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Complete Question
Select all decimals that are equivalent to ( 9 × 100 ) + ( 2 × 10 ) + ( 3 × 1/10 ) + ( 5 × 1/100 ) . A. 92.35 B. 920.350 C. 902.35 D. 92.350 E. 920.35 F. 920.035
Answer:
E. 920.35
Step-by-step explanation:
( 9 × 100 ) + ( 2 × 10 ) + ( 3 × 1/10 ) + ( 5 × 1/100 )
Step 1
(900) + (20) + (3/10) + (5/100)
Step 2
900 + 20 + 0.3 + 0.05
Step 3
920.35
Therefore, the answer = 920.35
Answer:
The Answer is actually B & E if doing this via Connexus. Connexus doesn't view putting an extra zero at the end to be incorrect (as it really isn't, it is just pointless) but Connexus does view NOT selecting that one as incorrect.
So while E is the correct answer, you will only get partial credit if you don't also select B. (With Connexus you can tell ones that are supposed to have multiple answers if they have check boxes instead of radio buttons.)
Step-by-step explanation:
What is the value of the expression below when y = 7?
y2+ 5y + 6
90
Plug in 7 for x and solve.
[tex]{y}^{2} + 5y + 6[/tex]
[tex]{(7)}^{2} + 5(7) + 6[/tex]
[tex]49 + 35 + 6[/tex]
[tex]90[/tex]
Square root of 9610 by division method
Answer:98.03060747
Step-by-step explanation:
Square root 9610
A bus makes a stop at 2:30, letting off 12 people and letting on 9. The bus makes another stop ten minutes later to let off 4 more people. How does the number of people on the bus after the second stop compare to the number of people on the bus before the 2:30 stop?
Answer: bus makes a stop at 2:30, letting off 15 people and letting on 9
-15 + 9 = -6
The bus makes another stop ten mins later to let off 4 more people
-4
Happy to Help! (Now i must go back to my planet ^^)
Figure A was translated 5 units left to create Figure B.
Figure B was reflected over the line y=1 to create Figure
C. Figure C was rotated 90 degrees clockwise around
the origin to create Figure D. Are Figure A and Figure D
congruent?
А A
Prove your answer using any tools and explain
reasoning in the box below:
10
Answer:
a
Step-by-step explanation:
What is the equation for g, which is f(x) = 2x2 + 3x − 1 reflected across the y-axis? Group of answer choices g(x) = −2x2 − 3x − 1 g(x) = 2x2 + 3x − 1 g(x) = −2x2 − 3x + 1 g(x) = 2x2 − 3x − 1
Answer:
[tex]g(x) = 2x^2 - 3x - 1[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 2x^2 + 3x - 1[/tex]
Required
Determine g(x), if f(x) is reflected across the y axis
When a function (x,y) is reflected across the y axis, the new function becomes (−x,y).
In other words,
[tex]g(x) = f(-x)[/tex]
Calculating f(-x)
[tex]f(-x) = 2(-x)^2 + 3(-x) - 1[/tex]
[tex]f(-x) = 2x^2 - 3x - 1[/tex]
Substitute g(x) for f(-x)
[tex]g(x) = 2x^2 - 3x - 1[/tex]
Hence;
[tex]g(x) = 2x^2 - 3x - 1[/tex]
Tim has a bag of 36 orange-flavored sweets and Peter has a bag of 44 grape-flavored sweets. They have to divide up the sweets into small trays with equal number of sweets; each tray containing either orange-flavored or grape-flavored sweets only. If there is no remainder, find the largest possible number of sweets in each tray.
Answer:
Largest possible number of sweets in each tray[tex]=4[/tex]
Step-by-step explanation:
Given:
Number of orange-flavored sweets = 36
Number of grape-flavored sweets = 44
To find: largest possible number of sweets in each tray
Solution:
HCF(highest common factor) of two or more numbers refers to the greatest number which can divide the given numbers
To find largest possible number of sweets in each tray, find the HCF(highest common factor) of 36 and 44.
[tex]36=2^{2}\times 3^{2}\\44=2^{2}\times 11[/tex]
So,
[tex]HCF(36,44)=2^{2}=4[/tex]
So,
Largest possible number of sweets in each tray[tex]=4[/tex]
The largest possible number of sweets in each tray is 4.
In order to determine the largest possible sweets in each tray, the highest common factor of the number of sweets have to determined. The highest common factor is the highest factor that is common to two or more numbers.
Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, and 36.
Factors of 44 = 1, 2, 4, 11, 22, 44.
Common factors = 1, 2, 4
Highest common factor - 4
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Write an equation in slope-intercept form of the line with slope 3 that contains the point (1, 2).
Answer:
Step-by-step explanation:
y - 2 = 3(x - 1)
y - 2 = 3x - 3
y = 3x - 1
Express 0.1 as a fraction.
Step-by-step explanation:
Write 0.1 as
0.1
1
Multiply both numerator and denominator by 10 for every number after the decimal point
0.1 × 10
1 × 10
=
1
10
Reducing the fraction gives
1
10
In fraction form the number 0.1 can be written as 1/10.
Use the concept of fraction defined as:
A fraction is a part of the whole number and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called a fraction. It can be written in the form of p: q, which is equivalent to p/q.
The given number is: 0.1
Since the given number is a decimal number,
And it has only in digit after decimal.
Therefore,
Divide and multiply by 10 with this number,
[tex]0.1 \times \dfrac{10}{10} = \dfrac{1}{10}[/tex]
Hence,
The fraction from of the number 0.1 is 1/10
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Please Help Brainliest to whoever can give a clear explanation for this problem!
In triangle ABC, [tex] \angle A = 90 [/tex], AC = 1, and AB = 5. Point D lies on ray AC such that [tex]\angle DBC = 2\angle CBA[/tex]. Compute AD.
See the attached sketch. Let [tex]\beta[/tex] denote angle ABC and [tex]\beta'[/tex] denote angle CBD. Then [tex]\beta'=2\beta[/tex].
From the sketch, we see that
[tex]\tan\beta=\dfrac15[/tex]
[tex]\tan(\beta+\beta')=\tan(3\beta)=\dfrac{AD}5[/tex]
Write [tex]\tan(3\beta)[/tex] in terms of [tex]\tan\beta[/tex]. Recall the angle sum identity for tangent:
[tex]\tan(x+y)=\dfrac{\tan x+\tan y}{1-\tan x\tan y}[/tex]
This gives us
[tex]\tan(3\beta)=\dfrac{\tan\beta+\frac{2\tan\beta}{1-\tan^2\beta}}{1-\tan\beta\cdot\frac{2\tan\beta}{1-\tan^2\beta}}=\dfrac{\tan\beta(\tan^2\beta-3)}{3\tan^2\beta-1}[/tex]
and plugging in [tex]\tan\beta=\frac15[/tex] leaves us with
[tex]\tan(3\beta)=\dfrac{37}{55}[/tex]
and so AD = 5 * 37/55 = 37/11.
Expand and simplify the expression
(p-4q) (3p+q) - (2p+3q) (4p-7q)
Answer:
[tex]-5p^2-9pq+17q^2[/tex]
Step-by-step explanation:
[tex](p-4q) (3p+q) - (2p+3q) (4p-7q)\\\\\mathrm{Expand}\:\left(p-4q\right)\left(3p+q\right):\quad 3p^2-11pq-4q^2\\=3p^2-11pq-4q^2-\left(2p+3q\right)\left(4p-7q\right)\\\\\mathrm{Expand}\:-\left(2p+3q\right)\left(4p-7q\right):\quad -8p^2+2pq+21q^2\\=3p^2-11pq-4q^2-8p^2+2pq+21q^2\\\\\mathrm{Simplify}\:3p^2-11pq-4q^2-8p^2+2pq+21q^2:\\\quad -5p^2-9pq+17q^2[/tex]
Answer:
-5p² -9pq +17q²
Step-by-step explanation:
Please see attached picture for full solution.
REALLY IN NEED OF HELP!! please do the best you can<3 Many companies make products to sell, either to other businesses or directly to consumers. The amount of money that a company collects from sales of its products is called its revenue. When a business produces a product, there are costs associated with production. For example, if a cola company is producing a diet cola, they incur costs from purchasing ingredients, aluminum to make cans, cardboard to make boxes, as well as the cost of paying their employees, and more. The profit that a company earns is the difference between the amount earned and the amount spent. Consider the lip color product from each of the two competing high-end cosmetic companies described below. The Alcone Company Besame Beauty This company makes a popular shade of lip color that retails for $45 per tube. The lip color costs The Alcone Company $36 per tube to make and the monthly costs associated with manufacturing just this color are $1,500. A popular shade of lip color from this company costs the consumer $55 per tube. The process to make the lip color costs Besame Beauty $44 per tube and the monthly costs associated with this are $2,200. Use the information given to explore some of the mathematical concepts you have practiced so far by answering the questions below. 1. Develop a single formula you can use to find the profit earned by both The Alcone Company and Besame Beauty for their lip color. Explain why your formula will work for both companies. 2. Write an expression that each company can use to describe the amount of money they will earn from selling their lip colors. Let x represent the number of tubes of lip color each company sells. 3. Write an expression that each company can use to describe the amount of money it costs them to manufacture the lip color each month. Let x represent the number of tubes of lip color each company sells. 4. Use your responses to questions 1, 2, and 3 to write fully simplified expressions each business could use to find their monthly profit. State which property of algebra you are using at each step. Remember that x represents the number of tubes of lip color each company sells. 5. If each company makes 225 tubes of their lip color this month, what amount of profit can they expect? Interpret your answers in terms of the problem’s context. 6. If each company makes and sells 150 tubes of their lip color this month, what amount of profit can they expect? Interpret your answers in terms of the problem’s context. 7. Explain how you used the order of operations to help you answer questions 5 and 6. 8. Explain how you figure out the number of tubes of lip color each company would need to manufacture and sell in order to earn a profit that is greater than 0. 9. Implement your plan from question 8. What is the minimum number of lip color tubes each company would need to manufacture and sell in order to earn a profit that is greater than 0? Interpret your answers in context of the question
Answer:
1. Profit = Revenue - Cost
2. For the Alcone Company Revenue = $45 × x
For the Besame Beauty Revenue = $55 × x
3. Alcone Company; Cost = $1,500 + $36×x
Besame Beauty; Cost = $2,200 + $44×x
4) For Alcone Company, we have;
Profit = $9 × x - $1,500
For Besame Beauty, we have;
Profit = $11 × x - $2,200
5) For Alcone Company;
Profit= $525
For Besame Beauty;
Profit = $275
6) For Alcone Company;
Profit = -$150
For Besame Beauty;
Profit -$550
7) Order of operations is used to ensure that the revenue is first calculated before the cost is subtracted to find the costs
8) In order to find the number of tubes that the company would need to manufacture in order to have a profit of greater than 0, we equate the expression using the inequality of greater than 0 to find the value of x that must be surpassed to have a profit greater than 0
9) For Alcone Company;
The profit will be > 0 at x = 167 tubes
For Besame Beauty;
The profit will be > 0 at x = 201 tubes
Step-by-step explanation:
The given parameters are;
The Alcone Company
The price at which the shade of lip color is sold = $45 per tube
The cost incurred to make the lip color = $36 per tube
The monthly manufacturing cost of manufacturing the lip color = $1,500
For Besame Beauty
The price at which the shade of lip color is sold = $55 per tube
The cost incurred to make the lip color = $44 per tube
The monthly manufacturing cost of manufacturing the lip color = $2,200
1. The formula for finding the profit is given as follows;
Profit = Revenue - Cost
Revenue = Sale price × Number of tubes sold
Cost = The monthly manufacturing cost + The cost incurred to make the lip color × Number of tubes
2. The expression for revenue for the Alcone Company is given as follows;
Revenue = $45 × x
The expression for revenue for the Besame Beauty is given as follows;
Revenue = $55 × x
3. The expression for the cost for the manufacture of the lip color by the Alcone Company per month is given as follows;
Cost = $1,500 + $36×x
The expression for the cost for the manufacture of the lip color by the Besame Beauty per month is given as follows;
Cost = $2,200 + $44×x
4) For Alcone Company, we have;
Revenue = $45 × x
Cost = $1,500 + $36×x
By transitive property and distributive property, we have
Profit = Revenue - Cost = $45 × x - ($1,500 + $36×x) = $9 × x - $1,500
Profit = $9 × x - $1,500
For Besame Beauty, we have;
Revenue = $55 × x
Cost = $2,200 + $44×x
By transitive property and distributive property, we have;
Profit = Revenue - Cost = $55 × x - ($2,200 + $44×x) = $11 × x - $2,200
Profit = $11 × x - $2,200
5) With the number of tubes produced = 225 tubes, we have;
For Alcone Company;
Profit = $9 × x - $1,500 = $9 × 225 - $1,500 = $525
ForBesame Beauty;
Profit = $11 × x - $1,500 = $11 × 225 - $2,200 = $275
6) With the number of tubes produced = 150 tubes, we have;
For Alcone Company;
Profit = $9 × x - $1,500 = $9 × 150 - $1,500 = -$150
For Besame Beauty;
Profit = $11 × x - $2,200 = $11 × 150 - $2,200 = -$550
7) Order of operations is used to ensure that the revenue is first calculated before the cost is subtracted to find the costs
8) In order to find the number of tubes that the company would need to manufacture in order to have a profit of greater than 0, we equate the expression using the inequality of greater than 0 to find the value of x that must be surpassed to have a profit greater than 0
9) For Alcone Company;
Profit = $9 × x - $1,500 >0
$9 × x >0 + $1,500
$9 × x > $1,500
x > $1,500/$9
x > 500/3
x > [tex]166\frac{2}{3}[/tex]
Therefore, the profit will be > 0 at x = 167 tubes
For Besame Beauty;
Profit = $11 × x - $2,200 > 0
$11 × x > 0 + $2,200
$11 × x > $2,200
x > $2,200/$11
x > 200
Therefore, the profit will be > 0 at x = 201 tubes
Pete and his friend Danny volunteered to bring sandwiches for lunch at a homeless shelter. They bought 7 loaves of bread. Each loaf had 18 slices of bread. The boys used up all the bread to make the sandwiches. They used 2 slices to make each sandwich. How many sandwiches did they make for the shelter?
Answer:
63 sandwiches
Step-by-step explanation:
Pete and his friend Danny volunteered to bring sandwiches for lunch at a homeless shelter
They brought 7 loaves of bread
Each loaves have 18 slices
They used 2 slices each to make the sandwich
The first step is to calculate the total number of slices
Sinces 7 loaves of bread are used and each of them contain 18 slices then, the total number of slices can be calculated as follows
= 7 ×18
= 126 slices
Therefore since 2 slices of bread is used to make one sandwich then, the number of sandwiches that was made can be calculated as follows
= 126/2
= 63
Hence 63 sandwiches were made for the shelter
What is m2 + m 23? Pls I need ASAP
Answer:
90 degrees
Step-by-step explanation:
the answer is 90 degrees because when the triangle is a right triangle, the two smaller angles equal 90 degrees.
What is Uche's pumping rate in \dfrac{\text{mL}}{\text{s}} s mL start fraction, start text, m, L, end text, divided by, start text, s, end text, end fraction?
Step-by-step explanation:
Pumping rate my be defined as the the rate ta which a liquid is pumped through a system. It is measured as the flow of the liquid at a unit time. It may be referred to as the capacity of the pump which defines how much liquid is being passed through the pump in a certain given time.
The pumping rate in mL/s refers to the amount of liquid passed in one second of time.
I know it’s a lot but I’m pretty stupid and could use help online class ain’t easy when you’re internet sucks thanks!
Problem 5
There are 2 answers and they are choice B and choice C
We can tell by looking at the factors. For something like choice B, the factor (x+6) shows up twice, so that means x = -6 is a double root. Something like choice A has roots x = -6 and x = 6 which aren't the same.
========================================
Problem 6
Ted is correct. He set each factor equal to 0 and solved each equation that resulted from doing so.
Note how 3x-2 = 0 turns into 3x = 2 after adding 2 to both sides. Then he divided both sides by 3 to get x = 2/3. That's the first solution. The second solution x = -5 results from solving x+5 = 0. You subtract 5 from both sides.
To fix Maggie's mistake, you just need to correct her steps to mirror Ted's steps.
What’s 13/19 as a decimal rounded to the nearest hundredth?
Answer:
0.68
Step-by-step explanation:
We can use long division to find the decimal equivalent of [tex]\frac{13}{19}[/tex] since a fraction is just another way of writing a division statement.
[tex]19\overline{\smash{)}#13}\\\\0.\\19\overline{\smash{)}#130}\\\\0.6\\19\overline{\smash{)}#130-114=16}\\\\0.6\\19\overline{\smash{)}#160}\\\\0.68\\19\overline{\smash{)}#160-152 = 8}\\\\0.68\\19\overline{\smash{)}#80}\\\\0.684\\19\overline{\smash{)}#80}[/tex]
0.684 to the nearest hundredth is 0.68.
Hope this helped!
please help ill give 10 points and a brainly to who ever who can answer this. thanks!!!
Answer:
Step-by-step explanation:
I WILL MARK BRAINIEST ZWYX and ZZYX are supplementary angles. mZWYX 8x + 12 and mZZYX = 2x + 28. What is mZWYX? mZWYX
Answer:
124 degrees
Step-by-step explanation:
Look at the equation from the information they gave you. Supplementary angles always add up to 180 degrees, so make up the equation of 8x + 12 + 2x + 28 = 180. Simplify to get 10x + 40 = 180. Subtract 40 from both sides to get 10x = 140. Divide both sides by 10, and you will get x=14. Substitute the value of 10 into the variable x in the angle ZWYK to get 8(14) + 12. This will simplify into 112 + 12, which will eventually get you 124 degrees.
Answer:
mZWYX = 124°Step-by-step explanation:
Since angles ZWYX and ZZYX are supplementary it means that the sum of their angles sum up to 180°
To find mZWYX we must first find x
To find x add ZWYX and ZZYX and equate them to 180 to find x
That's
ZWYX + ZZYX = 180
8x + 12 + 2x + 28 = 180
10x + 40 = 180
10x = 180 - 40
10x = 140
Divide both sides by 10
x = 14°
From the question
mZWYX = 8x + 12
Substitute the value of x into the expression
We have
mZWYX = 8(14) + 12
= 112 + 12
We have the final answer as
mZWYX = 124°Hope this helps you
Which of the following measures of central tendency are resistant to outliers? (May be more than one correct answer) Group of answer choices Median Mode Mean Range Inter-quartile Range (IQR) Standard Deviation
Answer
Median
Step-by-step explanation:
It should be noted that medians are resistant to outliers.
Outliers simply means the data records which are different from every other record. It escapes normality. The outlier affects mean, inter-quartile range, mode and the range.
It should be noted that the median isn't affected by outliers. The reason for this is that the median depends on the arrangement and the order of the data. For example, when one changes the lowest score in a given set of numbers, the order won't be affected.
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you deposit $3000 into an account that pays 8% compounded quarterly. how much will you have in 10 years?
Answer:
$5400 USD
Step-by-step explanation:
Investment=3,000
Interest=8% = .08
Time=10 years
([3000 x .08 x 10] + 3,000
[240 x 10] + 3,000
2,400 + 3,000= 5,400
Using four or more complete sentences, contrast race and ethnicity and provide an example of each.
Answer:
Race and Ethnicity are considered to be social constructs that enable humans to be grouped or categorized. They are sometimes used interchangeably but most argue that they are different and give them different definitions.
Race is generally used to refer to people that have the same physical characteristics such as skin color or the same texture of hair for instance Black and White/Caucasian.
Ethnicity on the other hand relates to people sharing a common culture, language, nation, and/ or tribal heritage for instance, the English, the Irish and the Igbo.
Answer:
The terms race and ethnicity are often used interchangeably throughout society. However, there is a distinct difference between the two. Race refers to a classification system based on inherited physical or biological traits, such as eye, hair, or skin color. In contrast, ethnicity refers to a group of people that can be linked together by common characteristics such as shared experiences, history, culture, or beliefs. Examples of ethnic groups include Native Americans, French Canadians, and Kongos.
Step-by-step explanation:
(edg2020)
Please help me? -4(7+2x)=-7x-33
Answer:x=5
Step-by-step explanation:
First we do the parenthesis
-4(7+2x)=-7x-33
To get
-28+-8x=7x+-33
and
-8x-28=-7x-33
Then we Add 7x to both sides.
-8x-28+7x=-7-33+7x
-x-28=-33
Then we Add 28 to both sides.
-x-28+28=-33+28
-x=-5
Lastly Divide both sides by -1.
-x/-1=-5/-1
X=5
a2+ 12a− 7 − 3a2− 5a+ 8
What are the roots of the equation? x² + 3x - 18 = 0
Answer:
[tex]x[/tex] = -6
[tex]x[/tex] = 3
Step-by-step explain
[tex]x^{2}[/tex] = 3[tex]x[/tex] - 18 =0
[tex]x^{2}[/tex] =6[tex]x[/tex] - 3[tex]x[/tex] - 18 = 0
[tex]x[/tex] x ([tex]x[/tex] + 6) -3[tex]x[/tex] - 18 = 0
[tex]x[/tex] x ([tex]x[/tex] + 6) - 3([tex]x[/tex] = 6)=0
([tex]x[/tex] = 6) x ([tex]x[/tex] 3) = 0
[tex]x[/tex] +6 = 0
[tex]x[/tex] - 3 = 0
[tex]x[/tex] = -6
[tex]x[/tex] = 3
Type the correct answer in each box. A company manufactures three types of cabinets, type A, type B, and type C. Last week, the number of type B cabinets produced was 30 more than the number of type A cabinets produced. The number of type C cabinets produced was 20 more than times the number of type A cabinets produced. If the company made the same number of type B and type C cabinets last week, then the number of type A cabinets produced was _____ . The total number of cabinets produced last week was ____.
Hi There!!
B = 1/2A + 30
C = 3/2A + 20
B = C
1/2A + 30 = 3/2A + 20
30 - 20 = 3/2A - 1/2A
10 = A
B = 1/2A + 30
B = 1/2(10) + 30
B = 5 + 30
B = 35
C = 3/2A + 20
C = 3/2(10) + 20
C = 15 + 20
C = 35
type A cabinets produced was 10
type B and type C cabinets produced were both 35
Good Luck!!
[tex]Itsbrazts[/tex]
Answer:
If the company made the same number of type B and type C cabinets last week, then the number of type A cabinets produced was 10. The total number of cabinets produced last week was 80.
Step-by-step explanation:
I took the test.
Given the following functions, find g(f(x)). f(x) = 2x + 1 g(x) = x2 + 6
Answer:
Step-by-step explanation:
g(x) = x^2 + 6
f(x^2 + 6) = 2(x^2 + 6) + 1 = 2x^2 + 12 + 1 = 2x^2 + 13
what is the decimal that is greater than 3/10 and less than 2/5
Answer:
0.31 - 0.39
Step-by-step explanation:
3/10 = 0.3
2/5 = 0.4
All the values between 0.3 and 0.4 excluding 0.3 and 0.4 (can't be 0.3 or 0.4)
The decimal number that is greater than 3/10 and less than 2/5 will be;
⇒ 0.35
What is Decimal number?A decimal number is a number that consists of a whole and a fractional part.
Given that;
A decimal number is greater than 3/10 and less than 2/5.
Now,
Let a decimal number = x
So, We get;
⇒ 3/10 < x < 2/5
Since, We have;
⇒ 3/10 = 0.3
⇒ 2/5 = 0.4
Thus, The decimal number that is greater than 3/10 and less than 2/5 is 0.35.
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20 Points!!! any absurd answers, I will report. In which expression should the exponents be multiplied? 2 to the 9th over 2 to the 7th (610)−7 one half to the 3rd times one half to the 5th 52 ⋅ 54
Answer:
it would be 2 to the 9th over 2 to the 7th
Step-by-step explanation:
Answer:
it would be 2 to the 9th over 2 to the 7th
Step-by-step explanation:
If you add two negative integers, what will the sign on the sum be? Explain.
Answer:
Negative
Step-by-step explanation:
If both are negative, they can't grow when you add them. If I owe someone 3 dollars, then I owe them 3 more, I don't owe them 0, I owe them 6. The equation would be My amount of money-3-3
Given the polynomial 21x^4+3y-6x^2+34 1. What polynomial must be subtracted from it to obtain 29x^2-7? 2. What polynomial must be added to it to obtain a first degree polynomial?
Answer:
[tex]21x^4+3y-35x^2+41[/tex] must be subtracted
As you can see, we added -x+2 to this polynomial to obtain a first degree polynomial. (Though really anything with an x would do. For example, 3x, 2221x, or -224x would all work)
Step-by-step explanation:
We have the following polynomial
[tex]21x^4+3y-6x^2+34[/tex]
And need to find a polynomial to subtract from it to get
[tex]29x^2-7[/tex]
This means that if we subtract these two polynomials, we will get our desired polynomial
[tex]21x^4+3y-6x^2+34-(29x^2-7)\\\\21x^4+3y-6x^2+34-29x^2+7\\\\21x^4+3y-35x^2+41[/tex]
Just to be sure, we can then check our work by finding the difference of the first polynomial and the one that we just found
[tex]21x^4+3y-6x^2+34-(21x^4+3y-35x^2+41)\\\\21x^4+3y-6x^2+34-21x^4-3y+35x^2-41\\\\-6x^2+34+35x^2-41\\\\29x^2-7[/tex]
As we got the desired result, we know that this answer is correct.
And now for the second part of the problem. What polynomial must be added to it to obtain a first degree polynomial?
Recall that a first degree polynomial is one that has the total sum of 1. For example the polynomial x+5 is a first degree polynomial, but x+y+5 has a degree of 2.
This means that our desired polynomial needs to only have some amount of x's and constants.
We can do the same thing as the first time and simply subtract our desired result from the first polynomial. For simplicity, let us use the simple polynomial x+2
[tex]21x^4+3y-6x^2+34-(x-2)\\\\21x^4+3y-6x^2+34-x+2\\\\21x^4+3y-6x^2-x+36[/tex]
As you can see, we added -x+2 to this polynomial to obtain a first degree polynomial. (Though really anything with an x would do. For example, 3x, 2221x, or -224x would all work)