The cover of a photo album has an area of 97.5 square inches. Find its area in square centimeters.(1cm =
0.3937 inches)

Let

x------>  the first even integer

x+2---->the second even integer

x+3---->the third even integer

we know that

[tex]x+(x+2)+(x+4)=36[/tex] -----> equation that represent the situation

solve for x

Combine like terms in the left side

[tex](x+x+x)+(2+4)=36[/tex]

[tex]3x+6=36[/tex]

therefore

the answer is the option B

[tex]3x+6=36[/tex]

The equation that can be used to find the first integer is B) 3x + 6 = 36

Solving linear equation mean calculating the unknown variable from the equation.

Let the linear equation : y = mx + c

If we draw the above equation on Cartesian Coordinates , it will be a straight line with :

m → gradient of the line

( 0 , c ) → y - intercept

Gradient of the line could also be calculated from two arbitrary points on line ( x₁ , y₁ ) and ( x₂ , y₂ ) with the formula :

[tex]\large {m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]

If point ( x₁ , y₁ ) is on the line with gradient m , the equation of the line will be :

[tex]\boxed {y - y_1 = m ( x - x_1 )}[/tex]

Let us tackle the problem.

Given:

The First Integer = x

The Second Integer = x + 2

The Third Integer = x + 4

The sum of three consecutive even integers is 36.

[tex]\texttt{The First Integer + The Second Integer + The Third Integer = 36}[/tex]

[tex]x + (x + 2) + (x + 4) = 36[/tex]

[tex]x + x + x + 2 + 4 = 36[/tex]

[tex]\large {\boxed {3x + 6 = 36} }[/tex]

Grade: High School

Subject: Mathematics

Chapter: Linear Equations

Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point

One bag of sugar can make 19 batches of chocolate chip cookies.

To determine how many batches of chocolate chip cookies can be made with one bag of sugar, we need to divide the total amount of sugar in the bag by the amount of sugar used in each batch of cookies. Since the bag holds 23 3/4 cups of sugar, and the recipe uses 1 1/4 cups of sugar per batch, we can set up the following division:

23 3/4 ÷ 1 1/4 = (95/4) ÷ (5/4) = (95/4) × (4/5) = 95/5 = 19

Therefore, one bag of sugar can make 19 batches of chocolate chip cookies.

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Answer:

x=32

Step-by-step explanation:

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The value of x is 32.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 9 is an equation.

We have,

x/8 + 12 = 16

Solve for x.

x/8 + 12 = 16
Subtract 12 on both sides.

x/8 = 16 - 12

x/8 = 4

Multiply 8 on both sides.

x = 8 x 4

x = 32

Thus,

The value of x is 32.

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A line is a straight, infinite, one-dimensional entity with no thickness or endpoints. It can be represented mathematically, intersects at points or can be parallel to other lines.

Given that,

To find the characteristic of a line.

Now, A line is a fundamental geometric concept characterized by several key properties.

Firstly, it is straight and extends infinitely in both directions.

Secondly, it has no thickness, meaning it is one-dimensional and can be represented by a mathematical equation or equation system.

Thirdly, any two points on a line can be connected to form a segment, making it possible to measure distances along the line.

Now, Additionally, a line has no endpoints, which distinguishes it from a line segment.

Lastly, lines can intersect each other at a single point or be parallel, maintaining a constant distance from one another throughout their lengths.

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sqrt(60) =7.745967 rounded to nearest 100th = 7.75

58/8 = 7.25

7.3 rounded to nearest 100th = 7.33

7 3/5 = 7.6

7.6 +7.33 +7.25+7.75 = 29.93/4 = 7.4825 = 7.48km

The value of the variable t is greater than or equal to 3.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

Fifteen is no more than a number t divided by 5 will be given in the mathematical form. Then the inequality is given as,

15 ≤ 5t

t ≥ 15 / 5

t ≥ 3

The value of the variable t is greater than or equal to 3.

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Answer:

[tex]x=\frac{m-9}{3-d}[/tex]

Step-by-step explanation:

We have been given an equation [tex]m=9+3x-dx[/tex]. We are asked to solve the given equation for x.

Subtract 9 from both sides:

[tex]m-9=9-9+3x-dx[/tex]

[tex]m-9=3x-dx[/tex]

Factor out x from right side:

[tex]m-9=x(3-d)[/tex]

Switch sides:

[tex]x(3-d)=m-9[/tex]

Divide both sides by [tex](3-d)[/tex]:

[tex]\frac{x(3-d)}{3-d}=\frac{m-9}{3-d}[/tex]

[tex]x=\frac{m-9}{3-d}[/tex]

Therefore, the value of x is [tex]\frac{m-9}{3-d}[/tex].

break 96 into multiples of 6

96 = 60 +30 +6

60/6 =10

30/6 = 5

6/6 =1

10+5+1 = 16

so 96/6 = 16

Answer:

The correct option is 3.

Step-by-step explanation:

The slope intercept form of a line is

[tex]y=mx+b[/tex]                  ..... (1)

where, m is slope and b is y-intercept.

From the given graph it is clear that the graph intersect the y-axis at (0,2). So, the y-intercept of the line is 2.

The line passes through the points (0,2) and (4,3). So, the slope of the line is

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{3-2}{4-0}[/tex]

[tex]m=\frac{1}{4}[/tex]

Substitute [tex]m=\frac{1}{4}[/tex] and b=2 in equation 1.

[tex]y=\frac{1}{4}x+2[/tex]

The equation of line is [tex]y=\frac{1}{4}x+2[/tex].

Therefore the correct option is 3.