The remainder of given polynomial is 10 . An expression that consists of variables, constants, and exponents and is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
What distinguishes a polynomial?In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only involves non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1. The word "polynomial" is derived from the Greek words "poly" and "nominal," which together translate to "many terms."
Given,
[tex]fx=x^3+2x^2-5x-6[/tex]
By using remainder theorem
[tex]f(2)=2^3+2*2^2-5*2-6\\f(2)=0[/tex]
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According to th given question x³ - 2x² - 5x + 6 is divided by x + 2 it gives remainder zero.
A split fraction is what?The act of dividing a fraction into further equal portions is known as fraction division. For instance, if you cut a slice of pizza in half and had three-fourths of the pizza left, you would have eaten six slices total, or four of the entire pizza. In mathematics, division is the procedure of dividing a sum into equal parts. For illustrate, we may divide a group of 20 individuals into small groups of 4, 5, 6, and so on.
Given that p(x) = x³ - 2x² - 5x + 6 and g(x) = x + 2
We have to track down the rest.
So let's get started!
Remainder theorem is used;
g(x) = x + 2 = 0
g(x) = x = -2
By substituting the value x = -2
x³ - 2x² - 5x + 6
Substituting the values:
(-2)³ - 2(-2)² - 5(-2) + 6
= - 8 + 10 + 6
= -16 + 16
= 0
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Does a have to be greater than 1 in standard form?
The mantissa of scientific notation or standard form is between 1 and 10 in absolute value, or 1 ≤ |a| < 10. It can be 1, hence, it does not have to be greater than 1.
Standard form is also called scientific notation and has the form:
a x 10ᵇ
Where b is an integer and is called exponent.
a is a real number between 1 and 10 (in absolute value), it includes 1 but not 10, or we can write a should satisfy 1 ≤ |a| < 10.
Usually, a is called mantissa.
Example:
2467 can be written in standard form as:
2467 = 2.467 x 10³
0.0095 can be written in standard form as:
0.0095 = 9.5 x 10⁻³
150 x 10² can be written in standard form as:
150 x 10² =1.5 x 10⁴
-0.062 can be written instandard form as:
-0.062 = -6.2 x 10⁻²
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What is the least common denominator of 3 4 and 5 6?
The least common denominator (LCD) of 3/4 and 5/6 is 12
How do you determine the common denominator?To discover the least common denominator, list the multiples of both denominators until you find the smallest multiple that both denominators share. Because 20 is the first shared multiple of 4 and 5, it must be the fractions’ least common denominator.
Step 1: Using the repeated division method, find the prime factors of the given integers. Step 2: Express the numbers in exponent form. Determine the product of just the prime components with the greatest power. Step 3: The LCM of the provided numbers is the product of these factors with the greatest powers.The least common denominator (LCD) of a group of fractions is the least common multiple (LCM) of their denominators.
In this case, the denominators of the fractions are 4 and 6. The least common multiple (LCM) of 4 and 6 is 12. Therefore, the least common denominator of 3/4 and 5/6 is 12.
You can also find the LCM by finding the prime factorization of the numbers, and then take the highest power of each prime factor and then multiply those.
[tex]4 = 2^2\\6 = 2*3[/tex]
The highest power of 2 and 3 are [tex]2^2[/tex] and 3 respectively, so LCM(4,6) = [tex]2^2 * 3 = 12[/tex]
So the LCD of 3/4 and 5/6 is 12.
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Complete question is: What is the least common denominator of 3/4 and 5/6?
what is 3/5 divided by 9 equal?
Answer:
1/15
Step-by-step explanation:
Dividing a fraction by a whole number
3/5 ÷ 9
Copy dot flip
3/5 * 1/9
Rewriting
3/9 * 1/5
1/3 * 1/5
1/15
Answer:
1/15
Step-by-step explanation:
3/5 ÷ 9
3/5 × 1/9
1/5 × 1/3
1/15
An arithmetic sequence k starts 4,13….. explain how you would calculate the value of the 5000th term
Therefore , the solution of the given problem of arithmetic mean comes out to be a 5000th term = 44995
The definition of arithmetic meanThe sum of all values in a list multiplied by the total no. all items in the list yields the arithmetic average, often known as the group's means. The growth in arithmetic follows a similar pattern. The following equation + 7 + 9 equals 21, but 21 multiplied by 3 (there's several currently three numbers) equals 7, proving that the mean of the numbers 5, 7, while 9 is 4, and the median of the real numbers 5, 8, and 9 is 3.
Here,
Given : sequence is -
=> 4, 13, 17, 18,21...….
a = 4
d = 9
for
=> a 5000th term = a + 4999d
=> a 5000th term = 4 + 4999*9 = 44995
Therefore , the solution of the given problem of arithmetic mean comes out to be a 5000th term = 44995
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PLEASE HELP ASAP!!!!!!!!!
Answer: x=-5
Step-by-step explanation:
first answer
Wrote an expression that is equivalent to 2.5 +(-5y)-2.5
Answer: -5y
Step-by-step explanation:
2.5+-5y-2.5
=-5y
or 0+-5y
2(c+1)=10 solve for c
Answer:
c = 4
Step-by-step explanation:
Solve for c:
2 (c + 1) = 10
Divide both sides of 2 (c + 1) = 10 by 2:
(2 (c + 1))/2 = 10/2
2/2 = 1:
c + 1 = 10/2
The gcd of 10 and 2 is 2, so 10/2 = (2×5)/(2×1) = 2/2×5 = 5:
c + 1 = 5
Subtract 1 from both sides:
c + (1 - 1) = 5 - 1
1 - 1 = 0:
c = 5 - 1
5 - 1 = 4:
Answer: c = 4
Answer:
[tex]\boxed{\sf c=4}[/tex]
Step-by-step explanation:
[tex]\sf 2(c+1)=10[/tex]
Distribute:-
[tex]\sf 2c+2=10[/tex]
Subtract 2 from both sides:-
[tex]\sf 2c+2-2=10-2[/tex]
[tex]\sf 2c=8[/tex]
Divide both sides by 2:-
[tex]\sf \cfrac{2c}{2}=\cfrac{8}{2}[/tex]
[tex]\sf c=4[/tex]
Therefore, c = 4!!!
_________________
Hope this helps!
Have a great day!
Wyatt runs a farm stand that sells blueberries and raspberries. Each pound of blueberries sells for $1.50 and each pound of raspberries sells for $3. Wyatt sold 12 more pounds of blueberries than pounds of raspberries and made $72 altogether. Graphically solve a system of equations in order to determine the number of pounds of blueberries sold, x, and the number of pounds of raspberries sold, y
In linear equation, The number of pounds of apples is 12 and the number of pounds of raspberries is 20.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Given that, the cost of a pound of apples = $2.25 and the cost of a pound of raspberries = $1.50.
What is an equation?
In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the number of pounds of apples be x, then the number of pounds of raspberries(y) be y=x+ 12
Now, the total cost of apples = The number of pounds of apples × The cost of a pound of apples
=x × 1.50
= 1.50x
The total cost of raspberries = The number of pounds of raspberries × The cost of a pound of raspberries
=(x+12) × 3
=3x+ 36
So, the total cost = The total cost of apples + The total cost of raspberries
⇒ 72 = 1.50x+ 3x+ 36
⇒ 72 = 4.5x + 36
4.5x = 72-36
x = 8
So, y= x+ 12 = 20
Therefore, the number of pounds of apples is 12 and the number of pounds of raspberries is 20.
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The map that 1cm =50mile
Answer:
jejejdhudsjhshsiwvvjsjsjd
I realllyyy need helppp plssss helppp meee
Answer:
84 divided by 7 - 5x
Step-by-step explanation:
Solve the inequality n - 3/8 > -2/5 for n
The solution of the inequality for n is n > 31/40
What is inequality ?Inequality is a statement of an order relationship greater than or equal to less than between two numbers or algebraic expressions.
Inequalities are not only driven by and measured by income but are also determined by other factors including gender origin, ethnicity, disability, class and religion. Moreover inequalities are determined not only by income but also by other factors.
How to solve the inequality?
The inequality is given as
n minus three eighths is greater than negative two fifths
Rewrite properly as
n - 3/8 > 2/5
Add 3/8 to both sides
n > 3/8 + 2/5
Evaluate the sum
n > 31/40
Hence, the solution of the inequality for n is n > 31/40
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which of the following states the phytagorean theorem
The
hypotenuse's square
of a right triangle is equal to the sum of its legs' squares.
What is Pythagorean theorem?
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in
Euclidean
geometry.
According to this rule, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse, or the side across from the right angle.
This theorem can be expressed as the Pythagorean equation, which is an equation connecting the lengths of the sides a, b, and the
hypotenuse
c.
There are several ways to generalize the theorem, including to higher-dimensional spaces, non-Euclidean spaces, objects other than right triangles, and even things that are not triangles at all but n-dimensional solids.
Hence, The hypotenuse's square of a right triangle is equal to the sum of its legs' quares.
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What are the zeros of the function defined by the expression x^2 - 7x - 30 ? A. 3 and -10 B. 10 and -3 C. 15 and 2 D. 15 and -2
Answer:
C. 15 and 2
Step-by-step explanation:
arrange the following lengths in ascending order
1)15m 2)7km 3)1,800
Answer:
15m, 1,800cm, 7km
Step-by-step explanation:
Ascending order mean from smallest value to largest value
We know
1km = 1000m
1km = 100000cm
1) 15m = 0.015km
2) 7km
3) 1800cm = 0.018km
So, the order is
15m, 1,800cm, 7km
URGENTTT PLEASE!! in middle of test help!
I WILL MARK BRAINIEST! if you answers in under 5mins!
Answer:
equation: 2(2w + 2) = 60
length = 16
width = 14
Step-by-step explanation:
width = w
length = w + 2
perimeter = 2(w + w + 2) = 60
equation: 2(2w + 2) = 60
4w + 4 = 60
4w = 56
w = 14
width = 14
length = w + 2 = 14 + 2 = 16
length = 16
What does the purple peace emoji mean?
Therefore , the solution of the given problem of expressions comes out to be it means to promote peace and love.
Expression is what?It is required to multiply, divide, add, or take away in mathematics. The following is how an expression is put together: Number, expression, and mathematical operator The components of a mathematical statement, such as multiplication, subtraction, multiplied, or division, etc., include numbers, variables, and functions. It is possible to contrast expressions and phrases.
Here,
Given : purple peace emoji
Thus,
An easy approach to find a peace sign online is to use the peace symbol emoji,
which is used to signify a variety of emotions such as, well, peaceful, love, unity, harmony, togetherness, and general everyone-getting-along-ness. Sleep well, Divergents Be genuine.
Promote peace and love.
Therefore , the solution of the given problem of expression comes out to be it means to promote peace and love.
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What is the slope of the given line?
Help me
Please
Answer:
y = -2/3x
Step-by-step explanation:
Use technology to find points and then graph the function y=-2\log_2(x+3)+2,y=−2log 2 (x+3)+2, following the instructions below.
The graph of the given function is attached below.
What is the function?A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
The graph of the function y = -2log2(x+3) + 2 is a downward-sloping curve that approaches the x-axis as x approaches infinity.
The curve is defined only for positive values of x, as the logarithm is undefined for negative values.
As x increases, the logarithm term inside the parentheses becomes larger in magnitude, causing the value of y to decrease rapidly.
The curve approaches the x-axis but never touches it, as the logarithm term will never reach zero.
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In a right triangle, the side opposite angle x is 19 units and the hypotenuse is 26 units. What is the measure of angle
x to the nearest whole number?
A. 37 degrees
B. 27 degrees
C. 57 degrees
D. 4.6 degrees
Answer:
x=47 degrees
Step-by-step explanation:
We can use trigonometry to solve this problem.
the sine of the angle is equal to the side opposite the angle divided by the hypotenuse
so we have [tex]sin(x)=\frac{19}{26}[/tex]
now, in order to get x by itself, we have to take the inverse sine of both sides.
[tex]x=sin^{-1} (\frac{19}{26} )[/tex]
now we can plug this into a calculator.
we get 46.95 degrees
I think there is a typo in option D. because it says to find the nearest whole number but 4.6 is not a whole number.
Given the function h(x)=-x²+4x+12, determine the average rate of change of the function over the interval -1≤x≤8
The average rate of change of h(x) on the interval [-1, 8] is r = -3.6
How to find the average rate of change?For any function, the average rate of change on an interval [a, b] is given by:
r = ( f(b) - f(a))/(b - a)
In this case, the function is:
h(x) = -x^2 + 4x + 12
And we want to find the average rate of change on the interval [-1, 8]
Evaluating the function in these values we will get:
h(-1) = -(-1)^2 + 4*(-1) + 12
h(-1) = -1 - 4 + 12 = 7
h(8) = -(8)^2 + 4*8 + 12 = -20
Then the average rate of change is:
r = ( h(8) - h(-1) )/(8 + 1)
r = (-20 - 12)/9
r = (-32/9) = -3.6
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Simplify the expression
61/4 divided by 6 10/3
Is convex real or virtual?
Plane mirrors and convex mirrors only produce virtual images.
A mirror is a surface that nearly always images the light that strikes it. Mirrors are divided into two types: Plane mirrors and the second one is spherical mirrors. As the name says, plane mirrors have a plain, polished surface, while spherical mirrors are curved throwback surfaces.
Spherical mirrors are further divided into convex and concave mirrors based on their curves. Yet, to distinguish between Concave and Convex Mirror, it is fundamental to understand what they are and how they differ.
To put it simply, mirrors with a reflecting surface that bump outwards are convex mirrors, whereas concave mirrors have a reflecting surface that bulges inwards.
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What is the only even number that is prime?
Answer:
The only even prime number is 2.
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Maine has a cold climate in the water. Which statement
The statement about the probability of temperatures falling below 32°F in Maine in January, that is true, is B. The probability is 100.
How to describe probability ?Probability is a measure between 0 and 100 % or 0 and 1 that measures the likelihood of something happening. Probabilities that are closer to 1 or 100 % are more likely than not to happen.
Maine has a cold climate in the winter and January is a winter month. This means that there is a hundred percent chance that in January, the temperatures will fall below the temperature of 32 ° F, is 100 %.
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Full question is:
Maine has a cold climate in the winter. Which statement about the probability of temperatures falling below 32°F in Maine during the month of January is most likely true?
The probability cannot be determined before FebruaryThe probability is 100.The probability could be -1.The probability is closer to 1 than to 0.Is 4 cm and 7 cm are the lengths of two sides of a triangle then the length of the third side may be?
If 4 cm and 7 cm are the lengths of two sides of a triangle then the length of the third side should be 6 cm.
In the given question we have to check 4 cm and 7 cm are the lengths of two sides of a triangle then the length of the third side may be.
Any two sides of a triangle can have a sum of lengths that is always greater than the length of the third side.
Any two triangle sides' length differences will never be greater than the triangle's third side's length.
The sum of 4cm and 7cm is 11cm, and their difference is 3cm.
The third side's possible length must be larger than 3 cm and less than 11 cm to ensure that the aforementioned rule is not broken.
6 cm is therefore larger than 3 cm and less than 11 cm from the possibilities presented.
The triangle's third side measures 6 cm in length.
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Analyze the diagram to answer the questions.
Another way to name AngleSAC would be Angle
.
A point on ray AS is
.
Line segment A R and Line segment A B create Angle
.
Angle CAS is another name for Angle SAC. It is necessary to come up with another name for Angle SAC.
What is line?A line is a one-dimensional straight shape with no thickness that extends endlessly in both directions. A line is made up of a series of points that stretch in opposite directions indefinitely. Two points in a two-dimensional plane determine it. Collinear points are two points that are located on the same line.
Given:
Given a ray diagram,
Ray RS is given and point A & T are on between R & S.
Another ray DC cuts the ray RS at point A.
The ray AS cuts the point A.
One more ray is AB ,there is no any point to cut.
<SAC, we can also write this angle in form < CAS.
So,
∠SAC = ∠CAS (same angle)
Angle SAC is also known as Angle CAS. Angle SAC requires a new name.
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Diagram is missing
Why is the midpoint formula used to calculate elasticity?
The midpoint formula is used to calculate elasticity because it overcomes the limitations of the traditional method.
The old point-slope method has significant drawbacks that are overcome by the midpoint formula, which determines the elasticity of demand. The elasticity of demand refers to how sensitively a good's quantity desired is to a price shift. Inelastic goods are those in which a little price shift causes a large change in quantity demanded, while elastic goods are those in which a small drop causes a small change in quantity demanded.
The conventional point-slope formula for elasticity employs the change in quantity and price at a particular point, which might be deceptive in some circumstances. Contrarily, the midpoint formula determines the elasticity of demand by averaging the quantity and price at the beginning and end and utilising the percentage change in both.
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find the length of the diagnol please.
The length of the diagonal of the rectangle is 6.4 meters
How to determine the diagonalFrom the question, we have the following parameters that can be used in our computation:
Length = 5 meters
Width = 4 meters
The length of the diagonal can be calculated as
diagonal = √(length² + width²)
substitute the known values in the above equation, so, we have the following representation
diagonal = √(5² + 4²)
Evaluate
diagonal = 6.4
Hence, the diagonal is 6.4 meters
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What is the formula used for finding the equation of a line given two points?
Answer:
y=mx+c
Step-by-step explanation:
y=mx+c
PLEASE HELP!!! I NEED HELP WITH MY HOMEWORK!!!!
(GEOMETRY)
WILL MARK BRAINLIEST!!!!!!
Answer: v would be root2 and u would be 2
Step-by-step explanation: