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3 years ago

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A graph passes through the points (0, 2), (2, 6), and (3, 12). Does this graph represent a linear function or a non-linear funct

ion?

1 answer:

pychu [463]3 years ago

5 0

A linear function is <span>the answer</span>

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/// WORTH 70 points /// ASAP ////

belka [17]

A community is developing plans for a pool and hot tub. The community plans to form a swim team, so the pool must be built to certain dimensions. Answer the questions to identify possible dimensions of the deck around the pool and hot tub.

Part I: The dimensions of the pool are to be 25 yards by 9 yards. The deck will be the same width on all sides of the pool. Including the deck, the total pool area has a length of (x + 25) yards, and a width of (x + 9) yards.

Write an equation representing the total area of the pool and the pool deck. Use y to represent the total area. Hint: The area of a rectangle is length times width. (1 point)

$y = (x+25)(x+9)$

Rewrite the area equation in standard form. Hint: Use the FOIL method. (1 point)

$y = x^2 + 9x + 25x + 9(25)$

$y = x^2 +34x + 225$

Rewrite the equation from Part b in vertex form by completing the square. Hint: Move the constant to the other side, add to each side, rewrite the right side as a perfect square trinomial, and finally, isolate y. (4 points: 1 point for each step in the hint)

$y-225 = x^2 +34x$

$y-225 + 17^2 = x^2 +34x + 17^2$

$y-225 + 289 = (x+17)^2$

$y = (x+17)^2 - 64$

What is the vertex of the parabola? What are the x- and y-intercepts? Hint: Use your answer from Part a to identify the x-intercepts. Use your answer from Part b to identify the y-intercept. Use your answer from Part c to identify the vertex. (4 points: 1 point for each coordinate point)

The vertex is where the squared term is zero, x=-17 , y =-64, (-17,-64)

The y intercept is y at x=0, so (0,225)

The x intercepts are the zeros; so at x=-25 and x=-9, aka (-25,0), (-9,0)

Graph the parabola. Use the key features of the graph that you identified in Part d. (3 points)

[Plot the points we generated and connect the dots. I'll leave the graphing to you]

In this problem, only positive values of x make sense. Why? (1 point)

<em>x</em> is the width of the pool edge; it must be positive.

What point on your graph shows a total area that includes the pool but not the pool deck? (1 point)

x=0, y=225 i.e. (0,225)

The community decided on a pool area that adds 6 yards of pool deck to both the length and the width of the pool. What is the total area of the pool and deck when x = 6 yards? (2 points)

(9+6)(25+6)=15(31)=465

Part II: A square hot tub will be placed in the center of an enclosed area near the pool. Each side of the hot tub measures 6 feet. It will be surrounded by x feet of deck on each side. The enclosed space is also square and has an area of 169 square feet. Find the width of the deck space around the hot tub, x.

Step 1: Write an equation for the area of the enclosed space in the form y = (side length)2. Hint: Don't forget to add x to each side of the hot tub. (1 point)

$y=(x+6)(x+6)=(x+6)^2$

Step 2: Substitute the area of the enclosed space for y in your equation. (1 point)

169 = (x+6)^2

Step 3: Solve your equation from Part b for x. (3 points)

$x + 6 = \pm \sqrt{169}$

$x = -6
 \pm 13$

$x= 7 \quad \textrm{ or } \quad x= -19$

Step 4: What is the width of the deck around the hot tub? Hint: One of the answers from Part c is not reasonable. (1 point)

Only the positive root works,

x=7 feet

5 0

3 years ago

What is the answer?<br><br> [(12 − 5) • 12] ÷ 6

Sever21 [200]

(7 × 12 )/ 6
= 7×2
= 14

6 0

4 years ago

Read 2 more answers

In November 2010 the average price of 5 gallons of regular unleaded gasoline in the United states was $14.46. what was the price

Lapatulllka [165]

Propecia:

5 gallons ====== $ 14.46.

16 gallons ======= x dollars

X=16*14.46: 5=46.27

Answer: $ 46.27.

3 0

3 years ago

pls help, i need to write an essay explaining what the difference is between finding the volume and total surface of a shape

Vinil7 [7]

Answer:

The surface area applies to how much space a SOLID objects occupies while volume is the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains, so volume can be anything.

Step-by-step explanation:

you can't really write an essay-

8 0

3 years ago

Read 2 more answers

Suppose researchers test 100 college students, whose ages range from 18 to 23. They also test 100 people at a nearby community c

prisoha [69]

Answer:

b. You would conclude that the differences in the average scores can be traced to differences in the working memory of the two groups.

Step-by-step explanation:

Though the average scores of the two sets could have lead to various conditions, but retentive ability deminishes with respect to an increase in age. With respect to the age of the elderly people involved, it is expected that some of them would not be able to retain information for a long period of time. Thus, their average score is 72%.

The college students' are younger, so it is expected that they should be able to retain more information. That ability is one of the reasons why their average score is 85%.

It can be concluded from the research that the differences in the average scores is probably due to the working memory of the two groups.

6 0

3 years ago