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Ganezh [65]
3 years ago
14

A box contains 4 red pencils and 6 black pencils. What fraction of he pencils are red? What fraction of pencils are black? Draw

a model.
Mathematics
1 answer:
Scorpion4ik [409]3 years ago
3 0

Answer:

The fraction of the pencils that are red is 4/10. The fraction of the pencils that are black is 6/10.

Step-by-step explanation:

[I can't draw you a model but I reccomend that when you do, you seperate it into 10 pieces and mark 4 as red pencils and 6 as black pencils. You could also simplify 4/10 to 2/5 and 6/10 to 3/5, but instead you'd seperate the model into 5 pieces and mark 2 as red pencils and 3 as black pencils.]

First, let's add this up so we have our denominator.

4 + 6 = 10.

Now that we know that the denominator is 10, we apply it to the question.

<em>The box has 4/10 red pencils and 6/10 black pencils.</em>

<em>The box has 4/10 red pencils and 6/10 black pencils.If you were to simplify, it'd be 2/5 red pencils and 3/5 black pencils.</em>

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What is the x in the inaquality -x+8&gt;6
Zina [86]

Answer:

x < 2

Step-by-step explanation:

-x + 8 > 6 is our equation.

We can subtract 8 from both sides:

-x > -2

Then, we can flip the inequality sign so that it is positive:

(multiply both sides by -1)

(-x) (-1) < (-2)(-1)

Simplifying gives our answer of:

x < 2

7 0
3 years ago
/// 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
42+__________=68 vhrvwfruybtglh
Hitman42 [59]

Answer:

42 + 26 = 68

Step-by-step explanation:

I hope this helped :)

8 0
3 years ago
The height of the house is 26 feet. What is the height x of each story?
Iteru [2.4K]
X = stories of houses.

x ÷ 26 = the amount of the hiegth of the story.

It would all depend on the amount of stories this house or building would contain.
4 0
3 years ago
Need help with this math question
maw [93]

ANSWER

The vertex of this parabola is (-7,4)

EXPLANATION

The given parabola has equation:

{y}^{2}  - 4x - 8y - 12 = 0

{y}^{2}  - 8y = 4x +12

Complete the square for the quadratic equation in y.

{y}^{2}  - 8y +  {( - 4)}^{2}  = 4x + 12 +  {( - 4)}^{2}

{y}^{2}  - 8y +  {( - 4)}^{2}  = 4x + 12 +  16

{( y- 4)}^{2}  = 4x + 28

{( y- 4)}^{2}  = 4(x +7)

The vertex of this parabola is (-7,4)

5 0
4 years ago
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