Use Pascal's Triangle to determine the sixth term of the expansion of (x + 5)^7

Answers

Answer 1

Pascal's triangle up to the 7th row (starting with 0)

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

1 7 21 35 35 21 7 1

Then the 6th term in the expansion of (x + 5)⁷ is

7 • x¹ • 5⁶ = 109375x


Related Questions

The admission fee at a local zoo is $1.50 for children and $3.00 for adults. On a certain day, 2400 people enter the zoo and $4,800.00 is collected. How many children and how many adults?​

Answers

Answer:

Step-by-step explanation:

c = children

a = adults

2200 people enter the zoo mean :

c + a = 2200

$4,550.00 is collected mean :

1.5 c + 4 a = 4550

Now you must solve system:

c + a = 2200

1.5 c + 4 a = 4550

c + a = 2200 Subtract c to both sides

c + a - c = 2200 - c

a = 2200 - c

1.5 c + 4 a = 4550

1.5 c + 4 ( 2200 - c ) = 4550

1.5 * c + 4 * 2200 - 4 c = 4550

1.5 * c + 8800 - 4 c = 4550

- 2.5 c + 8800 = 4550 Subtract 8800 to both sides

- 2.5 c + 8800 - 8800 = 4550 - 8800

- 2.5 c = - 4250 Divide both sides by - 2.5

c = - 4250 / - 2.5

c = 1700

a = 2200 - c = 2200 - 1700 = 500

1700 children and 500 adults

Proof :

c + a = 1700 = 2200

$ 1.5 * c + $ 4 * a =

$ 1.5 * 1700 + $ 4 * 500 =

$ 2550 + $ 2000 = $ 4550

The number of children and the number of adults are 1600 and 800, respectively.

What is the solution to the equation?

The allocation of weights to the relevant variables that produce the calculation's optimum is referred to as a direct consequence.

A nearby zoo charges $1.50 for kids and $3.00 for adults to enter. 2400 persons visit the zoo on a certain day, and $4,800.00 is gathered.

Let x be the number of children and y be the number of adults. Then the equation is written as,

x + y = 2400           ...1

1.5x + 3y = 4800

x + 2y = 3200    ...2

Subtract equation 1 from equation 1, then

2y - y = 3200 - 2400

y = 800

Then the value of x is calculated as,

x + 800 = 2400

x = 2400 - 800

x = 1600

The number of children and the number of adults are 1600 and 800, respectively.

More about the solution of the equation link is given below.

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You are asked to prepare 900mls of 3% sucrose. How much sucrose do you need?

Answers

Answer:

27g of sucrose

Step-by-step explanation:

You would need 3g of sucrose per ever 100ml and you have 900ml therefore 27g

consider h(x)=x^2+8+15. identify its vertex and y-intercept.

Answers

Answer:

Vertex: (-4, -1)

Y-intercept: (0, 15)

Step-by-step explanation:

Given the quaratic function, h(x) = x² + 8x + 15:

In order to determine the vertex of the given function, we can use the formula, [tex][x = \frac{-b}{2a}, h(\frac{-b}{2a})][/tex].

Use the equation:  [tex][x = \frac{-b}{2a}, h(\frac{-b}{2a})][/tex]

In the quadratic function, h(x) = x² + 8x + 15, where:

a = 1, b = 8, and c = 15:

Substitute the given values for a and b into the equation to solve for the x-coordinate of the vertex.

[tex]x = \frac{-b}{2a}[/tex]

[tex]x = \frac{-8}{2(1)}[/tex]

x = -4

Subsitute the value of the x-coordinate into the given function to solve for the y-coordinate of the vertex:

h(x) = x² + 8x + 15

h(-4) = (-4)² + 8(-4) + 15

h(-4) = 16 - 32 + 15

h(-4) = -1

Therefore, the vertex of the given function is (-4, -1).

Solve for the Y-intercept:

The y-intercept is the point on the graph where it crosse the y-axis. In order to find the y-intercept of the function, set x = 0, and solve for the y-intercept:

h(x) = x² + 8x + 15

h(0) = (0)² + 8(0) + 15

h(0) = 0 + 0 + 15

h(0) = 15

Therefore, the y-intercept of the quadratic function is (0, 15).

Fill in the blank with a number to make a true statement. *
0.25 / ? = -0.25

Answers

0.25/-1=-0.25 because +/- = -

If you earn 15% on your investment how long will it take for your money to double using the rule of 72

Answers

Answer:

If you earn 15% the answer will be 10.8

Step-by-step explanation:

I know this because if you use the rule of 72 you will have to divide the two numbers together and the you will come out with 10.8

At an airport, it costs $7 to park for up to one hour and $5 per hour for each additional hour. Let x
represent the number of hours parked. Write the function that models the cost, C(x), of parking x
hours, where x is an integer greater than 1. A:c(x)

Answers

Answer:

C(X)=5(x-1)+7  

Step-by-step explanation:

because x-1 represents the fact that the first hour costs $7 and then x times 5 represents the fact that each hour after that costs $5

Help pls!!!!!!


Yghhjjhgf

Answers

Answer:

[tex]\sf{Exact\:form:\\\sqrt[4]{81}\\[/tex]

[tex]\bold{Decimal\:form:-3}[/tex]

Step-by-step explanation:

[tex]-81^\frac{1}{4}[/tex]

[tex]\mathrm{Convert\: to\: radical\: form\: using\: the\: formula\:}\: a^\frac{x}{n} = \sqrt[n]{a^x}[/tex]

[tex]\mathrm{If\:} n \mathrm{\:is\: a\: positive\: integer\: that\: is\: greater\: than\:} x\mathrm{\:and\:} a \mathrm{\:is\: a\: real\: number\: or\: a\: factor, then} \\a^\frac{x}{n} = \sqrt[n]{a^x}[/tex]

[tex]\mathrm{Use\: the\: rule\: to\: convert\: -81^\frac{1}{4}\: to\: a\: radical, where\:} a=-81,\ x=1, \mathrm{and\:} n=4\\\sqrt[4]{81}[/tex]

[tex]\mathrm{Plug\: the\: points:}\\\\a^\frac{x}{n} = \sqrt[n]{a^x}\\-81^\frac{1}{4} =\sqrt[4]{81}[/tex]

[tex]\mathrm{Solve}\\\\\mathrm{The\: result\: can\: be\: shown\: in\: multiple\: forms.}[/tex]

PLEASE HELP EXPLAIN !! SHOW WORK FOR BRAINLIEST Acidity is measured on the pH scale. The acidity of a substance is given by pH=−logH, where H is the concentration of Hydrogen ions. If a substance has an H value of 0.0004, what is the pH of the substance, rounded to the nearest tenth?

Answers

3.4

Step-by-step explanation:

The pH or acidity of a solution is given by the equation

[tex]pH = -\log{[H]}[/tex]

where [H] is the concentration of [tex]H^+[/tex] ions. If the [tex]H^+[/tex] concentration is 0.0004 (=[tex]4×10^{-4}),[/tex] then its pH level is

[tex]pH = -\log{(4×10^{-4})} = 3.4[/tex]

identify the pair of similar triangles in each of the groups of triangle below​

Answers

Answer:

its triangle ABC and XYZ

Step-by-step explanation:

Grace collected 7 2/3 bins of glass bottles to recycle. Kenneth collected 7 5/6 times as many
bins as Grace. How many bins of bottles did Kenneth collect?

Answers

Answer:

Kenneth collected 60 bins of bottles.


Solution:

(7 2/5) * (7 5/6) = 60.05


which inequality has he same solutions as d < -5

Answers

-d < 5 has the same the same solution

Mary was asleep from 9:pm to 5:am. How long was she asleep for?​

Answers

Answer:

8 hours

Step-by-step explanation:

Answer:

8hours

Step-by-step explanation:

A group of 6 friends rent a cabin on a campsite. It costs $62.88 to rent the cabin. if they divide the cost evenly between them, how much does each friend need to pay?

Answers

Answer: Each friend needs to pay $10.48

Benji took out a $10,000 loan at a 13% interest rate. Benji will not make a payment for the next 3 years. How much will be owed in 3 years with monthly compounding?

Round your answer to the nearest cent.
(please help)

Answers

Answer:

Plug into calc

Step-by-step explanation:

A= P(1+r/n)^nt

A= 10000(1+.13/12)^12*3

Gabby read 98 pages of a book then stopped. She later decided to continue the book and read 37 more pages every day.
Let d represent the number of days since Gabby decided to continue the book and p represent the total number of pages of the book she had read.

Answers

Answer:

number of days = 3

total number of pages=135

Step-by-step explanation:

98÷49= 2

37=1 day

total number of days=3days

Total number of pages read=135 pages

The letters A, B, and C can be arranged in six ways. Five ways are listed below.
Find the sixth way.
АВС ACB BAC ВСА САВ

Answers

Answer:

CBA would be the sixth

Step-by-step explanation:

CBA would be the sixth and and final one

Would anyone help me with this please, worth 20 pts.

Answers

Answer:

Below in bold.

Step-by-step explanation:

The perimeter = length of 3 sides of the square + 1/2 the circumference of the circle. The radius of the circle = 2.5 in and its circumference = 2π r and 1/2 of this is π r.

So the perimeter = 3*5 + π  r

= 15 + 2.5π

= 22.85 in  to the nearest hundredth.

Find the cardinal number of the set:
C={1/x x is an integer that's greater than or equal to 4 and less than or equal to 9}.

Answers

Answer: 6

Step-by-step explanation:

Ok lemme actually format this set

[tex]$C = \left\{\frac 1x : x \in \mathbb{Z}\ \text{and}\ 4 \leq x \leq 9\right\}$[/tex]

Well the only integers from 4 to 9 are 4, 5, 6, 7, 8, 9. So this set is just

[tex]$C = \left\{\frac 14, \frac 15, \frac 16, \frac 17, \frac 18, \frac 19\right\}$[/tex]

which has cardinality [tex]\boxed{6}[/tex] .

Lindsey drew a scale of a city. the scale of the drawing is 1 inch = 3 yards. If the actual length of a neighborhood park is 114 yards, how long is the park in the drawing?

Answers

Answer:

38 in

Step-by-step explanation:

114 yds divided by 3 = 38 in

I need help really bad! I have literally no clue what the answer is to this question

Answers

Answer: C is the answer

Answer:

The second answer: {(-1, 4),(2, 7),(3,7)} because every x value has one y value

I need word form and decimal

(I already shaded it in so that is all I need​

Answers

The shading is correct for each of the three problems. Nice work.

==========================================

Problem 13

Word form = one tenth

Decimal form = 0.1

Explanation: The 1 is in the tenths place for the decimal value 0.1 to represent the fraction 1/10.

==========================================

Problem 14

Word form = eighty-five hundredths

Decimal form = 0.85

Explanation: The 8 is in the tenths place, and the 5 is in the hundredths place. Overall, 0.85 represents 85 out of 100, aka 85/100.

==========================================

Problem 15

Word form = thirty-nine thousandths

Decimal form = 0.039

Explanation: The second zero is in the tenths place. The 3 is in the hundredths place. The 9 is in the thousandths place. The decimal represents 39/1000 which you can think of it as 039/1000.

One tenth, 0.1
Eighty five hundredths, 0.85
Thirty nine thousandths, 0.039

Hope this helps!!!

Which equation has a solution of r = 1/3

Answers

Answer:

                 

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

A.

2 2/3 + r = 3

r = 3 - 2 2/3

r = 1/3

B.

r - 1 = 2/3

r = 1 2/3

C.

3r = 1/3

r = 1/9

D.

4r = 12

r = 3

Answer: A.

Choose all of the equations that are equivalent to 8k = 20.

Answers

Answer:

D

Step-by-step explanation:

it's 100% I'm super sure

Use the table below to answer the following question,
2:
хо 1 2 3 4 5 6
y 100 200 400 800 1,600 3,200 6,400
Which equation BEST fits the data given in the table?
se 3:
Of(x) = { (200)*
Of(x) = 100(2)*
uge 4
f(x) = 200)
age 5
Of(x) = 200(2)*
5
Previous Page
Next Page
Page 2 of 11

Answers

Answer Of(x) = 200(2)

Step-by-step explanation:

Of(x) = 200(2)

Martin is buying inkjet cartridges that cost $22 each. He has $100 to pay for the cartridges.

Which number line shows the number of cartridges Martin can buy?

Answers

Answer: C

Step-by-step explanation:

lets think about it

you can totally buy 0 ink cartridges. you can just be like "nope ok im gone, no ink today, the prices are so high.. maybe another time. maybe ill use the school printer or smth"

so that ELIMINATES B.

and now A and D are strange because how exactly are we going to buy half of an ink cartridge? or a fraction of an ink cartridge? that simply isnt feasible

so this eliminates A and D

now C is the best because you can buy 0, 1, 2, 3, 4 ink cartridges. but not 5 because that is $110 and Martin dont got that money, am i right fellas?

Answer:

The Answer Is C

Step-by-step explanation:

Dеtеrmіnе tһе rаnցе օf tһе fսnсtіօn f(х) = 2х + 1 ԝһеn tһе ԁօmаіn іѕ {-3, 9, 15}.

Answers

Answer:

Range: {-5, 19, 31}

Step-by-step explanation:

Given the linear function, f(x) = 2x + 1, and the domain, {-3, 9, 15}.

In order to determine the range of the given linear function, simply substitute each domain value as inputs into the function.

x = -3

f(x) = 2x + 1

f(-3) = 2(-3) + 1

f(-3) = -6 + 1

f(-3) = -5

x = 9

f(9) = 2x + 1

f(9) = 2(9) + 1

f(9) = 18 + 1

f(9) = 19

x = 15

f(15) = 2x + 1

f(15) = 2(15) + 1

f(15) = 30 + 1

f(15) = 31

Therfore, the range of the function is: {-5, 19, 31}.

This graph gives Selma's distance from home over time What does the slope of the line show in this situation? 20 18 16 Select from the drop-down menus to correctly complete each statement 14 12 Distance from home (miles) 100 For this situation, the slope of the line represents 81 60 Choose 40 20 The slope is Choose... which means that Selma's distance 0 from home Choose... by Choose... miles per hour.​

Answers

Answer:

The amount Selma's distance from home changes per unit of time.

The slope is 38, which means that Selma's distance from home increases by 38 miles per hour.

Step-by-step explanation:

I just took the the test in k12 and I got it right.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. Selma's distance from home increases by 38 miles per hour.

What is Slope of Line?

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The given two points from graph are (2, 91) and (4,167)

x₁=2,y₁=91,x₂=4, y₂=167

Substitute in the formula

167-91/4-2

76/2

38

The amount Selma's distance from home changes per unit of time.

So slope is 38, which means that Selma's distance from home increases by 38 miles per hour.

Hence Selma's distance from home increases by 38 miles per hour.

To learn more on slope of line click:

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Name the postulate or theorem that you can use to show the triangles are congruent. Then explain why the statement is true.


I’ll choose brainliest

Answers

4. EA ≅ MA

In ΔTAE and ΔTAM,

TE = TM (Given)

∠ETA = ∠MTA (Given)

TA = TA (Common)

∴ ΔTAE ≅ ΔTAM

∴ EA = MA (CPCT)

5. In ΔJUN and ΔJEN,

JU = JE (Given)

NE = NU (Given)

JN = JN (Common)

∴ ΔJUN ≅ ΔJEN (By SSS Criteria)

∴ ∠U = ∠E (CPCT)

Hope it helps you....

Please mark as brainlliest

27 red bikes out of 33 bikes

Answers

The total is 33 bikes. 27 out of the 33 bikes are red. Therefore, we have a number of parts to a whole, so we can create a fraction to calculate the percentage of red bikes.

27/33 = .818

.818 x 100 = 81.81%.

• To calculate a percentage, divide the numerator by the denominator and multiply by 100. Here’s a formula to remember: n/d•100, where n=numerator and d=denominator.

Therefore, 81.81% of the bikes are red.

Feel free to give Brainliest!

Devaughn's age is two times Sydney's age. The sum of their ages is 21. What is Sydney's age?

Answers

Answer:

The age is 7

Step-by-step explanation:

Devaughn's age is two times Sydney's age

and the sum of their ages is ? Let’s Sydney's age is X, Devaughn's age is (2X+X=21)

Therefore 3X=21

Rearranged is X= 21 divide 3

Therefore Sydney’s age is 7

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