Algebra

To determine the value that the function ( f(x) = \frac{2x - 1}{x - 3} ) approaches as the magnitude of ( x ) increases, we can analyze the behavior of the function as ( x ) approaches infinity. Dividing the numerator and denominator by ( x ) gives ( f(x) = \frac{2 - \frac{1}{x}}{1 - \frac{3}{x}} ). As ( x ) approaches infinity, the terms ( \frac{1}{x} ) and ( \frac{3}{x} ) approach zero, leading to ( f(x) ) approaching ( \frac{2}{1} = 2 ). Thus, the value that the function approaches is 2.

NO!!!!

The word 'perpendicular' means 'at right-angles'. or '90 o'.

Cot (45 o) = Cos(45) / Sin(45)

Note the inversion of Cos and Sin.

Cos(45) = sqrt(2) / 2

Sin(45) = sqrt(2) /2

Applying division of fractions.

Cot(45) = Cos(45)/Sin(45) = [sqrt(2)/2] / [sqrt(2)/2] =>

sqrt(2)/2 X 2/Sqrt(2)

Note the change of sign and the inversion of terms.

Cancel down by '2'

sqrt(2)/1 X 1 / sqrt(2)

Cancel down again by 'sqrt(2)' .

1/1 x 1/1

= 1/1 = 1

Hence Cot (45 o) = 1

To simplify the expression (3(y - 1 + 2y)), first combine the terms inside the parentheses: (y - 1 + 2y = 3y - 1). Then, distribute the 3: (3(3y - 1) = 9y - 3). Therefore, the expression (3(y - 1 + 2y)) is equivalent to (9y - 3).

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The clitellum is a thickened, glandular section of the body wall in certain annelids, such as earthworms. Its primary function is to produce a mucus secretion that helps in the formation of a cocoon for fertilized eggs, facilitating reproduction. The clitellum also plays a role in the alignment and transfer of sperm during mating.

To determine the net gain in steps when climbing 3 up and 1 down, you can calculate it as follows: each complete cycle of climbing 3 steps up and then 1 step down results in a net gain of 2 steps (3 - 1 = 2). To reach 15 steps, you would perform this cycle 7 times to gain 14 steps (7 cycles x 2 steps), and then you would need 1 more step to reach 15. Therefore, the total number of steps taken is 7 cycles (which involves 28 steps) plus the final step, resulting in 29 steps.

Someone might choose to use the y-intercept and slope to graph a line because this form, known as slope-intercept form (y = mx + b), provides a clear and straightforward way to understand the line's behavior. The y-intercept (b) indicates where the line crosses the y-axis, while the slope (m) shows the rate of change or steepness of the line. This approach makes it easier to plot the line accurately and visualize relationships in data, especially in linear equations. Additionally, it simplifies the process of identifying and interpreting key features of the graph.

To find the vertex of the quadratic function ( f(x) = (x - 6)(x - 2) ), we first expand it to get ( f(x) = x^2 - 8x + 12 ). The vertex form of a quadratic function ( ax^2 + bx + c ) has its vertex at ( x = -\frac{b}{2a} ). Here, ( a = 1 ) and ( b = -8 ), so the x-coordinate of the vertex is ( x = \frac{8}{2} = 4 ). Substituting ( x = 4 ) back into the function gives ( f(4) = (4 - 6)(4 - 2) = (-2)(2) = -4 ). Therefore, the vertex is at the point ( (4, -4) ).

The equation that represents a parabola opening to the right with its vertex at the origin (0,0) and a focus at (4,0) is given by ( y^2 = 4px ), where ( p ) is the distance from the vertex to the focus. Since the focus is located at (4,0), ( p = 4 ). Therefore, the equation of the parabola is ( y^2 = 16x ).

x X x = x^(2) ; said as ' x squared '. ( NOT 2x).

It depends what x is. If you do not know the value of either variable it would be 2x.

CosX(Sin^(2)X) = 1

Use trig. identity ; Sin^(X) =

(1 - Cos^(2)X)

Hence

CosX(1 - Cos^(2)(X)) = 1

CosX = 1

X = 0

&

1 - Cos^(2)x = 1

Cos^(2)X = 0 ( 1 - 1)

Square rooting

CosX = 0

X = 90, 270 ....

Cos(x) equals zero at 90 degrees and 270 degrees. If x exceeds 360 degrees, cos(x) will equal zero at any increment of 90 + 180(n) degrees. In radians, this is equivalent to (pi/2) + pi(n) radians.

Cos(47) = Cos(313) = 0.681998 ( 6 d.p.).

The points where a graph intersects the x-axis are called x-intercepts, and they occur when the value of y is zero. Conversely, the points where a graph intersects the y-axis are known as y-intercepts, and these occur when the value of x is zero. Each type of intercept represents a solution to the equation of the graph at those respective points.

The inequality you provided seems to be missing an operator (like <, >, ≤, or ≥) between 5x and 13y. Assuming you meant to write an inequality such as 5x < 13y, one possible ordered pair that satisfies this inequality is (3, 2), since 5(3) = 15 and 13(2) = 26, and 15 < 26. If you meant a different inequality, please specify, and I can provide a corresponding solution.

First, we need to find the slope of the line given by the equation (2x - 3y = 6). Rearranging it to slope-intercept form (y = mx + b) gives us (y = \frac{2}{3}x - 2), so the slope is (\frac{2}{3}). The slope of a line perpendicular to this would be the negative reciprocal, which is (-\frac{3}{2}). Using the point-slope form of the equation with the point (1, 4), we get (y - 4 = -\frac{3}{2}(x - 1)), which simplifies to (y = -\frac{3}{2}x + \frac{11}{2}).

In the expression (3x^2y^4), the coefficient is the numerical factor that multiplies the variables. Here, the coefficient is 3, while (x^2) and (y^4) are the variable parts of the expression. Thus, the entire expression can be interpreted as 3 times (x) squared times (y) raised to the fourth power.

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The phonograph solved the problem of sound reproduction, enabling the recording and playback of audio. Before its invention, music and spoken word could only be experienced live, limiting access to performances. The phonograph allowed people to enjoy recorded sounds at their convenience, revolutionizing entertainment and communication. This innovation laid the groundwork for the modern music industry and transformed how people interacted with audio content.

To find the zeros of the function ( f(x) = x^2 - 8x + 16 ), we can set it equal to zero: ( x^2 - 8x + 16 = 0 ). This can be factored as ( (x - 4)(x - 4) = 0 ), which gives us a double root. Therefore, the zero of the function is ( x = 4 ).

3.41 x 1,3019234 /12347 x 8 + 13- 1804351 x 235-135425 x2 105 + 1- 1243818723847= 68935013828483769314151163591716 The hardest math problem is the one that you don't understand an therefore can't do.

A shallow slope represents a gradual change in the relationship between two variables, indicating that small changes in one variable result in only minor changes in the other. In graphical terms, it appears as a line that is relatively flat compared to steeper slopes. This can suggest a weaker correlation or lower sensitivity in the data being analyzed. In practical applications, such as economics or physics, a shallow slope may signal lower rates of return or slower reaction times.

The algebraic expression for the quotient of ( z ) and ( 9 ) is ( \frac{z}{9} ). This expression indicates that ( z ) is divided by ( 9 ).