The book costs $49.95 with 3% sales tax. What is the total cost?

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 equation of the graph below? A graph shows a parabola that opens up with a vertex at negative three comma negative o

Tomtit [17]

Answer:

$y=(x+3)^2-1\\y=x^2+6x+8$

Step-by-step explanation:

Given:

Vertex of the parabola is, $(h,k)=(-3,-1)$

Equation of the parabola in vertex form is given as:

$y=(x-h)^2+k$

Plug in $h=-3,k=-1$ . This gives,

$y=(x-(-3))^2+(-1)\\y=(x+3)^2-1$

Therefore, the equation of the given graph is

$y=(x+3)^2-1\\y=x^2+6x+8$ .

5 0

3 years ago

Li Ping says a square with 3 inch sides has greater area than a parallelogram that is not a square but has sides that have the s

Kipish [7]

Answer:

Li Ping's statement makes sense.

Step-by-step explanation:

The area of a square with side lengths a inches is given by, $A_1 = a^{2}$ .

Now, the area of a parallelogram with equal sides a inches, which is not a square is given by, $A_2 = ah$ , where, h is the perpendicular distance between the opposite sides.

See the diagram attached.

Since a is the hypotenuse of as right triangle with height h, hence, a > h.

So, $A_1 > A_2$

Therefore, Li Ping's statement makes sense. (Answer)

8 0

3 years ago

PLS HELP ME!! STATE THE DOMAIN AND RANGE OF EACH RELATION AND WHETHER ITS A FUNCTION

muminat

Domain is everything below 0. Range is all real numbers. It is a function as it passes the vertical line test.

5 0

3 years ago

Emma borrowed $89.40 from her sister. She determines that she can pay her back the total over six months. Which number reflects

omeli [17]

Answer:

$14.9

Step-by-step explanation:

Step one:

given data

we are told that Emma borrowed $89.40 from her sister to pay her back in 6 months.

let us solve for the amount she is to pay her sister every month.

amount to be paid per month= 89.40/6

=$14.9

So that every month she pays back her sister $14.9

we don't know her balance but every month there will be a deduction.

Hence the monthly change in her balance is reflected by a deduction of $14.9

5 0

3 years ago