Answers
a) Yes, the function is in standard form.
Degree = 2
Exponent = 2
Constant term = -1
b) No, the function is not in standard form.
And it doesn't have the degree, exponent and constant term.
Firstly, let's consider the function f(x) = x(x-1). To determine if it is a polynomial function, we need to check if all of its terms have non-negative integer exponents. In this case, we see that f(x) can be written as x² - x, which has only two terms, and each term has a non-negative integer exponent. Therefore, f(x) is a polynomial function.
In this case, the degree of f(x) is 2 because the highest exponent of x is 2.
In this case, the leading term of f(x) is x², and its leading coefficient is 1.
Finally, the constant term is the term that does not have the variable in it. Here, the constant term of f(x) is -1.
Next, let's consider the function f(x) = 3 - 1/2 x. We can see that f(x) is not a polynomial function because it has a term with a negative exponent.
Polynomial functions must have non-negative integer exponents on all terms.
Therefore, the answer to the first question is 'no.'
Since f(x) is not a polynomial function, it does not have a degree, leading term, or constant term.
To know more about polynomial here
https://brainly.com/question/12976257
#SPJ1
Related Questions
Help with math problems
Answers
The surd forms are simplified to give;
21. 10√6 - 12√10
23. -56a - 5√2a - 25
25. -4√15x - 25x + 3
What are surds?Surds are described as values in square root that can no longer be simplified into whole numbers or integers
They are also seen as irrational numbers.
From the information given, we have that;
√15(2√10 - 4√6)
Expand the bracket and multiply the surd forms
2√150 - 4√90
Factorize the forms
2√25 ×√6 - 4√9 × √10
find the square root
10√6 - 12√10
23. (√2a - 5)(7√2a - 5)
expand the bracket
7√4a² - 5√2a - 35√4a² + 25
find the square root, we have;
7×2a - 5√2a - 35×2a + 25
collect the like terms
14a - 70a - 5√2a - 25
-56a - 5√2a - 25
25. (√3 + √5x)(√3 - 5√5x)
expand the bracket
3 - 5√15x + √15x - 5√25x²
find the square root
3 - 5√15x + √15x - 25x
collect the like terms
-4√15x - 25x + 3
Learn about surds at: https://brainly.com/question/840021
#SPJ1
x+2y=5
4x+8y=20
I need help asap
Answers
Answer:
(x, -1/2x + 5/2) or infinitely many solutions
Step-by-step explanation:
We can solve the system of equations using substitution. We can start by isolating x in the first equation. Then, we can plug in the entire equation made from isolating for x in the second equation, which will allow us to find y:
Isolating:
x = -2y + 5
Plugging in and solving for y:
4(-2y + 5) + 8y = 20
-8y + 20 + 8y = 20
20 = 20
We see that we get a constant equal to another constant. Whenever you get this as a solution to a system of equations, this means that there are infinitely many solutions. We can express the general rule for the solution in coordinate form by isolating y in at least one of the equations:
y = -1/2x + 5/2
Thus, the general rule for the solution to the system of equations is
(x, -1/2x + 5/2), so you can either put this general rule as the answer or write solution = infinitely many solutions
You can see that there are infinitely many solutions by plugging in any number for x into the two equations and see that you get 5 for the equation and 20 for the second equation. Let's try 4 for x and 0 for x:
4 for x in first equation:
4 + 2(-1/2(4) + 5/2) = 5
4 + 2(0.5) = 5
4 + 1 = 5
5 = 5
4 for x in the second equation
4(4) + 8(-1/2(4) + 5/2) = 20
16 + 8(0.5) = 20
16 +4 = 20
20 = 20
0 for x in the first equation:
0 + 2(-1/2(0) + 5/2) = 5
0 + 2(2.5) = 5
5 = 5
0 for x in the second equation:
4(0) + 8(-1/2(0) + 5/2) = 20
0 + 8(2.5) = 20
20 = 20
In complex numbers what is the multiplicative inverse of 2i
Answers
To find the multiplicative inverse of 2i, we need to find a complex number z such that:
(2i) * z = 1
Multiplying both sides by -i, we get:
z = -i/2
Therefore, the multiplicative inverse of 2i is -i/2.
Find the volume of the solid obtained by rotating the region underneath the graph of the function over the given interval about
the y-axis.
f(x)=√x² +9, [0,2]
(Use symbolic notation and fractions where needed.)
Answers
The volume of the solid obtained by rotating the region over the function is given by the integral and V = 44.46 units³
Given data ,
The volume of the solid obtained by rotating the region underneath the graph of the function f(x)=√x² +9 over the interval [0,2] about the y-axis
The formula for Area under definite integral is
∫ₐᵇ f ( x ) = f ( b ) - f ( a )
Since we are rotating the region about the y-axis, the radius is simply the x-coordinate of each point on the curve, or r = x
The height h of each shell is equal to the difference between the y-coordinates of the curve at x and x + Δx, or h = f(x + Δx) - f(x)
Using these expressions for r and h, we can write the volume of each cylindrical shell as:
V(x) = 2πx[f(x + Δx) - f(x)]Δx
V = ∫₀² 2πx[f(x + Δx) - f(x)]dx
As Δx approaches zero, this integral becomes:
V = ∫₀² 2πx√(1 + (f'(x))²) dx
where f'(x) is the derivative of f(x), which is:
f'(x) = x/√(x² + 9)
Substituting this expression for f'(x) into the integral, we get:
V = ∫₀² 2πx√(1 + (x/√(x² + 9))²) dx
This integral can be evaluated using a substitution, u = x² + 9, du/dx = 2x, and dx = du/2x, to get:
V = ∫₉¹³ 2π(x² + 9)^(3/2)/2 dx
V = [4/5 π(x² + 9)^(5/2)]₉¹³
V = 44.46 units³
Hence , the volume of the solid is 44.46 units³
To learn more about definite integral click :
https://brainly.com/question/14279102
#SPJ1
Explain by using an example why you need to multiply when converting from a larger unit to a smaller unit
Answers
Multiplying is necessary because each larger unit contains a certain number of the smaller units and we need to account for that conversion factor.
Why is multiplication necessary with examples?For example, when converting from meters to centimeters where we know that 1 meter is equal to 100 centimeters.
To convert 3 meters to centimeters, we need to multiply by the conversion factor of 100 which gives us:
= 3 meters * 100 centimeters/meter
= 300 centimeters
So, without the multiplication, we would not account for the fact that each meter contains 100 centimeters. This principle applies to all conversions from larger units to smaller units and it is important to remember to ensure accurate conversions.
Read more about multiplication
brainly.com/question/28768606
#SPJ1
Mr Tan calculated the average amount of money collected by all the students in his class during a fund-raising event. If three of his students each collected $32 less, the average amount of money collected would be $146. If eight of his students each collected $18 more, the average amount of money collected would be $156. How many students were there in Mr Tan's class?
Answers
There were 56 students in Mr Tan's class.
To solve this problem, we can use the formula for average: average = (sum of all values) / (number of values). Let's assume that there were initially n students in Mr Tan's class, and the average amount collected was x. Then, we can write:
nx = sum of all amounts collected
Now, if three students each collected $32 less, the new sum of amounts collected would be:
(nx - 3*32) = (n-3)(x-32)
And the new average would be:
(n-3)(x-32) / n = 146
Similarly, if eight students each collected $18 more, the new sum of amounts collected would be:
(nx + 8*18) = (n+8)(x+18)
And the new average would be:
(n+8)(x+18) / n = 156
Now we have two equations with two unknowns (n and x). We can solve them using algebraic manipulation. After some simplification, we get:
n = 56 and x = 104
To learn more about : Mr Tan's
https://brainly.com/question/29082921
#SPJ11
If g(q) = 2q-4 / q-A
and g(-3) = 2, what is the value of A?
Answers
Answer:
To find the value of A, we can substitute g(-3) = 2 into the given equation and solve for A.
g(q) = (2q-4) / (q-A)
2 = (2(-3)-4) / (-3-A)
Multiplying both sides by (-3-A), we get:
2(-3-A) = -10 - 2A
Expanding the left side, we get:
-6 - 2A = -10 - 2A
Adding 2A to both sides, we get:
-6 = -10
This is a contradiction, which means that there is no value of A that satisfies the given conditions. Therefore, the answer to the question is:
There is no value of A that satisfies the given conditions.
if there are 15 people from the bronx, brooklyn, manhattan queens and staten island and each borough has 3 people, if the people from each borough insist on standing together, how many possible ways are there to stand
Answers
There are 10,080 possible ways for the 15 people to stand if the people from each borough insist on standing together.
If there are 15 people from the Bronx, Brooklyn, Manhattan, Queens, and Staten Island, and each borough has 3 people, then there are 5 groups of 3 people. If the people from each borough insist on standing together, we can treat each group of 3 people as a single entity. So, we have 5 entities that need to be arranged.
The number of ways to arrange these 5 entities is 5!, which is equal to 120. However, within each group of 3 people, there are 3! ways to arrange the people. So, we need to multiply the number of ways to arrange the groups by the number of ways to arrange the people within each group. We will get the answer
5! × (3!)⁵ = 120 × 3⁵ = 10,080
To know more about possible ways here
https://brainly.com/question/1216161
#SPJ1
Help please
Expand the logarithm as much as possible
logy^10
Answers
Using some logarithm properties we will get the expanded expression:
log(y^10) = 10*ln(y)/ln(10)
How to expand the logarithm?So there are two logarithm properties that we can use here, these are:
logₙ(x) = ln(x)/ln(n)
and:
logₙ(x^a) = a*logⁿ(x)
Now let's go to our expression, it is:
log(y^10)
Using the second property we can remove the exponent, then we will get:
log(y^10) = 10*log(y)
Now we can use the first rule, remember that log(x) has a base of 10, then we can write:
10*log(y) = 10*ln(y)/ln(10)
That is the expession expanded.
Learn more about logarithms at:
https://brainly.com/question/13473114
#SPJ1
Solve for x, in terms of y: 23 x + 15 y = 2
MAKE BRAINLYST AND 100
Answers
To solve for x in terms of y in the equation 23x + 15y = 2, we can start by isolating the term with x on one side of the equation. We can do this by subtracting 15y from both sides of the equation to get 23x + 15y - 15y = 2 - 15y, which simplifies to 23x = 2 - 15y.
Next, we can solve for x by dividing both sides of the equation by 23 to get 23x/23 = (2 - 15y)/23, which simplifies to x = (2 - 15y)/23.
Therefore, the solution for x in terms of y is x = (2 - 15y)/23.
Need answer asap. Thank you for helping me.
Answers
The estimate of the cost for a 20-ft cord is given as follows:
$74.66.
How to find the equation of linear regression?To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator.
The points in the context of the problem are given as follows:
(3, 12.75), (5, 16), (6, 25.99), (50, 185).
Inserting these points into a calculator, the regression equation is given as follows:
y = 3.6794x + 1.06462.
Hence the estimate of the cost for a 20-ft cord is obtained when x = 20 as follows:
y = 3.6794(20) + 1.06462
y = $74.66.
More can be learned about linear regression at brainly.com/question/29613968
#SPJ1
A glass jug can hold (p+6) quarts less water than a plastic container. 2 glass jugs and 2 plastic containers contain 6p quarts of water in all.
How much water can the plastic container hold? Give your answer im terms of p.
Answers
The amount of water that the plastic container can hold is -p + 3.
How to determine the amount of water that can be heldTo determine the amount of water that can be held, we will first assume that the container can hold x quantity of water.
So, the glass jug can hold:
p + 6 - x
2 glass jugs and 2 plastic containers can hold 6p quarts of water.
= 2(p + 6 - x) - 2x = 6p
2p + 12 - 2x -2x = 6p
2p + 12 -4x = 6p
12 - 4x = 6p - 2p
-4x = 6p -2p - 12
-4x = 4p -12
x = 4p - 12/-4
x = -p - 3
or -p + 3
Learn more about algebraic expressions here:
https://brainly.com/question/4344214
#SPJ1
Express each of the following as (i)Percentage (ii)Decimal :
a) 3¾ (b) 6½/50
Answers
ii) 3¾ = 3.75
b) i) 6½/50 = 6.5/50/100 = 0.0013
ii) 6½/50 = 6.5/50 = 0.13
How to solve -10(x-1.7)=-3 by expanding first
Answers
To solve the equation -10(x-1.7)=-3 by expanding first, we need to apply the distributive property of multiplication.
Expanding -10(x-1.7), we get
-10x + 17 = -3
Now we can solve for x by isolating the variable on one side of the equation. To do this, we'll add 10x to both sides of the equation
-10x + 17 + 10x = -3 + 10x
Simplifying, we get
17 = 10x - 3
Next, we add 3 to both sides of the equation
17 + 3 = 10x - 3 + 3
Simplifying, we get
20 = 10x
Finally, we divide both sides of the equation by 10 to isolate x
20/10 = 10x/10
Simplifying, we get
2 = x
Therefore, the solution to the equation -10(x-1.7)=-3 by expanding first is x = 2.
To know more about distributive property here
https://brainly.com/question/6276874
#SPJ1
A graph is shown.
6987654321
10
0 1 2 3 4 5 6 7 8 9 10
Which ordered pair describes a point that should be removed from the graph so that the graph represents a function?
Answers
An ordered pair that describes a point that should be removed from the graph so that the graph represents a function include the following: A. (1, 1).
What is a function?In Mathematics and Geometry, a function can be defined as a mathematical equation which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.
Based on the graph shown below, we can reasonably infer and logically deduce that it does not represent a function because the input values (domain or independent values) are not uniquely mapped to the output values (range or dependent values);
3 → 1
1 → 1
In this context, we can reasonably infer and logically deduce that either (3, 1) or (1, 1) must be removed from the graph in order to represent a function.
Read more on function here: https://brainly.com/question/27862183
#SPJ1
Missing information:
The question is incomplete and the complete question is shown in the attached picture.
what principal will earn $67.14 interest at 6.25% for 82 days?
Answers
Answer:
I'm pretty much confused abt this one bc I didn't get an exact answer. Anyway I think it's 13.1
Step-by-step explanation:
The pic
What is the equation through the points: (6, 5), (8, -2)
ASAP please
Answers
The equation of the line passing through the points (6, 5) and (8, -2) is[tex]y = -\frac{7}{2} x + 26[/tex].
What is the equation of the line?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Determine the slope of the line.
Given the two points are (-7, -3) and (1, 2)
We can find the slope of the line by using the slope formula:
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values:
m = (-2 - 5) / (8 - 6)
m = -7/2
Using the point-slope form, plug in one of the given points and slope m = -7/2 to find the equation of the line.
Let's use the point (6, 5):
y - y₁ = m(x - x₁)
[tex]y - 5 = -\frac{7}{2}( x - 6 )\\\\y - 5 = -\frac{7}{2} x + 21\\\\y = -\frac{7}{2} x + 21 + 5\\\\y = -\frac{7}{2} x + 26[/tex]
Therefore, the equarion of the line is [tex]y = -\frac{7}{2} x + 26[/tex].
Learn more about equation of line here: brainly.com/question/2564656
#SPJ1
Which expression is equivalent to 6^2/7 ?
Answers
Answer: A
Step-by-step explanation:
well i did alll of them and got A
Look at this pictograph:
Library books checked out
December
January
February
March
April
Each = 5 books
How many more books were checked out in March than in April?
books
Answers
There were no more books checked out in March than in April.
What is the pictograph about?The pictograph provided shows the number of books checked out from the library during the months of December, January, February, March, and April. Each picture represents 5 books.
The pictograph tells us that for each of these months, 5 books were checked out. So, in March, 5 books were checked out, and in April, 5 books were also checked out.
To find the difference between the number of books checked out in March and April, we subtract the number of books checked out in April from the number of books checked out in March:
5 books (March) - 5 books (April) = 0 books
Therefore, The result shows that there were no more books checked out in March than in April. Both months had the same number of books checked out, which is 5.
Learn more about pictograph from
https://brainly.com/question/768035
#SPJ1
A gas station sells regular gas for $2.20 per gallon and premium gas for $2.75 a gallon. At the end of a business day 340 gallons of gas had been sold, and receipts totaled $803. How many gallons of each type of gas had been sold?
Answers
Using a system of equations, the quantities of each type of gas sold by the gas station for the business day are as follows:
Regular Gas = 240 gallonsPremium Gas = 100 gallons.What is a system of equations?A system of equations refers to two or more equations solved concurrently.
A system of equations is also known as simultaneous equations because they can be solved at the same time.
Regular Premium
Price per gallon $2.20 $2.75
Total number of gallons of gas sold = 340
The total receipts for the 340 gallons = $803.
Let the number of gallons of the regular gas = x
Let the number of gallons of the premium gas = y
Equations:x + y = 340 ...Equation 1
2.2x + 2.75y = 803 ...Equation 2
Multiply Equation 1 by 2.2:
2.2x + 2.2y = 748 ...Equation 3
Subtract Equation 3 from Equation 2:
2.2x + 2.75y = 803
-
2.2x + 2.2y = 748
0.55y = 55
y = 100
x = 240 (340 - 100)
Learn more about a system of equations at https://brainly.com/question/13729904.
#SPJ1
b/8 < 8 help me please I also need the graphic
Answers
The solution of the inequality given is b < 64
the graph is attached
How to solve for bIn the equation, let us replace b with x
To solve the inequality x/8 < 8 for x, we need to isolate x on one side of the inequality.
We can do this by multiplying both sides of the inequality by 8, which will cancel out the 8 in the denominator on the left side:
Therefore, the solution to the inequality x/8 < 8 is x < 64.
This means that any value of x that is less than 64 will make the inequality true.
Learn more about inequality at
https://brainly.com/question/25275758
#SPJ1
Which statements are true about a decagonal (10-sided) pyramid? Select 3 options.
It has one face that is a decagon.
It has two faces that are decagons.
It has 11 faces.
It has 20 edges.
It has 20 vertices.
Answers
The correct statements are,
B)It has two faces that are decagons.
C)It has 11 faces.
D)It has 20 edges.
What is decagonal pyramid?
A decagonal pyramid is a solid whose base is a decagon or a ten sided figure, regular or irregular. The surfaces are ten isosceles triangles, in case of a regular decagonal pyramid with all the ten vertices meeting at a point.
Here The decagonal prism is formed by two regular decagons as its bases and 10 squares as its other faces. the top of the decagonal prism is a regular decagon, so is the bottom face.
We know that decagonal pyramid has 11 faces and 20 edges and 11 vertices.
Hence the correct statements are,
B)It has two faces that are decagons.
C)It has 11 faces.
D)It has 20 edges.
To learn more about decagonal pyramid refer the below link
https://brainly.com/question/22585969
#SPJ1
pls answer asap
A traveler has 9 pieces of luggage.
How many ways can the traveler select 3 pieces of luggage for a trip?
Responses
84
84
504
504
60,480
60,480
362,880
Answers
Answer:
84
Step-by-step explanation:
Trust me
Answer:
84
Step-by-step explanation:
There are 9 pieces of luggage.
We can select the first piece 9 different ways, the second piece 8 different ways, since there are only 8 pieces left. The third piece can be selected 7 different ways.
9*8*7
504
But order doesn't matter since we are taking 3 pieces.
Divide by (3*2*1)
504/6 = 84
There are 84 different combinations of luggage
Solve 8 • w ≤ 72. Graph the solution.
Please help
Answers
Answer:
w≤9
Step-by-step explanation:
8w ≤ 72
Divide by 8 on both sides
w ≤ 9
For graph, draw a number line and label a point as 9. Draw a solid line facing to the left and having a closed point at 9. The line should not extend past 9.
9. What is the volume of a rectangular prism with a length of 11 meters, width of 26 meters, and height of 38 meters?
Answers
Answer:
10868
Step-by-step explanation:
11x26=286
286x38=10868
Determine the solution to the equation shown below.
3.2 - 1/2 (x+4) = 4.8x + 2 - 5.2x
Answers
Answer:x=-8
Step-by-step explanation:
3.2+(−1/2)x−2=4.8x+2−5.2x
−0.1x=0.8
x=-8
Answer:
x=-8
Step-by-step explanation:
x=-8
Mo is running the tracks where one lap is 400m. After completing some laps, he found that he has completed 40% of the total distance. After another 2, 50% is done. What is the total distance that he needs to cover in meters?
I REALLY NEED THE ANSWER SOON,
IF YOU CAN DO IT WELL THANK YOU.
Answers
Answer:
Total distance is 8000 m------------------
According to the problem, 2 laps make a difference of 10% as:
50% - 40% = 10%Hence the total distance in terms of laps is:
100% / 10% = 10 times the 2 laps:Find the total distance:
Total distance = 10*2 = 20 lapsTotal distance = 20*400 m = 8000 mWhich of the following is the graph of the quadratic function y = x² - 4x+4?
A. Graph C
B. Graph B
C. Graph D
D. Graph A
Answers
Answer:
The correct answer is C, Graph D.
x^2 - 4x + 4 = (x - 2)^2.
tamara. Find the sum of two number cubes rolled at the same time. The chart below shows all possible sums from 36 possible combinations how many times should tamara expect the sum of two cubes to be equal to five if she rolls the cubes 180 times
Answers
Answer:
Step-by-step explanation:
There are 6 possible outcomes when rolling a single cube (1, 2, 3, 4, 5, or 6). When rolling two cubes, the possible sums range from 2 (1+1) to 12 (6+6). Using the chart provided, we can see that the sum of two cubes being equal to 5 only occurs once in the 36 possible combinations: when one cube shows a 1 and the other cube shows a 4.
To find the expected number of times this sum will occur if Tamara rolls the cubes 180 times, we need to multiply the probability of this event occurring on any given roll by the number of rolls. The probability of rolling a sum of 5 is 1/36, since there is only one way to get a sum of 5 out of the 36 possible combinations. Therefore, the expected number of times this sum will occur in 180 rolls is:
(1/36) x 180 = 5
So Tamara should expect to roll a sum of 5 about 5 times in 180 rolls of two cubes.
The distance between Kingston and Sunny Place is 35 km. At 8.30 a.m. , Joel cycles from Kingstown towards Sunny place at an average speed of 12 Km/h. At the same time, Ryan cycles from Sunny place towards Kingstown, along the same route, at an average speed of 8 Km/h.
a) At what time will the cyclists meet on the way?
b)How far will each cyclist have travelled when they meet?
Answers
Answer:
Distance = Speed × Time.
Let's break down the problem into two parts:
a) At what time will the cyclists meet on the way?
Let's assume t represents the time in hours when the cyclists meet.
The distance Joel travels in t hours is given by: Distance = Speed × Time = 12t km.
The distance Ryan travels in t hours is given by: Distance = Speed × Time = 8t km.
Since they are cycling towards each other, the sum of their distances should equal the total distance between Kingston and Sunny Place, which is 35 km.
So, we can set up the equation: 12t + 8t = 35.
Simplifying the equation, we have: 20t = 35.
Dividing both sides of the equation by 20, we get: t = 35/20 = 1.75 hours.
Therefore, the cyclists will meet on the way after 1.75 hours, which is equivalent to 1 hour and 45 minutes.
b) How far will each cyclist have traveled when they meet?
To find the distance traveled by each cyclist, we can substitute the value of t into their respective equations:
Distance traveled by Joel = 12t = 12 × 1.75 = 21 km.
Distance traveled by Ryan = 8t = 8 × 1.75 = 14 km.
Therefore, when the cyclists meet, Joel would have traveled 21 km and Ryan would have traveled 14 km.