Mathematics
ALG2 James Madison High School Pythagorean Theorem Questions Response

ALG2

James Madison high school

Question Description

I need help with a Algebra question. All explanations and answers will be used to help me learn.

Algebra 2 worksheet with functions, graphing, linear equations. Also solving inequalities and graphing.

Unformatted Attachment Preview

Name: Directions: Use what you have learned in this course to answer the following questions. Justify your responses completely. Each question is worth 5 points. 1. Solve for n: –6(n – 8) = 4(12 – 5n) + 14n. 2. For f(x) = 2|x+3| – 5, name the type of function and describe each of the three transformations from the parent function f(x) = |x|. 3. Determine whether f(x) = –5𝒙𝟐 – 10x + 6 has a maximum or a minimum value. Find that value and explain how you know. 4. The median weekly earnings for American workers in 1990 was $412 and in 1999 it was $549. Calculate the average rate of change between 1990 and 1999. 5. Find the roots of the parabola given by the following equation. 2x2+ 5x - 9 = 2x 6. Describe the end behavior and determine whether the graph represents an odd-degree or an even-degree polynomial function. Then state the number of real zeros. 7. GEOMETRY Recall the formula for finding the area of a rectangle. Define a variable for the width and set up an equation to find the dimensions of a rectangle that has an area 144 square inches, given that the length is 10 inches longer than its width. DIMENSIONS: Length: Width: 8. The amount f(t) of a certain medicine, in milligrams, in a patient’s bloodstream t minutes 𝟔𝟎𝒕 after being taken is given by f(t) = 𝟐 . 𝒕 +𝟒𝟔 Find the amount of medicine in the blood after 20 minutes. 9. Graph f(x) = x2 + 2x - 3, label the function’s x-intercepts, y-intercept and vertex with their coordinates. Also draw in and label the axis of symmetry. 10. Determine whether the relation shown is a function. Explain how you know. 11. Solve the inequality and graph the solution on a number line. –3(5y – 4) ≥ 17 12. Assume that the wooden triangle shown is a right triangle. a. Write an equation using the Pythagorean Theorem and the measurements provided in the diagram. Hint: (leg 1)2 + (leg 2)2 = (hypotenuse)2 b. Transform each side of the equation to determine if it is an identity. 13. Use long division or synthetic division to find the quotient of 14. Simplify (9𝒌𝟔 + 8𝒌𝟒 – 6𝒌𝟐 )(4𝒌𝟐 – 5). 𝟐𝒙𝟑 + 𝒙𝟐 + 𝟏 𝒙+𝟏 . 15. Find the inverse of h(x) = 𝟐𝒙 + 𝟔 . 𝟓 16. If f(x) = 2x – 1 and g(x) = 𝒙𝟐 – 2, find [g ◦ f](x). 17. Graph the function y = √𝒙 + 𝟒 – 2. Then state the domain and range of the function. Domain: Range: 18. If f(x) = 3x2 – 2 and g(x) = 4x + 2, what is the value of (f + g)( 2) ? The price of a sweatshirt at a local shop is twice the price of a pair of shorts. The price of a T-shirt at the shop is $4 less than the price of a pair of shorts. Brad purchased 3 sweatshirts, 2 pairs of shorts, and 5 T-shirts for a total cost of $136. 19. Let w represent the price of one sweatshirt, t represent the price of one T-shirt, and h represent the price of one pair of shorts. Write a system of three equations that represents the prices of the clothing. 20. Solve the system. Find the cost of each item. ...
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Final Answer

Attached.

Name:
Directions: ​Use what you have learned in this course to answer the following
questions. Justify your responses completely. Each question is worth 5
points.
1. ​Solve for ​n​: ​–6(​n ​– 8) = 4(12 – 5​n​) + 14​n​.
● Switch the equation
○ 4(12 − 5n) + 14n = − 6(n ...

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University of Virginia

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