The closed form sum of

$$12 \left[ 1^2 \cdot 2 + 2^2 \cdot 3 + \ldots + n^2 (n+1) \right]$$
for $n \geq 1$ is $n(n+1)(n+2)(an+b).$ Find $an + b.$

Answer:

2 x^2 sqrt(13)

Step-by-step explanation:

sqrt( 52x^4)

sqrt( 4*13 * x^2 * x^2)

We know that sqrt(ab) = sqrt(a) sqrt(b)

sqrt( 4)*sqrt(13) *sqrt( x^2) *sqrt( x^2)

2 sqrt(13) x*x

2 x^2 sqrt(13)

52|2

26|2

13|13

1

[tex]\sqrt{52x^4}=\sqrt{2^2\cdot13\cdot(x^2)^2}=2x^2\sqrt{13}[/tex]

Answer:

The regular bottle holds 9 fl oz less

Step-by-step explanation:

Given

Family Size =  12 fl oz

Required

Determine the size held less by the regular bottle

From the question, we have that the regular bottle holds 75% less;

[tex]Regular\ Size = 75\% * Family\ Size[/tex]

Substitute 12 fl oz for Family Size

[tex]Regular\ Size =75\% * 12\ fl\ oz[/tex]

Convert percentage to fraction

[tex]Regular\ Size = \frac{75}{100} * 12\ fl \oz[/tex]

[tex]Regular\ Size = \frac{75 * 12\ fl\ oz}{100}[/tex]

[tex]Regular\ Size = \frac{900\ fl\ oz}{100}[/tex]

[tex]Regular\ Size = 9\ fl\ oz[/tex]

Hence, the regular bottle holds 9 fl oz less

Answer:

[tex]9\ days[/tex]

Step-by-step explanation:

[tex]We\ are\ given:\\No.\ of\ days\ A\ takes\ to\ complete\ some\ amount\ of\ work=15\ days\\No.\ of\ days\ B\ takes\ to\ complete\ the\ same\ amount\ of\ work=12\ days\\No.\ of\ days\ C\ takes\ to\ complete\ the\ same\ amount\ of\ work\ as\ A\ and\ B\ =20\ days\\[/tex]

[tex]Now,\\We\ can\ say\ that\ an\ object\ has\ to\ complete\ \frac{1}{n}th\ of\ the\\ work\ daily,\ to\ complete\ the\ work\ in\ n\ number\ of\ days.\ This\ is\ however\\ only\ true\ if\ the\ object\ covers\ equal\ amounts\ of\ work\ each\ day.[/tex]

[tex]Here,\\In\ 1\ day,\\A\ would\ cover\ \frac{1}{15}th\ of\ the\ work.\\B\ would\ cover\ \frac{1}{12}th\ of\ the\ work.\\C\ would\ cover\ \frac{1}{20}th\ of\ the\ work.[/tex]

[tex]Now,\\We\ are\ also\ given\ that:\\They\ work\ together\ for\ 2\ days\ on\ the\ same\ work.\\Hence,\\Total\ work\ done\ in\ 1\ day\ by\ A,B\ and\ C=\frac{1}{15}+\frac{1}{12}+\frac{1}{20}=\frac{4+5+3}{60}=\frac{12}{60}=\frac{1}{5}\\Hence, Total\ work\ done\ in\ 2\ days\ by\ A,B\ and\ C=2*\frac{1}{5}=\frac{2}{5}[/tex]

[tex]Hence,\\The\ portion\ of\ the\ total\ work\ left=1-\frac{2}{5}=\frac{5-2}{5}=\frac{3}{5}\\So,\\Since\ A\ has\ to\ complete\ \frac{3}{5}th\ of\ the\ work,\ lets\ compute\ the\ no.\ of\ days\ it\ takes\ to\ do\ so.\\Hence,\\No.\ of\ days\ A\ takes\ to\ complete\ the\ entire\ work=15\ days\\Hence,\\No.\ of\ days\ A\ takes\ to\ complete\ \frac{3}{5}th\ of\ the\ entire\ work=15*\frac{3}{5}=9\ days[/tex]

Answer:

9 days

Step-by-step explanation:

A does in 15days, so A in 1day does 1/15part

B does in 12days, so B in 1day does 1/12part

C does in 20days, so C in 1day does 1/20part

So. A+B+C in 1 day-- 1/15+1/12+1/20=(4+5+3)/60= 12/60=1/5 and in 2days 2/5 part..hence remaining work=1/1–2/5=(5–2) =3/5part.

Now A in 1/15 part takes 1day

So, in 3/5 part 15×3/5 = 9 days.

Answer:

c=13.42

Step-by-step explanation:

[tex]A^2+B^2=C^2\\6^2+14^2=C^2\\C^2=144+36\\C^2=180\\\sqrt{c^2}=\sqrt{180} \\c=13.42[/tex]

alright I can help!

so to find the two values of x that are roots of the equation we need to put the variables all on one side so that we can set up the quadratic formula.

3x^2+2x-5=0 (the -3x^2 becomes positive when moved across the equal sign)

now we can set up the quadratic formula. the equation is x= (-b+-(sqrt of b^2 -4ac))/ 2a

so now we just plug in our variables.

x= (-2+-(sqrt of 2^2 -4×3×-5))/ 2×3

x= (-2+-8)/6

now we just seperate the equations so that we have the two roots. and then just solve!

x= (-2-8)/6 -> x= -5/3

x= (-2+8)/6 -> x=1

hope this helps! best wishes and best of luck!!

Answer:

8x

Step-by-step explanation:

Using differentiation from first principles

f'(x) = [tex]lim_{h>0}[/tex]  [tex]\frac{f(x+h)-f(x)}{h}[/tex]

      = [tex]lim_{h>0}[/tex] [tex]\frac{4(x+h)^2-2-(4x^2-2)}{h}[/tex]

      = [tex]lim_{h>0}[/tex]  [tex]\frac{4x^2+8hx+4h^2-4x^2+2}{h}[/tex]

      = [tex]lim_{h>0}[/tex] [tex]\frac{8hx+4h^2}{h}[/tex]

      = [tex]lim_{h>0}[/tex] [tex]\frac{4h(2x+h)}{h}[/tex] ← cancel the h on numerator/denominator

      = 4(2x)

      = 8x

Answer:

8x

Step-by-step explanation:

Pls I hope this helps

Answer:

you need to be more specific.

Step-by-step explanation:

Answer:

Let's call the length of the field "l", and the width of the field "w".

If the area of the field is 72 square meters, then we have:

l x w = 72

And if the length is 6 meters longer than the width, we have:

l = w+6

So looking at the first equation (l x w = 72), we can substitute the l for a w+6.

And we obtain:

(w+6) x (w) = 72

Which simplifies to w^2 + 6w = 72.

This quadratic equation is pretty easy to solve, you just need to factor it.

w^2 + 6w - 72 = 0

(w-6)(w+12)

This leaves the roots of the  quadratic equation to be 6 and -12, but in this case, a width of -12 wouldn't make sense.

So, the width of the rectangular field is 6, and the length of the field is 12.

Let me know if this helps!

Answer:

we assume one side is x and other side must be x+6 and when we multiple it together we can find x²+6x =72

Step-by-step explanation:

one side is 6 and. other is 12 so the lenght= 12 the width=6

5 buses is the answer pls mark me brainliest

Least number of bus require for trip = 5 buses

It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.

Steps to Use Unitary Method

First, let us make a note of the information we have. There are 5 ice-creams. 5 ice-creams cost $125.

Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams. The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.

Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams. The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.

Given:

Total number of classes = 9

Number of student in each class = 25

Number of teacher = 4

Number of chaperones = Double of teacher

Bus hold = 45 people

Now,

Total number of student = 9 × 25

                                         = 225

Number of chaperones = 4 × 2

                                         = 8

Total people = 225 + 8 + 4

                     = 237

Least number of bus require for trip = Total people / Bus hold

= 237 / 45

= 5.266

Learn more about unitary method here:

https://brainly.com/question/22056199

#SPJ2

Add the ratio: 3 + 5 = 8

Divide total students by that:

32/8 = 4

The ratio for girls is 3, multiply the 4 by 3:

4 x 3 = 12

There are 12 girls

Answer:

12

Step-by-step explanation:

If the ratio of girls to boys is 3:5, that means that for every 8 total students, 3 would be girls and 5 would be boys. Therefore 3/8 of the students are girls and 5/8 are boys. If 3/8 are girls, then:

[tex]\frac{3}{8}[/tex] of 32

= [tex]\frac{3}{8} * 32[/tex]

[tex]=\frac{3 * 32}{8} \\= \frac{96}{8} \\= 12[/tex]

There are 12 girls.

Answer:

Step-by-step explanation:

[tex]\frac{9}{11}=0 .818181....[/tex]

     __  

= 0.81

Answer:

B 2x - 31 = -2x - 31 have exactly one solution

Step-by-step explanation:

Which of the following equations have exactly one solution?

Choose all answers that apply:

A 2x - 31 = 2x - 31

B 2x - 31 = -2x - 31

C 2x + 31 = 2x - 31

D 2x - 2 = 2x - 31

A. 2x - 31 = 2x - 31

2x-31=2x-31

Collect like terms

2x-2x= -31+31

0=0

Infinite number of solutions

B 2x - 31 = -2x - 31

2x - 31 = -2x - 31

Collect like terms

2x+2x=-31+31

4x=0

x=0

One solution

C 2x + 31 = 2x - 31

2x + 31 = 2x - 31

Collect like terms

2x-2x= -31-31

0= -62

No solution

D 2x - 2 = 2x - 31

2x - 2 = 2x - 31

Collect like terms

2x-2x= -31+2

0= -29

No solution

Answer:

32

Step-by-step explanation:

The sum of the angles of a triangle is 180

58+90+x = 180

148+x = 180

x = 180-148

x=32

The angle sum property of a triangle:

The total measure of the three angles of a triangle is 180°

[tex]\large\bf \longrightarrow \: {\underline{\red{x \: + \: 58 \degree \: + \: 90 \degree \: = \: 180 \degree}}}[/tex]

[tex]\large\bf \longrightarrow \: {\underline{\red{x \: + \: 148 \: = \: 180 \degree}}}[/tex]

[tex]\large\bf \longrightarrow \: {\underline{\red{x \: = \: 180 \degree \: - \: 148 \degree}}}[/tex]

[tex]\large\bf \longrightarrow \: {\underline{\red{x \: = \: 32 \degree}}}[/tex]

Answer:

A

Step-by-step explanation:

The solution to a system of equations is the point of intersection of the 2 lines.

The lines intersect at (6, 9 ) ← solution

Answer:

A(6, 9)

Step-by-step explanation:

The intersecting points of the two lines gives the solution of the equation.

Answer:

-8

Step-by-step explanation:

Hello!

What we do to one side of the equation we do to the other side

7 * p = -56

Divide both sides by 7

p = -8

The answer is -8

Hope this helps!

Answer:

63/8

Step-by-step explanation:

3 1/2 = 7/2

4 1/3 = 13/3

[tex] \frac{ \frac{7}{2} + 7 }{ \frac{13}{3} - 3} [/tex]

[tex] = \frac{ \frac{21}{7} }{ \frac{4}{3} } [/tex]

[tex] = \frac{63}{8} [/tex]

Question 7: Choose the correct simplification of the expression (3x − 6)(2x2 − 4x − 5)

Answer:

C) 6x³ - 24x² + 9x + 30

Step-by-step explanation:

(3x - 6)(2x² - 4x - 5)

3x • 2x² = 6x³

3x • -4x = -12x²

3x • -5 = -15x

-6 • 2x² = -12x²

-6 • -4x = 24x

-6 • -5 = 30

Combine terms.

6x³ - 12x² - 15x - 12x² + 24x + 30

Combine like terms.

6x³ - 24x² + 9x + 30

Learn with another example:

https://brainly.com/question/28001380

Answer:

x = 5

Step-by-step explanation:

The measure of an arc equals the measure of the central angle that intercepts it.

The measure of an arc intercepted by a diameter is 180 deg.

m(arc)EH = 180

m(arc)EF + m(arc)FG + m(arc)GH = m(arc)EH

10x + 8 + 67 + 11x = 180

21x + 75 = 180

21x = 105

x = 5

Answer:

C. (-13, -7)

Step-by-step explanation:

The location of a point O(x, y) that divides a line AB with location A[tex](x_1,y_1)[/tex] and B[tex](x_2,y_2)[/tex] in the ratio m:n is given by:

[tex]x=\frac{m}{m+n} (x_2-x_1)+x_1\\\\y=\frac{m}{m+n} (y_2-y_1)+y_1[/tex]

Therefore the coordinates of point X That divides line segment from Y(-8, 8) to T(-15, -13) in the ratio 5:2 is:

[tex]x=\frac{5}{5+2} (-15-(-8))+(-8)\\\\x=\frac{5}{7} (-15+8)-8=\frac{5}{7}(-7)-8=-5-8=-13 \\\\\\y=\frac{5}{5+2} (-13-8)+8\\\\y=\frac{5}{7} (-21)+8=5(-3)+8=-15+8=-7[/tex]

Therefore the coordinates of point X is at (-13, -7)

Answer:

D(-2,5;1); C(-1,1); E(0.5,3).

Step-by-step explanation:

Imagine that there is a line AB, it is divided into 4 equal parts. If there are 4 parts, There are 4+1=5 points. That's obvious that if parts are equal , the third point is on the middle of the line AB, suppose it is the point C

xc= (xa+xb)/2

xc=( -4+2)/2= -1

yc= (-3+5)/2=1

(-1,1)

There are to unknown points D (between A and C), and E (between C and B). D is on the middle of AC .

Xd= (-4-1)/2=-2.5

yd= (-3+1)/2=-1

(-2,5;1)

E is on the middle of CB

xe= (-1+2)/2= 0.5

ye=(1+5)/2=3

(0.5, 3)

Answer:

7

Step-by-step explanation:

the median is the middle value of the list. first off, write the list of numbers in ascending order (small to big)

3, 4, 4, 5, 7, 7, 8, 10, 10, 10

since there are 10 values, there are two middle numbers which are 7 and 7. since they are both 7, the median is 7

Answer:

stop cheating

Step-by-step explanation:

get smart

Answer:

Domain : any real number

Range : y ≥0

Step-by-step explanation:

The domain is the values that x can be

X can be any real number

The range is the values the y can be

Y can be zero or any positive value since y = x^2

Domain : any real number

Range : y ≥0

Answer:

[tex]\boxed{\sf Option \ A}[/tex]

Step-by-step explanation:

[tex]y=x^2[/tex]

[tex]\sf The \ domain \ of \ a \ function \ is \ all \ possible \ values \ for \ x.[/tex]

[tex]\sf There \ are \ no \ restrictions \ on \ the \ value \ of \ x.[/tex]

[tex]\sf The \ domain \ is \ all \ real \ numbers.[/tex]

[tex]\sf The \ range \ of \ a \ function \ is \ all \ possible \ values \ for \ y.[/tex]

[tex]\sf When \ a \ number \ is \ squared \ the \ result \ is \ always \ greater \ than \ or \ equal \ to \ 0.[/tex]

[tex]\sf The \ range \ is \ \{y:y\geq 0\}[/tex]

Answer:

8, 19

Step-by-step explanation:

let group 1 have x students and group 2 have y students

x + y = 27

but group 2 has 2x + 3 students

the sum of students from both groups is 27

x + 2x + 3 = 27

3x + 3 = 27

3x = 24

x = 8

y = 2x + 3

y = 19

[tex]\huge\blue{ANSWER}:—[/tex]

Plz mark me as brainliest as I have solve all the questions for you

Answer:1 : x is 95/3

4 x is -32/10

7 b is 6

10 x is 20/7

13 x is 9/2

Step-by-step explanation:

Answer:

the mixed form is 28 [tex]19/100[/tex]

the improper form is ( 28 x 100) = 19 / 100

2819 / 00

Answer:

Amount after 8 month (A) = $3775 (Approx)

Step-by-step explanation:

Given:

Amount invested (P) = $3,700

Rate of interest (r) = 3% = 0.03 / 12 = 0.0025 monthly

Number of month (n) = 8 month

Find:

Amount after 8 month (A)

Computation:

[tex]A=P(1+r)^n\\\\ A=3700(1+0.0025)^8\\\\A=3700(1.02017588)\\\\ A = 3774.650676[/tex]

Amount after 8 month (A) = $3775 (Approx)

Answer:

The answer is D

Step-by-step explanation:

use the quadratic formula, plug and chug, and voila!

Answer:

Ascending- 10%, 0.2, 1/4, 30%

Descending- 30%, 1/4, 0.2, 10%

Step-by-step explanation:

0.2 = 2/10 = 4/20

1/4 = 5/20

30% = 30/100 = 6/20

10% = 10/100 = 2/20

Ascending

-2/20, 4/20, 5/20, 6/20

- 10%, 0.2, 1/4, 30%

Descending

- 6/20, 5/20, 4/20, 2/20

- 30%, 1/4, 0.2, 10%

Answer:

C

Step-by-step explanation:

The end of a slinky is moved vertically up and down to simulate a wave.