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iren2701 [21]
2 years ago
15

What is an expression that is equivalent to 6(7x-x)

Mathematics
2 answers:
soldi70 [24.7K]2 years ago
7 0

Answer:

6(7x - x)

= 42x - 6x

= 36x

Step-by-step explanation:

\blue{ \frak{iuynsm}}

BigorU [14]2 years ago
3 0

6(7x-x)= 6(6x) = 36x

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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&#10; \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
a local company uses 13 1/2 tons of paper in one week. It recycles about 1/3 of its waste. how many tons of paper does the compa
bogdanovich [222]

Answer:

4 1/2 tons of recycled paper

Step-by-step explanation:

13.5/3 = 4.5 or 4 1/2

3 0
2 years ago
hello could you please help me with this math problem with full explanation which I am unable to solve? Thanks.
neonofarm [45]

Answer:

8 / sqrt(3)

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp / adj

tan A = BC / AC

tan 30 = BC / 8

8 tan 30 = BC

8 * sqrt(3)/3 = BC

8/3 sqrt(3) = BC

7 0
3 years ago
Plz Urgently for today !!!!!!!!!!!
Elden [556K]
Block one is 17
Block 2 is 15
Block 3 is -8 (negative 8)
Block 4 I need to see the options
Block 5 I need to see the option
Block 6 is she does live in the area
3 0
3 years ago
The expression below represents the number of boxes of cookies sold by a girl scouts troop with 14 members at the school fair, w
Zinaida [17]
I think it would be The first term indicates that the 14 girl scouts each sold 22 boxes of cookies per additional day of the fair. The second term indicates that the 14 girl scouts each sold 25 boxes of cookies on the first day of the fair.
4 0
3 years ago
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