It took Lou 2 1/2 gallons of paint to paint one fence.   How many gallons of paint will it take Lou to paint 6 fences that are the same size? Express your answer in simplest form.  

In mathematics, the roster form is when we call a group of set members that is placed inside between brackets, and is separated by commas. So in this case, natural numbers which are less than 8 are 1 to 7, hence the roster form is:

{1, 2, 3, 4, 5, 6, 7}

Rachel collects 3/4 or 75% of Bryce's goal if they both meet their goals in the canned goods drive

The question involves determining what fraction of Bryce's goal Rachel collects if they both meet their personal goals for a canned goods drive. Bryce's goal is to collect 32 items, and Rachel's goal is to collect 24 items. To find the fraction of Bryce's goal that Rachel collects, you divide Rachel's goal by Bryce's goal.

Here's the calculation:

Rachel's collection / Bryce's collection = 24 / 32 = 3/4

This means that Rachel collects 3/4 or 75% of the number of items that Bryce collects

The number of ounces left after one brick is sold is 591.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Willard gold nuggets = 788 ounces

The number of equal-sized bricks = 4

Now,

The number of ounces in each of the 4 bricks.

= 788/4

= 197 ounces

Number of bricks sold = 1

The remaining ounces.

= 788 - 197

= 591 ounces

Thus,

The number of ounces left is 591.

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Answer:

Step-by-step explanation:

78

Answer: 5ft - 7.2ft +2.2 ft = 0

When he finishes the trick he will be in the starting point.

Step-by-step explanation:

Hi, to write the expression we have to analyze the information given:

So, we simply have to sum the tricks that takes him forward and subtract the tricks that take him backwards.

Mathematically speaking:

When he finishes the trick he will be in the starting point, because the expression equals 0.

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the three sides of the triangle are 42 feet, 21 feet, and 43 feet,

Let's denote the second side of the triangle as ( x ). According to the problem, the first side is twice the length of the second side, which makes it ( 2x). The third side is 20 feet less than three times the second side, so it is ( 3x - 20 ).

Now, we can write the equation for the perimeter of the triangle:

[tex]\[ \text{Perimeter} = \text{First side} + \text{Second side} + \text{Third side} \][/tex]

[ 106 = 2x + x + (3x - 20) ]

Now, combine like terms and solve for \( x \):

[ 106 = 6x - 20 ]

Add 20 to both sides:

[ 6x = 126 ]

Divide both sides by 6:

[ x = 21 ]

So, the second side is 21 feet. Using this, we can find the other two sides:

First side = [tex]\( 2x = 2 \times 21 = 42 \) feet[/tex]

Third side = [tex]\( 3x - 20 = 3 \times 21 - 20 = 63 - 20 = 43 \) feet[/tex]

Therefore, the three sides of the triangle are 42 feet, 21 feet, and 43 feet, respectively.

To recap the process:

1. Let ( x ) represent the second side of the triangle.

2. Write the equation for the perimeter using the given information.

3. Simplify the equation and solve for ( x ).

4. Substitute the value of ( x ) back into the expressions for the first and third sides to find their lengths.

5. Confirm the final answer by checking that the sum of the three sides equals the given perimeter.

complete question

Solve by making an equation

The first side of a triangle is twice the length of the second side; the third side is 20 feet less than three times the second side. The perimeter of the triangle is 106 feet. Find the three sides.

Answer:

We have that for the Question "A scooter travels 30 ft in 2 seconds.  

What is the speed of the scooter in feet per second?

" it can be said that the speed of the scooter in feet per second is mathematically given as

V=15ft/s

From the question we are told

A scooter travels 30 ft in 2 seconds.  

What is the speed of the scooter in feet per second?

Generally the equation for the speed of the scooter in feet per second is mathematically given as

[tex]V=\frac{v}{s}\\\\Therefore\\\\V=\frac{v}{s}\\\\V=\frac{30}{2}\\\\[/tex]

V=15ft/s

Therefore

the speed of the scooter in feet per second is mathematically given as

V=15ft/s

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the solution to the system of equations by graphing is [tex]\( (0,1), (-5/2,6) \)[/tex]

The correct option is (C).

The generated image above represents a graphical solution to the system of equations given:

[tex]\[ y = 2x^2 + 3x + 1 \][/tex]

[tex]\[ y = -2x + 1 \][/tex]

However, the graph does not clearly show the exact points of intersection between the parabola and the line. To find the solutions accurately, we would typically set the two equations equal to each other and solve for [tex]\( x \)[/tex]:

[tex]\[ 2x^2 + 3x + 1 = -2x + 1 \][/tex]

Solving this equation algebraically will give us the [tex]\( x \)[/tex]-coordinates of the points of intersection. The corresponding [tex]\( y \)[/tex]-values can then be found by substituting these [tex]\( x \)[/tex]-values back into either of the original equations.

Since I cannot perform this algebraic computation at the moment, you can solve the equation using the following steps:

1. Move all terms to one side of the equation to set it to zero.

2. Solve the resulting quadratic equation, either by factoring, completing the square, or using the quadratic formula.

3. Substitute the [tex]\( x \)[/tex]-values back into one of the original equations to find the [tex]\( y \)[/tex]-values.

Therefore, the correct option that represents the solution to the system of equations by graphing is:

C. [tex]\( (0,1), (-5/2,6) \)[/tex]

complete question given below:

Solve the system by graphing. y=2x^2+3x+1 y=-2x+1

A. (1,3), (4,7)

B. (1,3), (1/2,3)

C. (0,1), (-5/2,6)

D. (-5,5), (4,-2)

a)Carrie's map indicates Greenville and North Valley are 90 miles apart. b) On Krystal's map, using a scale of 1 inch = 18 miles, the distance is 5 inches.

Part a:

On Carrie's map, Greenville and North Valley are 4.5 inches apart. The scale on her map is 1 inch = 20 miles. To determine the distance between the two locations:

Measure the distance on the map: 4.5 inches.

Multiply by the scale: 4.5 inches * 20 miles/inch.

Result: The actual distance is 4.5 * 20 = 90 miles.

Part b:

The scale on Krystal’s map is 1 inch = 18 miles. To find how far apart Greenville and North Valley are on Krystal's map, we use the actual distance calculated from part a (90 miles) and apply Krystal’s map scale:

Divide the actual distance by the scale: 90 miles / 18 miles/inch.

Result: The distance between Greenville and North Valley on Krystal's map is 90 / 18 = 5 inches.