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3 years ago

LMNP is a rectangle. Find the value of x and the length of each diagonal. LN =7x+9 and MP=9x-9

Mathematics

1 answer:

PilotLPTM [1.2K]3 years ago

7 0

Answer:

see explanation

Step-by-step explanation:

The diagonals of a rectangle are congruent, thus

MP = LN , substitute values

9x - 9 = 7x + 9 ( subtract 7x from both sides )

2x - 9 = 9 ( add 9 to both sides )

2x = 18 ( divide both sides by 2 )

x = 9

LN = 7x + 9 = (7 × 9) + 9 = 63 + 9 = 72

MP = 9x - 9 = (9 × 9) - 9 = 81 - 9 = 72

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Answer:

Given the statement: if y =3x+6.

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Substitute the value of y ;

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Distribute the terms;

$f(x)= 3x^4 + 6x^3$

The derivative value of f(x) with respect to x.

$\frac{df}{dx} =\frac{d}{dx}(3x^4+6x^3)$

Using $\frac{d}{dx}(x^n) = nx^{n-1}$

we have;

$\frac{df}{dx} =(12x^3+18x^2)$

Set $\frac{df}{dx} = 0$

then;

$(12x^3+18x^2) =0$

$6x^2(2x + 3) = 0$

By zero product property;

$6x^2=0$ and 2x + 3 = 0

⇒ x=0 and x = $-\frac{3}{2} = -1.5$

then;

at x = 0

f(0) = 0

and

x = -1.5

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Step-by-step explanation:

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$\bold{\huge{\orange{\underline{ Solution }}}}$

$\bold{\underline{ Given :- }}$

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$\bold{\underline{ To \: Find :- }}$

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$\bold{\underline{ Let's \: Begin :- }}$

According to the question,

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$\sf{ = 140 × 18.75 }$

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