1.
Simplify: 5x^{3}(2x^{3} - 4x^{2} + 3x)remember: just put x3 for x^{3}
Explanation
The given expression can be simplified by distributing the 5x3 to each term within the parentheses. This results in 5x3(2x3) - 5x3(4x2) + 5x3(3x). Simplifying each term separately gives us 10x6 - 20x5 + 15x4.
2.
Simplify: (2x^{2}y^{3})^{4}remember: just put x3 for x^{3}
Explanation
The given expression is (2x^2y^3)^4. To simplify this expression, we need to raise each term inside the parentheses to the power of 4.
For the term 2, since it does not have any variables, it remains the same.
For the term x^2, we need to multiply the exponents, so x^2 raised to the power of 4 becomes x^(2*4) = x^8.
For the term y^3, we also need to multiply the exponents, so y^3 raised to the power of 4 becomes y^(3*4) = y^12.
Putting it all together, the simplified expression is 2x^8y^12.
Therefore, the correct answer is 16x8y12.
3.
Simplify: (4x - 3y)(4x + 3y) remember: just put x3 for x^{3}
Explanation
The given expression is a product of two binomials, (4x - 3y) and (4x + 3y). When multiplying these binomials using the distributive property, the result is a difference of squares. The first term is obtained by squaring the first term of the first binomial, which is 4x, resulting in 16x^2. The second term is obtained by squaring the second term of the second binomial, which is 3y, resulting in 9y^2. Therefore, the simplified expression is 16x^2 - 9y^2.
4.
Simplify: (y^{2} - 4y + 3) - (4y^{2} + 5y - 2)remember: just put x3 for x^{3}
5.
Simplify: (x^{2} + 10x + 16)/(x + 2)
Explanation
The correct answer is x + 8. This can be obtained by factoring the numerator, which is a quadratic expression, and then canceling out the common factor of (x + 2) from both the numerator and denominator. The remaining expression is x + 8.
6.
Simplify: 3√(80) - 5√(45)√ is square root sign, copy and paste it for your answer
Explanation
The given expression involves simplifying the square roots of 80 and 45. The square root of 80 can be simplified to 4√5, while the square root of 45 can be simplified to 3√5. Therefore, the expression simplifies to 4√5 - 5(3√5), which further simplifies to 4√5 - 15√5. Combining like terms, we get -11√5. Therefore, the correct answer is -3√5.
7.
Simplify: (c/d) ÷ (c - d)/d
Explanation
The given expression is (c/d) ÷ (c - d)/d. To simplify this expression, we can multiply the numerator and denominator of the first fraction by d to get c ÷ (c - d). This is the same as c/(c-d). Therefore, the correct answer is c/(c-d). The other options are just different ways of writing the same simplified expression.
8.
Factor: x^{2} - x - 6
Explanation
The correct answer is (x - 3)(x + 2),(x + 2)(x - 3),(x -3)(x +2),(x-3)(x+2),(x +2)(x -3). This is because the given factor x^2 - x - 6 can be factored into (x - 3)(x + 2). The order of the factors does not matter, so all the given options are correct.
9.
An equation of a line is y = 4x + 8. What is the x-intercept?
Explanation
The x-intercept of a line is the point where the line crosses the x-axis. To find the x-intercept, we set y equal to zero and solve for x. In this equation, y = 4x + 8, when y is zero, we have 0 = 4x + 8. By rearranging the equation, we get 4x = -8, and dividing both sides by 4 gives x = -2. Therefore, the x-intercept is -2. The answer choices (-2, 0), (-2,0), -2, 0, -2,0 all represent the same point on the coordinate plane, which is the x-intercept of the line.
10.
Factor: 12x^{2}y + 21xy^{2} - 3xyremember: just put x3 for x^{3}
Explanation
The given expression can be factored by finding the common factors of the terms. The common factor in this case is 3xy. When we factor out 3xy from each term, we are left with (4x + 7y - 1). Therefore, the correct answer is 3xy (4x + 7y - 1).
11.
If x = 3 and y = -2, evaluate (x^{2} - xy)/(x^{2} + 2y)
Explanation
The given expression is (x^2 - xy)/(x^2 + 2y). Substituting the given values of x = 3 and y = -2, we get (3^2 - 3*(-2))/(3^2 + 2*(-2)). Simplifying this expression, we have (9 + 6)/(9 - 4), which further simplifies to 15/5. Finally, dividing 15 by 5 gives us the answer of 3.
12.
Write an equation of the line that passes through the point (1, -2) and is parallel to the line with equation y = 3x + 7.Write in y-intercept form.
Explanation
The line that passes through the point (1, -2) and is parallel to the line y = 3x + 7 will have the same slope as the given line, which is 3. Using the point-slope form of a linear equation, we can substitute the values of the point (1, -2) and the slope (3) into the equation y - y1 = m(x - x1). Simplifying the equation will give us the equation of the line in y-intercept form, which is y = 3x - 5.
13.
Solve: 5/(x + 2) = 3/(x - 1)
Explanation
The equation 5/(x + 2) = 3/(x - 1) can be solved by cross-multiplying. Multiplying both sides of the equation by (x + 2) and (x - 1) gives 5(x - 1) = 3(x + 2). Expanding both sides gives 5x - 5 = 3x + 6. Combining like terms gives 2x = 11. Dividing both sides by 2 gives x = 11/2. Therefore, the correct answer is 11/2. Additionally, the answer choices 5 1/2, 5.5, and (11/2) are equivalent to 11/2 and also correct.
14.
Solve: 4x - 3 = 9x + 7
Explanation
The given equation is 4x - 3 = 9x + 7. To solve for x, we need to isolate the variable on one side of the equation. By subtracting 4x from both sides, we get -3 = 5x + 7. Then, by subtracting 7 from both sides, we have -10 = 5x. Finally, dividing both sides by 5, we find that x = -2. Therefore, the correct answer is x = -2.
15.
Solve: x^{2} - 8x + 15 = 0(use a comma to separate multiple answers)
Explanation
The given quadratic equation is x^2 - 8x + 15 = 0. To solve this equation, we can factorize it as (x - 3)(x - 5) = 0. This implies that either (x - 3) = 0 or (x - 5) = 0. Solving these equations, we find that x = 3 or x = 5. Therefore, the correct answer is x = 3, 5.