Perhaps you know that
[tex]S_2 = \displaystyle\sum_{k=1}^n k^2 = \frac{n(n+1)(2n+1)}6[/tex]
and
[tex]S_3 = \displaystyle\sum_{k=1}^n k^3 = \frac{n^2(n+1)^2}4[/tex]
Then the problem is trivial, since
[tex]\displaystyle\sum_{k=1}^n k^2(k+1) = S_2 + S_3 \\\\ = \frac{2n(n+1)(2n+1)+3n^2(n+1)^2}{12} \\\\ = \frac{n(n+1)\big((2(2n+1)+3n(n+1)\big)}{12} \\\\ = \frac{n(n+1)\big(4n+2+3n^2+3n\big)}{12} \\\\ = \frac{n(n+1)(3n^2+7n+2)}{12} \\\\ = \frac{n(n+1)(3n+1)(n+2)}{12}[/tex]
Then
[tex]12\bigg(1^2\cdot2+2^2\cdot3+3^2\cdot4+\cdots+n^2(n+1)\bigg) = n(n+1)(n+2)(3n+1)[/tex]
so that a = 3 and b = 1.
Find the measure of each angle indicated.
A) 95°
C) 26°
B) 92°
D) 20°
Answer:
D) 20°
Step-by-step explanation:
Using the triangle sum theorem, you know that every triangle's interior angles add up to 180°. Therefore the bottom triangle's missing angle can be found by giving it the variable x.
57° + 30° + x = 180°
Simplify: 87° + x =180°
x=93°
By the vertical angles theorem, the vertical angle directly across this angle is congruent to this one. Meaning that the top triangle's angle are 67°, 93°, and unknown, which we can assign y. We can use the same method from above here.
67° + 93° + y = 180°
Simplify: 160° + y = 180°
y=20°
Answer:
(C). 26°
Step-by-step explanation:
mutual sold an item for sh.3250 after allowing his customers a 12% discount on the marked price.if he had sold the article without giving a discount,he would have made a profit of 25%.calculate the percentage profit he made by selling the article at a discount?
Answer:
lol Step-by-step explanation:
solve |2x+2|=10 ap3x
Answer:
solving for x
Step-by-step explanation:
4 or -6
Answer:
x = 4
Step-by-step explanation:
Those absolute value signs are a trick, well at least for this problem. Solve it how you usually would. However, if +2 was -2 or +/-2, then you would need to pay attention. Basically, those signs make the whole equation incased positive no matter what.
Geometry, please answer question ASAP
Answer:
C) 81 degrees
Step-by-step explanation:
all quadrilateral's sum of interiror angles is 360 degrees
right angles are 90 degrees
call measure of angle C =y
360=90+90+99+y
180=99+y
y= 81
Whats 5867 times 382?
Whats 5867 times 382?
answer;
5867×382
=2241194
Hope it helps you.........
Find the dimensions of a rectangle whose perimeter is 52 m and whose area is 160 m (2)
Answer:
10, 16
Step-by-step explanation:
List the factors of 160.
1 × 160 = 160
2 × 80 = 160
4 × 40 = 160
5 × 32 = 160
8 × 20 = 160
10 × 16 = 160
(there are more, but we don't need them)
Check to see which factors can be added together to make 26, half of 52.
10 and 16 make 26.
That's the answer!
I hope this helps!
pls ❤ and mark brainliest pls!
the vertex of this parabola is at (-2 -3). When the y value is -2, the x value is -5. What is the coefficient of the squared term in the parabolas equation.
Answer:
1/9
Step-by-step explanation:
The vertex form is
y =a(x-h)^2 +k where (h,k) is the vertex
The vertex is (-2,-3)
y =a(x--2)^2 +-3
y =a(x+2)^2 -3
Substitute the point into the equation
-2 = a(-5+2)^2 -3
-2=a(-3)^2-3
Add 3 to each side
-2+3 = a(9)
1 = 9a
1/9 =a
y =1/9(x+2)^2 -3
The coefficient of the x^2 is 1/9
Answer:
[tex]\frac{1}{9}[/tex]
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k ) = (- 2, - 3) , then
y = a(x + 2)² - 3
To find a substitute (- 5, - 2 ) into the equation
- 2 = a(- 5 + 3)² - 3 ( add 3 to both sides )
1 = a(- 3)² = 9a ( divide both sides by 9 )
[tex]\frac{1}{9}[/tex] = a
y = [tex]\frac{1}{9}[/tex] (x + 2)² - 3
The coefficient of the x² term is therefore [tex]\frac{1}{9}[/tex]
Use the given information to prove that f║g (f is parallel to g).
please help
Answer:
Not Enough Information
Step-by-step explanation:
Unfortunately, you did not give us the "given information", so there is no way to prove the two parallel.
Need help with 1 and 2
Answer:
1a. 128
1b. 81
1c. 64
1d. 25
1e. 343
1f. 100000
1g. 64
1h. 0
1i. 13
1j. 1
2a. 243
2b. 64
2c. 36
2d. 625
2e. 1331
2f. 10000000
2g. 81
2h. 0
2i. 17
2j. 1
Ryan just got hired for a new job and will make $48,000 in his first year Ryan was told that he can expect to get raises of $3,500 every year going forward.how much money in salary would Ryan make in his 24th year working at this job ?
Answer:
128500
Step-by-step explanation:
This is an arithmetic sequence with a common difference of 3500
The formula for an arithmetic sequence is
an = a1+d(n-1) where a1 is the first term and d is the common difference
an = 48000+ 3500(n-1)
We want n = 24
a24 = 48000+3500(24-1)
= 48000+3500(23)
=48000+80500
=128500
State the transformations on the graph of f(x) = ^ x that result in the graph of the given functions.
Write the transformation rule.
2. Sum of two numbers = 16
Difference of the numbers = 6
Find the numbers.
What is their product?
Answer:
Step-by-step explanation:
let the numbers be x and y.
x+y=16
x-y=6
add
2x=22
x=22/2=11
11+x=16
x=16-11=5
product xy=11×5=55
find the distance traveled in 27.9 minutes
Answer:
A
Step-by-step explanation:
d = 0.5 * t There are no conversions. You just substitute the value for t.
d = 0.5 * 27.9
d = 13.95 which is A
Find the area of a regular
polygon with 7 sides that has a
perimeter of 63 inches and an
apothem of 8 inches.
Answer:
The area of a regular polygon is A = (1/2)ap, where a is the apothem and p is the perimeter of the polygon.
The apothem is 8 inches and the perimeter is 6(7) = 42 since there are 7 sides of 6 inches.
Then the area is
A = (1/2)(8)(42) = 336/2 = 168 in2
I hope this helped!
The function f(t) = 4t2 − 8t + 7 shows the height from the ground f(t), in meters, of a roller coaster car at different times t. Write f(t) in the vertex form a(x − h)2 + k, where a, h, and k are integers, and interpret the vertex of f(t).
A) f(t) = 4(t − 1)2 + 3; the minimum height of the roller coaster is 3 meters from the ground
B) f(t) = 4(t − 1)2 + 3; the minimum height of the roller coaster is 1 meter from the ground
C) f(t) = 4(t − 1)2 + 2; the minimum height of the roller coaster is 2 meters from the ground
D) f(t) = 4(t − 1)2 + 2; the minimum height of the roller coaster is 1 meter from the ground
Answer:
A) f(t) = 4(t − 1)^2 + 3; the minimum height of the roller coaster is 3 meters from the ground
Step-by-step explanation:
f(t) = 4t^2 − 8t + 7
Factor out 4 from the first two terms
f(t) = 4(t^2 − 2t) + 7
Complete the square
(-2/2)^2 =1 But there is a 4 out front so we add 4 and then subtract 4 to balance
f(t) = 4( t^2 -2t+1) -4 +7
f(t) = 4( t-1)^2 +3
The vertex is (1,3)
This is the minimum since a>0
The minimun is y =3 and occurs at t =1
Answer:
The above answer is correct.
Step-by-step explanation:
Please help me factorise these brackets and expand them
Answer:
5ba^2 +ab^2 6a^2 + 2b
Step-by-step explanation:
ab(6a+b)-3a^2 (b-2)+2b(a^2 +1)
6ba^2 +ab^2 -3ba^2 +6a^2 + 2ba^2 +2b
6ba^2 -3ba^2 +2ba^2 +ab^2 +6a^2 +2b
5ba^2 +ab^2 6a^2 + 2b
i need help with this
Answer:
A) (-8, -16)
B) (0, 48)
C) (-4, 0), (-12, 0)
Step-by-step explanation:
A) the vertex is the minimum y value.
extremes of a function we get by using the first derivation and solving it for y' = 0.
y = x² + 16x + 48
y' = 2x + 16 = 0
2x = -16
x = -8
so, the vertex is at x=-8.
the y value is (-8)² + 16(-8) + 48 = 64 - 128 + 48 = -16
B) is totally simple. it is f(0) or x=0. so, y is 48.
C) is the solution of the equation for y = 0.
the solution for such a quadratic equation is
x = (-b ± sqrt(b² - 4ac)) / (2a)
in our case here
a=1
b=16
c=48
x = (-16 ± sqrt(16² - 4×48)) / 2 = (-16 ± sqrt(256-192)) / 2 =
= (-16 ± sqrt(64)) / 2 = (-16 ± 8) / 2 = (-8 ± 4)
x1 = -8 + 4 = -4
x2 = -8 - 4 = -12
so the x- intercepts are (-4, 0), (-12, 0)
please please please help me with this assignment :)
Answer:
$45.63
Step-by-step explanation:
[tex]50,145 cm^{3} * 2.6 g/cm^3 = 130,377 g\\130,377 g = 130.377 kg\\130.377 kg * $0.35/kg = $45.63\\[/tex]
or all together
50,145 cm³ * 2.6 g/cm³ * 0.35/kg = $45.63
evaluate : 8/-5+(4/-3)+1/3
Explain full steps
with easy method
Answer:
-39/15
Step-by-step explanation:
=-8/5-4/3+1/3
Taking LCM of 5,3 and 3.
=3(-8)-5(4)+5(1)/15
=-24-20+5/15
=-44+5/15
=-39/15
Note:if you need to ask any question please let me know.
The sine of angle θ is 0.3.
What is cos(θ)? Explain how you know.
Answer:
cos(θ) = -0.95
Step-by-step explanation:
Remember the relation:
sin(θ)^2 + cos(θ)^2 = 1
So if we have:
sin(θ) = 0.3
we can replace that in the above equation to get:
0.3^2 + cos(θ)^2 = 1
now we can solve this for cos(θ)
cos(θ)^2 = 1 - 0.3^2 = 0.91
cos(θ) = ±√0.91
cos(θ) = ± 0.95
Now, yo can see that there are two solutions, which one is the correct one?
Well, you can see that the endpoint of the segment that defines θ is on the second quadrant.
cos(x) is negative if the endpoint of the segment that defines the angle is on the second or third quadrant.
Then we can conclude that in this case, the correct solution is the negative one.
cos(θ) = -0.95
Given: PSTK is a rectangle
Area of PSTK=562m^2
m∠TOK=75
Find:PS, PK
(HELP! ILL GIVE BRAINLIEST)
Answer:
See picture below
Step-by-step explanation:
Let PK be the length and PS be the width of the rectangle.
Then LW =562
Assuming O is the center of the rectangle then ∠KST = ∠STO = 75/2
Hence tan ( 75/2 ) = PS/PK
Now solve the system of the equations
PS*PK=562
tan ( 75/2 ) = PS/ PK
Hello, have anyone can help me to solve this question?
Answer:
24 days LCM
prime factor :
4- 2, 2
8-2,2,2
12- 2,2,3
largest factors- 2,2,2,3
2*2*2*3 = 24
Step-by-step explanation:
Calculate the average speed in km/h for a plane that travels 1300km in 4 hours??
Answer:
The plane is going 325 kilometers per hour :)
Step-by-step explanation:
To find the average speed per hour, divide 1300 by 4.
1300/4 = 325
after allowing 20% discount an article is sold for rs.672 levying 12% VAT, find its market price
The market price is Rs. 750 which was obtained by creating a mathematical relationship from the given parameters.
PERCENTAGE DISCOUNT = 20%
VAT LEVIED= 12%
PRICE SOLD = 672
Let the MARKET PRICE = m
Hence,
market price * (1 - discount) * (1 + VAT) = price sold
m * (1 - 20%) * (1 + 12%) = 672
m * (1 - 0.2) * (1 + 0.12) = 672
m * 0.8 * 1.12 = 672
0.896m = 672
m = 672 / 0.896
m = Rs. 750
Learn more :
https://brainly.com/question/20418815
The Market Price of the product is RS. 750.
The Market Price is calculated by dividing the components associated to Discount, which is less than 1, and the Value Added Tax, which more than 1, to the Resulting Price.
[tex]c_{M} = \frac{c_{R}}{\left(1-\frac{r_{D}}{100} \right)\cdot \left(1+\frac{r_{T}}{100} \right)}[/tex] (1)
Where:
[tex]c_{M}[/tex] - Market price, in monetary units.
[tex]c_{R}[/tex] - Resulting price, in monetary units.
[tex]r_{D}[/tex] - Discount rate, in percentage.
[tex]r_{T}[/tex] - Tax rate, in percentage.
If we know that [tex]c_{R} = 672[/tex], [tex]r_{D} = 20[/tex] and [tex]r_{T} = 12[/tex], then the market price is:
[tex]c_{M} = \frac{672}{\left(1-\frac{20}{100} \right)\cdot \left(1+\frac{12}{100} \right)}[/tex]
[tex]c_{M} = 750[/tex]
The market price of the product is RS. 750.
A square has a side length of 36 feet. This square is dilated by a scale factor of 23 to create a new square. What is the side length of the new square?
Answer:
828
Step-by-step explanation:
Multiple the side length by the dilation
36 x 23 = 828
Maritza is comparing cell phones plans and notices that verizon offers a plan that is $60 for 10GB of data and $12 for each extra GB of data ore month. Create an expression to model this situation
Answer:
60 + 12 * g, with g representing the number of extra gigabytes
Step-by-step explanation:
First, we know that Maritza has to pay $60 for 10GB of data, no matter what. Therefore, the base cost of the cell phone plan is 60 dollars, and all extra costs must be added to that. Currently, our expression is therefore 60 + something = cost of cell phone plan.
After that, the plan costs $12 for each gigabyte of data past 10 GB. This means that, for example, if Maritza uses 11 gigabytes, the plan will cost 60 (the base amount) + 12 for each gigabyte past 10 GB. There are 11-10=1 extra gigabytes, so the cost is 60 + 12 * 1 = 72 dollars. For each extra gigabyte, 12 dollars are added, so we can represent this as
60 + 12 * g, with g representing the number of extra gigabytes
The mean of data set A is 43.5 and the MAD is 3.7. The mean of data set B is 12.8 and the MAD is 4.1. What differences would you expect to see when comparing the dot plots of the two data sets?
Answer:
MAD - mean absolute deviation is indication of the distance of data points from the mean.
Data set B shows the greater variability since has greater MAD.
It means the B data set is more spread compared to A data set.
determinar el decimal correspondiente
A)71% B)172% C)6%
[tex]71\% = \frac{70}{100} = \frac{7}{10} = 0.7 \\ 172\% = \frac{172}{100} = 1.72 \\ 6\% = \frac{6}{100} = 0.06[/tex]
Find the value of each variable. Lines that appear tangent are tangent, and the dot is the center. (Answer in the form a=? b=? c=? d=?)
Answer:
a = 60°/2 = 30°
b = 84/2 = 42°
c = (100+60)/2 = 80°
d = 360-100-60-84 = 116°
Answered by GAUTHMATH
if m JUST NUMBER 10. PLEASE HELP
pls snap the picture well so that the pre information can be seen and considered
