Questions in mathematics

Questions in mathematics

[Done] Simplify the polynomial. 1. \(4a^2b + 5 - 6a^3b - 3a^2b + 2a^3b\)

[Done] A circular logo is enlarged to fit the lid of a jar. The new diameter is 50 percent larger than the original. By what percentage has the area of the logo increased?

[Done] Rounding: 1. 8.238; round to the tenths 2. 3.666; round to the tenths 3. 4.47; round to the ones 4. 10.86; round to the ones 5. 3.299; round to the hundredths 6. 20.687; round to the hundredths 7. 2.3654; round to the thousandths 8. 69.0678; round to the thousandths 9. 5.58214; round to the hundredths 10. 468.09156; round to the thousandths 11. 46.49; round to the tens 12. 1358.761; round to the tens

[Done] The product of two whole numbers is 10,000. If neither number contains a zero digit, what are the two numbers?

[Done] If \( f(x) = x^2 - 3 \), where \( x \) is an integer, which of the following could be a value of \( f(x) \)? a. 6 b. 0 c. -6 Explain your answer.

[Done] A water skier is pulled behind a boat by a rope. The rope has a tension of 290 N and is at an angle of 33 degrees. What is the x component of the tension? A. 192 N B. 215 N C. 243 N D. 158 N

[Done] Patrick owns an apartment building. The money he earns in a month depends on the rent he charges. The relationship can be modeled by: \[ E = \frac{1}{50}R(1650 - R) \] where \( E \) is Patrick's monthly earnings, in dollars, and \( R \) is the amount of rent, in dollars, he charges each tenant. If Patrick wants to earn at least $13,000, between what two values should he set the rent?

[Done] Multiply the polynomials: \[ (2n + 2)(6n + 1) \]

[Done] What is: \[ (49^x)(7^{x^2}) = 2401^2 \]

[Done] Simplify the expression: \(\frac{5}{6} - \frac{1}{6}\)