Simplify (x+3)^2 - 6x

Answer:

[tex]t_7 =\frac{5}{729} [/tex]

Step-by-step explanation:

We are given that:

First term (a) = 5

common ratio (r) =[tex]\frac{1}{3}[/tex]

The nth term of a geometric sequence is given as:

[tex]t_n =ar^{n-1} \\\therefore t_7 =5\times \bigg(\frac{1}{3}\bigg) ^{7-1} \\\therefore t_7 =5\times \bigg(\frac{1}{3}\bigg) ^{6} \\\therefore t_7 =5\times \bigg(\frac{1}{3}\bigg) ^{6} \\\therefore t_7 =5\times \frac{1}{729}\\\\\huge\red{\boxed{\therefore t_7 =\frac{5}{729} }}[/tex]

Answer:

Step-by-step explanation:

x+2/3=2

multiply by 3

3x+2=6

3x=6-2

3x=4

x=4/3

if it is (x+2)/3=2

multiply by 3

x+2=6

x=6-2=4

Answer:

[tex]x=\frac{4}{3}[/tex]

Step-by-step explanation:

[tex]x+\frac{2}{3}=2[/tex]

to find the value of x we subtract 2/3 on both sides

[tex]x+\frac{2}{3}-\frac{2}{3}=2-\frac{2}{3}[/tex]

taking LCM AS 3

[tex]x=\frac{2*3}{1*3}-\frac{2}{3}[/tex]

[tex]x=\frac{6}{3}-\frac{2}{3}[/tex]

[tex]x=\frac{4}{3}[/tex]

[tex]i hope this will help you:)[/tex]

Answer:

$675

Step-by-step explanation:

If it is 24% less than the regular price then it is 76% of the original price

$675 multiplied by 0.76 is $513

Answer:9 packets

Step-by-step explanation:

You simply divide 144 by 16: )

Answer:

9 packages

Step-by-step explanation:

Take 144 ounces and divide by 16 ounces per package

144/16 = 9

You will get 9 packages

Answer:

C. x=(p−ny)/m

Step-by-step explanation:

mx + ny = p

Subtract ny from each side

mx + ny -ny= p -ny

mx = p-ny

Divide each side by m

mx/m = (p-ny)/m

x=(p−ny)/m

Answer:

v = -1

Step-by-step explanation:

First, you will need to solve it step-by-step:

(4v − 9)(1 + v) = 0

Next, you need to simplify both sides of the equation:

4v(2) − 5v − 9 = 0

Now, factor the left side of equation:

(4v − 9)(v + 1) = 0

The last thing you need to do is to set all of the factors to equal to zero:

4v − 9 = 0 or v + 1 = 0

So, that means that you answer:

v=9/4 or in your case, v = −1

Answer:

Step-by-step explanation:

The geometric mean has a set up it must follow in order to "work". If you look at #3, x is a side of the smaller triangle that has a base of 3, but it's also a side of the large triangle that has a base of 3 + 8 which is 11.  That means that x is your geometric mean. Setting up the geometric mean will look like this:

[tex]\frac{3}{x}=\frac{x}{11}[/tex]

where x is the geometric means and the 3 and the 11 (the positions they are in) are the geometric extremes.

Now we cross multiply to solve for x:

[tex]x^2=33[/tex] and

[tex]x=\sqrt{33}[/tex]

That's the length of x in #3.

For #4, x is the side of the small triangle with the base of 7 and it's also the side of the large triangle with the base of 7 + 13 which 20. That means that x is the geometric mean. Setting up like above:

[tex]\frac{7}{x}=\frac{x}{20}[/tex] and

[tex]x^2=140[/tex] so

[tex]x=\sqrt{140}[/tex]

Answer:

(–4, 1)  

Step-by-step explanation:

1. Calculate the slope of AB

m₁ = (y₂ - y₁)/(x₂ - x₁) = (-4 - 4)/(0 -(-2))= -8/2 = -4

2. Calculate the slope of the perpendicular line

m₂ = -m₁ = ¼

3. Calculate its y-intercept

Point Z, (0,2), is the y-intercept.

4. Write the equation for the line

Insert the values of m and b

y = ¼x + 2

5. Check the points

(a) (-4,1)

1 = ¼(-4)+ 2

1 = -1 + 2

1 = 1

TRUE

(b) (1,-2)

-2 = ¼(1) + 2

-2 = ¼ + 2

-2 = 2¼

FALSE

(c) (2,0)

0 = ¼(2) + 2

0 = ½ + 2

0 = 2½

FALSE

(d)  

4 = ¼(4) + 2

4 = 1 + 2

4 = 3

FALSE

Only (-4,1) is on the perpendicular line.

The diagram shows the line going through AB in red and the perpendicular line in purple.

Answer:

-4,1

Step-by-step explanation:

Answer:

198.5 cm²

Step-by-step explanation:

The figure is composed of a central rectangle and 2 congruent semi- circular ends, equivalent to 1 circle with diameter = 10 cm, thus radius of 5 cm

length of rectangle = 22 - 5 - 5 = 12 cm, thus

area of rectangle = 10 × 12 = 120 cm²

area of circle = πr² = π × 5² = 25π ≈ 78.5 cm² ( to 1 dec. place )

Total area = 120 + 78.5 = 198.5 cm²

Answer:

The distance between park and museum is 12km.

Step-by-step explanation:

Given that the map shows 1cm represents 3km. In this question, the distance between park and museum is 4cm so in order to find the real-life distance, you have to multiply by 4 :

[tex]1cm = 3km[/tex]

[tex]4cm = 3km \times 4[/tex]

[tex]4cm = 12km[/tex]

Hence, the real-life distance between the park and the museum is [tex]12km[/tex].

What is the simplification?

Simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

Here given that,

Here is a map of a town.The map shows a centimetre ruler [tex]1[/tex] cm represents [tex]3[/tex] km.

In a map it is mentioned that [tex]1[/tex]cm which represents the [tex]3[/tex] km. So, the distance between park and museum is

[tex]1+3=4[/tex]cm

So for the real-life distance, we multiply by [tex]4[/tex]

then,

[tex]1cm=3km\\\\4cm=3(4)km\\\\4cm=12km[/tex]

Hence, the real-life distance between the park and the museum is [tex]12km[/tex].

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Answer:

30° and 110°

55° and 85°

70° and 70°

Step-by-step explanation:

Given that:

[tex]\angle B = 90^\circ[/tex]

To find the possible values for the other two angles [tex]\angle A\ and\ \angle C[/tex].

Property of a triangle is that the sum of all three angles is always equal to [tex]180^\circ[/tex].

OR

[tex]\angle A +\angle B +\angle C = 180^\circ\\\Rightarrow \angle A + 40^\circ + \angle C = 180^\circ\\\Rightarrow \angle A + \angle C = 180^\circ - 40^\circ\\\Rightarrow \angle A + \angle C = 140^\circ[/tex]

So, the sum of [tex]\angle A\ and\ \angle C[/tex] should be [tex]140^\circ[/tex]. We can select our answers according to this condition.

Option 1: 20° and 30°: the sum is [tex]50^\circ \neq 140^\circ[/tex] hence, not correct.

Option 2: 30° and 110°: the sum is [tex]140^\circ[/tex] hence, correct.

Option 3: 55° and 85°: the sum is [tex]140^\circ[/tex] hence, correct.

Option 4: 60° and 90°: the sum is [tex]150^\circ \neq 140^\circ[/tex] hence, not correct.

Option 5: 70° and 70°: the sum is [tex]140^\circ[/tex] hence, correct.

Hence, the possible answers can be:

30° and 110°

55° and 85°

70° and 70°

Answer:

30º and 110º

55º and 85º

70º and 70º

Step-by-step explanation:

got it right on edge. !

Answer:

Set of ordered pairs = { ( 0 , 2 ),  ( π / 2 , 0) ,  ( π , -2) , ( 2 π , 2)}

Step-by-step Explanation:

Given  y = 2 cos x

i) Let  x =0 ⇒ y = 2 cos (0) = 2

The ordered pair ( 0 , 2 )

ii) Let x = π / 2  ⇒ y = 2 cos (π/2) = 2(0) =0

The ordered pair ( π / 2 , 0)

iii) let x = π ⇒ y = 2 cos(π) = 2 (-1) = -2

The ordered pair ( π , -2)

iv)

let x = 2π ⇒ y = 2 cos(2π) = 2 (1) = 2

The ordered pair ( 2 π , 2)

Set of ordered pairs = { ( 0 , 2 ),  ( π / 2 , 0) ,  ( π , -2) , ( 2 π , 2)}

Answer:

What aspect of culture does the following excerpt from "What For" by Garrett Hongo celebrate?

I lived for stories about the war

my grandfather told over hana cards,

slapping them down on the mats

with a sharp Japanese kiai.

Step-by-step explanation:

Answer:

[tex]-\frac{443}{420}[/tex]

Step-by-step explanation:

Answer:

2/3

Step-by-step explanation:

2/9+4/9

The denominator is the same, so we add

6/9

Divide the top and bottom by 3

2/3

6/9simplified = 2/3 or ≅ 0.6666667

9514 1404 393

Answer:

  43/120 ≈ 0.3583

Step-by-step explanation:

Adding up the folks who use two facilities counts the folks who use all three 3 times. So, the number who use two or more facilities is ...

  21 +16 +24 -2(9) = 43 . . . . people who use 2 or more facilities

The probability that a person chosen randomly from the 120 at the sports center uses at least 2 facilities is ...

 43/120 ≈ 0.3583

_____

The given numbers add up as follows:

  Gym only: 42

  Pool only: 18

  Track only: 14

  Gym and Pool only: 12

  Gym and Track only: 15

  Pool and Track only: 7

  Gym and Pool and Track: 9

  No facilities: 3

Answer:

see below

Step-by-step explanation:

Take the miles and divide by the hours

242/4 =

divide the top and bottom by 2

121/2 miles per hour as an improper fraction

60 1/2 miles per hour  as a mixed number

Answer:

C^5d^5

Step-by-step explanation:

The equivalent expression is,

⇒ c⁵ × d⁵

We have to given that,

An expression is,

⇒ (cd)⁵

Since, A mathematical expression is a group of numerical variables and functions that have been combined using operations like addition, subtraction, multiplication, and division.

Now, Solve the expression by rule of exponent as,

⇒ (cd)⁵

⇒ c⁵ × d⁵

Therefore, The correct equivalent expression is,

⇒ c⁵ × d⁵

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Answer:

83/10 ; 9.01 ; 97/10 ; 9.87

Step-by-step explanation:

Simplify the fractions, and then you can easily see the answer.

Answer: 83/10, 9.01, 97/10, 9.87

Step-by-step explanation:

We can choose to either write all the numbers indecimals or fractions. Let's choose decimals.

83/10=8.30

97/10=9.70

9.87

9.01

Now that we know the decimals, we can put them in order.

8.30, 9.01, 9.70, 9.87

Though this is correct, it is not the answer we are looking for. When we were given the problem, we had fractions. We must change the decimals back into fractions.

83/10, 9.01, 97/10, 9.87

This is our correct answer.

Answer:

V = 6.26 (2.5)

Step-by-step explanation:

The volume of a cube is given by

V = s^3 where s is the side length

V = (2.5)^3

V = 6.26 (2.5)

Answer:

12 sec

Step-by-step explanation:

After 1 sec distance between the deer and the bear = (8 + 5) = 13 feet.

After x sec distance is 13x.

13x = 156

x= 156/13=12 sec

Answer:

36

Step-by-step explanation:

First we will add the bear and the deer's speed. 8+5=13. now we will divide by the distance, but the speed is in feet not yards, so multiply 156 by 13=468/ then do 13x=468 so x is equal to 36.

Answer:

85 - 85 = 0

Step-by-step explanation:

so answer is 0

hope this helps u

Answer:

85 - 85 = 0

Step-by-step explanation:

hope this helps u

Answer:

The answer is

A[tex].5x^2+9x+15[/tex]

Step-by-step explanation:

kindly find attached the solving for proper understanding and solution flow.

Given Data

the divisor=  [tex]6x-10[/tex]

dividend= [tex]30x^3+4x^2-150[/tex]

firstly for us to perform the division we need to re write the dividend and include the missing coefficient of x

dividend [tex]=30x^3+4x^2+0x-150[/tex]

Answer:

[tex]2x^2-25x+63[/tex]

Step-by-step explanation:

You have to multiply both terms from the first one by both term in the second on, it'll look like this:

[tex](x-9)*(2x-7)=(x*2x)+(x*-7)+(-9*2x)+(-9*-7)\\(x-9)*(2x-7)=(2x^2)+(-7x)+(-18x)+(63)[/tex]

Once you combine like terms it'll be the final answer:

[tex](x-9)*(2x-7)=2x^2-25x+63[/tex]

You can use foiling to get any other questions like this:

Answer:

x = 7

Step-by-step explanation:

Parallel sides have to be the same length

5x+3 = 38

Subtract 3 from each side

5x+3-3 = 38-3

5x = 35

Divide by 5

5x/5 = 35/5

x = 7

There are two rectangles.

1= 8 x 4 = 32

2= 2x6 = 12

Total = 32 + 12 = 44 square km

Answer:

44 sq. KM

Step-by-step explanation:

To find the total area, we have to add the area's of each rectangle. For the bigger rectangle, we will go base times height.

[tex](8)(4)=32[/tex]

For the smaller rectangle, the width is 2 and height is 6 so we will multiply those.

[tex](2)(6)=12[/tex]

Now we have to add the two areas to get the grand area.

[tex]32+12=44[/tex]

The area is 44 square km

Answer:

40

Step-by-step explanation:

The number of gift baskets Nikki can make varies directly with the amount of time she spends making the baskets .

Let n be the number of baskets and let t be the mount of time it takes to make the basket. This means that:

n α t

=> n = kt

where k = constant of proportionality

She can make 4 baskets in every 1/2 hour.

This means that:

4 = k * 1/2

=> k = 4 * 2 = 8 baskets per hour

The time is now 5 hours (t = 5). Therefore:

n = 8 * 5 = 40 baskets

She can make 40 baskets in 5 hours.

Answer: The correct answer is C

Answer:

[tex]17[/tex]

Step-by-step explanation:

[tex]\sqrt{285}[/tex]

[tex]=16.8819430161[/tex]

Answer:

it is a horizontal stretch by 2.

Step-by-step explanation:

AB=3-1=2

A'B'=6-2=4

[tex]\frac{A'B'}{AB} =\frac{4}{2} =2\\A'B'=2(AB)[/tex]

Answer:

101[tex]cm^{2}[/tex]