Algebra 1 Tutor Competency Quiz

Explanation
To divide a number by a fraction, we can multiply the number by the reciprocal of the fraction. In this case, we have 26 divided by -13/3. To find the reciprocal of -13/3, we flip the fraction, resulting in -3/13. Now we can multiply 26 by -3/13, which gives us -78/13. Simplifying this fraction, we get -6. Therefore, the correct answer is -6.

Explanation
The expression 4(9a + 10b) - (10a - 7b) can be simplified by applying the distributive property to remove the parentheses. This results in 36a + 40b - 10a + 7b. Combining like terms, we get 26a + 47b.

Explanation
The given expression is a polynomial expression with terms of different degrees. To combine the terms, we add or subtract the coefficients of the terms with the same degree. In this case, the terms -5x³, 10x², -7x, and 5 have the same degrees and can be combined. Combining them gives us -5x³ + 10x² - 7x + 5. Therefore, the correct answer is -5x³ + 10x² - 7x + 5.

Explanation
The given polynomial can be factored completely as (x+9)(x-5). This is the correct answer.

Explanation
The given ordered pair (-4, 3) can be substituted into the equation 4x - 6y = -34. When we substitute x = -4 and y = 3 into the equation, we get 4(-4) - 6(3) = -16 - 18 = -34. Since the left side of the equation is equal to the right side, the ordered pair satisfies the equation. Therefore, the answer is Yes.

Explanation
To solve the quadratic equation (x - 4)(x + 3) = 8, we need to expand the equation and set it equal to zero. Expanding the equation gives us x^2 - x - 12 = 8. Moving all the terms to one side, we get x^2 - x - 20 = 0. To solve this quadratic equation, we can use factoring or the quadratic formula. Factoring the equation gives us (x - 5)(x + 4) = 0. Therefore, the solutions are x = 5 and x = -4. Therefore, the correct answer is {-4, 5}.

Explanation
The correct answer is Width = 26 ft; length = 59 ft. This can be determined by setting up an equation using the given information. Let's assume the width of the room is x. According to the given information, the length of the room is 7 feet longer than twice the width, which can be expressed as 2x + 7. The perimeter of a rectangle is calculated by adding the lengths of all its sides, which in this case is 2(width + length). Therefore, we can set up the equation 2(x + 2x + 7) = 170. Solving this equation gives x = 26, which is the width, and 2x + 7 = 59, which is the length.

Explanation
The sum of three consecutive integers can be found by adding the first and the last integer and then adding the middle integer. In this case, if we let the first integer be x, then the second integer would be x+1 and the third integer would be x+2. So, the sum of these three integers would be x + (x+1) + (x+2) = 3x + 3. We know that this sum is equal to 387, so we can solve for x by setting up the equation 3x + 3 = 387. Solving this equation gives us x = 128. Therefore, the three consecutive integers are 128, 129, and 130.

Explanation
The answer (18, -9) is the solution to the system of equations because when we substitute these values into the equations, they satisfy all the equations simultaneously.