In dividing an irregular shape into polygons it is permissible for the polygons to overlap

Answer:

  y = (-x -6)/2

Step-by-step explanation:

You want to solve x +2y = -6 for y.

The first step here is to get the y-term by itself on one side of the equal sign. We can do that by subtracting x from both sides of the equation.

  x +2y -x = -6 -x

  2y = -6 -x

Now, we divide by the coefficient of y to get y by itself.

  2y/2 = (-6 -x)/2

  y = (-x -6)/2

We can also write this as ...

  y = -x/2 -3

Answer:

The expression represents [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex] is [tex]\( y = \frac{-6 - x}{2} \)[/tex]

Explanation:

To solve the equation [tex]\(x + 2y = -6\)[/tex] for [tex]\(y\)[/tex], follow these steps:

1. Subtract [tex]\(x\)[/tex] from both sides of the equation to isolate the term containing [tex]\(y\)[/tex]:

[tex]\[2y = -6 - x\][/tex]

2. Divide both sides of the equation by [tex]\(2\)[/tex] to solve for [tex]\(y\):[/tex]

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

So, the solution for [tex]\(y\) is \(y = \frac{-6 - x}{2}\).[/tex]

Answer: The value of x = 5

Step-by-step explanation:

Given : ∠E and ∠F are vertical angles  m∠E = 8x + 8 and m∠F = 2x + 38.

We know that the vertical angles are congruent.

It means [tex]\angle{E}\cong\angle{F}[/tex]

[tex]\Rightarrow\ m\angle{E}=\ m\angle{F}[/tex]

[tex]\Rightarrow\ 8x+8=2x+38[/tex]

Subtract 2x and 8 from both sides , we get

[tex]6x=30[/tex]

Divide both sides by 6 , we get

[tex]x=5[/tex]

Hence, the value of x = 5

Answer:

Option C - [tex]2\frac{1}{6}-5\frac{2}{3}=-3\frac{1}{2}[/tex]

Step-by-step explanation:

Given : Expression [tex]2\frac{1}{6}-5\frac{2}{3}[/tex]

To find : Perform the indicated operation in the expression ?

Solution :

Expression [tex]2\frac{1}{6}-5\frac{2}{3}[/tex]

Write mixed fraction into fraction,

[tex]2\frac{1}{6}-5\frac{2}{3}=\frac{13}{6}-\frac{17}{3}[/tex]

Taking Least common denominator,

[tex]2\frac{1}{6}-5\frac{2}{3}=\frac{13-34}{6}[/tex]

[tex]2\frac{1}{6}-5\frac{2}{3}=-\frac{21}{6}[/tex]

[tex]2\frac{1}{6}-5\frac{2}{3}=-\frac{7}{2}[/tex]

Write improper fraction into mixed fraction,

[tex]2\frac{1}{6}-5\frac{2}{3}=-3\frac{1}{2}[/tex]

Therefore, Option C is correct.

Answer:

P = 0.43h + 0.65p + 1.31d  represents the total profit, in dollars that the stand will make on a day when they sell h hot dogs, p pretzels, and d drinks

Step-by-step explanation:

Given :  The concession stand at a ballpark makes $0.43 profit from each hot dog sold. It also makes a profit of $0.65 from each pretzel sold and $1.31 from each drink sold

We have to find an expression that represents the total profit, in dollars that the stand will make on a day.

Let the stand sells h hot dogs, p pretzels, and d drinks on a day

Since profit of one hot dog is $ 0.43

So , profit of h hot dogs is $ 0.43h

also, profit of one pretzels is $ 0.65

So , profit of p pretzels is $ 0.65p

also, profit of one drink is $1.31

So , profit of d drinks  is $ 1.31d

Total profit of a day is the total profit he earned from selling each item.

thus, total profit is given by equation

P = 0.43h + 0.65p + 1.31d

Thus, P = 0.43h + 0.65p + 1.31d  represents the total profit, in dollars that the stand will make on a day when they sell h hot dogs, p pretzels, and d drinks

area of a square = S^2

to find length of side take square toot of area

sqrt(59) = 7.68114

to nearest tenth = 7.7 inches

The two consecutive even integers whose sum is 126 are 62 and 64.

Let's represent the first even integer as x. Since the next consecutive even integer would be the next even number, we can represent it as x + 2.

The problem states that the sum of these two consecutive even integers is 126. We can set up the equation:

x + (x + 2) = 126

Now, let's solve for x by simplifying and combining like terms:

2x + 2 = 126

Subtract 2 from both sides of the equation:

2x + 2 - 2 = 126 - 2

2x = 124

Divide both sides of the equation by 2 to isolate x:

(2x) / 2 = 124 / 2

x = 62

Now that we have found the value of x, we can find the second consecutive even integer:

x + 2 = 62 + 2 = 64

Therefore, the two consecutive even integers whose sum is 126 are 62 and 64.

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When adding make sure you add 4 sides worth of calculations. You have to consider the left and right side (for length) and front and back for the width.

The solution for this problem is:

Side 1 (8+36+8) 
+ 
Side 2 (8+48+8) 
+ 
Side 3 (8+36+8) 
+ 
Side 4 (8+48+8) 
= 232 

The perimeter of the glass tabletop is 232 inches. The option (E) is correct.

To find the perimeter of the glass tabletop, we need to determine its dimensions first. According to the problem, the glass tabletop is 8 inches wider than the pedestal on each side.

Dimensions of the Pedestal:

- Width: 36 inches

- Length: 48 inches

Since the tabletop extends 8 inches beyond the pedestal on each side, we add 16 inches (8 inches on each side) to both the width and the length of the pedestal.

Width of the glass tabletop:

[tex]\[ \text{Width} = 36 \, \text{inches} + 16 \, \text{inches} = 52 \, \text{inches} \][/tex]

Length of the glass tabletop:

[tex]\[ \text{Length} = 48 \, \text{inches} + 16 \, \text{inches} = 64 \, \text{inches} \][/tex]

The perimeter [tex]\( P \)[/tex] of a rectangle is given by:

[tex]\[P = 2 \times (\text{Length} + \text{Width})\][/tex]

Substituting the dimensions:

[tex]\[P = 2 \times (64 \, \text{inches} + 52 \, \text{inches})\\P = 2 \times 116 \, \text{inches} = 232 \, \text{inches}\][/tex]

The correct perimeter of the glass tabletop is [tex]\( 232 \)[/tex] inches.

The complete question is:

A glass tabletop is supported by a rectangular pedestal. If the tabletop is 8 inches wider than the pedestal on each side, what is the perimeter of the glass tabletop?

A) 92 inches

B) 116 inches

C) 176 inches

D) 184 inches

E) 232 inches

Answer:

[tex]\frac{b^2}{2}[/tex]

Step-by-step explanation:

We are supposed to write an algebraic expression for given word phrase.

The square of b would be 'b' raised to second power: [tex]b^2[/tex].

Half the square of b would be [tex]b^2[/tex] divide by 2: [tex]\frac{b^2}{2}[/tex].

Therefore, our required expression would be [tex]\frac{b^2}{2}[/tex].

The required speed of the current is given as 9 miles per hour.

Given that,
A boat traveled 252 miles downstream and back. The trip downstream took 12 hours. The trip back took 84 hours. What is the speed of the boat in still water is to be determined.

Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.

Here,

let the speed of the current be y, and the speed of the boat at still water be x,
According to the question,
Downstream speed,
252 / 12 = x + y - - - -(1)
upstream speed,
252 / 84 = x - y  - - - (2)
Adding equations 1  and 2
21  + 3 = 2x
x = 24 / 2
x = 12 miles/hour
Now,
3 = 12  - y
y = 9 miles/ hour

Thus. the required speed of the current is given as 9 miles per hour.

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Final answer:

To find the speed of the boat in still water and the current, we used the relation of speed, distance, and time for downstream and upstream travel to set up equations. We solved these to determine that the boat's speed in still water is 12 miles per hour, and the current's speed is 9 miles per hour.

Explanation:

The question asks to determine the speed of the boat in still water and the speed of the current given the distances and times for traveling downstream and upstream. Using the given data, we can set up two equations based on the speed-distance-time relationship:

Downstream speed = Speed of boat in still water + Speed of current

Upstream speed = Speed of boat in still water - Speed of current

Let v represent the speed of the boat in still water, and c represent the speed of the current. We have the equations:

(v + c) = 252 miles / 12 hours = 21 miles/hour (downstream)

(v - c) = 252 miles / 84 hours = 3 miles/hour (upstream)

Adding these two equations gives us:

2v = 24 miles/hour

Dividing by 2:

v = 12 miles/hour

Substituting v in either equation to find c:

c = 21 miles/hour - v = 21 miles/hour - 12 miles/hour

c = 9 miles/hour

Therefore, the speed of the boat in still water is 12 miles/hour, and the speed of the current is 9 miles/hour.

Triangle DPW was translated 1 unit to the left, then it was translated 5 units down and then it was rotated by 90 degrees counterclockwise.

Answer:

[tex]8r^6s^3-5r^5s^4+r^4s^5+5r^3s^6[/tex]

Step-by-step explanation:

We want to simplify;

[tex](8r^6s^3-9r^5s^4+3r^4s^5)-(2r^4s^5-5r^3s^6-4r^5s^4)[/tex]

We expand the bracket to obtain;

[tex]8r^6s^3-9r^5s^4+3r^4s^5-2r^4s^5+5r^3s^6+4r^5s^4[/tex]

We now group the like terms to obtain;

[tex]8r^6s^3-9r^5s^4+4r^5s^4+3r^4s^5-2r^4s^5+5r^3s^6[/tex]

We now simplify to get;

[tex]8r^6s^3-5r^5s^4+r^4s^5+5r^3s^6[/tex]

The correct answer is C

Answer:

c

Step-by-step explanation:

Answer: Hence, option 'A', 'B', 'D' , 'E' are correct.

Step-by-step explanation:

There are many different types of variations  as follows:

1) Direct variations in which the relationship between two different variables is direct.

2) Inverse variations in which the relationship between two different variables is opposite.

3) Joint variations in which the relationship between one variable varies directly with the product of two or more variables.

4) Combined variations in which one variable is directly proportion to second variable but inversely proportion with third variables.

Hence, option 'A', 'B', 'D' , 'E' are correct.