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4 years ago

Help please!!!!!!!!!!!!!!!

Mathematics

1 answer:

just olya [345]4 years ago

7 0

A. The width of the dining area is x+15+x; the length is x+10+x. The area (=length*width) must be 1800. That gives us the following equation:

(2x+15)(2x+10) = 1800 => 4x² + 50x + 150 = 1800 =>
4x² + 50x - 1650 = 0

Put 4, 50 and -1650 in the quadratic formula to find x=15 (or x=-27.5 but that is not applicable to this real-world problem).

b. width = 2x+15 = 45, length = 2x+10 = 40

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3. 3(a + 1) - 5 = 3a - 2 a=

Vera_Pavlovna [14]

Answer:

Step-by-step explanation:

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4 years ago

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What is the GCF of the numerator & denominator below? (x-2)(x+3)/x^2+4x+3

Ganezh [65]

Answer:

Step-by-step explanation:

Factorize the denominator

Sum = 4

Product = 3

Factors = 1 , 3 {1*3 = 3 and 1+3 = 4}

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= x(x + 1) + 3(x + 1)

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If the diagonal of a square is approximately 12.73, what is the length of its sides?

Alja [10]

Answer:

The length of the sides of the square is 9.0015

Step-by-step explanation:

Given

The diagonal of a square = 12.73

Required

The length of its side

Let the length and the diagonal of the square be represented by L and D, respectively.

So that

D = 12.73

The relationship between the diagonal and the length of a square is given by the Pythagoras theorem as follows:

$D^{2} = L^{2} + L^{2}$

Solving further, we have

$D^{2} = 2L^{2}$

Divide both sides by 2

$\frac{D^{2}}{2} = \frac{2L^{2}}{2}$

$\frac{D^{2}}{2} = L^2$

Take Square root of both sides

$\sqrt{\frac{D^{2}}{2}} = \sqrt{L^2}$

$\sqrt{\frac{D^{2}}{2}} = L$

Reorder

$L = \sqrt{\frac{D^{2}}{2}}$

Now, the value of L can be calculated by substituting 12.73 for D

$L = \sqrt{\frac{12.73^{2}}{2}}$

$L = \sqrt{\frac{162.0529}{2}}$

$L = \sqrt{{81.02645}$

$L = 9.001469325$

$L = 9.0015$ (Approximated)

Hence, the length of the sides of the square is approximately 9.0015

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3 years ago

What is the equation of the oblique asymptote? h(x) = x² – 3x - 4/x + 2

NNADVOKAT [17]

Simplifying h(x) gives

h(x) = (x² - 3x - 4) / (x + 2)

h(x) = ((x² + 4x + 4) - 4x - 4 - 3x - 4) / (x + 2)

h(x) = ((x + 2)² - 7x - 8) / (x + 2)

h(x) = ((x + 2)² - 7 (x + 2) - 14 - 8) / (x + 2)

h(x) = ((x + 2)² - 7 (x + 2) - 22) / (x + 2)

h(x) = (x + 2) - 7 - 22/(x + 2)

h(x) = x - 5 - 22/(x + 2)

An oblique asymptote of h(x) is a linear function p(x) = ax + b such that

$\displaystyle \lim_{x\to\pm\infty} h(x) - p(x) = 0$

In the simplified form of h(x), taking the limit as x gets arbitrarily large, we obviously have -22/(x + 2) converging to 0, while x - 5 approaches either +∞ or -∞. If we let p(x) = x - 5, however, we do have h(x) - p(x) approaching 0. So the oblique asymptote is the line y = x - 5.

4 0

2 years ago