Question

The Data

Decorative glass pebbles are often used in vases for their appearance, and to have their weight stabilize the vase. The table below gives the total weight of a vase full of uniform glass pebbles.


TABLE OF DATA ATTACHED BELOW*


The Analysis

1- Using the table of data above, determine if this relationship is linear or not. Explain how you know.


2-Write an equation that best represents this relationship:
Explain how you reach your answer and show your work below.


3- Graph the data on the grid to the right, label both axes, and label it Line 1.

4-
a) What is the meaning of the initial value in this scenario?

b) What is the meaning of the slope in this scenario?


5- How would the graph AND equation change if a Styrofoam cup is used to collect the data, instead of a glass vase? Explain your reasoning.


6- Based on your equation in question #2, how much will 112 pebbles weigh with the vase?


7- If the total weight is 504 g, how many pebbles are in the vase?


8- Your friend Wilma shares her analysis of similar data about pebbles and a vase, but her equation is W = 10p + 80.


a) Graph it on the same grid as question #3. Label it Line 2.


b)What are the coordinates of the point of intersection?


c)What does it mean in this scenario?


9- Write a SIMPLIFIED algebraic expression to represent the area of the following trapezoid. Show all your work.
(Hint: area of a trapezoid = $\frac{h(a+b)}{2}$)

TRAPEZOID ATTACHED BELOW*

10- Tanya is 12 years older than Leah. Three years ago, Tanya was five times as old as Leah. What is the age of Tanya and Leah now?

I NEED IT TODAY PLESE!

Answer 1

With the aid of the attached diagrams in the question, we have;

1- Linear relation

2- W = 8•P + 80

3- Please find attached the graph created using a graphing calculator.

4- a) The initial value is the mass of the vase

b) The slope is the mass of each pebble

5- The initial value is lesser than 80

6- 1.2 kilograms

7- 53 pebbles

8- a)

b) (0, 80)

c) The masses are the same

9- Trapezoid area, A = 14•x² - 4•x

10- Tanya and Leah are 18 and 6 years old respectively

How can the table and diagram be analyzed?

1- The relationship between two variables (x and y) is linear if the difference between the terms of the x-values and the terms of the y-values are both constant.

From the table we have;

• The difference between consecutive terms of the x-values is constant and equal to 10

• The difference between consecutive terms of the y-values is constant and equal to 80

The relationship between the x and y-values in the table is therefore;

• A linear relationship

2. The slope, m, of the linear function is found as follows;

m = (360 - 280)/(30 - 20) = 8

The equation is therefore;

W - 360 = 8•(P - 30)

W = 8•P - 240 + 360 = 8•P + 80

• The equation is; W = 8•P + 80

3. Please find attached the graph drawn with a graphing calculator.

4. The initial value is the output variable (W-value) when the input variable (P-value) is zero.

Therefore;

y = 8×0 + 80 = 80

a) The initial value indicates when the input, P-value is zero, which gives the mass of the vases

b) The slope indicates the number of times an additional pebble increases the weight of the vase and pebble, which is the mass of one pebble

5- A styrofoam cup is lighter than a glass cup, therefore, the initial value, which is the constant term, c, reduces.

• The change is that, the initial value reduces and becomes less than 80

6- The weight, W, of 112 pebbles is therefore;

W = 10 × 112 + 80 = 1,200

• The weight of 112 pebbles is 1,200 g, which is 1.2 kg.

7- 504 = 8•P + 80

Which gives;

504 - 80 = 8•P

P = 424 ÷ 8 = 53

• The number of pebbles in the vase when it weighs 504 g. is 53 pebbles

8- Wilma's equation is; W = 10•P + 80

a) Please find the second graph showing the graphs of the two equations combined.

b) The point of intersection is given by the relation 10•P + 80 = 8•P + 80

2•P = 0

P = 0

Therefore, at the point of intersection, W = 80

The coordinates of the point of intersection is therefore;

• (0, 80)

c) The point of intersection means that the weight of Wilma's vase and the vase in question 1 are the same.

9. The area of the trapezoid, A, can be expressed as follows;

A = 4•x × ((2•x + 5)+(5•x - 7))/2

A = 2•x × (7•x - 2) = 14•x² - 4•x

• Area of the trapezoid = 14•x² - 4•x

10. Let T represent Tanya's age now and let L represent Leah's current age, we have;

T = L + 12

T - 3 = (L - 3) × 5

Solving gives;

L + 12 - 3 = (L - 3) × 5 (Substitution property)

L + 9 = 5•L - 15

4•L = 9 + 15 = 24

L = 24 ÷ 4 = 6

• Leah's age now, L = 6 years

T = L + 12

Therefore;

T = 6 + 12 = 18

• Tanya's age now, T = 18 years

Learn more about writing equations here:

https://brainly.com/question/18713037

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