In mathematics, a polynomial is a mathematical expression that is the sum of a number of terms that contain the same variable raised to different powers. These come up all the time in the study of mathematics, so it is important to be familiar with them and the different forms we can write them in.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
To write a polynomial in standard form, we make sure that any like terms are combined, and then we arrange the terms so that the exponents of each term go in descending order.
For example, consider the following polynomial:
8x - x⁵ + 2x + 3x² - 7x⁴ + 3To write this polynomial in standard form, we first look for any like terms that need to be combined, where like terms are terms that have the same variable raised to the same power. We see that 8x and 2x are like terms, so we add these together to turn our polynomial into the following:
10x - x⁵+ 3x² - 7x⁴ + 3Now, we just rearrange the polynomial so that the term with the highest degree goes first, the term with the second highest degree goes second, and so on until the polynomial is arranged so that the exponents go in descending order from highest to lowest.
-x⁵ - 7x⁴+ 3x² + 10x + 3This gives us our polynomial in standard form.
A polynomial with 3 terms : x² + 3x³ + 27 - x
___________________________________________
Determine the value of the variable that makes the equation true.
b + (-8.3) = 0
The value of the variable that makes the equation true is: b = 8.3.
How to Determine the value of a Variable in an Equation?By isolating the given variable in an equation to one side of the equation, we can find out its value which will make the equation true.
Given the equation, b + (-8.3) = 0
b - 8.3 = 0 [plus times minus = minus]
Add 8.3 to both sides of the equation, to isolate variable b
b - 8.3 + 8.3 = 0 + 8.3
b = 8.3
Let's check if the value of b would make the equation true by plugging in the value of b:
b + (-8.3) = 0
8.3 + (-8.3) = 0
8.3 - 8.3 = 0
0 = 0 [true]
Therefore, the value of the variable that makes the equation true is: b = 8.3.
Learn more about equation on:
https://brainly.com/question/1429964
#SPJ1
Find the value of ax9 when a=8
Step by step Explanation= if a=8
then a×9 =8×9=72
Answer =72
Given f\left(x\right)=8-3xf(x)=8−3x, find the following
The value of the function f(2) for the function with the equation f(x) = 8 - 3x is 2
How to determine the value of the function?The function value is given as
f(x) = 8 - 3x
The above is a linear function
As a general rule
Linear functions are function that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
From the question, we have the value to be
f(2)
The above means that we determine the value of the function when x = 2
i.e., f(x) = ? when x = 2 or we substitute 2 for x in f(x)
Next, we test the above function with the x value
So, we have
f(x) = 8 - 3x
Substitute 2 for x in f(x)
f(2) = 8 - 3 x 2
Evaluate the product in the above equation
So, we have
f(2) = 8 - 6
Evaluate the difference in the above equation
So, we have
f(2) = 2
Hence, the value of the function f(2) for the function with the equation f(x) = 8 - 3x is 2
Read more about functions at
https://brainly.com/question/1415456
#SPJ1
Possible question
Given f(x)=8−3x, find the following: f(2)
HELP ME IF U HELP ME ILL GIVE U A SURPRISE!!!!!!
Abbie, Chloe, and Xander are playing a dice game. The game consists of ten rounds. In each round, each person takes a turn rolling two dice and earns or loses points based on what they role. Points are awarded according to the following table:
Roll Points
Same number on both dice +3
Different numbers, with an even sum +1
An odd sum -2
At the end of ten rounds, the person with the highest number of points wins.
In the first five rounds, Abbie got four odd sums and one pair of threes. How many points does she need to have an exact score of zero? What is the least number of rounds it will take her to have an exact score of zero? Explain your reasoning using complete sentences.
Answer:
okay so she got and odd sum 5 times which will mean she has -10 points and then she got a pair of threes which gives her 3 points so now she has -7 which means she needs 7 more points so the least amount would be 3
Step-by-step explanation:
Romina buys a bag of cookies that contains 8 chocolate chip cookies, 4 peanut butter cookies, 6 sugar cookies and 7 oatmeal cookies. What is the probability that Romina randomly selects an oatmeal cookie from the bag, eats it, then randomly selects a sugar cookie?
The probability that Romina randomly selects an oatmeal cookie from the bag, eats it, then randomly selects a sugar cookie is 7/100.
What is the probability?Probability determines the odds that a random event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0. The more likely the event is to happen, the closer the probability value would be to 1.
The probability of picking an oatmeal cookie then a sugar cookie = (number of oatmeal cookies / total number of cookies) x (number of sugar cookies / total number of cookies -1)
Total number of cookies = 8 + 4 + 6 + 7 = 25
The probability of picking an oatmeal cookie then a sugar cookie = (7/25) x (6/24) = 7/100
To learn more about probability, please check: https://brainly.com/question/13234031
#SPJ1
Evaluate.
(7/12+1/3)−(1/2+2/8)
Enter your answer as a fraction in simplest form by filling in the boxes.
Answer:
7/12+1/3_1/2+2/8
lcm of 12 and 3 is 12-lcm of 2 and 8 is 8
8/12-3/8
=5/24
Add. Write your answer in scientific notation.
(9.2×102)+(5.3×103)
Triangle ABC has been translated to create triangle A′B′C′. Which of the following statements is true? Group of answer choices m∠B′ = 63° m∠C = 63° m∠A′ = 63° m∠B = 63°
We have to know about translation inorder to understand the question.The correct answer for the question is m∠A'=63°.
A translation is a rigid transformation where a figure is moved from one location to another without changing it's size,shape or orientation.This means that the triangle that we get after translation is same as it's pre-image. So here we can say that traingles ABC and A'B'C' are congruent.When two triangles are congruent their respective sides and angles are congruent too,se we can say that
AB=A'B' and m∠A=m∠A'
BC=B'C' m∠B=m∠B'
AC=A'C' m∠C=m∠C'
It is given that in triangle ABC, m∠A=63° thus we can say that m∠A'=63°
Thus we see that using the concept of traingle translation and congruency we found that m∠A'=63° is the correct answer.
Learn more about traingle translation from here:
https://brainly.com/question/10451235
#SPJ9
A random sample of students were surveyed as to how much non-school screen time
they had each week (for purposes of the survey, screen time was defined as: time
spent online, on social media, watching TV, or playing video games) and if their grade
average was above or below 80.
Screen Time
Answer:
above below
9
9
16
15
17
less than 4 hours
4-8 hours
8-12 hours
more than 12 hours 14
%
11
What percent of the students who spend less than 4 hours a week on screens reported
a grade average below 80? Round your answer to the nearest whole number percent.
20
Submit Answer
p
attempt 2 out of 2
The percentage of students who spend less than 4 hours a week on screens which reported a grade average below 80 is 50%
Given, we have the report representing children spending time online, on social media or watching T.V, which has there effect on there grades as above or below 80.
By the question we know that the number of students who spends less than 4 hours a week on screen is:
9 + 9
= 18
And among the 18 students there are 9 students whose grade average is below 80.
So the percentage of the students who spends 4 hours a week on screen is:
= 9 ÷ 18 × 100%
= 100/2
= 50%
hence 50% students spend less than 4 hours a week on screens.
Learn more about Percentage here:
brainly.com/question/843074
#SPJ1
A food truck vendor sells small drinks for $1.15, medium drinks for $1.75, and large
drinks fro $2.25. The vendor sold a total of 1,385 drinks for a full week of business.
During the same week, his total sales were $2,238.75. During the week, he also sold
twice as many small drinks as medium drinks. Write a 3X3 system of equations that
models the vendors situation. Use s for small drinks, m for medium drinks, and g for
large drinks.
The system of equations is given by :
s + m + g = 1385
1.15 s + 1.75 m + 2.25 g = 2238.75
s = 2m
A group of equations comprising one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations.
We shall employ the linear combination method to resolve a system of three equations in three variables. This time, we will solve for the third variable while eliminating the second variable using the equations that follow from the elimination of the first.
Given the number of small drinks by the vendor is s , number of medium drinks is m and the number of large drinks is g.
The vendor sold all three drinks total of 1385, hence the equation:
∴ s + m + g = 1385.
Each small drink costs 1.15 , medium drinks cost 1.75 and large drinks cost 2.25, hence the equation:
∴ 1.15 s + 1.75 m + 2.25 g = 2238.75
He sold twice as many small drinks as medium drinks, hence the equation:
∴ s = 2m
The system of equations is given by:
s + m + g = 1385
1.15 s + 1.75 m + 2.25 g = 2238.75
s = 2m
To learn more about system of equations visit:
https://brainly.com/question/21620502
#SPJ1
Circle the problem in which you need to regroup use the strategy that is easier to find the sum. a 496 + 284. B 482 + 506
Correct answer is B. In A, there is no number from which to regroup (all the numbers may be added together), so you must regroup. In B, the number 6 cannot be added to the number 2, therefore you must regroup.
What is regrouping in mathematics?Making groups of ten while doing math operations like addition or subtraction is known as regrouping. This frequently occurs while dealing with double digits. Technically speaking, it also happens whenever you get a response that is more than 10.
Additionally, if the numbers you are adding result in a two-digit number and they are not in the farthest left column, you must regroup. When the numbers you are subtracting from are more than the ones you are subtracting from, you regroup.
To learn more about regrouping from given link
https://brainly.com/question/20490807
#SPJ9
You started this year with $447 saved and you continue to save an additional $27 per month. Write an algebraic expression to represent the total amount of money saved after m months.
Answer:
s = 13m + 384
hope this helped <3
10n + 2 =43 what is the value of n
Answer:
n = 41/10 OR 4.1
Step-by-step explanation:
10n + 2 =43
10 + 2 - 2 = 43 - 2
10n = 43 - 2
10n = 41
10n/10 = 41/10
n = 41/10
Answer:
n = 41/10Step-by-step explanation:
10n + 2 = 43 what is the value of n
10n + 2 = 43
10n = 43 - 2
10n = 41
n = 41/10
-------------------
check
10 * 41/10 + 2 = 43
41 + 2 = 43
43 = 43
the answer is good
ANSWER THE FOLLOWING WITH COMPLETE SOLUTION:
Step-by-step explanation:
try this option (see the attachment).
Can someone help with this question?✨
Answer:
the answer is y=3x - 9
Step-by-step explanation:
From y=mx+c
;m=3 (slope)
Therefore y=3x+c
SOLVING FOR C
y=3x+c
From (2,-3)
x=2
y=-3
-3=3(2)+c
-3=6+c
SUBTRACTING (6) FROM BOTH SIDES
-3-(6)=6-(6)+c
-3-(6)=0+c
c= -3-(6)
c=-9
THEREFORE THE EQUATION OF THE LINE IS
y=3x-9
The ratio table below shows the number of eggs per omelet.
Omelets
Number of eggs
Number of omelets
18
?
9
3
6
2
3
1
How many omelets can be made with 18 eggs?
4
6
9
12
Answer:
6
Step-by-step explanation:
The ratio of omelets and egg is calculated as:
omelets: egg = 3:9
omelets: egg = 1:3
The number of the omelets made by 18 eggs will be calculated as below:
omelets: egg = 1:3
omelets: 18 = 1:3
omelets = 18 x (1/3)
omelets = 6
Therefore, the number of omelets made by 18 eggs will be 6.
Last year's sales at Mel's Cinema totaled $144,600. This year's sales should increase by 1/3. How much should sales increase by, and what will sales be in the new year?
A grocery store sells a bag of 8 oranges for $4.48. What is the cost of oranges, in
dollars per orange?
The grocery store sells each orange at $0.56.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, A grocery store sells a bag of 8 oranges for $4.48.
∴ The cost per orange is $(4.48/8) = $0.56.
The cost of each orange is $0.56.
learn more about the unitary method here :
https://brainly.com/question/28276953
#SPJ6
If the profit was given by P(x)=-0.5x^2+400x-6,000, how many downloads would give you a profit of $30,000 the next month?
The downloads that would give you a profit of $30,000 the next month is 700 download.
How to illustrate the function?From the information, the profit was given by P(x)=-0.5x²+400x-6,000.
The number of downloads that would give you a profit of $30,000 the next month will be:
P(x)= -0.5x² + 400x - 6,000.
3000 = -0.5x² + 400x - 6,000.
-0.5x² + 400x - 6,000 - 3000 = 0
0.5x² - 400x + 9000 = 0
Divide through by 5
0.1x² - 80x + 1800 = 0
Using almighty formula, the value of x is 700.
Therefore, the downloads that would give you a profit of $30,000 the next month is 700 download.
Learn more about functions on:
brainly.com/question/25638609
#SPJ1
Geometry. I need help because ive been stuck for hours
Answer:look at the variable and it will all fall together
Step-by-step explanation:
A rectangular page is designed to contain 81 square inches of print. The margins at the top and bottom of the page are each 1 inches deep. The margins on each side are 1½ inches wide. What should the dimensions of the page be so that the least amount of paper is used?
The dimensions of the rectangular page will be 11.02 inches in width and 7.35 inches in height so that the least amount of paper is used.
Given that,
The area of the rectangular print = 81 square inches
The margins at the top of the page = 1inches, and
The margins at the bottom of the page = 1inches,
And,
The margins on each side = 1(1/2) inches wide.
Now,
Let, the width of the print = x
And,
The height of the print = y
Now,
According to the question,
The width of the page = x + (1.5 + 1.5) = x + 3
And,
The height of the page = y + (1 + 1) = y + 2
Now,
i.e.
xy = 81
we get,
y = (81/x)
Now,
The area of the page (A) = (x + 3)(y + 2) = (x + 3) [(81/x) + 2],
Now,
For the least amount of paper to be used,
dA/dx = (x + 3) [(81/x) + 2]
We get,
dA/dx = [(81/x) + 2] + (x + 3) [-81/x²] = 0
[(81+2x)/x] = [(x + 3) * 81]/x²
81 + 2x² = 81x + 243
2x² = 243
We get,
x = 11.02 inch
So,
y = 81/x = 81/11.02 = 7.35 inch
Hence we can say that the dimensions of the rectangular page will be 11.02 inches in width and 7.35 inches in height so that the least amount of paper is used.
Learn more about rectangles here:
https://brainly.com/question/10046743
#SPJ1
The entire graph of the function g is shown in the figure below.
Write the domain and range of g
as intervals or unions of intervals. What is the domain and range?
The domain and range of the given graph is [tex][-3,-2) \sqcup (-1,5][/tex] and [tex][-5,4)[/tex] respectively .
The set of all possible values that qualify as inputs to a function is called the function's domain. The set of all output of the function is called range after replacing the scope, or domain, of the function.From the graph , we can see that the left most point is when x = -3 and this point is closed in endpoint, so we will include this value of x in the domain.
Whereas its another point is on x = -2 which is not filled up so , we will not consider this value of x in the domain. In the interval , domain can be represented by [tex]-3\leq x < -2[/tex] .This interval can be written as [tex][-3,-2)[/tex]
Now , the right most point is when x = 5 which is filled up so we will include this value of x in the domain. Whereas it's another endpoint is at x = - 1 , we will not consider this value of x in the domain as it is not filled up. In the interval , domain can be represented by [tex]-1 < x\leq 5[/tex] .This interval can be written as [tex](-1,5][/tex] .
In order to get the full domain of the function we will use union symbol
[tex][-3,-2) \sqcup (-1,5][/tex]
For the range , we will observe the values of y . The lowest point is when y = -5 which is filled up so we will include this value of y in the range.
Whereas the highest point is when y = 4 which is not filled up so , we will not consider this value of y in the range . In the interval , range can be represented by [tex]-5\leq y < 4[/tex] .Since there are no gaps in the range, we don't use any union symbols here and hence range is [tex][-5,4)[/tex]
Learn more about domain and range here :
https://brainly.com/question/17204393
#SPJ9
Drag and drop the range of each data set into the boxes.
PLEASEE
The range of data set 1 is 4
The range of data set 2 is 4.
What is the range?A line plot is a graph that is made up of a number line and check marks above the number line. The check mark above the number represents the frequency of the number in the data set. For example, if the number 3 on the number line has 2 checkmarks above it, it means 3 has a frequency of 2.
The range is the difference between the highest number in a dataset and the smallest number in the dataset. Range is a measure of variation.
Range = highest number - lowest number
The range of data set 1 = 7 - 3 = 4
The range of data set 2 : 7 - 3 = 4
To learn more about range, please check: https://brainly.com/question/26348529
#SPJ1.
The admission fee to a carnival is $5.00, and each game costs an additional $1.50 to play. The carnival also has a
special admission price of $14 that includes unlimited games. What is the minimum number of games a customer
must play to make the special admission price less than paying for each game separately?
Answer:
9.3333333
Step-by-step explanation:
14÷1.50=9.333333
Determine the value of x.
Answer:
C
Step-by-step explanation:
5 = sin(30) × x = 0.5 × x
x = 5 / 0.5 = 10
Translate the English phrase into an algebraic expression: the sum of 11 times 4x2 and 5x.
Answer:
I believe it is 44x^2+5x
Step-by-step explanation:
A 16-ounce bottle of orange juice says that it contains 200 milligrams of vitamin C, which is 250% of the daily recommended dosage of vitamin C for adults. What is the daily recommended dosage of vitamin C for adults? Be sure to include units in your answer.
80 milligrams is the amount of vitamin C that is considered to be 100% of the daily recommended requirement for adults.
What is the daily recommended dosage of vitamin C for adults?Parameter
The amount of liquid included in the bottle is 16 ounces.The vitamin C content of the bottle comes to a total of 200 milligrams.Since the orange juice container that has a capacity of 16 ounces states that it has 200 milligrams of vitamin C, this means that it fulfills 250% of an adult's recommended daily requirement for vitamin C. Then, for one hundred percent of the daily allotment,
As a result, we are able to draw the conclusion that the amount of vitamin C that is considered to be 100% of the daily recommended requirement for people is 80 milligrams.
Read more about vitamin C
https://brainly.com/question/15080220
#SPJ1
if sin 22.6°=5/13, what is cos 67.4° ?
The value of cos 67.4° is 5/13.
According to trigonometric identities used in mathematics, sin of an angle is equal to cos of 90 - the given angle. Mathematically, this means that, suppose we have an angle x, then-
sin(90 - x) = cos x
Here, we are given that sin 22.6° = 5/13. As we can observe that (90 - 67.4) is equal to 22.6, and we need to find the value of cos 67.4° only. Thus we can write the given equation as follows-
sin22.6° = sin(90 - 67.4°)
= cos 67.4°
Thus, sin 22.6° = cos 67.4°
Hence, cos 67.4° = 5/13
Thus, the value of cos 67.4° comes out to be 5/13.
Learn more about trigonometric identities here-
https://brainly.com/question/7331447
#SPJ9
Two cars, initially at rest and 5 km apart at t=0 , simultaneously move toward each other. Car A travels at a constant speed of 55 km/hour, while car B travels at a constant speed of 12 km/hour. How far will car A travel before meeting car B in the middle?
Car A travel before meeting car B in the middle is 268 second.
Constant Speed Motion
An object is said to travel at constant speed if the ratio of the distance traveled by the time taken is constant.
Expressed in a simple equation, we have:
v= d/t
Where
v = Speed of the object
d = Distance traveled
t = Time taken to travel d.
From the equation above, we can solve for d:
d = v . t
And we can also solve it for t:
t = d/v
Two cars are initially separated by 5 km are approaching each other at relative speeds of 55 km/h and 12 km/h respectively. The total speed at which they are approaching is 55+12 = 67 km/h.
The distance of an object can be defined as the complete path travelled by an object. For example. if a car travels east for 5 km and takes a turn to travel north for another 8 km, the total distance travelled by car shall be 13 km.The time it will take for them to meet is:
t = 5/67
t = 0.0746 hours
Converting to seconds: 0.0746*3600 = 268.56
Therefore the closest answer is d. 268 s.
to know more about distance ;
visit ; brainly.com/question/10960571
#SPJ9
On April 11, Maria's checking account balance was $922. She wrote a check on April 29 for $280, withdrew
$40 on May 1, and deposited $150 into her account on May 14. What is her account balance on May 15?
Write your answer as a whole dollar amount, such as: $148.