Algebra

To find the inverse of the equation ( y = 3x + 1 ), we first solve for ( x ) in terms of ( y ). Rearranging gives ( x = \frac{y - 1}{3} ). Therefore, the equation of the inverse is ( y = \frac{x - 1}{3} ).

Yes, the square root of a whole number is either an integer or an irrational number. If the whole number is a perfect square (like 0, 1, 4, 9, etc.), its square root is an integer. However, if the whole number is not a perfect square (like 2, 3, 5, etc.), its square root is an irrational number.

To solve the equation (5x - 17 - x + 7 = 0), first combine like terms. This simplifies to (4x - 10 = 0). Adding 10 to both sides gives (4x = 10), and dividing by 4 results in (x = \frac{10}{4} = 2.5). Therefore, (x = 2.5).

To find the tens digit of the difference ( x - y ), first calculate the difference to obtain the result ( z = x - y ). Then, isolate the tens digit by using the formula ((z \mod 100) \div 10). This operation extracts the last two digits of ( z ) and divides by 10, effectively giving you the tens digit.

The distributive property allows us to break down a multiplication problem into simpler components. To multiply 16 by 102 using the distributive property, we can express 102 as 100 + 2. Then, we can calculate: (16 \times 102 = 16 \times (100 + 2) = (16 \times 100) + (16 \times 2) = 1600 + 32 = 1632). Thus, (16 \times 102 = 1632).

You can order replacement parts for a Quest 10 x 10 canopy from several sources. Check the manufacturer's website for direct parts sales or contact their customer service for assistance. Additionally, online retailers like Amazon, eBay, or specialized outdoor equipment stores may carry compatible parts. Be sure to have your canopy model number handy to ensure you order the correct items.

A positive times a negative results in a negative product. This is because the multiplication of a positive number (greater than zero) by a negative number (less than zero) reflects the concept of direction in mathematics: the positive number's direction is reversed by the negative. Therefore, the outcome is always negative.

To find the value of x in the equation (2x + 3 = 9), first subtract 3 from both sides to isolate the term with x: (2x = 9 - 3), which simplifies to (2x = 6). Next, divide both sides by 2 to solve for x: (x = \frac{6}{2}). Thus, (x = 3).

The function ( f(x) = x^2 - 4x + 5 ) is a quadratic function that opens upwards. To find its range, we first determine the vertex using the formula ( x = -\frac{b}{2a} ), where ( a = 1 ) and ( b = -4 ). This gives us ( x = 2 ). Evaluating ( f(2) ) results in ( f(2) = 2^2 - 4(2) + 5 = 1 ). Since the parabola opens upwards, the minimum value is 1, and the range of the function is ( [1, \infty) ).

To calculate the number of possible license plates, we consider two formats: three uppercase letters followed by three digits, and four uppercase letters.

1. For the first format (3 letters + 3 digits): There are 26 choices for each letter and 10 choices for each digit, resulting in (26^3 \times 10^3).
2. For the second format (4 letters): There are 26 choices for each letter, resulting in (26^4).

Adding these together gives the total number of license plates: (26^3 \times 10^3 + 26^4).

0.45 multiplied by 10 to the second power (10²) is calculated as follows: 10² equals 100, so 0.45 x 100 equals 45. Therefore, 0.45 x 10² is 45.

To write an expression that represents (4 \times 4 \times 8 \times 8 \times 8), you can use exponents to simplify it. Since there are two 4's and three 8's, the expression can be written as (4^2 \times 8^3). This compact form captures the same multiplication without listing all the factors explicitly.

The p orbitals are dumbbell-shaped and are oriented along the x, y, and z axes. Specifically, these orbitals are designated as (p_x), (p_y), and (p_z), corresponding to their alignment with the respective axes. Each p orbital has two lobes, with a nodal plane at the nucleus where the probability of finding an electron is zero.

To find the intercepts of the equation (3xy = 15), we first rewrite it as (y = \frac{15}{3x} = \frac{5}{x}). The x-intercept occurs when (y = 0), which does not exist for this equation since (y) is undefined when (x = 0). For the y-intercept, we set (x = 0), but again, this results in division by zero, indicating there is no y-intercept either. Therefore, the graph has no x- or y-intercepts.

To simplify the expression -3 - (2y + 3z), you first distribute the negative sign across the terms inside the parentheses. This changes the expression to -3 - 2y - 3z. Therefore, the final simplified expression is -3 - 2y - 3z.

The equation ( y = x^2 - 3x + 4 ) is a quadratic function. To determine the number of roots, we can use the discriminant ( D = b^2 - 4ac ), where ( a = 1 ), ( b = -3 ), and ( c = 4 ). Calculating the discriminant gives ( D = (-3)^2 - 4(1)(4) = 9 - 16 = -7 ). Since the discriminant is negative, the equation has no real roots, indicating that the graph does not intersect the x-axis.

The square root of 30, denoted as √30, is an irrational number because it cannot be expressed as a fraction of two integers. Its decimal expansion is approximately 5.477, which goes on forever without repeating. The rationale behind its classification as irrational lies in the fact that 30 is not a perfect square, meaning there is no integer that, when multiplied by itself, equals 30. Thus, √30 is often left in its radical form for exactness in mathematical expressions.

15b + 13c - 12b + 10c + 8 = 3b + 23c + 8

The graph of ( y = f(x) = x ) is transformed into the graph of ( g(x) = 3x + 7 ) through two main transformations. First, the graph is vertically stretched by a factor of 3, which increases the slope, making it steeper. Second, the graph is shifted upward by 7 units, which moves the entire line up on the y-axis. These transformations result in a new line with a slope of 3 and a y-intercept of 7.

14c^(2)d &(+) 42c^(3)d

This factors to

14c^(2)d(1 + 3c)

Hence the GCF is 14c^(2)d

Method

We have '14' & '3 X 14 = 42'. So '14' is a common factor

We have c^(2) = c X c & c^(3) = c X c X c . Sp c^(2) is a common factor.

Finally we have 'd' & 'd' . So 'd' is the final common factor.

Combining 14 x c^(2) X d

= 14c^(2)d as the GCF .

C^ (2) - D^(2) Factors to (C -D )(C + D)

If we apply FOIL to these bracketed terms. (C -D )(C + D), then we have

F ; C^(2)

O = CD

I = -DC

L = -D^(2)

'Stringing out'

C^(2) + CD - DC - D^(2)

NB Remember CD= DC ; just like 2 x 3 = 6 & 3 x 2 =6

Hence

C^(2) + CD - CD _ D^(2)

Adding terms we have C^(2) - D^(2)

NB THe (+)CD - CD = 0

This is the inverse function, done to show how C^(2) - D^(2) factors.

NB Remember two squared terms with a negative(-) between WILL Factor.

However, two squared with a positive(+) between them does NOT factor.

As a n example, take the Pythagorean Eq'n.

h^(2) = x^(2) + y^(2)

This does NOT factor .

However,

h^(2) - y^(2) = x^(2)

Does factors to

(h - y)(h + y) = x^(2)

Hope that helps!!!!!

d

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, ...

15th Term: 610

The nucleolus is a prominent substructure within the nucleus of eukaryotic cells, primarily responsible for the synthesis and assembly of ribosomal RNA (rRNA) and ribosomal subunits. It plays a crucial role in the production of ribosomes, which are essential for protein synthesis. The nucleolus also participates in the regulation of the cell cycle and stress responses. Overall, it is vital for maintaining cellular function and protein production.

The y-intercept of a distance vs. time graph represents the initial distance at time zero. If the graph starts at the origin (0,0), it indicates that the object began its motion from the starting point. If the y-intercept is greater than zero, it shows the object started from a distance away at the initial time. Conversely, a y-intercept of zero means no initial distance was present.

To simplify the expression (\frac{x + 1}{x^2 + x - 6} \div \frac{x^2 + 5x + 4}{x - 2}), first rewrite it as (\frac{x + 1}{x^2 + x - 6} \cdot \frac{x - 2}{x^2 + 5x + 4}). Next, factor the denominators: (x^2 + x - 6 = (x - 2)(x + 3)) and (x^2 + 5x + 4 = (x + 1)(x + 4)). This results in (\frac{x + 1}{(x - 2)(x + 3)} \cdot \frac{x - 2}{(x + 1)(x + 4)}), allowing cancellation of (x + 1) and (x - 2), leading to the simplified form (\frac{1}{x + 3}) when (x \neq -1, -4, 2).