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kykrilka [37]
3 years ago
9

The length of a rectangle is the sum of the width and 2. The area of the rectangle is 48 units. What is the length, in units, of

the rectangle?
Mathematics
1 answer:
suter [353]3 years ago
6 0

Length of the rectangle is 8 units

Step-by-step explanation:

  • Step 1: Find the length, let width be x.

Area of the rectangle = 48 units

Length = x + 2

⇒ Area = Length × Breadth

48 = x (x + 2)

48 = x² + 2x

x² + 2x - 48 = 0

x² + 8x - 6x + 48 = 0 (Product Sum rule to factorise)

x(x + 8) - 6(x + 8) = 0

(x - 6)(x + 8) = 0

⇒ x = 6, -8 (negative value is neglected)

∴ x = 6

x + 2 = 8

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Answer:

YES

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NO

Step-by-step explanation:

The given polynomial is: $ f(x) =  x^3 + 4x^2 - 25x - 100 $

(x - a) is a factor of a polynomial iff x = a is a solution to the polynomial.

To check if (x - 5) is a factor of the polynomial f(x), we substitute x = 5 and check if it satisfies the equation.

∴ f(5) = 5³ + 4(5)² - 25(5) - 100

        = 125 + 100 - 125 - 100

        = 225 - 225

        = 0

We see, x = 5 satisfies f(x). So, (x - 5) is a factor to the polynomial.

Now, to check (x + 2) is a factor.

i.e., to check x = - 2 satisfies f(x) or not.

f(-2) = (-2)³ + 4(-2)² - 25(-2) - 100

      = -8 + 16 + 50 - 100

     = -108 + 66

     ≠ 0

Therefore, (x  + 2) is not a factor of f(x).

To check (x - 4) is a factor.

∴ f(4) = 4³ + 4(4)² - 25(4) - 100

        = 64 + 64 - 100 - 100

        = 128 - 200

        ≠ 0

Therefore, (x - 4) is not a factor of f(x).

7 0
3 years ago
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jeka57 [31]
Point-slope equation=y+1=5(x+2)
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3 years ago
-2(4х + 4) — 3х – 2 = 34<br> Find x
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Answer:

x = -4

Step-by-step explanation:

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Then combine the -8x and -3x as well as the -8 and -2 to have -11x - 10 = 34

Add 10 to both sides and get -11x = 44

Divide both sides by -11 for x=-4

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Answer:

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Step-by-step explanation:

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5 0
2 years ago
Read 2 more answers
2X + 4 = 14<br> what is X
Simora [160]

Hello!

2X  + 4 = 14

X = 5

2 * 5 = 10

10 + 4 = 14

I hope this helps, and have a nice day!

3 0
3 years ago
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