The polynomial in standard form is as follows;
8x⁵ - 5y⁴ - 2xy⁵ + x²y
How to find the standard form of polynomial?A polynomial can have constants, variables and exponents, but never division by a variable. example of a polynomial is as follows:
4xy² + 2y + 5
Polynomial can be named base on the number of terms. For example monomial, binomial and trinomial.
The standard form of a polynomial is expressed by writing the highest degree of terms first then the next degree and so on.
Therefore, the polynomial in standard form is as follows;
8x⁵ - 5y⁴ - 2xy⁵ + x²y
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Answer: its b
8xy5 -5y4 -2xy5 +x2y
Step-by-step explanation:
I got it right on edge
Find the sum Sn of the first n terms from the given sequence.
1, 1+2, 1+2+3, 1+2+3+4, ...
Please show your work and use Sigma Notation too. Thank you!
The Sequence:
1 , 1+2 , 1+2+3 , 1+2+3+4, ...
here, every term is an AP. finding the general formula for the sum of the elements of each term is:
Sₙ = [tex]\frac{x}{2}(2a + (x-1)d)[/tex] [where x = number of term, a = first term and d = common difference]
here, the first term is always 1 and so is the common difference.
Sₙ = [tex]\frac{x}{2}(2 +x-1)[/tex]
Sₙ = [tex]\frac{x}{2}(1 +x)[/tex] = [tex]\frac{1}{2}(x + x^{2})[/tex]
which is the formula for a general term in our series
now, we need to find the sum of the first n terms of this series
[tex]\displaystyle\sum_{x=1}^{n} [\frac{1}{2}(x + x^{2})][/tex]
[tex]\displaystyle\frac{1}{2} [\sum_{x=1}^{n} (x) + \sum_{x=1}^{n}(x^{2})][/tex]
in this formula, for the first term, it's just an AP from x = 1 to x = n
for the second term, we have a general formula [tex]\frac{n(n+1)(2n+1)}{6}[/tex]
[tex]\frac{1}{2}[\frac{n}{2}(2a + (n-1)d)+ \frac{n(n+1)(2n+1)}{6} ][/tex]
in this AP (first term), the first term and the common difference is 1 as well
[tex]\frac{1}{2}[\frac{n}{2}(2 + n-1)+ \frac{n(n+1)(2n+1)}{6} ][/tex]
[tex]\frac{1}{2}[\frac{n}{2}(n+1)+ \frac{n(n+1)(2n+1)}{6} ][/tex]
[tex][\frac{n}{4}(n+1)+ \frac{n(n+1)(2n+1)}{12} ][/tex]
[tex]\frac{n}{4}(n+1) [1+\frac{(2n+1)}{3} ][/tex]
[tex]\frac{n}{4}(n+1) [\frac{(3+2n+1)}{3} ][/tex]
[tex]\frac{n}{4}(n+1) [\frac{(2n+4)}{3} ][/tex]
[tex]\frac{n}{2}(n+1) [\frac{(n+2)}{3} ][/tex]
[tex]\frac{n(n+1)(n+2)}{6}[/tex]
which is the sum of n terms of the given sequence
please help easy maths
Answer:
A
Step-by-step explanation:
Answer:
Step-by-step explanation:
The y intercept occurs when x = 0.
All you have to do is read the table until you come to x = 0.
When you do, read down to get the y value.
The answer is A (0,2)
The angle,2Θ, lies in the third quadrant such that cos2Θ=-2/5. Determine an exact value for tanΘ . Show your work including any diagrams if you plan to use them. (3 marks)
Answer:
[tex]tan(\theta)=\frac{\sqrt{21}}{3}[/tex]
Step-by-step explanation:
1. Approach
One is given the following information:
[tex]cos(2\theta)=-\frac{2}{5}[/tex]
One can rewrite this as:
[tex]cos(2\theta)=-0.4[/tex]
Also note, the problem says that the angle ([tex]2\theta[/tex]) is found in the third quadrant.
Using the trigonometric identities ([tex]cos(2\theta)=2(cos^2(\theta))-1[/tex]) and ([tex]cos(2\theta)=1-2(sin^2(\theta))[/tex]) one can solve for the values of ([tex]cos(\theta)[/tex]) and ([tex]sin(\theta)[/tex]). After doing so one can use another trigonometric identity ([tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]). Substitute the given information into the ratio and simplify.
2. Solve for [tex](cos(\theta))[/tex]
Use the following identity to solve for ([tex]cos(\theta)[/tex]) when given the value ([tex]cos(2\theta)[/tex]).
[tex]cos(2\theta)=2(cos^2(\theta))-1[/tex]
Substitute the given information in and solve for ([tex]cos(\theta)[/tex]).
[tex]cos(2\theta)=2(cos^2(\theta))-1[/tex]
[tex]-0.4=2(cos^2(\theta))-1[/tex]
Inverse operations,
[tex]-0.4=2(cos^2(\theta))-1[/tex]
[tex]0.6=2(cos^2(\theta))[/tex]
[tex]0.3=cos^2(\theta)[/tex]
[tex]\sqrt{0.3}=cos(\theta)[/tex]
Since this angle is found in the third quadrant its value is actually:
[tex]cos(\theta)=-\sqrt{0.3}[/tex]
3. Solve for [tex](sin(\theta))[/tex]
Use the other identity to solve for the value of ([tex]sin(\theta)[/tex]) when given the value of ([tex]cos(2\theta)[/tex]).
[tex]cos(2\theta)=1-2(sin^2(\theta))[/tex]
Substitute the given information in and solve for ([tex]sin(\theta)[/tex]).
[tex]cos(2\theta)=1-2(sin^2(\theta))[/tex]
[tex]-0.4=1-2(sin^2(\theta))[/tex]
Inverse operations,
[tex]-0.4=1-2(sin^2(\theta))[/tex]
[tex]-1.4=-2(sin^2(\theta))[/tex]
[tex]0.7=sin^2(\theta)[/tex]
[tex]\sqrt{0.7}=sin(\theta)[/tex]
Since this angle is found in the third quadrant, its value is actually:
[tex]sin(\theta)=-\sqrt{0.7}[/tex]
4. Solve for [tex](tan(\theta))[/tex]
One can use the following identity to solve for [tex](tan(\theta))[/tex];
[tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]
Substitute the values on just solved for and simplify,
[tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]
[tex]tan(\theta)=\frac{-\sqrt{0.7}}{-\sqrt{0.3}}[/tex]
[tex]tan(\theta)=\frac{\sqrt{0.7}}{\sqrt{0.3}}[/tex]
[tex]tan(\theta)=\frac{\sqrt{\frac{7}{10}}}{\sqrt{\frac{3}{10}}}[/tex]
Rationalize the denominator,
[tex]tan(\theta)=\frac{\sqrt{\frac{7}{10}}}{\sqrt{\frac{3}{10}}}[/tex]
[tex]tan(\theta)=\frac{\sqrt{\frac{7}{10}}}{\sqrt{\frac{3}{10}}}*\frac{\sqrt{\frac{3}{`0}}}{\sqrt{\frac{3}{10}}}[/tex]
[tex]tan(\theta)=\frac{\sqrt{\frac{7}{10}*\frac{3}{10}}}{\sqrt{\frac{3}{10}*\frac{3}{10}}}[/tex]
[tex]tan(\theta)=\frac{\sqrt{\frac{21}{100}}}{\frac{3}{10}}[/tex]
[tex]tan(\theta)=\frac{\frac{\sqrt{21}}{10}}{\frac{3}{10}}[/tex]
[tex]tan(\theta)=\frac{\sqrt{21}}{10}*\frac{10}{3}[/tex]
[tex]tan(\theta)=\frac{\sqrt{21}}{3}[/tex]
Can you guys help me find a flag that has at least one reflection and a translation in it? If not, then two flags that show these transformations.
This is very urgent and I need to get it done soon, whoever is willing to help me I'll mark you as brainliest. Thank you!
Answer:
The united nations flag the translation can be any of the blue triangles and the reflection if the flag itself as it is symmetrical
Step-by-step explanation:
The united nations flag the translation can be any of blue triangles and the reflection if the flag itself as it is symmetrical.
How does reflection across axis work?When a graph is reflected along an axis, say x axis, then that leads the graph to go just in opposite side of the axis as if we're seeing it in a mirror.
If we study it more, you will find that its symmetric, thus each point is equidistant from the axis of reflection as that of the image of that point.
If you're reflecting a point (x,y) along x axis, then its abscissa will stay same but ordinates will negate. Thus (x,y) turns to (x, -y)
Similarly, if you're reflecting a point (x,y) along y axis, the resultant image of the point will be (-x,y)
Therefore, The united nations flag the translation can be any of blue triangles and the reflection if the flag itself as it is symmetrical.
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Six times a number increased by five is fifty-three. What is the number?
Answer:
8
Step-by-step explanation:
6x+5=53
6x=48
6x/6=48/6
x=8
AAAAAAAAAAHHHHHHHHHHHH
Answer:
[tex] \sqrt{45 {x}^{2} } + \sqrt{5 {x}^{2} } + 4x \sqrt{5} \\ = 3 \sqrt{5} x + \sqrt{5} x + 4x \sqrt{5} \\ = 8x \sqrt{5} \\ thank \: you[/tex]
Simplify: 2(a-4)+15=13
Answer:
a = 3
Step-by-step explanation:
2(a−4)+15=132
a−8+15=132
a=13−15+82
a=6
a=6/2
a=3
all the number sets that apply to -4/5
-8/10,-12/15,-16/20,-20/25,-24/30,etc.
The number sets that apply to -4/5 is the fractions.
What is a fraction?Fractions represent the parts of a whole or collection of objects.
A fraction has two parts. The number on the top of the line is called the numerator and the number on the top of the line is called the denominator.
Now the given number is,
-4/5
-4/5 is a fraction. A fraction has two components numerator and denominator. This can positive or negative. Other example of fractions include 1/2,3/2,-5/2,-1/3.
The numbers who are not fractions are 0, 3, 6, 7.7.
Thus, the number sets that apply to -4/5 is the fractions.
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Sarah ran 4 7/8miles, then walked 1 11/12 miles.
Find the total distance she traveled.
Answer:
6 19 /24
Step-by-step explanation:
find the lcd and add
I need help guys like rn please someone!!
Answer:
B
Step-by-step explanation:
The correct answer is B, because you have -4 +(-6)+(-2) which is really just
-4-6-2 which is -12. Think of it as getting rid of the plus sign and just leaving the negative sign. Which this would make the answer to the equation be -12, but for the answer of the question, it would be B because it is accumulating the drops in temperatures making the numbers go down in temperature, therefore making them negative.
A is not the answer because although it is similar to letter B, the difference is the final sentence, "What was the overall change in temperature?" Since -4 is listed as the pre-existing temperature, that would make -6 - 2 be equal to negative eight (-8).
C is not the answer because it includes a temperature rising by 18 degrees.
D is not the answer either because it is saying the temperature rose, which is shouldn't have risen.
The only time C and D could be right, is if they included bigger number that equaled out to negative twelve (-12), like saying the temperature rose 18 degrees, but fell by 26 degrees by midnight, that would make the equation look like -4 + 18 - 26 = - 12
Even in that case, C and D would be wrong immediately because of the use of numbers outside of the expression given.
Hope this helps!
please help angles on a Cartesian plane
Answer:
a) 16/25
b)3/2
Step-by-step explanation:
all explaination is in picturw below
find the GCF of 3,14,5?
Factors for 3: 1 and 3
Factors for 5: 1 and 5
Factors for 14: 1, 2, 7, and 14
Answer:
1
Step-by-step explanation:
Factors for 3: 1 and 3
Factors for 5: 1 and 5
Factors for 14: 1, 2, 7, and 14
Since 1 is the greatest common factor in 3,5,14 ,
GCF = 1
Joe was driving on the highway a car ahead of him was driving far below the speed limit so he decided to pass. In the first second he gained(gained means to get nearer to something you are chasing) 5m on the car and as he accelerated he gained 1.5 times as much distance in each second as he had the second before. If there was 30 m between joe and the car he was passing then how long did it take him to pass
Answer:
537/100s.
Step-by-step explanation:
factorize 6(a+1)²+4(a+1)
Answer:
[tex]2(a + 1) \times (3a + 5)[/tex]
Step-by-step explanation:
[tex]6(a + 1 {)}^{2} + 4(a + 1)[/tex]
➡️ [tex]2(a + 1) \times (3(a + 1) + 2)[/tex]
➡️ [tex]2(a + 1) \times (3a + 3 + 2)[/tex]
➡️ [tex]2(a + 1) \times (3a + 5)[/tex]
7x-5y<-15 graph and shade
Answer:
Slope: 7/5
y intercept: (0,3)
Step-by-step explanation:
Janelle is shopping around for the best cell phone plan. The best company is offering a $50 set up fee plus $60 per month. If the contract is for one year, how much will Janelle end up paying after one year?
$650
None of these choices are correct.
$770
$700
$720
Answer:
770
Step-by-step explanation:
12 month ×60 per month
Plus 50 set up fee
=770
A motorcycle can travel 48 miles for every gallon of gas used
Use the unit rate to complete the table for the miles traveled by motorcycle
Answer:
A-96
B-144
C-192
:) have a nice rest of your day!
Step-by-step explanation:
d) The shadow of a vertical tower on a level ground increases by 10m, when the altitude of sum changes from angle of elevation 45° to 30°. Find the height of the towe correct to one place of decimal. (Take root 3 = 1.732)
Help As soon as possible please with picture please
Answer:
Below.
Step-by-step explanation:
I cant draw you a picture but it will be one right triangle inside the other where the vertical tower will be one leg common to 2 triangles and the base of the 2 triangles will be x and x+10 metres.
Tan 30 = h/ (x + 10)
tan 45 = h/x where h is the height of the tower.
From the second equation x = h / tan45
Substituting in the first equation;
tan30 = h / (h/tan45 + 10
Tan 30 = 1/ √3 and tan 45 = 1 so
1/ 1.732 = h/ (h + 10)
0.5774 = h/(h + 10)
h = 0.5774h + 57.74
0.4226 h = 57.74
h = 136.6 m to nearest tenth.
the expression x - 0.10 X gives the cost of an item that is discounted 10% write this expression in the other way
Answer:
Step-by-step explanation:
Take out a common factor (x)
x ( 1 - 0.10 )
Now do the subtraction
0.90x
Please no links because they dont work :).
Answer:
semoga jawapan ini dapat membantu
ASAP PLS
The soda shop has 11 flavors of soda, 2 kinds of fruit syrup, and 6 sweeteners. How many different sodas can be made with one flavor of soda, one fruit syrup, and one sweetener?
The radius of the circle below is 5 inches. What is the diameter of the circle?
Answer:
10 inches
Step-by-step explanation:
radius = 5 inches
Diameter = radius x 2 = 5 x 2 = 10 inches
Five times the sum of a number and 7 is 8
Answer:
5(n+7) = 8
Step-by-step explanation:
this is the equation you are look for if its the value of n it would be -27/5
Answer:
Step-by-step explanation:
5(x + 7) = 8
x + 7 = 8/5
x = 8/5 - 7 = -27/5 = -5.4
Points A, B, and C are collinear. Point B is between A and C. Find the length indicated.
Answer:
TR = 23
Step-by-step explanation:
first we have to find TS, so we subtract 16 from 4 to get 12. then we can add 12 and 11 to get TR
Write as an algebraic expression five times the sum of a number and 4
Answer:
5(x+4)
Step-by-step explanation:
It's basically asking for the sum of a number and four to be multiplied by 5. Since the sum is made up of the unknown number and four, you'd put four and the unknown number in parenthesis while putting five on the outside, making it 5(x+4).
4. Complete the following explanation to show that the sum of two rational numbers a
rational number.
Let a,b,c and d be integers. Let x and y be rational numbers. Consider the following
expression:
* = and y =
The above expressions represent the
If x + y = y + x
represents the
then, we can use the
to show that x +y = 3+. Using the rule for addition of
fractions to write an equivalent expression for x + y = 4+we obtain
The product of two integers results in an integer, so bd, ad and cb are all integers. Also.
since the sum of two integers results in an integer, ad + cb is an integer. Therefore,
xty is
6x + 3y - 9 when
x = 6, y = 9
Answer:
63
Step-by-step explanation:
6x + 3y - 9
x = 6
y = 9
6(6) + 3(9)
36 + 27
= 63
A design for a banner includes a striped background. The stripes are colored in the repeating order: yellow, blue, orange, green, and purple. What calor is the 37th stripe?
Answer:
purple.orang.blue.yellow and green
purple.orang.blue.yellow and green
hey please help i’ll give brain
Answer:
First, the dropdown is 9. Second, put in 9. The answer is 81.
Step-by-step explanation:
10* what equals 90? Well, let's do 90/10, our answer is 9. Then We are given 1 nine or 9 to put on the second slot. Our answer would be 90-9, or 81. Khan Academy is teaching you how to multiply.
Answer:
[tex]9 \times 9 = 10nines - 1nine \\ 9 \times 9 = 90 - 9 \\ 9 \times 9 = 81 \\ than \: you[/tex]
Mrs. Richards had a coupon for one-third off her total bill at the local
grocery store. She bought 2 boxes of cereal for $3.49 each, three cartons
of ice-cream for $2.99 each, and a six pack of soda for $1.99. How much
was her bill with the discount?
Answer: The bill with a discount is $18.59
Step-by-step explanation:
Given information
2 boxes of $3.49 cereal
3 cartons of $2.99 ice-cream
6 packs of $1.99 soda
1/3 discount off total bill
Given expression
Bill = (1 - 1/3) (2 × 3.49 + 3 × 2.99 + 6 × 1.99)
Simplify values in parentheses
Bill = (2/3) (6.98 + 8.97 + 11.94)
Simplify by addition
Bill = (2/3) (27.89)
Simplify by multiplication
Bill = $18.59 (Rounded to the nearest hundredth because the usual money ends in nearest cent)
Hope this helps!! :)
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