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Scilla [17]
3 years ago
15

Which of the following expression is equivalent to 6x2−13x−28

Mathematics
1 answer:
SSSSS [86.1K]3 years ago
5 0

Answer:

I, III and IV

Step-by-step explanation:

Required

Determine equivalent expressions to 6x^2 - 13x - 28

To do this, we simplify each of the given options.

I.\ 6x2+8x-21x-28

Simplify like terms

6x2+8x-21x-28

= 6x2-13x-28

<em>This is equivalent to the given expression</em>

<em></em>

II.\ 2x(3x + 4) + 7x(3x - 4)

Open Bracket

2x(3x + 4) + 7x(3x - 4)

2x*3x + 2x*4 + 7x*3x - 7x*4

6x^2 + 8x - 21x^2 - 28x

Collect Like Terms

6x^2 - 21x^2 + 8x  - 28x

-15x^2 - 20x

<em>This is not equivalent to the given expression</em>

III.\ 2x(3x+4)-7(3x+4)

Open Bracket

2x(3x+4)-7(3x+4)

2x*3x + 2x*4 - 7*3x - 7*4

6x^2 + 8x - 21x - 28

Simplify Like Terms

6x^2 -13x - 28

<em>This is equivalent to the given expression</em>

IV.\ (3x + 4)(2x-7)

Open Brackets

3x * 2x - 3x * 7 + 4*2x-4*7

6x^2 - 21x+ 8x-21

Simplify like terms

6x^2 -13x-21

<em>This is equivalent to the given expression</em>

<em></em>

<em>Hence: I, III and IV are equivalent to the given expression</em>

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3 0
3 years ago
The sum of two numbers is 153. if four times the smaller number is subtracted from the larger​ number, the result is 18. find th
sleet_krkn [62]
X = larger number and y = smaller number

x + y = 153....x = 153 - y
x - 4y = 18

153 - y - 4y = 18
153 - 5y = 18
-5y = 18 - 153
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y = -135/-5
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4 0
3 years ago
Joshua gave away 1/3 of his marbles to Kale.If Kale got 25 marbles,how many marbles did Joshua have at first?​
OLEGan [10]

Answer:

75

Step-by-step explanation:

joshua - x

kale - 1/3x

1/3x = 25

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6 0
2 years ago
A rectangle box with a square base and no top needs to be made using 300ft^2 of material. Find the dimensions of the box with th
Yuri [45]

The dimensions of the box are 10 ft and 5 ft

The maximum volume is 500 ft³

Step-by-step explanation:

A rectangle box with

  • A square base and no top
  • It needs to be made using 300 ft² of material
  • It has greatest volume

Surface area of a box without top (SA) = perimeter of base × height + area of the base

Volume of a box (V) = base area × height

Assume that the length of the side of the square base is x and the height of the box is y

∵ It needs to be made using 300 ft² of material

∴ The surface area of the box is 300 ft²

∵ Its base is a square of side length x ft

∴ Perimeter of the base = 4 × x = 4 x

∴ Area of the base = x²

∵ The height of the box = y ft

∵ SA = perimeter of base × height + area of the base

∵ SA = (4x)(y) + x²

∴ SA = 4xy + x²

∵ SA of the box = 300 ft²

- Equate the two expressions of SA

∴ 4xy + x² = 300

Now let us find y in terms of x

- Subtract x² from both sides

∴ 4xy = 300 - x²

- Divide each term by 4x to find y

∴ y=\frac{75}{x}-\frac{1}{4}x

∵ V = area of the base × height

∴ V = x² × y = x²y

- Substitute y by the equation of it above

∴ V=x^{2}(\frac{75}{x}-\frac{1}{4}x)

∴ V=75x-\frac{1}{4}x^{3}

∵ The volume of the box is greatest

- That means differentiate V and equate it by 0

∵ \frac{dV}{dx}=75-\frac{3}{4}x^{2}

∵ \frac{dV}{dx}=0 ⇒ greatest volume

∴ 75-\frac{3}{4}x^{2}=0

- Subtract 75 from both sides

∴ -\frac{3}{4}x^{2}=-75

- Divide both sides by -\frac{3}{4}

∴ x² = 100

- Take √ for both sides

∴ x = 10

Substitute the value of x in the equation of y

∵ y=\frac{75}{10}-\frac{1}{4}(10)

∴ y = 5

The dimensions of the box are 10 ft and 5 ft

∵ V=75x-\frac{1}{4}x^{3}

∵ x = 10

∴ V=75(10)-\frac{1}{4}(10)^{3}

∴ V=750-\frac{1}{4}(1000)

∴ V = 750 - 250

∴ V = 500 ft³

The maximum volume is 500 ft³

Learn more:

You can learn more about the volume in brainly.com/question/6443737

#LearnwithBrainly

6 0
3 years ago
Write 1.67% as a decimal. thx :)
Bas_tet [7]

Answer:

0.0167

Step-by-step explanation:

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6 0
3 years ago
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