First, simplify the expression inside the parentheses: \( 3(2 - 5) = 3 \times (-3) = -9 \). Then add the multiplication: \( 3 \times 7 = 21 \). Now add the two results: \( -9 + 21 = 12 \).

The common difference between consecutive terms in the arithmetic sequence is \( 3 \). Therefore, the next term after 11 is \( 11 + 3 = 14 \).

Simplify each part separately: \( (-2)^3 = -8 \) and \( 5^2 = 25 \). Then add the results: \( -8 + 25 = 17 \).

Simplify by canceling common factors in the numerator and denominator: \( \frac{5x^3y^2}{15x^2y} = \frac{5}{15} times \frac{x^3}{x^2} \times \frac{y^2}{y} = \frac{1}{3} \times x \times y = \frac{xy}{3} \).

Using the definition of the operation, substitute \( a = -1 \) and \( b = -5 \). This gives \( (-1) (-5) = 3(-1)^2 - (-5) = 3(1) + 5 = 8 \).

The prime numbers between \( 100 \) and \( 120 \) are \( 101, 103, 107, 109, 113 \). Only \( 107 \) and \( 109 \) have digit sums greater than 5. Therefore, there are 2 integers that meet both conditions.

An isosceles triangle has two equal angles, but an equilateral triangle has three equal angles. A triangle with angles 55°, 55°, and 70° is isosceles but not equilateral, so it is a counterexample.

The equation \( 3x - 5 = 0 \) simplifies to \( x = \frac{5}{3} \), which represents a vertical line. Vertical lines have an undefined slope.

For the quadratic equation to have one solution, the discriminant must be zero. Solving \(b^2 - 16 = 0\) gives \(b = pm 4\). Therefore, \(b\) could be 4.

From the first equation, solve for \(y\): \(y = 10 - x\). Substitute into the second equation: \(-x + 2(10 - x) = 2\). Simplifying gives \(x = 6\).

The slope of the line \(y = -3x + 7\) is -3. The slope of a line perpendicular to it is the negative reciprocal, \(frac{1}{3}\). Therefore, the line \(y = frac{1}{3}x - 7\) is perpendicular.

Simplify the expression by subtracting the exponents of \(x\) and \(y\). This gives \(x^{7 - 5}y^{3 - 2} = x^2y\).

The surface area of the cylindrical side is given by the formula \(2pi rh\), where \(r\) is the radius and \(h\) is the height. Substituting \(r = 10\) and \(h = 100\), the surface area is \(2000pi\) square centimeters.

\((cd)^2\) is positive and larger than both \(c\) and \(d\). Therefore, \((cd)^2\) must be greater than \(d^3c\).

In an isosceles triangle, two angles are equal. The sum of the angles in a triangle is 180°. If one angle is 20°, the sum of the other two angles is 160°, so each must be 80°.

Since \( m^2 \) is the square of an odd number, it is positive, and multiplying by \( -1 \) makes it negative. Therefore, \( -m^2 \) is an odd negative integer.

In any triangle, the largest angle is opposite the longest side. The longest side here is AB = 15 in, so the largest angle is \( C \).

First, calculate the proportion of the remaining pets. After removing the rabbits and cats, \(\frac{1}{3}\) of the pets remain. Based on the given ratios, birds, ferrets, and guinea pigs can be distributed as follows: Ferrets and guinea pigs each make up \(\frac{1}{9}\) of the total, and birds make up \(\frac{2}{9}\) of the total.

Just sub in values and ensure to take absolute value function into account. Subbing in -2, produces 6 which is indeed greater than 5.

The transformation involves reflecting the point across the y-axis, changing the sign of the x-coordinate while keeping the y-coordinate the same.

To calculate 20% more than 20, multiply 20 by 1.2: \( 20 times 1.2 = 24 \). Therefore, there are 24 students in her English class.

Each equilateral triangle has a perimeter of 24 in, so each side of the triangle is \( 24/3 = 8 \) in. The trapezoid has a base made up of two triangle sides (8 + 8 = 16 in), plus two more triangle sides for the legs, and another side for the top. Thus, the perimeter is \( 16 + 8 + 8 + 8 = 40 \) in.

The formula for the circumference of a circle is \( C = pi \times d \), where \( d \) is the diameter. Since the diameter is 12 cm, the circumference is \( 12pi \) cm.

The ratio of hydrogen atoms to potassium and oxygen atoms in one molecule is 7:3. If there are 56 hydrogen atoms, this corresponds to 8 molecules of potassium sorbate. Therefore, the sample contains \( 8 times 3 = 24 \) total potassium and oxygen atoms.

This is an increase in percentage problem. Imagine we have 100milliliters of air in a balloon. Apply the new percentage change and you will see the answer is B.

The four consecutive integers are 2, 3, 4, and 5. Among them, 2, 3, and 5 are prime numbers. The sum of these integers is \( 2 + 3 + 4 + 5 = 14 \).

Car C's velocity at time \( t \) is three times that of Car A and Car B. Since Car D's velocity is 1/6 that of Car C, the velocity ratio is 2:1:6 for Car A, Car D, and Car C.

Since m is an odd negative integer, \( -m^3 \) is an odd positive integer.

In any triangle, the largest angle is opposite the longest side. The longest side here is AB = 17 in, so the largest angle is C.

From the given fractions, we calculate the proportions for ferrets, guinea pigs, and birds. Ferrets make up \( \frac{1}{8} \), not \( \frac{1}{9} \).

By solving the inequality \( |2 + x^4| > 9 \), we find that the possible value of \( x \) is 3.

The set of integers \( 5, 6, 7, 8, 9 \)contains the primes 5 and 7. The sum of the set is 35.

Given the ratios of velocities, the correct conclusion is that the ratio of Car A to Car D to Car C is\( 4:1:8.\)

Using the definition of @, \( (-2)@(-6) = 4(-2)^2 - (-6) = 16 + 6 = 22. \)