### Mathematics Problem: Solving for Poster DimensionsHere are detailed steps and explanations for solving the given problem about the dimensions of a rectangular poster.---**Part A***The width of an extra large rectangular poster is 8 inches more than half its length. The area of this poster is 306 square inches. Write an equation in one variable that could be used to find the number of inches in the dimensions of this poster.*1. **Define the variables:** - Let $ L $ represent the length of the poster in inches. - The width $ W $ can be expressed as 8 inches more than half its length, i.e., $ W = \frac{L}{2} + 8 $.2. **Express the area relation:** - The area $ A $ of a rectangle is given by the formula $ A = L \times W $. - Here, $ A = 306 $ square inches.3. **Substitute the width expression into the area equation:** - $ 306 = L \times \left( \frac{L}{2} + 8 \right) $.4. **Form the equation:** - $ 306 = \frac{L^2}{2} + 8L $.5. **Simplify to get a standard form equation:** - Multiply through by 2 to clear the fraction: $ 612 = L^2 + 16L $. - Rearrange to form a standard quadratic equation: $ L^2 + 16L - 612 = 0 $.**On the right side of the box, click the "+" button to start a new line.**Click the box below to type your math work and answer.```Input Box```---**Part B***Solve this equation algebraically to determine the dimensions of this poster, in inches.*1. **Restate the quadratic equation from Part A:** - $ L^2 + 16L - 612 = 0 $.2. **Solve the quadratic equation using factoring, completing the square, or quadratic formula. Here we'll use the quadratic formula $ L = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $:** - For equation $ ax^2 + bx + c = 0 $, $ a = 1 $,

Name: ### Mathematics Problem: Solving for Poster DimensionsHere are detail
Uploaded: 2024-03-05T11:52:21.000Z
Channel: Bartleby
Description: ### Mathematics Problem: Solving for Poster DimensionsHere are detailed steps and explanations for solving the given problem about the dimensions of a rectangular poster.---**Part A***The width of an extra large rectangular poster is 8 inches more t

Math

Algebra

Part A The width of an extra large rectangular poster is 8 inches more than half its length. The area of this poster is 306 square inches. Write an equation in one variable that could be used to find the number of inches in the dimensions of this poster. In the box below, clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Utilize the information provided for the question to determine your answer. Click the box below to type your math work and answer. On the right side of the box, click the - button to start a new line. ) Part B Solve this equation algebraically to determine the dimensions of this poster, in inches. In the box below, clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Utilize the information provided for the question to determine your answer,

Part A The width of an extra large rectangular poster is 8 inches more than half its length. The area of this poster is 306 square inches. Write an equation in one variable that could be used to find the number of inches in the dimensions of this poster. In the box below, clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Utilize the information provided for the question to determine your answer. Click the box below to type your math work and answer. On the right side of the box, click the - button to start a new line. ) Part B Solve this equation algebraically to determine the dimensions of this poster, in inches. In the box below, clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Utilize the information provided for the question to determine your answer,

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Related questions

Q: Jada opens a 5-kg bag of dog food and fills her dog's dish with 0.25 kg of the content once a day.…

A: Solved below

Q: The diagram below shows the dimensions of the pane of glass inside a circular window. 6 inches Which…

A: The circumference of a circle is 2·π·r where r is the radius of the circle. Radius of the circle=…

Q: The first angle of a triangle is 14 degrees less than the second angle. The third angle of a…

A: Assume that x be the second angle of the Triangle. Then write the other two angles in terms of x.

Q: Marshall rectangular poster is 2 times it width if the perimeter is 24 inches what os the area of…

A: Given that, The Marshall rectangular poster is 2 times its width. The perimeter is 24 inches. Let x…

Q: end of each week, she will add $20 to the account. Write an equation to describe the total amount S,…

A: $35 initially After 1 week Total amount = 35 + 20 After 2nd week Total amount = 35 + 20 + 20 = 35…

Q: For each equation, determine what operation is performed on the variable. (a) x - 2 = 8 The…

A: (a) In the given equation the sign of subtraction is observed between the variable x and 2.

Q: 2. A box is made such that the height is 2 cm longer than the width and the length is twice the…

A: Given: Let the width of the box be x cm. Height=(2+x)cm. Length=2x cm.

Q: The hypotenuse of a right triangle is 13 inches. One of the legs of the right triangle is 5 inches.…

A: The hypotenuse of a right triangle is 13 inches. one of the legs of the right triangle is 5 inches.…

Q: Evaluate, please specify which formula or equation you used to answer the question. Th 2lnx

Q: Write an equation that represents the following statements: The height (H) of a shape is 6 less than…

A: Given:- The height (H) of a shape is 6 less than 3 times its volume (V). The weight (W) of an…

Q: The surface area of this cube is 486 square meters. What is the value of q? q 9 9

A: Given that the cube has a surface area of 486 square metres

Q: Type the correct answer in each box. Use numerals instead of words. What is the equation of the…

A: According to given, The given parabola with vertical axis given by, f(x)=y=ax²+bx+c -------equation…

Q: The length of a bedroom is 4 feet longer than the width. The perimeter of the bedroom is 40 feet. a.…

Q: day. It is 2 3/10 kilometers each way. How far does Riley walk to get to and from school each day?

A: Given, Riley walks to and from school each day. It is 2310 kilometers each way.

Q: A huge suspended LED screen is the centerpiece of The Place, a popular mall in Beijing, China. Find…

A: Length=L Width=W Area=A

Q: Find two integers whose sum is 140 and whose product is as large as possible.

A: Topic=Algebra Two integers are 70 and 70.

Q: During a recent storm clean up there is a mound of m tons of sand at the beach. Throughout the day…

A: topic - linear equations

Q: 8) The perimeter of a rectangular pool is 182 feet. The length of the pool is 5 feet less than twice…

Concept explainers

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.

Topic Video

Question

### Mathematics Problem: Solving for Poster Dimensions

Here are detailed steps and explanations for solving the given problem about the dimensions of a rectangular poster.

---
**Part A**

*The width of an extra large rectangular poster is 8 inches more than half its length. The area of this poster is 306 square inches. Write an equation in one variable that could be used to find the number of inches in the dimensions of this poster.*

1. **Define the variables:**
- Let $ L $ represent the length of the poster in inches.
- The width $ W $ can be expressed as 8 inches more than half its length, i.e., $ W = \frac{L}{2} + 8 $.

2. **Express the area relation:**
- The area $ A $ of a rectangle is given by the formula $ A = L \times W $.
- Here, $ A = 306 $ square inches.

3. **Substitute the width expression into the area equation:**
- $ 306 = L \times \left( \frac{L}{2} + 8 \right) $.

4. **Form the equation:**
- $ 306 = \frac{L^2}{2} + 8L $.

5. **Simplify to get a standard form equation:**
- Multiply through by 2 to clear the fraction: $ 612 = L^2 + 16L $.
- Rearrange to form a standard quadratic equation: $ L^2 + 16L - 612 = 0 $.

**On the right side of the box, click the "+" button to start a new line.**

Click the box below to type your math work and answer.
```
Input Box
```

---
**Part B**

*Solve this equation algebraically to determine the dimensions of this poster, in inches.*

1. **Restate the quadratic equation from Part A:**
- $ L^2 + 16L - 612 = 0 $.

2. **Solve the quadratic equation using factoring, completing the square, or quadratic formula. Here we'll use the quadratic formula $ L = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $:**
- For equation $ ax^2 + bx + c = 0 $, $ a = 1 $,

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Application of Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

Similar questions

Write an equation that can be used to determine the total cost C (t) for t months of the Star plan and find the total cost for 18 months of service. TV company charges $95 installation fee and $125 for Star plan.
What’s the answer
You fill a box with 6 more apples than pears. Create an equation that represents the number of fruit inside the box. First label the unknowns: Let a be the number of apples in the box. Let p be the number of pears.
Tonya has a rectangular rug with an area of 21 square feet. The rug is 4 feet longer than it is wide. Create an equation that can be used to determine the length and the width of the rug. Tonya adds a 1.5-foot boarder all the way around the rug. What is the area of the enlarged rug? Show all work.
A picture frame surrounds a picture that is 8 inches by 10 inches. The frame is the same width all the way around. If the total area of the entire framed picture is 143 in2, find the width of the frame. Hint: Draw a picture to help you write an equation.
Express the give quantity in terms of the indicated variable.