Twice the difference of a number and 9 is equal to three times the sum of the number and 6. Find the number

The numbers of ways can this be done, if the order of the choices is relevant is 181,440 ways and the numbers of  ways can this be done, if the order of the choices is not relevant is 36 ways.

a. N permutations

N permutations = nPr  = n!/ (n-r)!

N permutations = 9P7 = 9!/(9-7)!

N permutations = 9×8×7×6×5×4×3

N permutations= 181,440

b. N combinations :

N combinations = nCr = n!/((n-r)!r!)

N combinations = 9C7 = 9!/((9-7)!7!)

N combinations =9×8×7×6×5×4×3 ×2!/7!×2!

N combinations = 9×8×7×6×5×4×3 /7!

N combinations =181,440/7!

N combinations =36

Therefore the numbers of ways can this be done, if the order of the choices is relevant is 181,440 ways and the numbers of  ways can this be done, if the order of the choices is not relevant is 36 ways.

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Answer:

Step-by-step explanation:

Given square TUVW, you want the perimeter and area of square T'U'V'W' after it has been dilated by a factor of 5/2 and translated by (0, -8).

Counting grid squares, or reading coordinates, we find the length of a side of square TUVW to be 8 units. Then the perimeter is ...

  P = 4s = 4·8 = 32 . . . . units

After dilation, the perimeter of the square is the preimage value multiplied by the dilation factor.

 perimeter of T'U'V'W' = (5/2)(perimeter of TUVW) = (5/2)(32 units)

  perimeter of T'U'V'W' = 80 units.

The area is the square of the side length. The side length of T'U'V'W' is ...

  s' = (5/2)(8) = 20 . . . . units

Then the area is

  A' = (s')² = (20 units)² = 400 units²

area of T'U'V'W' is 400 units².

__

Additional comment

Translation is a rigid transformation. It does not change the dimensions, so does not change the perimeter or area of the dilated square.

Answer: The first 3 answers from the top

Step-by-step explanation:

Answer:

x = 3

y = 15

Step-by-step explanation:

The equation 4y = -4x + 2³​ is a linear function

A linear function can be explained as an algebraic equation, whose every  term is either a constant or the product of a constant and a variable (raised to the first power only).

The equation 4y = -4x + 2³​ is a linear function since both variables x and y meet the criteria, and both constants a and b do comply with rules as well

The exponent of x is 1, that is, it is raised to the first power only and the equation follows the definition of a function: for each input (x) there is only one output (y). The graph of any linear function in one variable  is always  a straight line.

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Answer:

X = 4

Step-by-step explanation:

Remove the fraction first by multiplying with 6 both sides.

Then leave the variable alone by diving with - 5

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Answer:  [tex]\textsf{x= 4}[/tex]

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Given: [tex]\textsf{-5/6x = -10/3}[/tex]

Find:  [tex]\textsf{The value of x}[/tex]

Solution: In order to get the value of x we must multiply both sides by -6/5 to help cancel the coefficient on the left side to leave x by itself.

Multiply both sides by -6/5

Simplify the expression

Therefore, the value of the unknown variable x is 4.

Answer:

310

Step-by-step explanation:

189+122=311

(311 rounded to the nearest ten is 310.)

Answer: [C] P = 5000T + 93,000

Step-by-step explanation:

I THINK X IS 2) : -0.75

With an HCF of 6 and an LCM of 60, the numbers 12 and 30 are greater than 6.

Two numbers with HCF 6 can be:

6a, 6b where a, b are coprime numbers a, b > 1 as numbers greater than 6.

As a result, a and b can be 2 or 5.

The numbers are 6 × 2 and 6 × 5.

Therefore, with an HCF of 6 and an LCM of 60, the numbers 12 and 30 are greater than 6.

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Answer:

horizontal line isywgwueve

66.00 divided by 4 equals 16.5

Answer:

the respuesta is 54

Step-by-step explanation:

are not

Answer:

Geometric sequence with a common ratio of 1/3

Step-by-step explanation:

Each term is 1/3 of the previous term:
First term is : 162
Second term: 162 x 1/3 = 162/3 = 54
Third term : 54 x 1/3 = 54/3 = 18

and so on

The ratio of a term to its previous term is therefore 1/3 and this is called a common ration

This kind of sequence where each term is a multiple (1/3) of the previous term is called a geometric sequence

Answer:

19 7/20 feet

Step-by-step explanation:

1. [tex]2\frac{5}{8}[/tex] pieces of wood

[tex]2\frac{5}{8} * 6 = 15\frac{3}{4}[/tex]

2. [tex]1\frac{1}{5}[/tex] pieces of wood

[tex]1\frac{1}{5} * 3 = 3\frac{3}{5}[/tex]

3. Combined

[tex]15\frac{3}{5} +3\frac{3}{5} = 19\frac{7}{20}[/tex]

The products that have 240 as a partial product are 3 x 3,388 and 6 x 4,345

The partial product is given as

240

Express 240 as a product of its factors

So, we have

240 =  1 * 240

240 =  2 * 120

240 =  3 * 80

240 =  4 * 60

240 =  5 * 48

240 =  6 * 40

240 =  9 * 30

Next, we test the options

3 x 3,388

Express all values other than the ten-place value as 0

3 x 0080

Evaluate the product

3 x 0080  = 240

8 x 2,612

Express all values other than the ten-place value as 0

8 x 0010

Evaluate the product

8 x 0010 = 80

4 x 5,376

Express all values other than the ten-place value as 0

4 x 0070

Evaluate the product

4 x 0070 = 280

6 x 4,345

Express all values other than the ten-place value as 0

6 x 0040

Evaluate the product

6 x 0040 = 240

3 x 6,828

Express all values other than the ten-place value as 0

3 x 0020

Evaluate the product

3 x 0020 = 60

Hence, the products that have 240 as a partial product are 3 x 3,388 and 6 x 4,345

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The time takes Ben to walk to the library is 80 minutes.

Given that, Ben can walk to the library 4 miles away, but it takes him 20 minutes longer than it would walk to school 3 miles away.

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. The proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

Let the time taken Ben to walk to the school be x, so the time taken to walk to the library be x+20.

Now, 4 : x+20 :: 3 : x

⇒4x=3(x+20)

⇒4x=3x+60

⇒x=60

So, x+20=80

Therefore, the time taken by Ben to walk to the library is 80 minutes.

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Keri's total score in her last gymnastics which had three different types of acts is 17.25.

A decimal separates the whole part and the integer part of a given number. Decimal can also be written as fractions.

Keri in her last gymnastics competition scored a 5.65 on the floor exercise, 5.85 on the vault, and 5.57 on balance.

∴ Her total score will be the sum of all the scores she obtained in all those three performances which are,

= ( 5.65 + 5.85 + 5.75).

= 17.25.

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Answer:The answer is 2

no time for explonations

Answer:

Step-by-step explanation:

sec(2a+6)cos (5a+3)=1

[tex]\frac{cos(5a+3)}{cos(2a+6)} =1\\[/tex]

cos(5a+3)=cos(2a+6)

cos(5a+3)-cos(2a+6)=0

[tex]-2sin(\frac{5a+3+2a+6)}{2} )sin(\frac{5a+3-2a-6)}{2} )=0\\-2sin(\frac{7a+9}{2} )sin(\frac{3a-3}{2} )=0\\either sin (\frac{7a+9}{2} )=0=sin ~n\pi \\\frac{7a+9}{2} =n~\pi \\7a+9=2n~\pi \\7a=2n~\pi -9\\a=\frac{2n\pi-9 }{7} \\where~n~is~an~integer.[/tex]

or

[tex]\sin\frac{3a-3}{2} =0=\sin ~n\pi \\3a-3=2n\pi \\3a=2n\pi+3\\a=\frac{2~n\pi+3 }{3}[/tex]

where n is an integer.

The volcano is growing larger by 1 cm/year.

In order to determine if the volcano is growing or wearing down, determine the cm that the volcano wears down each year. To do this, we would be dividing the total cm the volcano wears down by the number of years.

Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷.

The cm the volcano wears down each year = 20 cm / 5 = 4cm

10 / 2 = 5cm

5cm - 4cm = 1 cm

This means that the volcano is growing at 1 cm per year.

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Answer:

33124

Step-by-step explanation:

please rate as brainliest

f(x) = -2x² + 8x - 8 by computing f(-1) + f(1) we get -20 and we don't need to calculate f(1) - f(1) it will be 0.

A function can be thought of as an output for the given inputs.

According to the given question f(x) = -2x² + 8x - 8 we have to compute

A. f(-1) + f(1) = { -2(-1)² + 8(-1) - 8 } + { -2(1) + 8(1) - 8 }.

f(-1) + f(1) = { (-2 - 8 - 8) + (- 2 + 8 - 8) }

f(-1) + f(1) = - 18 - 2.

f(-1) + f(1) = - 20.

B.  f(1)-f(1) = 0 ( we don't need to calculate )

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Answer: x=-7, y=0

Step-by-step explanation:

You can see just by the set up that the x values cancel each other out without you having to do anything(-2x+2x=0). Because of this, you can add the two equations to eliminate the x values.

-2x+8y = 14

2x+8y= -14    -------->   16y=0

When you isolate the variable, you get y=0. Now you can choose one of the original equations and substitute 0 into the y value.

-2x+8y = 14 ---> -2x+8(0) = 14 ----> -2x+0 = 14 ---> -2x=14

When you divide both sides by -2, you get x=-7.

keeping in mind that a year has 12 months, thus 18 months is really 18/12 of a year.

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$300\\ r=rate\to 15\%\to \frac{15}{100}\dotfill &0.15\\ t=years\to \frac{18}{12}\dotfill &\frac{3}{2} \end{cases} \\\\\\ I = (300)(0.15)(\frac{3}{2})\implies I=67.5[/tex]

The coordinates of the new vertices of the rectangle are P''(x, y) = (- 1, - 4), Q''(x, y) = (- 6, - 4), R''(x, y) = (- 6, - 1) and S''(x, y) = (- 1, - 1).

In this question we find the coordinates of the four vertices of the rectangle, whose locations are described in the statement. Each point must be transformed by the following sequence of rigid transformations:

If we know that P(x, y) = (1, 4), Q(x, y) = (6, 4), R(x, y) = (6, 1) and S(x, y) = (1, 1), then the locations of the images of the four vertices are:

P'(x, y) = (1, 4) + (0, - 8)

P'(x, y) = (1, - 4)

P''(x, y) = (1, - 4) + (- 2, 0)

P''(x, y) = (- 1, - 4)

Q'(x, y) = (6, 4) + (0, - 8)

Q'(x, y) = (6, - 4)

Q''(x, y) = (6, - 4) + (- 12, 0)

Q''(x, y) = (- 6, - 4)

R'(x, y) = (6, 1) + (0, - 2)

R'(x, y) = (6, - 1)

R''(x, y) = (6, - 1) + (- 12, 0)

R''(x, y) = (- 6, - 1)

S'(x, y) = (1, 1) + (0, - 2)

S'(x, y) = (1, - 1)

S''(x, y) = (1, - 1) + (- 2, 0)

S''(x, y) = (- 1, - 1)

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Answer:

The Answer is D

Step-by-step explanation:

you just have to look for the letter that's giving you it not subtracting it. And look for the right amount.

Step-by-step explanation:

equivalent fractions are all fractions with different numbers in numerator and denominator, but after simplifying they have the same value.

like 1/2 and 3/6 are equivalent fractions to each other.

so, the equivalent fractions for 3/25 are

a/a × 3/25

for any "a".

e.g.

6/50, 15/125, 300/2500, ...

Answer:

The girls ran 8 laps in one hour, for the boys it is 48:6

Step-by-step explanation:

The girls ran 4 laps in 30 minutes so per hour is was be 8 laps because 4x2. So on the paper it would be 4x2=8

For the boys it would be 8x6 which is 48 dollars in one hour and 6 laps per hour so it would be 48:6 so just put 8x6=48 and it should work.

Carlos pays monthly for his cable bill $67.15

For over 5 months Carlos wrote a total of 5 checks for $335.75 to make payment for his cable TV service.

The same amount is paid for the cable bill every month.

Therefore the amount paid every month can be calculated as follows

= 335.75/5

= 67.15

Hence the amount paid monthly for the cable bill is $67.15

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Answer:

15

Step-by-step explanation:

Distribute where possible

10v + 30 - 4v -6v -6 -9

Combine like terms and do the math

15