The sum of the polynomial is obtained by adding the terms with the same power and variable together.
The steps to determine the sum of the polynomial :
Step 1: Arrange each polynomial with the term with the highest degree first then
in decreasing order of degree.
Step 2: Group the like terms : Like terms are defined as the terms whose variables and exponents are the same. For example 2x² and 3x² are like terms.
Step 3: Simplify by combining like terms.
For example, (2x² + 6x +5) +(-2x + 3x²- 1)
and we have determine sum of polynomial. Follows the above steps :
Arrange the polynomials are in decreasing order of degree.=> (2x² + 6x +5) + ( 3x²– 2x – 1)
Group the like terms.2x² + 3x² + 6x – 2x + 5 -1
Simplify by combining the like terms= 2x² + 3x² + 6x – 2x + 5 -1
= 5x² + 4x + 4
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What type of function always has an inverse?.
The type of function always has an inverse is one to one.
In math function is referred as a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Here we need to identify the type of the function always has an inverse.
As we all know that in each and every function has an inverse, here we have also know that but not every inverse will be a function.
Where as the inverse may fail the vertical line test.
Here we have identified that if the original function is a one-to-one function then its inverse will be a function.
Finally in a one-to-one function not only passes the vertical line test, then it also passes a horizontal line test.
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Graphing on a Number Line
18. Describe how to graph -6 and 5 on a number line.
Count 6 point from zero to the left side from zero for negative (-6) and for 5 count 5 points right from the zero on the number line.
What is number line?A number line in mathematics is a horizontal straight line with numbers spaced equally apart along that line. Some will have a defined beginning and end. We refer to these as closed number lines. Number lines may also be left empty or blank. A number ladder is almost a vertical number line.
Number lines are frequently used in elementary and middle school to help students develop skills like counting, adding, and subtracting numbers. They are typically introduced in kindergarten.
Additionally, it is very easy to read number lines. The values provided enable kids to compare and visualise the relationships between the numbers shown on the line, despite the fact that it isn't a ruler and the space between the numbers isn't fixed. In turn, this promotes the growth of number sense.
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All students in Ridgewood Junior High School either get their lunch in the school cafeteria or brought it from home on Tuesday. 10% of students brought their lunch. 40 students brought their lunch. How many students in total are in Ridgewood Junior High School?
Answer:
400!
Simple Step-by-step explanation:
40x10
=400
Sorry for being late <3
I'm unsure how to answer this question,can someone walk me through it?
Without evaluating, rewrite 3^10×37^9/9^12 as a single power with base 3
The simplified exponential expression 3^10×37^9/9^12 as a single power of 3 is given as follows:
3^70.
How to simplify the exponential expression?The exponential expression for this problem is defined as follows:
[tex]\frac{3^{10} \times (3^7)^{12}}{9^{12}}[/tex]
Applying the power of power rule, we have that:
(3^7)^12 = 3^(7 x 12) = 84.
When two terms with the same base and different exponents are multiplied, we keep the base and add the exponents, hence:
3^10 x 3^84 = 3^94.
For the denominator, we have that:
9^12 = (3²)^12 = 3^24.
When two terms with the same base and different exponents are divided, we keep the base and subtracted the exponents, hence:
3^94/3^24 = 3^(94 - 24) = 3^70.
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Lana ha 5 apple and her friend ha 10 time a much a her how many apple doe her friend have
Lana has 5 apples and her friend has 10 times as many as her So her friend will have 50 apples.
Here times mean The symbol is used in mathematics to represent the multiplication operation and the resultant product. It is sometimes referred to as the time sign or the dimension sign.
So if Lana has 5 apples
her friend has 10 times as many as her
By using the unitary method
The unitary approach is a methodology for problem-solving that involves first determining the value of a single unit and then determining the necessary value by multiplying the single unit value.
The unitary method's formula is to get the value of a single unit and then multiply that value by the number of units to obtain the required value.
5 time 10
50 apples
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Daniel travels 325 miles in 5 hours. How many miles did he travel in 11 hours
Answer:
Below
Step-by-step explanation:
The answer can be found by 11/5 * 325
here is how this comes about
ratios
325 is to 5 hours as 'd' is to 11 hours
325/5 = d/11 Multiply both sides by ' 11 '
11/5 * 325 = d ( the equation above )
d = 715 miles
Point M is online to LN given LN equals 10 and LM equals 8 determine the length of mn
Answer:
2 ...
Step-by-step explanation:
since LM = 8
and LN = 10
therefore MN = LN - LM .
MN = 10 - 8 .
MN = 2
MARK ME AS BRAINLIEST ...What is 5 less than 7 times a number is 0. In algebraic expressions
Answer:
Step-by-step explanation:
We can write this out as an equation and let x represent the number:
7x-5=0
Adding five on both sides gives us: 7x=5
Therefore, x=5/7
A line has a slope of -3 and includes the points (9, 4) and (8, t). What is the value of t?
According to the question A line has a slope of -3 and includes the points (9, 4) and (8, t) then the value of t is 7
How do I find the value of a slope?Typically, a line's slope provides information about the steepness and direction of the line. Finding the difference between the coordinates of the locations will allow you to quickly compute the slope of a straight line connecting two points, (x1,y1) and (x2,y2). The letter "m" is typically used to signify slope.
tan θ = Δy/Δx
the solution is -
Considering a line with a slope of -3 and also the point (9, 4), we could use the point-slope form of either a line to find the equation of a line:
y - 4 = -3(x - 9)
y = -3x + 27 + 4
y = -3x + 31
We are given some other point on the line (8, t) we can try substituting it in the equation above:
t = -3(8) + 31
t = -24 + 31
t = 7
And hence, the value of the t is 7.
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The total cost of attending a state university is $21,800 for the first year. A students parents will pay for 30% of this cost. An athletic scholarship will pay another $5,600. The student has $3,800 saved in the bank for college. Which amount is closes to the minimum that the student will need to save every month in order to pay off the remaining cost at the end of 12 months?
Answer:
$488.33 monthly savings
Step-by-step explanation:
Parent payment 30% of $21,800 is $6,540.
Subtract all payment from total cost.
21,800−6,540−5,600−3,800=5,680.
Split this into monthly payment by dividing 5,680 by 12 months.
5,680÷12= $488.33
How many solutions are there to the equation xi x2 x3 x4 17 where Xi x2 x3 and x4 are nonnegative integers?.
The number of solutions to an equation x₁ + x₂ + x₃ + x₄ = 17 are 1140
Consider given equation x₁ + x₂ + x₃ + x₄ = 17,
where x₁ , x₂ , x₃ and x₄ are non-negative integers.
As we know x₁ is the number of ones before the first zero, x₂ the number of ones between the first and the second zero, x₃ the number of ones between the second and the third zero, and x₄ is the number of ones after the third zero.
This means, there is a 1-1 correspondence between the solutions and reorderings of 17 ones and 3 zeros.
So, the number of solutions to given equation would be,
n = ²⁰C₃
Using combination formula [tex]^nC_r=\frac{n!}{r!\times(n-r)!}[/tex],
²⁰C₃ = 20! / (3! × (20 - 3)!)
²⁰C₃ = 1140
So, n = 1140
The possible number of solutions = 1140
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The complete question is:
How many solutions are there to the equation x₁ + x₂ + x₃ + x₄ = 17 where x₁ , x₂ , x₃ and x₄ are nonnegative integers?.
What function is f/x )= Logbx?.
The logarithmic function
[tex] f(x) = log_{b}(x) [/tex] is represent the inverse of an exponential function f(x)= bˣ.
A logarithmic function involves logarithms. Its basic form is
[tex]f(x) = log_{a}(x) ,[/tex] , where a > 0. It is Log functions include natural logarithm (ln) or common logarithm (log). For example f(x) = ln(x). An exponential function is defined as a mathematical function in the form f(x) = aˣ , where “x” represent a variable and “a” is a constant number which is known as the base of the function and it's value always be greater than zero. Transcendental number e is mostly used as a base of exponential function base is f. We have, the logarithmic function
[tex]f(x) = log_{b}(x) [/tex] , is the inverse of an exponential function f(x) =bˣ, and which means that
[tex]y = log_{b}(x) [/tex], is bʸ = x. The expression bʸ = x is said to be the “exponential form” for the logarithm
[tex]y = log_{b}(x) [/tex].
Here, b is called the base (of the logarithm) and it should be positive constant.
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Complete question:
What function is
[tex]f(x)= log_{b}(x) ?[/tex]
What is the example of perfect square trinomial?.
Answer:
x^2 + 6x + 9 and x^2 + 8x + 16 are examples of perfect-square trinomial
Step-by-step explanation:
1. x2 + 6x + 9
(x + 3)^2
= (x + 3)(x + 3)
= x2 + 6x + 9
2. x^2 + 8x + 16
x^2 + 8x + 16
= x^2 + 2(x)(4) + 4^2
= (x + 4)^2
Is 0 a real value of x?.
Yes. Zero is a real value of x.
Given,
Real value of x;
The non-negative value of a real number x, regardless of its sign, is its absolute value (or modulus), | x |. For instance, 5 has an absolute value of 5, and 5 has a value of 5.
How do you discover the true worth?
The influence of price level changes is subtracted from the nominal value of a good, service, or time-series data to create real value, which provides a more accurate view of economic trends. A deflator is used to alter the nominal value of time-series data, such as GDP and incomes, in order to produce real values.
Here,
The real value of x includes 0.
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Find (f∘g)(x).
f(x)=2x
g(x)=x+4
Write your answer as a polynomial in simplest form.
Answer:
(f∘g)(x) = 2x + 12
Step-by-step explanation:
(f∘g)(x) =
f(g(x)) =
2(g(x)) + 4 = ==> substitute g(x) for x in f(x) = 2x + 4
2(x + 4) + 4 = ==> substitute x + 4 for g(x)
2x + 2*4 + 4 = ==> use distribution property on x and 4
2x + 8 + 4 = ==> simplify
(f∘g)(x) = 2x + 12
What is a set of all X values *?.
The domain is actually the set of all "x" values, whereas the range is the set of all "y" values in an ordered pair.
Given,
What is the definition of the word "domain"?
Remember which of the following symbols corresponds to which ordered pair: (x, y).
When analyzing a set of ordered pairs, first list all the x values from the relation to establish the domain.To find the range, list each of the y values from the ordered pairs first.It is sufficient to list repeated values once as long as they fit within the domain or range.A relation cannot be a function unless each x value has a different value for the y value.If an x value has more than one y value connected with it, such as in the relation (4, 1), (4, 2), where the x value of 4 has y values of 1 and 2, a collection of ordered pairs is not a function.
Thus, the connection is referred to as a function if there is only one y value for every x value.
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Factor the expression completely. 14 x 4 − 35 x
How do you graph the equation y =- 3x?.
Equations of degree one and having two variables are known as linear equations in two variables. It is of the form, ax +by +c = 0, where a, b and c are real numbers, and both a and b not equal to zero.
Equations of the form a x +b y = 0; where a and b are real numbers, and a ,b ≠ 0, is also linear equations in two variable.
Since the solution of linear equation in two variable is a pair of numbers (x,y), we can represent the solutions in a coordinate plane.
To draw graph , we need to find some points
y =-3x
for y =-3x ,lets substitute value and check,
x=0
then y =0
x=1
then y =-3
x=2
then y =-6
x=3
then y =-9
x=-1
then y =3
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What is a negative exponential function called?.
Answer:
Step-by-step explanation:
Y = e−x
Answer: A negative exponential function or y = e−x, is otherwise known as exponential decay
Step-by-step explanation: I hope this helps!
What is logarithm class 11?.
The exponent or power that must be added to a base to produce a particular number is called the logarithm.
Indicated by the letter log n, the later class of logarithms, those with base 10, are referred to as common or Briggsian logarithms.
Logarithms, which were developed in the 17th century to expedite calculations, significantly decreased the amount of time needed to multiply integers with numerous digits. For more than 300 years, they served as the foundation for numerical labor, but the development of mechanical adding machines in the late 19th century and computers in the 20th century made them obsolete for large-scale calculations.
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(−8x+7)(4x+2)−(−8x+7)(6x−9)
Answer: [tex]16x^2-102x+77[/tex]
Step-by-step explanation:
1) distribute
[tex](-8x+7)(4x+2)\\-32x^2-16x+28x+14\\-32x^2+12x+14[/tex]
2) distribute
[tex](-8x+7)(6x-9)\\-48x^2+72x+42x-63\\-48x^2+114x-63[/tex]
3) solve
[tex](-32x^2+12x+14)-(-48x^2+114x-63)\\(-32x^2+12x+14)+(48x^2-114x+63)\\16x^2-102x+77[/tex]
How is substitution used to determine if an ordered pair is the solution to a system of equations?.
Substitution is a method for solving systems of equations by substituting the values from one equation into the other. To use substitution to determine if an ordered pair is the solution to a system of equations, first solve one of the equations for either x or y.
Then substitute this value into the other equation, and solve for the other variable. If the ordered pair you obtain is also found in both equations, then it is a solution to the system.
Take the equation set as an example.
2x + y = 5
3x – y = 1
To use substitution to determine if (2, 3) is a solution to this system, first solve one of the equations for either x or y:
2x + y = 5 ⇒ y = 5 – 2x
Add this value to the other equation after that:
3x – (5 – 2x) = 1
⇒ 5x = 6
⇒ x = 6/5
Finally, substitute 6/5 back into either equation to find y:
2(6/5) + y = 5
⇒ 12/5 + y = 5
⇒ y = 10/5
⇒ y = 2
Since (6/5, 2) is found in both equations, it is a solution to the system.
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how much work is done when a 100 lb rock is lifted to a height of 3 ft?
A. The work done is 300 ft-lbs when a 100 lb rock is lifted to a height of 3 ft.
To calculate the work done, we can use the formula: Work = force x distance x cos(Ф).In this case, the force is the force of gravity acting on the rock, which can be calculated using the formula:
force = m * g
where m is the mass of the rock and g is the acceleration due to gravity (32.17 ft/s^2).
force = 100 lb * 32.17 ft/s^2 = 3,217 ft-lbs
The distance is the height to which the rock is lifted, which is 3 ft.
The angle of the rock to the vertical is 90 degrees, so cos(90) = 0.
So,
Work = force x distance x cos(theta) = 3,217 ft-lbs * 3 ft * 0 = 300 ft-lbs
So, the work done is 300 ft-lbs.
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Alexis invests 40% of capitol needed to start a business. If he invests $15,000, how much total capital was needed ?
Answer:
37500
Step-by-step explanation:
40%=$15,000
100%=?
100%×$15,000/40%
$1,500,000/40
=37500
How do you find an inequality?.
When solving an inequality:
you can add the same quantity to each side. you can subtract the same quantity from each side. you can multiply or divide each side by the same positive quantity If you multiply or divide each side by a negative quantity, the inequality symbol must be reversed.In arithmetic, an inequality is a relation that makes a non-equal assessment between two numbers or other mathematical expressions. it is used most usually to evaluate numbers on the range line by using their size.
In mathematics, a dating between two expressions or values that aren't identical to every other is called 'inequality. ' So, a loss of balance consequences in inequality. The three facets and three angles proportion an important relationship. In arithmetic, the term “inequality” represents the that means “not equal”. allow us to bear in mind a simple example if the expressions in the equations are not the same, we can say it is inequality.
Whilst two actual numbers or algebraic expressions are represented with symbols like <, > or ≤, ≥ they can be called an inequality. as an example, 3x<20, or 4x+y>12. which means Of The Symbols used in Inequalities: The image < manner 'less than' and ≤ means much less than or same to.
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What is the slope of the line that passes through the points (4, 8) and (8, 6)? Write
your answer in simplest form.
PSSPY
Answer:
The slope is simply the gradient of the two points . use the gradient equation (Y2-Y1/X2-X1) to find the answer ;)
Solve the quadratic equation by the square root method and write the solutions in radical form. Simplify the solutions.
(4x+21)2=27
Answer:
8x+42=27
8x=-15
x=-1.875
Step-by-step explanation:
The length in inche and correponding weith in ounce of 15 different fih were meaured and recorded
what i the expected weith of the bluegill that i 11 inche
32.56 is the expected weight for a bluegill fish that is 11 inches long.
Equation: What is it?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" symbol and terms on both sides must always be present when writing an equation. Equal treatment should be given to each party. Multiple terms, operators, and variables are not required on each side of an equation. Without them, one can still create an equation, such as 5 + 10 = 15. There are no variables in the equation below.
given expression:
In(Weight) = -5.28 + 3.44 In(Length)
So, we have to find 11 inches then
In(weight) = -5.28 + 3.44 x 11
= -5.28 + 37.84
= 32.56
Hence, 32.56 is the expected weight for a bluegill fish that is 11 inches long.
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What is the nature of the roots for the given quadratic equation 5x 2 − 2x − 3 0?.
A quadratic equation has the generic form ax2 + bx + c = 0. Thus, the roots are hypothetical, meaning that they have two false roots.
What kind of thing is a root?The equation's nature of roots indicates whether it contains rational, irrational, or fictitious roots. Imaginary roots and unreal roots are synonyms.
What is a quadratic form's nature?Having just second-order terms, the quadratic form is a unique nonlinear function (either the square of a variable or the product of two variables).
2x2 - 3x + 5 = 0
a = 2 , b = -3, c = 5
b2 - 4ac = (- 3)2 - 4 (2) (5) (5)
= 9 - 40
= - 31
b2 - 4ac < 0
Therefore, the equation lacks any true roots.
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Full Question = Find the nature of the roots of the quadratic equations. If the real root exist, find them:
i) 2x2 - 3x + 5 = 0
Given triangles AABC and ADEF, if BC = EF, and AB = DE, What information do you need to prove the triangles congruent using the SAS postulate?
