilize specific terminology. The side opposing its right angle is always the tangent of a right triangle.
Briefing:Dimensions of the Right Triangular Base
Base = 20 feet
Height= 120 inches = 10 feet
Base Area of the Prism
1/2 * 20 * 10
= 150 sq.feet
Height of the Prism = 5 feet
Volume of the Prism = Base Area X Height
= 150 X 5
=750 cubic feet
Jake's Box
Length: 12 inches
Width: 4 inches
Height: 8 inches
Volume = 12 X 4 X 8 =384 cubic inches
Havana's box
Jake's shipment crate is comparable to the one in Havana, except it is only half as long overall.
Therefore:
Length: 12/2=6 inches
Width: 4/2=2 inches
Height: 8/2=4 inches
Volume = 6 X 2 X 4 =48 cubic inches
Now:
384/48=8
Therefore, Jake's box has an 8-times higher volume than Havana's box.
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Part A Find the y-intercept and slope of the line.
Answer:
y-intercept = (0,6)
slope = -2
Step-by-step explanation:
⭐What is the slope of a line?
The slope of a line is how steep the line is⭐How can we find the slope of a line?
Use the formula: [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]m = the slope[tex](x_1,y_1)[/tex] is one of the coordinates of the given line[tex](x_2, y_2)[/tex] is another coordinate of the given lineTo find the slope, pick two coordinates you see on the line, substitute them into the slope formula, and solve for the slope!
I am choosing the coordinates (0,6) and (3,0), but you can choose any 2 coordinates that you see on the line.
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m = \frac{0-6}{3-0}\\m = \frac{-6}{3}\\m = -2[/tex]
∴ The slope of the line is -2.
⭐ What is the y-intercept of a line?
The y-intercept of a line is the point (0,y) at which the line intersects the y-axis⭐How do we find the y-intercept of a line?
Look at the graphFind the corresponding y-coordinate for when x=0When x=0, y=6
∴ The y-intercept of the line is (0,6)
reasoning suppose le ol i and fe o gi. what else must you know in order to prove kfde and kghi are congruent by asa? by aas?
In order to prove that KFDE and KGHI are congruent by ASA, you need to know that KFDE and KGHI have two congruent angles (angle F and angle H) and a congruent side (side DE and side HI).
In order to prove that KFDE and KGHI are congruent by AAS, you need to know that KFDE and KGHI have three congruent angles (angle F, angle G, and angle H). This means that the angles in the triangle are equal, which implies that the sides in the triangle are also equal. Thus, for AAS, KFDE and KGHI must have two congruent sides (side DE and side HI).
Therefore, in order to prove that KFDE and KGHI are congruent by ASA or AAS, you must know that both triangles have two congruent angles and a congruent side (for ASA) or three congruent angles and two congruent sides (for AAS).
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What is the formula for three consecutive odd numbers?
The formula to determine the consecutive odd numbers of a specific value "x" is:
x + 2n
What are consecutive numbers?Consecutive numbers are those numerical values that are found just after a specific number or value, for example consecutive numbers from 5 will be 6 onwards.
If we want to know the consecutive numbers immediately we add +1, +2 and so on.
But as we only want the odd numbers we will add +2, +4 and +6, having as a result the following numbers:
x + 2 x + 4 x + 6If we generalize an equation we have
x + 2n
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How is the literal equation y = a( bx + c) similar to the equation for converting °F to °C?
How would you solve this equation for the variable x ?
ans is 4 I don't really know how to explain it
Sakhi old a watch at a profit of 15%. Had he bought it at 10% le and old for R. 28 le, he would have gained 20%. Find the cot of the watch
Based on the calculation, we get that the cost of the watch is Rs 22.50.
Cost is the amount of resources, time, money, or effort that must be expended to achieve a goal or achieve something. It can refer to the financial or monetary expense of something, but it can also refer to other types of resources or effort that must be invested.
Let C be the cost of the watch.
The profit that Sakhi made on the watch was 15% of C. We can express this as:
Profit = (15/100) * C
If Sakhi had bought the watch at 10% less than the price at which he sold it and sold it for Rs. 28 le, he would have gained 20% on the sale. We can express this as:
Profit = (20/100) * (C - (10/100) * C)
We can set these two expressions for profit equal to each other and solve for C:
(15/100) * C = (20/100) * (C - (10/100) * C)
This simplifies to:
15/100 = 20/100 - (10/100)^2
Which simplifies to:
15 = 20 - (10/100)
Solving for C, we find that the cost of the watch is:
C = Rs. 22.50
Therefore, the cost of the watch is Rs. 22.50.
The missing part in the question is shown below.
Sakhi sold a watch at a profit of 15%. Had he bought it at 10% le and sold for Rs. 28 le, he would have gained 20%. Find the cost of the watch
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What to numbers can equal 16?
1, 2, 4, 8, and 16 are the components that make up 16. Similarly, the negative components of 16 are -1, -2, -4, -8, and -16. factors of 16: 1, 2, 4, 8, and 16.
What two numbers make 16?The natural number 16 (or sixteen) comes after the number 15 and before the number 17. Since 42 = 4 4 is a square number, the number 16 is both a composite and a square. It has precisely five correct divisors, making it the lowest number. These are 1, 2, 4, and 8. The numbers 16 and 60 sound remarkably similar in English speech, which might lead to confusion.
There are three factor pairs of 16:
1 × 16 = 16.
2 × 8 = 16.
4 × 4 = 16.
1, 2, 4, 8, and 16 are the 16 factors. Likewise, the unfavorable factors of 16 are -1, -2, -4, -8, and -16. 1, 2, 4, 8, and 16 make up the number 16.
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