Answer:
3
Step-by-step explanation:
Find the sum of -6x^2 + 3 and 4x^2 - 2x
Resultant polynomial is [tex]-2x^2 -2x +3[/tex].
What is polynomial?An algebraic statement with variables, coefficients, and mathematical operations like addition, subtraction, multiplication, or division is referred to as a polynomial. Let's talk about the definition of polynomials in this article, along with their types, uses, and standard form.Similar terms are added while adding polynomials, and similar terms are deleted when subtracting polynomials. Keep in mind that in mathematics, the sign following addition or subtraction will always be that of the variable with larger value.(4x^2 - 2x )+ ( -6x^2 + 3)
[tex]4x^2 - 2x + 0[/tex] +
[tex]-6x^2 + 0x + 3[/tex]
[tex]-2x^2 -2x +3[/tex]
Resultant polynomial is [tex]-2x^2 -2x +3[/tex].
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How do you find the algebraic value?
Bring the variable to the left side and bring all the remaining values to the right side.
Now, According to the question:
Let's know:
What is an algebraic value?
An algebraic number is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients. For example, the golden ratio, , is an algebraic number, because it is a root of the polynomial x2 − x − 1.
An algebraic formula is an equation or a rule written using mathematical and algebraic symbols and terms. It is an equation that involves algebraic expressions on both sides. The algebraic formula is a short quick formula to solve complex algebraic calculations.
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Who invented [infinity]?
Infinity is a concept that refers to something that is unbounded, limitless, and endless. Mathematician John Wallis invented the standard sign for infinity,∞, in 1655.
Given that,
We have to find who invented the infinity.
We know that,
Infinity is a concept that refers to something that is unbounded, infinite, and endless. English mathematician John Wallis created the standard sign for infinity,∞, in 1655.
There are three basic categories of infinity: mathematical, physical, and metaphysical.
Examples of mathematical infinities are the quantity of points on a continuous line or the length of the never-ending series of the numbers 1, 2, 3, etc.
When one inquires if there are infinitely many stars or whether the universe will exist forever, they are posing spatial and temporal ideas of infinity.
There are issues about whether an ultimate entity must be infinite and whether lower things could also be infinite in a metaphysical discussion about God or the Absolute.
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Julie wanted to match Lisa's obstacle course record of 74.6 seconds. She has already spent forty and one-fourth seconds on wall climbing and 10.56 seconds on the ropes. How much time did she have left to match the record?
23.79 seconds
29.69 seconds
34.35 seconds
64.04 seconds
Julie has spent 40.25 + 10.56 = <<40.25+10.56=50.81>>50.81 seconds on wall climbing and the ropes.
She needs to complete the course in 74.6 - 50.81 = <<74.6-50.81=23.79>>23.79 seconds to match Lisa's record. Answer: \boxed{23.79}.
if l brought a computer for $1500.00 and used my 75% off coupon. How much was the computer originally?
Answer:
$6000
Step-by-step explanation:
So, we know that
$1500 = 25%
We find 1% by taking
1500 divided by 25% = $60
We have to find the 75% off by taking
60 times 75 = $4500
Then we have to find the original price by taking
4500 + 1500 = $6000
So, the original price is $6000
Answer:
$6000
Step-by-step explanation:
The total cost is 100%
The discount was 75%
then:
100% - 75% = 25%
The percentage paid was:
25%
then:
$1500 ⇒ 25%
$A ⇒ 100%
A = 1500*100/25 = 6000
A = $6000
Which of the following expressions are polynomials? Justify your answer:
(i) 8
(ii) sqrt 3x^2 −2x
(iii) 1− sqrt 5x
(iv) 1/5x −2 +5x+7
(v) (x−2)(x−4)/x
(vi) 1/x+1
(vii) 1/7 a^3 −1/sqrt 3a^2 +4a−7
(viii) 1/2x
(i), (ii), (iv) and (vii) are the given expressions that represents polynomial.
What is polynomial?An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
Name three types of polynomial.Monomial, binomial and trinomial are the three types of polynomials.
A polynomial may contain exponents, constants, and variables, but it never divides by a variable.
There cannot be a negative exponent in a polynomial.
No variable at all, one variable, two variables, or more are all possible for polynomials.
Exponents can only be multiples of 0, 1, or 2, not fractions.
Based on above definitions (i), (ii), (iv) and (vii) are the given expressions that represents polynomial.
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If I arrange my pawns in a square as large as possible, I have 7 left. If I had 6 more pawns, I could arrange all my pawns in a square without remainder would have one more pawn. How many pawns do I have?
Please give me an explanation!
Note that in the word problem above, the number of Pawns that you have is 14 pawns.
What is the rationale for the above answer?
To solve this problem, you can use the equation:
Number of pawns = (Number of pawns in the largest possible square) + (Number of pawns needed to fill in the square) + 1
Substituting the given information, we get:
Number of pawns = (7 pawns) + (6 pawns) + 1 pawn
Simplifying, we get:
Number of pawns = 14 pawns
Therefore, you have 14 pawns.
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What is the formula for a linear function?
Answer:
⭐ There are 3 ways you can write a linear function (⭐ = most common):
⭐[tex]y = mx + b[/tex] (slope-intercept form)⭐[tex]y-y_1 = m(x-x_1)[/tex] (point-slope form)[tex]Ax + By = C[/tex] (standard form)
What are the roots of 2x² 3x 5?
On solving the provided question we can say that, - the roots of the given equations are - x = -5/2 and x = 1
What are roots ?When referring to the values of a variable for which the supplied polynomial equals zero, we use the term "roots of a polynomial." The polynomial p(x) has zero roots if and only if an is its root. By setting each component to 0, you may solve for x to determine the roots, or solutions, of the polynomial equation P(x) = 0. Factoring is used to solve the polynomial equation. Set each component to a value of 0 (2x4), (x-6) or (x+1). Calculate x using the solution.
here,
[tex]2x^2 + 3x - 5[/tex]
(2x + 5)(x-1)
x = -5/2 and x = 1
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Is 1 is positive or negative?
The numeric value with no sign is positive so 1 is positive.
Can numeric value be negative?
There are whole numbers and fractional numbers, for instance, in the world of numerical data. There are both positive and negative numbers.
What is positive and negative in numbers?
Positive numbers are those that are greater than zero. It is possible to write positive numbers with or without a sign in front of them. A negative number is one that is less than zero. The minus symbol (-) is always written in front of negative values.
As 1 have no sign with it so it means 1 is positive. If any numeric value is negative it must have negative sign with it else numeric value is positive.
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What table does 64 come in?
The Multiplication table that comes in the number 64 is 1, 2, 4, 8, 16, 32, and 64.
What do we mean by multiples?Multiples are numbers that are multiplied by another number to get a particular number.
In mathematics, multiples are the results of multiplying an integer by a given number.
Multiples of 5 include, for instance, 10, 15, 20, 25, 30, etc.
Numerous 7s include 14, 21, 28, 35, 42, 49, etc.
A multiple in mathematics refers to the outcome of multiplying two numbers together.
Here, the number 7 is multiple by 56.
Because the result of multiplying 0 by any number is 0, 0 is a multiple of all numbers.
So, in order to know what tables come in 64, we need to check that what numbers multiples ae 64:
64/1 = 64
64/2 = 32
64/4 = 16
64/8 = 8
64/16 = 4
64/32 = 2
64/64 = 1
Therefore, the Multiplication table that comes in the number 64 is 1, 2, 4, 8, 16, 32, and 64.
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8. Amy throws a ball so that when it is at its highest point, it passes through the centre of a
hoop. The path of the ball is modelled by the equation y=h+kx-x², where y is the
height in metres of the ball above the ground and x is the horizontal distance in metres
from the point at which the ball was thrown. The centre of the hoop is at the point where
x=2 and y = 5.
(a) Find the values of h and k.
(b) Find the value of x at which the ball hits the ground.
The values of h and k would be =2 and 2 respectively.
The value of x would be = 5.2
What is a horizontal distance?A horizontal distance is the distance that is be covered by a moving object through a horizontal pathway.
y = h + kx - 0.5x^2
When X = 2 and y = 5 is the centre of the hoop.
To calculate for y;
X max = -k/2× (-0.5)
X max = k = 2
y max = 5
Substitute the given variables into the equation and make h the subject of formula.
5 = (h + 2×2) - (0.5x^2)
5= (h + 4)- 1
h +4 = 5+1
h +4 = 6
h = 6-4
h = 2
Also from the graph, the value for x as the ball hits the ground would be = 5.2
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solve by substitution:
y = x
y=x+2
Answer:
Step-by-step explanation:
No solution.
y=x
-1(y=x)
-1y=-1x
+1y=1x+2
-1y and 1y cancel each other out. -1x and 1x cancel each other out.
Leaving +2..so it's a no solution. Solved using elimination it's easier..
Charles spent 1/4 of his net salary on school fees,1/3 of the remainder on electricity and water bills.He then spent 1/9 of what was left on transport.If he finally had sh.3600,what was his net january salary
The net salary of Charles in the month of January is 8100.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Let, 'x' be the total salary of Charles in January.
Charles spent 1/4 of his net salary on school fees so the reaming amount is,
= {x - (1/4)x}
= (3/4)x.
(1/3)rd of the remainder on electricity and water bills which is,
= (1/3)×(3/4)x.
= (3/12)x.
= (1/4)x.
Now, The remaining amount is {(3/4)x - (1/4)x}.
= (2/4)x.
He then spent 1/9 of what was left on transport which is,
= (2/4)x×(1/9).
= (1/18)x.
Now, The remaining amount is {(2/4)x - (1/18)x}.
= [(18 - 2)/36]x.
= (16/36)x.
= (4/9)x.
So, as he left with 3600 it is equal to (4/9)x.
Therefore,
(4/9)x = 3600.
4x = 32400.
x = 8100.
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What is rational function and irrational function?
The ratio of polynomials with which the polynomial denominator should not be equal to zero is known as a rational function. A function with a radical sign is frequently thought of as being irrational.
The ratio of polynomials to which the polynomial denominator should not be 0 is known as a rational function. It is same as the rational number's definition.
It's common knowledge that functions with radical signs are irrational functions. Activities including square roots, cube roots, or other roots, for instance, are regarded as irrational functions. It is claimed that a function is irrational if it performs addition, subtraction, multiplication, division, and raising to power with rational, non-integral exponents on the right side of the equation y = f(x).
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Find the x and y intercepts of f(x) = 2x² + 7x - 9.
A. (1, 0); (-9/2, 0) and (0, -9)
B. (-1,0); (9/2,0) and (0-9)
C. (0, 1); (0, -9/2) and (-9, 0)
D. (1, 0); (-4, 0) and (0, -9)
O A
OB
O C
OD
Answer:
B
Step-by-step explanation:
The [tex]x[/tex] intercepts are where [tex]f(x)=0[/tex].
[tex]2x^2+7x-9=0 \\ \\ (2x+9)(x-1)=0 \\ \\ x=-\frac{9}{2}, 1[/tex]
The [tex]y[/tex] intercept is where [tex]x=0[/tex].
[tex]f(0)=2(0)^2+7(0)-9=-9[/tex]
If a=b^2 c^3 and c=j^2 k^5 , which of the following is a correct expression for a in terms of b,j, and k?
Step-by-step explanation:
If a = b^2 c^3 and c = j^2 k^5, then we can substitute c = j^2 k^5 into the expression for a to get:
a = b^2 (j^2 k^5)^3
= b^2 j^6 k^15
This is a correct expression for a in terms of b, j, and k.
The correct expression for a in terms of b, j, and k is [tex]a = b^2 j^6 k^{15}[/tex].
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol be used to indicate the logical syntax's order of operations and other features.
We are given the terms as a = b^2 c^3 and c = j^2 k^5, then
we can substitute c = j^2 k^5 into the expression for a to get:
[tex]a = b^2 (j^2 k^5)^3\\= b^2 j^6 k^{15}[/tex]
Which is a correct expression for a in terms of b, j, and k.
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I need help with this question.
Answer:
49
Step-by-step explanation:
Vertical angles are congruent.
8x-23=6x-5
8x-6x=23-5
2x=18
divide
x=9
8(9)-23
=49
if repeated samples of yogurt sales were taken, according to the central limit theorem, the mean of those repeated samples would tend to be normally distributed if the sample size is large enough. because the sample population is , it is safe to apply the central limit theorem, even if the sample size for each sample is 15. a.) uniformly distributed b.) positively distributed c.) normally distributed d.) negatively distributed
The correct option is C. It is safe to apply the central limit theorem, even if the sample size for each sample is 15, if the sample population is normally distributed.
The central limit theorem states that, if you take repeated samples of a population and calculate the mean of each sample, the distribution of the means of those samples will tend to be normally distributed, provided that the sample size is large enough. This means that, even if the original population is not normally distributed, the distribution of the means of the samples will tend towards a normal distribution as the sample size increases.
However, if the original population is already normally distributed, then you can apply the central limit theorem with a smaller sample size and still expect the distribution of the means of the samples to be normally distributed. Therefore, in order for it to be safe to apply the central limit theorem with a sample size of 15, the sample population must be normally distributed.
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in what circumstances is the t statistic used instead of a z-score for a hypothesis test? the t-statistic is used when the population variance (or standard deviation) is known you use the z-test when the sample size is less than 30 the t-statistic is used when the population variance (or standard deviation) is unknown
A t-statistic rather than a z-score is used when (C) the population's variance and standard deviation are unknown.
What do we mean by t-statistic?The t-statistic, which is used in statistics, measures how far a parameter's estimated value deviates from its hypothesized value relative to its standard error.
Through the Student's t-test, it is utilized in hypothesis testing.
In a t-test, the t-statistic is used to decide whether to accept or reject the null hypothesis.
When the variance and standard deviation of the population are unknown, a t-statistic is employed rather than a z-score.
The p-value is the likelihood that, if the null hypothesis is correct, each test will result in a t-value with an absolute value at least as great as the one we actually observed in the sample data.
The t-value is a way to measure the difference between population means.
Therefore, a t-statistic rather than a z-score is used when (C) the population's variance and standard deviation are unknown.
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Correct question;
In what circumstances is the t-statistic used instead of a z-score for a hypothesis test?
(A) the t-statistic is used when the population variance (or standard deviation) is known
(B) you use the z-test when the sample size is less than 30
(C) the t-statistic is used when the population variance (or standard deviation) is unknown
Does anyone know the answer?
Answer:
Step-by-step explanation:
if you move over from 2. 3 full lines you get to 2.6. draw the x in between 2.6 and 2.8.
each line is 0.2 so 3.5 lines is 2.7
Lauren builds a sandbox shaped like an octagon. Each side of the sandbox is the same length.
The perimeter of the sandbox is 18.8 feet.
An octagon with 8 equal sides, all with unknown length, in feet.
Part A
How long is each side of the sandbox? Enter your answer in the box.
feet ( Input Answer )
Part B
The total cost of sand to fill the sandbox is $59.48. Lauren and 3 friends divide the cost equally.
How much does each person pay? Enter your answer in the box.
$ ( Amount??? )
Answer:
To solve this problem, we need to first find the length of each side of the sandbox. Since the sandbox is an octagon with 8 equal sides, we know that the perimeter of the sandbox is 8 times the length of each side. Thus, we can use the formula for perimeter to find the length of each side:
Perimeter = 8 * Side Length
Substituting the given values into this formula, we get:
18.8 feet = 8 * Side Length
Dividing both sides of the equation by 8, we get:
Side Length = 2.35 feet
Therefore, each side of the sandbox has a length of 2.35 feet.
________________________________________________________
To find the amount of money that each person pays to fill the sandbox, we need to divide the total cost by the number of people involved. In this case, there are 4 people in total, so each person pays 1/4 of the total cost. Thus, the cost per person is $59.48 / 4 = $14.87.
If (3x÷4,2)=(3,y÷6)then find the value of x and y.
Answer:
If you want to learn something without me directly giving you the answer, then here's the explanation
Step-by-step explanation:
You are given two points with unclear coordinates. Because they are equal to each other, you know that they are both the exact same point, meaning that the x and y coordinate of each point is equal to eachother. Therefore,
[tex]3x/4=3\\y/6=2[/tex]
If you understand basic algebra, the rest should be easy.
A bowling alley charges a flat fee to rent shoes. There is an additional fee for each game played. The function y=3. 5x+4 represents the cost y of bowling x games. Interpret the parameters of the function.
The function is in the form of linear equation in two variables where y is the cost and x are number of games played.
Linear equation in two variables is referred to a function that can be expressed in the form y = ax + b where a, b are constant values and x and y are variables. x is the independent variable and y is the dependent variable. Here we have the function y = 3.5x + 4 and the independent variable x is the number of games played and dependent variable y is the cost of the games that are played. Now in the equation the additional fee is represented by the constant value 3.5 and the fee for shoe is represented by the number 4 and is not dependent as the shoe rent fee is constant and not depends on number of games played.
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Please Help!! 25 points!!
Write the equation of the function in vertex form that has the vertex (1, 2) and the point (-3, 6). If necessary, use reduced fractions and not
decimals.
The equation of the function in vertex form is f(x) = 1/4(x-1)²+2.
What is vertex form?
A different way to express the equation of a parabola is in its vertex form. A quadratic equation is typically represented as an x 2 + b x + c, and when graphed, it will look like a parabola.
Here, we have
Given
The vertex (1, 2) and the point (-3, 6).
we have to find the equation of the function in vertex form.
We know that
The vertex form of the equation is :
f(x) = a (x-h)² +k
Now, we put the value of x, h, and k and we get
6 = a(-3-1)² + 2
6 = 16a + 2
4 = 16a
a = 1/4
Now, we put the value of a in the vertex form equation and we get
f(x) = 1/4 (x-1)²+2.
Hence, the equation of the function in vertex form is f(x) = 1/4(x-1)²+2.
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How to make charts in Excel?
We can create charts in microsoft Excel by using new tab on the view menu.
What is microsoft Excel?It is a software programe created by Microsoft that uses spreadsheet to display numbers and data with formulas.It enables the users to format,organize and calculate data easily in a spreadsheet.
How to create charts in the Excel?Open Microsoft Excel and select new tab.
Enter the data you want to create a chart.
Click the insert tab.
Click the recommended charts.(chart type)
Create chart.(once you select the chart preview and description appear at the right).
Click OK.(The recommended chart inserted into worksheet).
Hence we can create Excel chart into worksheet or microsoft word.
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There are 2 seats on the left side of a plane and three seats on the right. If there are 45 seats on the right, how many are on the left?
Answer:
30 seats
Step-by-step explanation:
For every row, there are 2 seats on the left and 3 seats on the right.
If there are 45 seats total on the right side, then there must be 45/3 = 15 rows. Therefore, there are 15*2= 30 seats on the left.
of 5 employees, 3 are to be assigned an office and 2 are to be assigned a cubicle. if 3 of the employees are men and 2 are women, and if those assigned an office are to be chosen at random, what is the probability that the offices will be assigned to 2 of the men and 1 of the women?
The probability that the offices will be assigned to 2 of the men and 1 of the women will be 3/5
Lets find all the combinations of 2 men and 1 woman that can be chosen
(men, men, women) m m w
3/5 x 2/4 x2/3
(men, women, men) m w m
3/5 x 2/4 x 2/3
(women, men, men) w m m
2/5 x 3/4 x2/3
then just add those probabilities together:
= 3/5x2/4x2/3+3/5x2/4x2/3+2/5x3/4x2/3
= 12+12+12/60
this simplifies to 3/5
Simply put, probability measures how probable something is to occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics explains the examination of events that can occur subject to probability.
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Select all that apply.
Which of the following are proportions?
2/8 = 3/12
3/4 = 8/10
25/10 = 5/2
3/4 = 15/20
Answer:
3/4 = 15/20
3/4 = 8/10
Step-by-step explanation:
What is the size of image if m is equal to 1?
The size of image if magnification m is equal to 1 is calculated to be 2m.
Given
Height of object = 1 m
Height of image = h'
Magnification = m = 2
The formula to calculate magnification is
m = h'/h
2 = h'/1
h' = 2 m
Therefore , the height of the image formed will be 2m.
Magnification is a concept of physics which refers to the process of enlarging an object , the object itself does not become physically larger, but just appears larger as projected on a screen.
The magnification can take two forms, microscopic magnification and telescopic magnification. When we insert a small thing, it appears larger due to microscopic magnification.
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