solve for x:

mx + nx = p

1st piece = x

2nd piece = x+2

3rd piece = x+2+3 = x+5

37 = x +x+2 + x+5 =

37 = 3x+7

30=3x

x = 30/3 = 10

 1st piece = 10 inches

 2nd piece = 10+2 = 12 inches

 3rd piece = 10+5 = 15 inches

The correct answer is:

Ken will have run 3 laps and Hamid will have run 4.

Explanation:

To find this, we first find the number of seconds that will have passed when they meet again.  We use the LCM, or least common multiple, for this.  First we find the prime factorization of each number:

80 = 10(8)

10 = 5(2)

8 = 2(4)

4 = 2(2)

80 = 2(2)(2)(5)(2)

60 = 10(6)

10 = 5(2)

6 = 2(3)

60 = 2(2)(3)(5)

For the LCM, we multiply the common factors by the uncommon.  Between the two numbers, the common factors are 2, 2 and 5.  This makes the uncommon 2, 2, and 3, and makes our LCM

2(2)(5)(2)(2)(3) = 240

This means every 240 seconds they will both be at the start line.

Since Ken completes a lap in 80 seconds, he completes 240/80 = 3 laps in 240 seconds.

Since Hamid completes a lap in 60 seconds, he completes 240/60 = 4 laps in 240 seconds.

Ken will have run [tex]3[/tex] laps and Hamid will have run [tex]4[/tex] laps when they next meet on the start line.

Take LCM of [tex]80,60 =240\\[/tex]

After every [tex]240[/tex] seconds they will both be at the start line.

So in [tex]240[/tex] seconds Ken covered

[tex]\dfrac{240}{80}=3laps\\[/tex]

So in [tex]240[/tex] seconds  Hamid covered

[tex]\dfrac{240}{60}=4laps\\[/tex]

Ken will have run  [tex]3[/tex] laps and Hamid will have run [tex]4[/tex] Laps.

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The geometric plane is two-dimensional since there are two variables.

A geometric plane is a plane which is a flat surface.

The general equation of a plane is :

ax + by + c = 0

Here x and y are variables.

Since there are two variables, the plane is two dimensional.

Or in other words, there are two directions for the plane.

So the geometric plane is two-dimensional.

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To make a 16-gallon mix that costs $14 per gallon from a paint costing $19 per gallon and a thinner costing $3 per gallon, you need approximately 11.56 gallons of paint and 4.44 gallons of thinner.

This is a problem of Mathematics, specifically Systems of Equations. Let's denote the amount of paint as P (in gallons) and the amount of thinner as T (in gallons). We are looking for the values of P and T that satisfy these two conditions:

This gives us two equations,

Now, you can subtract the first equation from the second to solve for P,

18P = 208, therefore P = 208/18 = 11.56 gallons. Substitute P = 11.56 into the first equation to solve for T, T = 16 - 11.56 = 4.44 gallons. So, approximately 11.56 gallons of paint and 4.44 gallons of thinner should be mixed to get the desired 16-gallon mixture.

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To find the amounts of paint and thinner needed to make a $14 per gallon mix by mixing two different-priced liquids.

Mathematically, this problem can be solved using a system of equations.

Let x be the gallons of paint and y be the gallons of thinner. We have two equations based on the given information:

Solving this system of equations will give you the amounts of paint and thinner that need to be mixed to achieve a $14 per gallon mix.

Answer:

The value of the equation is [tex]x=\frac{12-y}{5+4k}[/tex].

Step-by-step explanation:

Consider the provided equation.

[tex]12-5x-4kx=y[/tex]

We need to solve the provided equation for x.

Subtract 12 both side.  

[tex]12-12-5x-4kx=y-12[/tex]

[tex]-5x-4kx=y-12[/tex]

Take -x common as shown:

[tex]-x(5+4k)=y-12[/tex]

Divide both sides by 5+4k.

[tex]-x=\frac{y-12}{5+4k}[/tex]

[tex]x=\frac{-y+12}{5+4k}[/tex]

[tex]x=\frac{12-y}{5+4k}[/tex]

Hence, the value of the equation is [tex]x=\frac{12-y}{5+4k}[/tex].

3x-82 = x-6

subtract 1 x from each side

2x -82 = -6

add 82 to each side

2x = 76

divide both sides by 2

x = 76/2 =38

x = 38

Check:

3(38)-82 = 38-6

3*38 = 114, 114-82 =32 and 38-6 = 32 32 = 32 TRUE

1x+5 2x+10 3x+15 4x+20 5x+25

Step-by-step explanation:

To write expressions equivalent to 20x + 100, we can use factoring, distributing, and properties of equality. Examples include 4(5x + 25), 10(2x + 10), and three other variations, all of which maintain the original value of the expression.

To write five expressions equivalent to 20x + 100, we can apply various mathematical techniques such as factoring, distributing, adding/subtracting terms, or using properties of equality. Here are five different equivalent expressions:

The equivalence of these expressions to 20x + 100 remains intact because they are simply restructured using basic algebraic principles without changing the value.

Answer:

Number of granola bars that Josh gave to each of his friend =3

Number of fruit drinks that Josh gave to each of his friend =4

Step-by-step explanation:

Number of granola bars with Josh = 42

Number of fruit drinks with Josh = 56

He wants to give the same number of granola bars and fruit drinks to each friend.

To find : Number of granola bars and fruit drinks Josh give to each friend.

First, find HCF of 42 and 56 .

[tex]42=2\times 3\times 7\,,\,56=2^3\times 7[/tex]

Therefore, HCF ( 42, 56 ) = Highest common factor of 42 and 56 = 14

Number of granola bars that Josh gave to each of his friend = Number of granola bars with Josh / HCF ( 42, 56 )

= 42/14 = 3

Number of fruit drinks that Josh gave to each of his friend =  Number of fruit drinks with Josh / HCF ( 42, 56 )

= 56/14 = 4

Answer:

x^2 + 3x - 2 - (2x^2 - x + 6) =

x^2 + 3x - 2 - 2x^2 + x - 6 =

-x^2 + 4x - 8

the answer is 8

Adding a negative number on a number line is equivalent to subtracting the absolute value of that number. Thus, 56+(−116) = -60, 34+(−212) = -178 and 1.3+(−2.4) = -1.1

When you are adding a negative number on a number line, you are essentially performing a subtraction operation. Let's look at the three problems you've posted:

1. 56+(−116): Start at positive 56 on the number line and then move 116 steps to the left because we're adding a negative number. Your final position will be -60. So, 56+(−116) equals -60.

2. 34+(−212): Similarly, start at 34 on the number line and move 212 spaces to the left which results a value of -178. Therefore, 34 + (-212) = -178.

3. 1.3+(−2.4): Starting at 1.3 on the number line, if we move 2.4 steps to the left we end up at -1.1. So, 1.3 + (-2.4) = -1.1

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The formula V=lWh is solved for W by dividing both sides of the equation by lh, providing the solution W = V / lh. This is a simple algebraic operation used for isolating the variable we're solving for, which is W in this case.

The question asks to solve for the variable, W, in the formula V =lWh, where V represents volume, l represents length, h represents height, and W is the width we are solving for. To isolate W, you need to perform some algebraic operations. Let's go step by step:

Remember, in algebra, the main goal is to isolate the variable we're trying to find on one side of the equation, which in this case is W.

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Answer:

3 g/ml

Step-by-step explanation:

After the marble was introduced into the graduated bottle, the volume change from 10 ml to 12.5 ml, this means that 12.5 - 10 = 2.5 ml is the volume occupied by the marble.

The mass of a marble is 7.5 g.

Density is defined as follows:

density  = mass / volume =

Replacing with the measures:

density = 7.5/2.5  =  3 g/ml