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2 years ago

Which of the following is equivalent to f(x)?

Mathematics

1 answer:

Fynjy0 [20]2 years ago

6 0

Answer:

D. $x^{-3/2}$

Step-by-step explanation:

Given function:

$f(x) = \frac{1}{x\sqrt{x} }$

Equivalent expression is:

$\frac{1}{x\sqrt{x} } = x^{-1}x^{-1/2} = x^{-1 - 1/2} = x^{-3/2}$

Correct choice is D

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Find the area of quadrilateral ABCD

andreev551 [17]

Answer:

A ≈ 28.5

Step-by-step explanation:

a, b, c

P = a + b + c

Semiperimeter s = $\frac{a+b+c}{2}$

A = $\sqrt{s(s-a)(s-b)(s-c)}$

~~~~~~~~~~~~~~~

$P_{ABC}$ = 4.3 + 2.89 + 6.81 = 14

s = 14 ÷ 2 = 7

$A_{ABC}$ = $\sqrt{7(7-4.3)(7-2.89)(7-6.81)}$ = √14.75901 ≈ 3.84

$P_{BCD}$ = 8.59 + 7.58 + 6.81 = 22.98

s = 22.98 ÷ 2 = 11.49

$A_{BCD}$ = $\sqrt{11.49(11.49-8.59)(11.49-7.58)(11.49-6.81)}$ = √609.7343148 ≈ 24.6928

$A_{ABCD}$ = 3.84 + 24.6928 ≈ 28.5

3 0

2 years ago

There is a parallelogram ABCD with diagonals AC and BD. The diagonals AC and BD intersects each other at point E. Side AB is con

grandymaker [24]

Answer:

SAS theorem

Step-by-step explanation:

Given

$\square ABCD$

$\[ \lvert \[ \lvert AB =\[ \lvert \[ \lvert CD$

$\angle BAC = \angle DCA$

Required

Which theorem shows △ABE ≅ △CDE.

From the question, we understand that:

AC and BD intersects at E.

This implies that:

$\[ \lvert \[ \lvert AE = \[ \lvert \[ \lvert EC$

and

$\[ \lvert \[ \lvert BE = \[ \lvert \[ \lvert ED$

So, the congruent sides and angles of △ABE and △CDE are:

$\[ \lvert \[ \lvert AB =\[ \lvert \[ \lvert CD$ ---- S

$\angle BAC = \angle DCA$ ---- A

$\[ \lvert \[ \lvert BE = \[ \lvert \[ \lvert ED$ or $\[ \lvert \[ \lvert AE = \[ \lvert \[ \lvert EC$ --- S

Hence, the theorem that compares both triangles is the SAS theorem

4 0

2 years ago

66.

Naddik [55]

Answer: 530.66 units²

Step-by-step explanation:

$Area_{(circle)}=\pi r^2\qquad and\qquad r=\dfrac{diameter}{2}\\\\\\\implies Area_{(circle)}=\pi \bigg(\dfrac{diameter}{2}\bigg)^2\\\\\\\text{It is given that the diameter = 26:}\\A=\pi\bigg(\dfrac{26}{2}\bigg)^2\\\\\\.\quad =\pi \cdot 13^2\\\\\\.\quad =169\pi\\\\\\.\quad =\large\boxed{530.66}$