A homeowner plans to hang wallpaper on one wall of a bedroom that is 10 feet long

663/3 = 21

21 is the middle number,

21+1 = 22

21-1 = 20

20 + 21 + 22 = 63

Our three consecutive integers can be represented as

X → first integer

X + 1 → second integer

X + 2 → third integer

If the sum of our three consecutive integers is 63, our equation will read...

X + X + 1 + X + 2 = 63

Now, we can simplify on the left. Once we simplify, our equation will now read

3x + 3 = 63

      -3    -3  ← subtract 3 on both sides

  3x = 60 ← divide both sides by 3

   X = 20

Our three consecutive integers can be represented as

X → first integer = 20

X + 1 → second integer = 21

X + 2 → third integer = 22

Therefore, the three consecutive integers are 20, 21, and 22.

Answer:

18.2

Step-by-step explanation:

Answer:

(x+3)(x-8)

Step-by-step explanation:

To solve the given system of equations using substitution, we'll start by solving the first equation for x in terms of y. We'll substitute this expression for x in the other two equations to find the values of y and z.

To solve the given system of equations using substitution, we'll start by solving the first equation for x in terms of y: x = -2y + 10. We'll substitute this expression for x in the other two equations to find the values of y and z. Substituting -2y + 10 for x in the second equation, we have -6y = 6(-2y + 10) - 6.

Simplifying this equation, we get y = -2. Substituting y = -2 in the first equation, we find x = -2*(-2) + 10 = 14. Finally, substituting x = 14 and y = -2 in the third equation, we find z = -3*14 + 10*(-2) = -52.

Option B, spinning "back 2 spaces" on a spinner, describes a simple event as it represents a single outcome from the experiment, in contrast to the other options which describe compound events.

A simple event is an event that consists of a single outcome of an experiment. When tossing a coin 5 times and getting heads twice, we're looking at a compound event because it involves a combination of outcomes. In the options given, option B, spinning "back 2 spaces" on a spinner represents a simple event because it describes a single outcome that can occur from the experiment. The other options involve multiple outcomes or combinations and are therefore not simple events.

Considering the additional information provided:
Coin tosses and the outcomes of 5 coin tosses just give us a set of possible results which help illustrate compound events. The idea of grouping real world observations into outcomes or events shows us that a simple event is a single, specific outcome, such as getting an even number when rolling a die, which can be defined as an event with a single characteristic and has a calculable probability.

20d +13 -12d = -14

 combine like terms

20d-12d = 8d

8d+13 = -14

subtract 13 from each side:

8d =-27

divide both sides by 8

d = -27/8 

The sum of the geometric series is approximately 324.

The sum of a geometric series can be found using the formula:

Sn = a1(1 - rn) / (1 - r)

Where Sn is the sum of the series, a1 is the first term, r is the common ratio, and n is the number of terms.

Plugging in the given values, we have:

Sn = 4(1 - 3n) / (1 - 3)

Now we can solve for n by plugging in the given value of an:

324 = 4(1 - 3n) / (1 - 3)

Cross-multiplying and simplifying:

324(1 - 3) = 4(1 - 3n)

324 - 972 = 4 - 12n

-648 = -8n

Dividing both sides by -8, we get:

81 = 2n

Taking the logarithm base 2 of both sides:

n = log2(81)

Using a calculator, we find that n is approximately 6.3398.

Now we can plug this value back into the formula:

Sn = 4(1 - 36.3398) / (1 - 3)

Simplifying further:

Sn ≈ -648 / -2

Sn ≈  324

The equivalent equation solving for volume is v = mass/density

Data;

The density of an object can be calculated using the formula

[tex]density = \frac{mass}{volume}[/tex]

Making the volume the subject of formula here

[tex]density = \frac{mass}{volume}\\ volume = \frac{mass}{density}[/tex]

The equivalent equation solving for volume is v = mass/density

Learn more on density here;

https://brainly.com/question/25693692

The answer is obtained by setting up a mathematical equation corresponding to the details given in the word problem. It is found that if the candies were 36 cents cheaper or dearer per dozen, it would affect the price by 3 cents for 39 candies.

The problem can be solved by translating the words into a mathematical equation. Let's denote the original price of a candy as Y cents. Therefore, a dozen candies would cost 12Y cents.

First, we acknowledge that if candies are X cents less per dozen, each candy will be X/12 cents cheaper. And if you buy x+3 such candies, you will pay (x+3)*X/12 cents less.

Simultaneously, the problem also mentions that x+3 candies would have cost 3 cents less if they had been X cents *more* per dozen. This implies that buying x+3 candies would cost an extra (x+3)*X/12 cents, yet it is still 3 cents less.

Therefore, these two costs should be equal: (x+3)*X/12 = (x+3)*X/12 +3. By solving this equation: X = 36. Therefore, if candies were 36 cents cheaper or dearer per dozen, it would affect the cost by 3 cents for x+3 or 39 candies.

https://brainly.com/question/32924529

#SPJ2

the men can be arranges in 5! ways

 and the women in 5! ways

so (5*4*3*2) = 120

120 *120 = 14,400 ways

The coordinates of the midpoint M, point A, and point C in the rhombus can be found using formulas. The coordinates of M are (4, 6), the coordinates of A are (0, 0), and the coordinates of C are (4, 2).

To find the coordinates of the midpoint of BD, we can use the midpoint formula:

M = ( (x1+x2)/2, (y1+y2)/2 )

Substituting the coordinates of B and D into the formula, we get:

M = ( (2+6)/2, (10+2)/2 )

Simplifying, we get:

M = (4, 6)

Since A lies on the x-axis, its y-coordinate is 0. Therefore, the coordinates of A are:

A = (0, 0)

To find the coordinates of C, we can use the fact that a rhombus has opposite sides equal in length and parallel. Since B and D have the same y-coordinate, the y-coordinate of C will also be the same. The x-coordinate of C will be the average of the x-coordinates of B and D. Therefore, the coordinates of C are:

C = ( (2+6)/2, 2 )

https://brainly.com/question/26994123

#SPJ12