Algebra

To solve the equation (\sin^2 \theta = 0.75), first take the square root of both sides to get (\sin \theta = \pm \sqrt{0.75} = \pm \frac{\sqrt{3}}{2}). Then, find the angles (\theta) for which (\sin \theta = \frac{\sqrt{3}}{2}) and (\sin \theta = -\frac{\sqrt{3}}{2}). The solutions are (\theta = \frac{\pi}{3} + 2k\pi) and (\theta = \frac{2\pi}{3} + 2k\pi) for the positive case, and (\theta = \frac{7\pi}{6} + 2k\pi) and (\theta = \frac{4\pi}{3} + 2k\pi) for the negative case, where (k) is any integer.

9 squared ?

To solve the equations (xy = 7) and (2x + 2y = 14), we can simplify the second equation to (x + y = 7). Substituting (y = 7 - x) into the first equation gives (x(7 - x) = 7). This leads to the quadratic equation (x^2 - 7x + 7 = 0). Using the quadratic formula, the solutions for (x) are (x = \frac{7 \pm \sqrt{49 - 28}}{2} = \frac{7 \pm \sqrt{21}}{2}), and corresponding (y) values can be found from (y = 7 - x).

A bulb serves as a source of artificial light, converting electrical energy into light through a filament or gas. It provides illumination for various environments, enhancing visibility and ambiance. Additionally, bulbs can come in different types, such as incandescent, LED, and fluorescent, each with specific energy efficiencies and applications. Overall, bulbs are essential for both practical and aesthetic lighting needs.

To find the solution to the system of equations ( y = 7x + 2 ) and ( y = 9x - 14 ), set the equations equal to each other: ( 7x + 2 = 9x - 14 ). Solving for ( x ), we get ( 16 = 2x ) or ( x = 8 ). Substituting ( x = 8 ) into either equation gives ( y = 58 ). Thus, the solution is the ordered pair ( (8, 58) ).

4x times 9 is calculated by multiplying the coefficients together. Therefore, 4x * 9 = 36x.

The four sections of a coordinate plane separated by the x and y axes are called quadrants. They are labeled as Quadrant I, Quadrant II, Quadrant III, and Quadrant IV, moving counterclockwise from the upper right. Each quadrant corresponds to a specific combination of positive and negative values for the x and y coordinates.

The dependent variable (DV) is typically plotted on the y-axis, while the independent variable (IV) is plotted on the x-axis. This arrangement allows for a clear visualization of how changes in the independent variable affect the dependent variable in a graph.

To solve the expression (12x^2 - 5x - 3), you need to either factor it or find its roots using the quadratic formula. The expression itself does not have a single numerical answer since it is a quadratic equation in terms of (x). If you are looking for specific values, you would need to set it equal to zero and solve for (x).

A polynomial is considered rational if all of its coefficients are rational numbers, meaning they can be expressed as the quotient of two integers. Conversely, a polynomial is deemed irrational if it contains at least one coefficient that is not a rational number, such as an irrational number (like ( \sqrt{2} ) or ( \pi )). Additionally, the polynomial itself must be expressed as a finite sum of terms, each consisting of a coefficient multiplied by a variable raised to a non-negative integer power.

To divide algebraic expressions, you first factor both the numerator and the denominator if possible. Then, cancel out any common factors between them. Finally, simplify the resulting expression to its lowest terms. If the expression involves polynomials, you may also use long division or synthetic division as appropriate.

If the function changes from ( y = x - 6 ) to ( y = x + 8 ), the new graph will be a vertical shift upward. Specifically, the entire graph will move up by 14 units, since ( 8 - (-6) = 14 ). The slope remains the same (1), so the lines will be parallel, but the new line will intersect the y-axis at ( y = 8 ) instead of ( y = -6 ).

To solve the problem (63 \times 0.52), you can first convert the decimal to a fraction for easier computation. Rewrite (0.52) as (\frac{52}{100}), making the multiplication (63 \times \frac{52}{100}). Then, calculate (63 \times 52) to get (3276) and divide by (100) to get (32.76). Thus, (63 \times 0.52 = 32.76).

The X-intercepts of a linear function are the points where the graph intersects the X-axis, occurring when the output (y) is zero. Conversely, the Y-intercept is the point where the graph intersects the Y-axis, occurring when the input (x) is zero. These intercepts can be found by setting the respective variables to zero in the linear equation. For example, in the equation (y = mx + b), the Y-intercept is (b), and the X-intercept can be found by solving (0 = mx + b).

To multiply monomial algebraic terms with like bases, first multiply the coefficients (numerical parts) of the terms together. Then, add the exponents of the like bases according to the exponent multiplication rule, which states that ( a^m \times a^n = a^{m+n} ). Finally, combine the results to form the new monomial. For example, for ( 3x^2 \times 4x^3 ), you would multiply ( 3 \times 4 = 12 ) and add the exponents ( 2 + 3 = 5 ), resulting in ( 12x^5 ).

In an interview, I typically approach problem-solving by first clearly understanding the problem at hand through active listening and asking clarifying questions. Then, I outline my thought process methodically, breaking the problem into manageable parts and considering various solutions. I prioritize logical reasoning and creativity, and I communicate my reasoning clearly to ensure the interviewer follows my approach. Finally, I reflect on the potential outcomes and any adjustments that might be necessary.

To write 250,000,000 in expanded notation using powers of 10, you can express it as (2.5 \times 10^8). This represents the number as 2.5 multiplied by 10 raised to the 8th power, indicating that the decimal point is moved 8 places to the right. Alternatively, it can also be written as (2 \times 10^8 + 5 \times 10^7).

To find angle A in triangle ABC with angles (x - 1), (2x + 1), and (3x), we can use the fact that the sum of the angles in a triangle is 180 degrees. Setting up the equation: ( (x - 1) + (2x + 1) + (3x) = 180 ). Simplifying gives ( 6x = 180 ), so ( x = 30 ). Substituting back, angle A, which is ( (x - 1) ), equals ( 30 - 1 = 29 ) degrees.

+/- means that the answer can be either a positive(+) number or a negative(-) number.

e.g.

the sqrt(4) = +/- 2

Because +2 x +2 = 4

&

-2 X -2 = 4

Similarly for any other square root values.

Same mathematical signs equal plus

Different mathematical signs equal minus

Plus Plus = Plus (+)(+) = +

Minus Minus = Plus (-)(-) = +

Plus Minus = Minus (+)(-) = -

Minus Plus = Minus (-)(+) = -

So the direct answer to your question would be: plus minus equals minus

2/8 - 2/4 + 5/8

Bring all fractions to a common denominator of '8' , and the numerators to equivalent values.

Hence

2/8 - 4/8 + 5/8

Add the numerators

2 - 4 + 5 = 3

Place over the denominator

Hence

3/8 The answer!!!!!

The square root of 45 is approximately 6.71, and the square root of 67 is approximately 8.19. Therefore, the square root of 45 minus the square root of 67 is approximately 6.71 - 8.19, which equals about -1.48.

Let the number be represented by ( x ). The algebraic equation for the quotient of five times this number and 7 being no more than 10 can be expressed as:

[ \frac{5x}{7} \leq 10 ]

Equations and inequalities are fundamental tools in various fields, including science, engineering, economics, and everyday decision-making. They help model relationships between variables, enabling predictions and analyses, such as calculating financial budgets, optimizing resource allocation, or determining physical laws. In everyday life, inequalities can guide choices based on constraints, like budgeting or time management, while equations can solve problems ranging from cooking measurements to construction planning. Overall, they provide structured ways to understand and navigate complex situations.

The square root of 174 can be simplified by factoring it into its prime factors. Since 174 = 2 × 3 × 29, and none of these factors are perfect squares, the simplest form of (\sqrt{174}) is (\sqrt{174}) itself. Therefore, it cannot be simplified further into a simpler radical form.