The constant f(a) is the result of dividing a polynomial f(x) by xa, and f(x)=q(x)(xa)+f(a), where q(x) is a polynomial of degree one lower than f(x )'s.
What are polynomials?Algebraic expressions called polynomials include constants and indeterminates.
Polynomials can be thought of as a type of mathematics.
Nearly all branches of mathematics employ them to express numbers, and calculus is one of those branches where they play a crucial role.
A specific kind of expression is a polynomial.
A mathematical statement without the equals symbol (=) is called an expression. Let's examine the definition and usage of polynomials as they are described below.
An algebraic expression known as a polynomial requires that all of its exponents be whole numbers.
Any polynomial must have variable exponents that are non-negative integers. Although a polynomial contains variables and constants, we are unable to divide a polynomial by a variable.
Hence, The constant f(a) is the result of dividing a polynomial f(x) by xa, and f(x)=q(x)(xa)+f(a), where q(x) is a polynomial of degree one lower than f(x )'s.
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The remainder theorem helps us find the remainder when dividing a polynomial by a linear expression, using the formula R = f(a), where a is the root of the linear expression. Using this formula, we can easily calculate the remainder without performing long division.
The remainder theorem is a concept in algebra that helps us find the remainder when we divide a polynomial by a linear expression. The formula for the remainder theorem can be stated as follows:
If we have a polynomial f(x) and we divide it by a linear expression x - a, then the remainder R is given by the formula:
R = f(a)
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How many answers are there in inequality?
There is no single answer to this question as there are many different types of inequalities and each one can have a different number of solutions.
Number of Solutions to InequalitiesInequalities are mathematical statements that compare two values or expressions using an inequality sign. These signs can be:
Greater than (>) Less than (<)Greater than or equal to (>=)Less than or equal to (<=)Depending on the type of inequality and the values involved, the number of solutions can vary.
For example, a linear inequality with two variables will have an infinite number of solutions as the two variables can take on any real number value.
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What must be added to 2xsquare-7xy+5ysquareto obtain xsquare+4xy-3ysquare with steps
A value which must be added 2x² - 7xy + 5y² to obtain x² + 4xy - 3y² include the following: -x² - 8y² + 11xy.
What is a quadratic function?In Mathematics, a quadratic function can be defined as a mathematical expression which defines and represent the relationship that exists between two (2) or more variable on a graph, with a maximum exponent of two (2).
In Mathematics, the standard form of a quadratic function is given by;
ax² + bx + c = 0
Let the variable k represent the value which must be added to the given quadratic function. Therefore, a mathematical expression which models and represent the situation is given by;
2x² - 7xy + 5y² + k = x² + 4xy - 3y²
k = x² + 4xy - 3y² - (2x² - 7xy + 5y²)
k = x² + 4xy - 3y² - 2x² + 7xy - 5y²
By collecting like terms, we have the following:
k = (x² - 2x²) + (-3y² - 5y²) + (4xy + 7xy)
k = -x² - 8y² + 11xy.
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Complete Question:
What must be added to 2x² - 7xy + 5y² to obtain x² + 4xy - 3y²?
What are the 7 rules of exponents?
The 7 rules of exponents are:
Product Rule: When multiplying two numbers with the same base, add the exponents. For example, [tex]a^m * a^n = a^{(m+n)}[/tex]Quotient Rule: When dividing two numbers with the same base, subtract the exponents. For example, [tex]a^m / a^n = a^{(m-n)}[/tex]Power Rule: When raising a power to a power, multiply the exponents. For example, [tex](a^m)^n = a^{(m*n)}[/tex]Zero Exponent Rule: Any non-zero number raised to the power of 0 is equal to 1. For example, [tex]a^0[/tex] = 1, where a is not equal to 0Negative Exponent Rule: When a number is raised to a negative exponent, it is the same as the reciprocal of the number raised to the positive exponent. For example, [tex]a^{-n}[/tex] = 1/[tex]a^n[/tex]One Exponent Rule: When a number is raised to the power of one, it stays the same. For example, [tex]a^1[/tex] = aZero Exponent Rule: Any number raised to the power of 0 is equal to 1. For example, [tex]a^0[/tex] = 1
It's worth noting that these rules are only valid for real numbers, with the exception of the zero exponent rule, which is valid for any number except for zero. Also, some rules may have restrictions such as the Negative exponent rule, where the base cannot be zero.
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The solve by substitution calculator allows to find the solution to a system of two or three equations in both a point form and an equation form .of the answer.true or false
Given statement is True.
A system of equations can be represented in different forms, such as point form (showing the x and y values that make the equations true) or equation form (showing the equations in standard form, with variables on one side and constants on the other). A solve by substitution calculator can be used to find the solution to a system of two or three equations in both point form and equation form of the answer.
The process of solving a system of equations by substitution involves isolating a variable in one equation and then substituting it into the other equation(s) to find the values of the other variable(s). The calculator can display the solution in point form by showing the values of x and y (or x, y, and z for a system of three equations) that make the equations true. It can also display the solution in equation form by showing the equations with the variable(s) replaced by the values found in the solution.
In conclusion, solve by substitution calculator can find the solution to a system of two or three equations in both point form and equation form of the answer, it can be a helpful tool for solving systems of equations.
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Points (-4,-8) and (-2,-5) fall on a line. Calculate the y-intercept of the line. What is the y-intercept?
Answer:
y-intercept: -2
Step-by-step explanation:
The Y-intercept is when x = 0. So, to find the y-intercept we just need to put in 0 for x and get the answer of -2. So, the y-intercept is located at (0, -2)
solve the following linear inequalities in one variable and show the solution set on the number line. 1 <2x<5
The solution of the given expression is x>1/2 and x<5.
What is Algebraic expression ?
Algebraic expressions are the idea of expressing numbers using letters or alphabets with out specifying their real values. The fundamentals of algebra taught us the way to specific an unknown value the usage of letters together with x, y, z, and so forth. those letters are called right here as variables.
An algebraic expression can be a aggregate of both variables and constants. Any cost that is positioned earlier than and expanded with the aid of a variable is a coefficient.
Given
linear equality in one variable,
and the expression ,
1<2x<5
so,
1<2x
2x>1
x>1/2
and another one x<5.
Hence, The solution of the given expression is x>1/2 and x<5.
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Your family decides to go to the Fox Theater to watch a
musical. There is valet parking (where someone parks your
car for you) available across the street. Your dad decides to
leave a tip of 15% to the valet person. The cost of parking
is $35. How much tip will he leave?
The cost of tip will he leave for the valet person is, $5.25.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
Your dad decides to leave a tip of 15% to the valet person.
And, The cost of parking is $35.
Here, The cost of parking is $35.
Hence, The cost of tip for the valet person = 15% of $35
= 15/100 × $35
= $5.25
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Find the domain and range of the function:
fx)=-5-x-3
Domain:
Range:
On solving the provided question we can say that the domain and Range of algebraic linear equation is all real number.
What is the scope and domain?Range and Domain. The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values. In mathematics, a real number is a quantity that may be represented by an endless number of decimal expansions. In contrast to the natural numbers 1, 2, 3,... that result from counting, real numbers are utilized in measurements of continuously altering quantities such as size and time.
f(x) = 5 - x - 3
Domain is all real number.
and Range is also all real number.
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A rectangle with area 12 square units is dilated by a scale factor of k. Match each given value of k with the area of the image.
(match the number with the letter it belongs with)
1.) k=2
2.) k=5
3.) k=1
4.) k=1/4
5.) k=1.2
A.) 48 square units
B.) 17.28 square units
C.) 300 square units
D.) 12 square units
E.) 0.75 square units
After calculating , when k = 2 the matching area could be 48 for k=5 ,the matching area could be 300 and for k=1.2 ,the matching area could be 17.28 and for k=1 ,the matching area could be 12,for k=1/4 ,the matching area could be 3/4 .
What is area of rectangle ?
area of rectangle is defined as the product of length and breadth is called as the area of rectangle.
Given,
A rectangle with area 12 square units is dilated by a scale factor of k.
When linear dimensions of similar figures are related by a factor of k, their areas are related by a factor of k².
For an original figure of area 12, each image figure dilated by a factor of k will have an area of 12k².
For k=2, the area is =
12(2)² = 12*4 = 48 square units
For k=5, the area is =
12(5)² = 300 square units
For k=1, the area is =
12(1)² = 12*1 = 12 . square units
For k=1/4, the area is =
12(1/4)² = 12/16 = 3/4 . square units
For k=1.2, the area is =
12(1.2)² = 12*1.44= 17.28 square units
Hence, After calculating , when k = 2 the matching area could be 48
for k=5 ,the matching area could be 300 and for k=1.2 ,the matching area could be 17.28 and for k=1 ,the matching area could be 12,for k=1/4 ,the matching area could be 3/4
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An item that cost $50.00 is marked 20% off. Sales tax for the item is 8%. What is the final price,including tax
Answer:
$43.20
20% off 50 Is 40 and 8% of 40 is 3.2 so 43.20
What are the signs of the first and second coordinates of a point in quadrant II?
The signs of the first and second coordinates of a point in quadrant II are negative.
To determine the signs of the coordinates of a point in quadrant II, we can use the following formula:
Sign of coordinate 1: (-1) * (x-axis)
Sign of coordinate 2: (-1) * (y-axis)
For example, if we need to determine the signs of the coordinates of the point (4, -5) in quadrant II, we can use the formula above. The sign of the first coordinate is (-1) * (+4), which is -4. The sign of the second coordinate is (-1) * (-5), which is +5. Therefore, the signs of both coordinates of the point (4, -5) in quadrant II are negative.
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Rename 1 foot with an equivalent factor in inches.
Answer:
12 inches
Step-by-step explanation:
1 foot = 12 inches
(12 inches)/(1 foot) = 1
1 foot × (12 inches)/(1 foot) = 12 inches
Use a trigonometric ratio to solve for y. Round to two decimal places as necessary!!
HELP, and can someone explain how to get the answer?
Using Trigonometric Identities, The value of y equals 20.36.
Trigonometric identities are equality conditions in trigonometry that hold for all values of the variables that appear and are defined on both sides of the equivalence. These are identities that, geometrically speaking, involve certain functions of one or more angles. They are not to be confused with triangle identities, which are identities that may involve angles but may also involve side lengths or other lengths of a triangle.
These identities are in use when trigonometric function-based expressions need to be made simpler. The integration of non-trigonometric functions is a crucial application; a typical method is employing the substitution rule with a trigonometric function first, and then simplifying the resulting integral with a trigonometric identity.
Using Trigonometric ratios,
Sin θ = perpendicular / hypotenuse
Sin 69 = 19 / y
0.933 = 19 / y
y = 19 / 0.933
y = 20.36
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what is the slope of a line that goes through the points (-5,-4) and (-2,-5).
Answer:
-1/3
The Slope
Slope is a measure of steepness of a line. In Algebra 1, It is how much the y-value changes when the x-value increases by 1.
Slope Formula:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Plug in your points accordingly to find the slope.
Q)What is the slope of a line that goes through the points (-5,4) and (-2-5)
1) To solve, first find your y-values and x-values. y-values are the second value in the coordinate form and a measure of height on a 2D coordinate plane. x-values are the first value in coordinate form and a measure of horizontal distance on a 2D coordinate plane.
(x,y)
y-values: -4, -5
x-values: -5, -2
2) Plug into the formula listed above.
[tex]\frac{-5-(-4)}{-2-(-5)}[/tex]
Simplify.
[tex]-\frac{1}3}[/tex]
Your slope is -1/3.
Answer:
-1/3
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-5-(-4))/(-2-(-5))
m=(-5+4)/(-2+5)
m=-1/3
Do the sides 7 cm 24 cm and 25cm form a right-angled triangle give reasons?
The sides 7 cm, 24 cm and 25 cm can form a right-angled triangle. The Pythagorean theorem can be used to verify this.
From Pythagorean theorem, it can be said that, the square of hypotenuse side is equal to the sum of other two sides of a right angles triangle.
Let AB, CA and BC be the sides of a right triangle. CA is the hypotenuse side, AB and BC are the base and height sides of the right triangle. Then the equation, can be written as,
CA² = AB² + BC²
Now, let us check this rule for the above given sides of the triangle.
Longest side² = Sum of squares of other two sides
25² = 24² + 7²
625 = 625
Thus, the sides 7 cm, 24 cm and 25 cm can form a right-angled triangle.
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Why is it called midpoint?
As the word himself says, "midpoint" means "the point in the middle or center". Finding a midpoint is not too hard and has applications in many areas of statistics, from confidence intervals to sketching distributions, to means.
To Find the Midpoint Between Two Numbers.
If the numbers are given, then the midpoint is become the average of the two numbers. To calculate or answer the midpoint, we first add them up and then divide the result by 2. The formula is as follows:
Let x and y be two numbers. So, the midpoint is:
M = x + y/2
A midpoint is a point that lying between two points and is in the center of the line joining the two points.
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Marge said that she subtracted 20 from both sides of an equation to solve it. Colin thinks that the equation she was solving could have been 6 + t = 20. Does Colin's reasoning make sense? Explain.
Answer:
Colin's reasoning makes sense. If Marge subtracted 20 from both sides of an equation, the equation she was solving could have been 6 + t = 20. On the left side of the equation, 6 + t would be simplified to t. On the right side of the equation, 20 would be subtracted from 20, resulting in a value of 0. So, the equation t = 0 would be the result of Marge's actions.
Answer: Colin's reasoning makes sense. If Marge subtracted 20 from both sides of an equation, the equation she was solving could have been 6 + t = 20. On the left side of the equation, 6 + t would be simplified to t. On the right side of the equation, 20 would be subtracted from 20, resulting in a value of 0. So, the equation t = 0 would be the result of Marge's actions.
Step-by-step explanation:
Yuri computes the mean and standard deviation for the sample data set 12, 14, 9, and 21. He finds the mean is 14. His steps for finding the standard deviation are below.
The mistake that Yuri has made is that : he divided the equation by n instaed of dividing the equation by n-1
What is the mistake that is made in the solution?While finding the standard deviation of a group of scores, the formula has the denominator as n - 1
where n is the total number of values in the data set.
the data set is 12, 14, 9 and 21. Hence n = 4
N - 1 = 3
Going ahead to work with n = 4 would give a wrong result.
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the correct question is
Yuri computes the mean and standard deviation for the sample data set 12, 14, 9, and 21. he finds the mean is 14. his steps for finding the standard deviation are below. what is the first error he made in computing the standard deviation
The image is attached as well to the question
What is the formula of mirror image?
A mirror equation is an equation relating object distance and image distance with focal length. It is also known as the mirror formula.
1/f= 1/u + 1/v.
u is the Object distance
v is the Image distance
f is the Focal Length given by f=R/2.
R is the radius of curvature of the spherical mirror
The above formula is valid under all situations for all types of concave and convex and for all object positions.
Linear magnification is defined as the ratio of the image size to the object size;
Magnification= Image size/ Object size.
it can be expressed as the ratio of the distance of the image to the distance v of object u from the mirror. Magnification has no unit.
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P 18 The circle C has equation (x-3)² + (y + 3)² = 52. The baselines, and are tangents to the circle and have gradient a Find the points of intersection, P and Q, of the tangents and the circle. b Find the equations of lines and 12, giving your answers in the form ax + by + c = 0.
Answer:
a) To find the points of intersection, P and Q, of the tangents and the circle, we can use the fact that a tangent line is perpendicular to the radius at the point of tangency. Therefore, the slope of the tangent line is the negative reciprocal of the slope of the radius.
We know that the equation of the circle is (x-3)² + (y + 3)² = 52. To find the slope of the radius, we can differentiate the equation of the circle with respect to x and y.
dx/dt = 2(x-3) and dy/dt = 2(y+3)
We know that the slope of the tangents is a. So, the slope of the radius is -1/a
Now we can use the point slope form of a line to find the equation of the tangent line.
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is a point on the line.
We can substitute the point of tangency, which is on the circle, into the point slope form.
y + 3 = -1/a(x - 3)
We can now substitute the point (3, -3) and the slope -1/a into the point slope form to find the equation of the line
y + 3 = -1/a(x - 3)
y = -1/a
Step-by-step explanation:
Not sure if this helps, hope it does!
Write an equation of the perpendicular bisected of the segment with endpoints (3,7) and (-1,-5)
The equation of the perpendicular bisector of the segment with endpoints (3,7) and (-1,-5) is y = -1/3x + 4/3.
What exactly is a perpendicular bisector?A triangle's perpendicular bisectors are lines that pass through the midpoint of each side and are perpendicular to the given side.
Here,
Given :
The perpendicular bisector is the line that passes through the midpoint and has an opposite-reciprocal slope.
The GH slope is:
m = (-5-7)/(-1-3)=-12/-4-3
The slope of a perpendicular line is: -1/m = -1/3
The GH midpoint is:
x=(3-1)/2=2/2=1
y= (7-5)/2=2/2=1
The slope of the line that passes through point (1, 1) is:
In point-slope form, 9-1-1/3(x-1) And
In slope-intercept form, y = -1/3 + 4/3.
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Which graph represents this equation?
Y=3/2x^2-6x
Answer: if The parabola is passing right through (0, 0) and (9, 0). Then the correct option is C. The correct graph is C. I did this assessment before
Step-by-step explanation:
Write the rule to describe the transformation.
Answer:
Dilation of 3
Step-by-step explanation:
Note [tex]DE=2[/tex] and [tex]D'E'=6[/tex].
The scale factor is defined as the ratio of the length of the side of the image to the length of the corresponding side of the preimage.
So, the scale factor is [tex]\frac{6}{2}=3[/tex].
Jerrod had scores of 75, 82, 94 and 77 on his first four history tests. What must he score on the next test to have an average of at least 85? (Note: Remember that average is found by dividing the sum of the numbers, by the number of numbers.)
Write as an inequality and show steps, please
Jerrod can score 97 on the next test to have an average of at least 85
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
Given that Jerrod had scores of 75, 82, 94 and 77 on his first four history tests.
We need to find the score on the next test to have an average of at least 85
Let x be the score of the next text.
75+82+94+77+x/5≥85
328+x/5≥85
328+x ≥ 85×5
328+x ≥425
Subtract 328 from both sides
x≥425-328
x≥97
Hence, Jerrod can score 97 on the next test to have an average of at least 85
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6/10-1/5+1/4+?????????
Answer:
13/20 or 0.65
Step-by-step explanation:
6/10=0.6
1/5=0.2
1/4=0.25
0.25+0.2+0.6=0.65
Halima is on her way home in her car. She has driven 9 kilometers so far, which is one-third of the way home. What is the total length of her drive?
Answer:
27
Step-by-step explanation:
If 9 kilometers is 1/3, the total length of her drive would be 9: 1/3=9•3/1=27
Answer:
27
Step-by-step explanation:
if 9 kilometers is 1/3 of her journey then you should take 9 times 3 to find the total distance she needs to travel which is 27 kilometers
Simplify your answer as much as possible. 4w=96
The value of "w" in the algebraic equation
4w = 96 which makes it true is equal to 24.
What is an algebraic equation?An algebraic equation is a mathematical statement that contains two equated algebraic expressions.
We shall evaluate for the value of w in the algebraic equation 4w = 96 as follows:
The coefficient of w is 4 and can be removed to allow w stand alone by dividing both sides of the equation by 4
4w/4 = 96/4
w = 96/4
96 = 24 × 4, so 4 can cancel out and we have;
w = 24
Therefore, 24 is the value of w in the algebraic equation 4w = 96 that makes it true.
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Help, please! I can not figure out this question.
The product of the given expression is option C. 6x^3 - 33x^2 + 45x - 6.
Product of numbers in brackets.The product of two or more numbers implies the final value that would be derived when the numbers are multiplied with each other.
The given expression in the question involves the expansion of brackets.
Thus it can be solved as;
(3x - 6) (2x^2 - 7x + 1)
Considering the first bracket, the first term is 3x and second term is -6. To solve the question thus require to first expand the second bracket by 3x, then by -6 to have;
(3x - 6) (2x^2 - 7x + 1) = 6x^3 - 21x^2 + 3x - 12x^2 + 42x - 6
= 6x^3 - 33x^2 + 45x - 6
Therefore, the product of given brackets is 6x^3 - 33x^2 + 45x - 6. Thus option C.
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A 10-ft ladder ret againt the ide of a houe. The ditance between the top of the ladder and the ground i 2 ft more than the ditance between the bae of the ladder and the bottom of the houe. Find both ditance
The distance from the base of the ladder to the bottom of the house is 6 feet and the distance between the top of the ladder and the ground is 8 feet.
Length of the ladder = 10 ft
Let the distance between the base of the ladder and the bottom of the house = x
Then the distance between the top of the ladder and the ground = (x+2)
x and x+2 distance are perpendicular to each other and making a right-angle triangle with the ladder of length 10-ft.
By applying pythagoras theorem,
(10)² = (x)² + (x+2)²
100 = x²+x²+4+4x
2x² + 4x - 96=0
x² + 2x - 48 = 0
x² + (8x-6x) - 48=0
x(x+8) - 6(x+8)
(x-6)(x+8) = 0
x = 6, x = -8
Taking the positive value
x= 6 feet, and (x+2) = 8 feet
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Algebra 2, I remember doing this but i’m confused bc I remember like (f)g)(x) something like that so do I multiply or what?
The (g·g)(t) of the function is (g·g)(t) = 16t - 15
How to find (g·g)(t) of the function?A function is an expression, rule, or law that defines a relationship between an independent variable and a dependent variable
Since g(t) = -4t + 5
What (g·g)(t) means is that you should replace t with the value of g(t) (i.e. -4t + 5) in the same equation. That is:
(g·g)(t) = g(g(t))
(g·g)(t) = -4(-4t + 5) + 5
(g·g)(t) = 16t - 20 + 5
(g·g)(t) = 16t - 15
Thus, the value of g·g)(t) is 16t - 15
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