Answer: 98
Step-by-step explanation: 25+24+25+24
There are two parts to a rectangle. The opposite sides are the same. You add them all up to equal 98.
Hope this helps and would appreciate getting brainliest to level up :)
Question 16
............................................................
Answer:
[tex]\boxed{x^7+14x^6y+84x^5y^2+280x^4y^3+560x^3y^4+672x^2y^5+448xy^6+128y^7}[/tex]
Step-by-step explanation:
To answer this question, you can use a number pattern that is well-known in algebra & higher mathematics called Pascal's Triangle. However, for simplification reasons, I will use the Binomial Theorem as it is quite difficult to create Pascal's Triangle without just attaching an image. A binomial is any two-term expression that are not like terms (for instance, both are integers that lack a variable).
Part I - Expanding the Binomial using the Binomial TheoremAfter constructing Pascal's Triangle, you can use this method to expand a binomial. To do this, it will require a lot of patience and a lot of space.
Using Pascal's Triangle, we can expand the binomial entirely by referencing the exponents given and the coefficients that we have now solved for using Pascal's Triangle.
Referring to the seventh exponent row of the triangle, we can expand the binomial using a formula referred to as the Binomial Theorem.
The binomial theorem states that:
[tex]\large\boxed{(a+b)^{n}=\sum_{k=0}^{n} \binom{n}{k}a^{n-k}b^{k}, \textsf{where} \binom{n}{k}=\frac{n!}{(n-k)!k!} \textsf {\: and \:} n! = 1 * 2 * 3... \textsf{n}}[/tex]
Therefore, we can use this information to begin defining values and expanding the binomial.
We are given an a, b, and n value. These are defined as a = 2y, b = x, and n = 7.
Therefore, [tex](x + 2y)^{7}=\sum_{k=0}^{7} \binom{7}{k}(2y)^{7-k}(x)^{k}[/tex].
Using this information, you can then solve for every k-value. This will be slightly extensive. To solve for each k-value, ignore the summation sign and everything before it. You only need the information that follows the summation sign: [tex]\binom{7}{k}(2y)^{7-k}(x)^{k}[/tex]. This will then extend and allow you to only use the portions of the equation that require factorials.
Be sure that when you get a final answer that you always apply the exponent (k) to the final result.
k = 0
[tex]\binom{7}{0}(2y)^{7-0}(x)^0 = \frac{7!}{(7-0)!0!}(2y)^{7}(x)^{0}\\[/tex]
[tex]\frac{7*6*5*4*3*2*1}{(7*6*5*4*3*2*1)}(2y)^{7}(x)^{0}[/tex]
[tex]1(2y)^{7} = 2y^7=(2y*2y*2y*2y*2y*2y*2y)= 128y^7[/tex]
[tex]\boxed{128y^7}[/tex]
k = 1
[tex]\binom{7}{1}(2y)^{7-1}(x)^{1}=\frac{7!}{(7-1)!1!}(2y)^{6}(x)^1[/tex]
[tex]\frac{7*6*5*4*3*2*1}{6*5*4*3*2*1} (2y)^{6}(x)^{1}[/tex]
[tex]7(2y)^{6}(x)^{1}=448xy^6[/tex]
[tex]\boxed{448xy^6}[/tex]
k = 2
[tex]\binom{7}{2}(2y)^{7-2}(x)^{2}=\frac{7!}{(7-2)!2!}(2y)^{5}(x)^2[/tex]
[tex]\frac{7*6*5*4*3*2*1}{(5*4*3*2*1)(2*1)}(2y)^{5}(x)^2[/tex]
[tex]\frac{42}{2}(2y)^{5}(x)^2[/tex]
[tex]21(2y)^{5}(x)^{2}=672x^2y^5[/tex]
[tex]\boxed{672x^2y^5}[/tex]
k = 3
[tex]\binom{7}{3}(2y)^{7-3}(x)^3=\frac{7!}{(7-3)!3!}(2y)^{4}(x)^{3}[/tex]
[tex]\frac{7*6*5*4*3*2*1}{(4*3*2*1)(3*2*1)}(2y)^4(x)^3[/tex]
[tex]\frac{210}{6}(2y)^4(x)^3[/tex]
[tex]35(2y)^4(x)^3=560x^3y^4[/tex]
[tex]\boxed{560x^3y^4}[/tex]
k = 4
[tex]\binom{7}{4}(2y)^{7-4}(x)^4 = \frac{7!}{(7-4)!4!}(2y)^3(x)^4[/tex]
[tex]\frac{7*6*5*4*3*2*1}{(3*2*1)(4*3*2*1)}(2y)^3(x)^4[/tex]
[tex]\frac{840}{24}(2y)^3(x)^4[/tex]
[tex]35(2y)^3(x)^4=280x^4y^3[/tex]
[tex]\boxed{280x^4y^3}[/tex]
k = 5
[tex]\binom{7}{5}(2y)^{7-5}(x)^5=\frac{7!}{(7-5)!5!}(2y)^2(x)^5[/tex]
[tex]\frac{7*6*5*4*3*2*1}{(2*1)(5*4*3*2*1)}(2y)^2(x)^5[/tex]
[tex]\frac{2520}{120}(2y)^2(x)^5[/tex]
[tex]21(2y)^2(x)^5 = 84x^5y^2[/tex]
[tex]\boxed{84x^5y^2}[/tex]
k = 6
[tex]\binom{7}{6}(2y)^{7-6}(x)^6=\frac{7!}{(7-5)!6!}(2y)^1(x)^6[/tex]
[tex]\frac{7*6*5*4*3*2*1}{(1)(6*5*4*3*2*1)}(2y)^1(x)^6[/tex]
[tex]\frac{5040}{720}(2y)^1(x)^6[/tex]
[tex]7(2y)^1(x)^6=14x^6y[/tex]
[tex]\boxed{14x^6y}[/tex]
k = 7
[tex]\binom{7}{7}(2y)^{7-7}(x)^7=\frac{7!}{(7-6)(7!)}(2y)^0(x)^7[/tex]
[tex]\frac{7*6*5*4*3*2*1}{(1)(7*6*5*4*3*2*1)}(2y)^0(x)^7[/tex]
[tex]\frac{5040}{5040}(2y)^0(x)^7[/tex]
[tex]1(2y)^0(x)^7=x^7[/tex]
[tex]\boxed{x^7}[/tex]
Part II - Adding/Subtracting all Terms TogetherNow, we have to take a look at the original binomial and discover whether or not we are to add or subtract these terms together. The original binomial was [tex](x+2y)^7[/tex], so we will add (that is the operation of the binomial).
Therefore, we will add all of the terms that we started with following algebraic notation (that is, alphabetically and highest exponent to lowest exponent).
[tex]\boxed{x^7+14x^6y+84x^5y^2+280x^4y^3+560x^3y^4+672x^2y^5+448xy^6+128y^7}[/tex]
This is the final expanded binomial (now a polynomial).
what is the greatest common factor of 35,10
Answer:
5
Step-by-step explanation:
Factors of 35: 1,5,7,35
Factors of 10: 1,2,5,10
5 is the greatest common factor.
this table shows values represented by an exponential function. What is the average rate of change for the function for the interval from x=2 to x=4?
Answer:
B
Step-by-step explanation:
2= 9
4= 64
64-9=55
If you subtract that
You will get 55
Answer:
the correct answer is 27.5
Step-by-step explanation:
Part A The dot plot shows the daily lunch money of a group of students. Each dot represents one student. What is the mean daily pocket money? A $1.50 B $2.00 C $2.15 D $2.20 Part B What is the mode of the daily pocket money? Answer:
Answer:
Mean= $ 1.96
Mode= No mode
Step-by-step explanation:
Mean is the value obtained by dividing the sum of all the observations by their numbers.
Mean is obtained by dividing the total number of the values with the number of values.
Mean= x1+ x2+ x3 + x4/ 4
Mean = $ 1.5 + $ 2.0 + $ 2.15 + $ 2.20/4= 7.85/4= 1.9625or 1.963 or $ 1.96
Mode is the most frequent occurring value in a data set. But since all the values in the given set occur only once the data does not have any mode .
There is no mode because every value has the same frequency, that is it occurs the same number of times.
please help me out! i have a few more of these questions, about 4
Step-by-step explanation:
You can make a table of values to find the points that belong to the line and then draw the line through those points. Here are some: (-6, -2), (0, -1), and (6, 5). You can use any value for x in your table. Hope this helps!
Answer:
Step-by-step explanation:
put a point in at negative 1 first; that is the y value.
Then, go up 1 then to the right six points. that should result in the next point being at (0,6).
Keep going and draw a line
The radius of a circle is 11.4 cm. Find the circumference \textit{to the nearest tenth}to the nearest tenth.
Answer:
71.60 cm
Step-by-step explanation:
To round 71.63 to the nearest tenth, consider the hundredths value of 71.63, which is 3 and less than 5. Therefore, the tenths value remains 6 and you get rid of the 3 since it is less than 5.
Answer:
the circumference is 71.63 but that number rounded to the nearest tenth is 71.60 cm. when a number is rounded to the nearest tenth in a decimal the last two numbers are rounded. because 3 is less than five then that means we turn it into a zero then we get 71.60
Step-by-step explanation:
Each side of a triangle is a different length. One side is 6, one side is greater than 6, and one side is less than 6. The perimeter of the triangle could not be
a) 13
b) 18
c) 22
d)24
Answer:
i think the correct answer is c sorry if im wrong
Answer:
The perimeter of the triangle could not be 24 - which is our solution.
Step-by-step explanation:
The first approach to this problem that comes to my mind, is to find the most " restricting " triangles possible. By that I mean the largest length of the side greater than 6 and the side less than 6.
The length of the side greater than 6 has to be less than 12 - considering it has to stretch the sum 6 + 6 - by the Triangle Inequality Theorem. Therefore, the most restricting triangle possible to the 1st decimal place should be the following -
{ 6, 5.9, 11.8 } ... the catch here is that this triangle does not need to be composed of lengths being whole numbers. If that was true the most " restricting " triangle would have lengths { 6, 5, 10 } throwing you off track as it's perimeter is 21.
{ 6, 5.9, 11.8 } adds to a sum of 23.7, eliminating answer choice c. Therefore, we can conclude that the perimeter of the triangle can't be 24. In fact this is only to the first decimal place, you could be more specific and go to the 100th decimal place even. Either way, the perimeter of the triangle has to be less than 24.
Cam has a budget of $3,000 per month. She puts $15% of that toward savings. How many months will it take Cam to save $4,050?
Answer:
9 months
Step-by-step explanation:
3000X(0.15)= 4050
X=9
The diameter of a circle is 8 cm. Which equation can be used to find its circumference? WILL MARK BRAINLIEST
A. C =π×88
B. C=π × 4
C. C = 16×π
D. C=π × 8
Answer:
The equation is D. C= π × 8.
Step-by-step explanation:
Regular hexagon FGHIJK shares a common shares a common center with square ABCD on a coordinate plane .
Answer:
"The answer is the yellow lines in the attached figure.Step-by-step explanation: As shown in the attached figure, regular hexagon FGHIJK and square ABCD shares common centre on the co-ordinate plane and AB || FG.
We are to find the line across which the combined figure will reflect onto itself.
In the attached figure, we see two lines which are yellow in colour. We can easily detect that the figure will be reflected onto itself if these two lines acts as a mirror separately.
Hence these yellow lines are the required lines."
Hope this helps!Consider this composite figure. A cone and half sphere. What formulas for volume will need to be applied to calculate the volume of the composite figure? check all that apply.
V = Bh
V = one-fourth B h
V = one-third pi r squared h
V = four-thirds pi r squared
V = four-thirds pi r cubed
Answer:
C and E on edge
Step-by-step explanation:
C- V = one-third pi r squared h
E- V = four-thirds pi r cubed
Answer:
c and e
Step-by-step explanation:
i agree
Which one is it??
A. Synonyms
B. Antonyms
C. Homographs
Answer:
anytomys
Step-by-step explanation:
15 points for this!! ( btw d is 90 it got cut off)
Answer:
The value of x is D) 90°
Step-by-step explanation:
The sum of interior angles in a quadrilateral is 360°
As the total interior angles in a quadrilateral is 360 to work this out you would first need to work out the total of the angles given You can do this by adding 101 and 75 and 94, this gives you 270. This is because it tells us how much of that 360 degree total has been used.
The next step is to work out the angle of x. You can do this by subtracting the total angles gives of 270 from the total of 360, this gives you 90 degrees. This is because by subtracting it we are isolating the value of x.
1) Add the values of 94, 101, 75.
[tex]101+94+75=270[/tex]
2) Minus 270 from 360.
[tex]360-270=90degrees[/tex]
Solve for x. Describe the steps taken to find the solution.
3( 4x - 3) + 8 = 2x + 10x -1
Answer:
see below
Step-by-step explanation:
3( 4x - 3) + 8 = 2x + 10x -1
Distribute
12x - 9 +8 = 2x+10x -1
Combine like terms
12x - 1 = 12x - 1
Subtract 12x from each side
12x - 1 -12x = 12x - 1-12x
-1 = -1
This is true for all values of x
x = all real numbers
Answer:
All real numbers are solutions.
Step-by-step explanation:
3 ( 4x - 3 ) +8 = 2x + 10x - 1 Example 1:
12x - 9 + 8 = 12x - 1 3 ((4*1) -3) + 8 = (2*1) + (10*1) - 1
- 12x = -12x 3 ((4) - 3) + 8 = (2) + (10) - 1
-9 + 8 = -1 ( 12 - 9 ) + 8 = 12 - 1
-1 = -1 3 + 8 = 12 - 1
Example 2 11 = 11
3 ((4*6) - 3) + 8 = (2*6) + (10*6) - 1
3 ((24) - 3) + 8 = (12) + (60) - 1
72 - 9 + 8 = 72 - 1
72 - 1 = 72 - 1
71 = 71
what line represents the relationship between r and s shown in the table r 0,1,2,3 s 10,11,12,13
Answer:4/13
Step-by-step explanation:
Find the side lengths for the nets
A solid oblique pyramid has a square base with an edge length of 2 cm. Angle BAC measures 45°.
What is the volume of the pyramid?
A. 2.4 cm3
B. 3.6 cm3
C. 4.8 cm3
D. 7.2 cm3
Answer: 4.8cm^3
Step-by-step explanation:
2020 edge
hope this helps
Answer: C
Source: Trust me bro
What is the definition of absolute value?
a) Positive and negative numbers
b) Rational numbers
c) A number line
d) The number away from zero
Answer:
The answer is D
Step-by-step explanation:
The absolute value number is its relationship to other numbers without regards for its sign. So say the question is asked: whats the absolute value of -1. The absolute value would be positive four because 1 is one place away from 0 on the number line.
Select all that apply to the graph
Emily is a very good student. She is more likely to attend class than to miss class. Which could be the probability that she misses class tomorrow?
A
–0.4
B
0.1
C
0.7
D
1.2
Answer:
Im pretty sure it is c
Step-by-step explanation:
Factor
x^2−6x+8
(x+4)(x−2)
(x+4)(x+2)
(x−4)(x+2)
(x−4)(x−2)
Answer:
(x-4)(x-2)
Step-by-step explanation:
Using The AC Method
What is the slope of the line that contains these points.
X -4 -3 -2 -1
Y 2 5 8 11
Answer: Hey! Since the other answer is obviously wrong. Here is the actual answer! (from Khan Academy) .
Step-by-step explanation:
The slope is 3.
Change in y = + 3
Change in x = +1
So, it is not 1/3 but it is 3/1 which is technically 3.
Here is the formula!:
Slope = rise/run = Change in y / change in x.
Always put the y above the x!!! :)
What is the y-coordinate of the solution of the system of equations? {y=3x−26 2x−y=19 Enter your answer in the box.
Answer:
The y-coordinate of the solution is -5.
Step-by-step explanation:
I graphed the equations on the graph below to find the solution of the system.
If this answer is correct, please make me Brainliest!
How can you use the mean absolute deviation of two
data sets to compare them?
Answer:
The mean absolute deviation tells you how spread out or how clustered around the mean a set of data is. This is the variation in the data. To compare sets, a higher mean absolute deviation indicates that the data points are more spread out from the mean. A lower mean absolute deviation indicates data points are more clustered around the mean.
Answer:
Sample Answer: The mean absolute deviation tells you how spread out or how clustered around the mean a set of data is. This is the variation in the data. To compare sets, a higher mean absolute deviation indicates that the data points are more spread out from the mean. A lower mean absolute deviation indicates data points are more clustered around the mean.
Which did you include in your explanation? Check all that apply. Make sure you have all of them
The mean absolute value is a measure of variation and indicates the spread of the data.
A higher mean absolute deviation indicates that the data points are more spread out from the mean.
A lower mean absolute deviation indicates data points are more clustered around the mean.
What is the value of x?
Enter your answer in the box. Round only your final answer to the nearest hundredth
Answer:
x = 12.5 yd
Step-by-step explanation:
To find the value of x, use the equation below
cos 37 = [tex]\frac{10}{x}[/tex]
0.80 = [tex]\frac{10}{x}[/tex] Take 10 divided by 0.80 to find x
x = 12.5
If this answer is correct, please make me Brainliest!
A triangle has lengths 4,7,9 Is it a right triangle why or why not?
Answer:
No
Step-by-step explanation:
4,7,9 is not a right angle triangle. If it was a right angle triangle then it show work in the formula a^2+b^2=c^2. But 4^2+7^2 doesn't equal 9^2. The hypotenuse or c should be 8.02 to be a right angle triangle.
help! question in photo.
Answer:
B
Step-by-step explanation:
negative 6 times negative 6 equals 36
Answer:
B.) 36
Step-by-step explanation:
plz answer below will make u brainliest help plz
Answer:
first one 5 - 30
second one 21 : 7
third one 16 : 32
Step-by-step explanation:
Answer:
Question 1: Gemma gets 5 biscuits and Zak gets 30 biscuits.
Question 2: Emily gets 21 marbles and Asif gets 7 marbles.
Question 3: Niamh gets 16 pencils and Jack gets 32 pencils.
Step-by-step explanation:
Just keep the ratios consistent
Solve 1/4 + 3/5 - 3/10
Answer:
it will be equal to 11/20
Answer:
11/20
Step-by-step explanation:
= (5+12-6)/20
= 11/20
!! Please help!!
With the exception of 1 and 63, find all the numbers that divide into 63 with no remainder
A. 2, 3,6
B. 3,9,21
c. 3,7
D 3,7,9, 21
E, 3,7,9
Answer:
the factors of 63 are:
1,3,7, 9, 21, 63
D. 3, 7, 9, 21, 63
Step-by-step explanation:
