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4 years ago

What is the simplest form of this expression? (x − 4)(x2 + 3x − 5)

Mathematics

2 answers:

valentina_108 [34]4 years ago

7 0

Answer:

x^3 - x^2 - 17 x + 20

Step-by-step explanation:

Expand the following:

(x - 4) (x^2 + 3 x - 5)

| | | | x | - | 4

| | x^2 | + | 3 x | - | 5

| | | | -5 x | + | 20

| | 3 x^2 | - | 12 x | + | 0

x^3 | - | 4 x^2 | + | 0 | + | 0

x^3 | - | x^2 | - | 17 x | + | 20:

Answer: x^3 - x^2 - 17 x + 20

Marina86 [1]4 years ago

4 0

For this case we must simplify the following expression:

$(x-4) (x ^ 2 + 3x-5) =$

We must apply distributive property term by term, taking into account that:

$+ * - = -\\- * - = +$

To multiply powers of the same base, we place the same base and add the exponents.

So:

$x ^ 3 + 3x ^ 2-5x-4x ^ 2-12x + 20 =$

We add similar terms:

$x ^ 3-x ^ 2-17x + 20$

Answer:

$x ^ 3-x ^ 2-17x + 20$

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Let |u| = 10 at an angle of 45° and |v| = 13 at an angle of 150°, and w = u + v. What is the magnitude and direction angle of w?

mixer [17]

Given:

$|u|=10$ at an angle of 45°.

$|v|=13$ at an angle of 150°.

$w=u+v$

To find:

Magnitude and direction angle of w.

Solution:

We have,

$w=u+v$

$\theta = 45^\circ, \phi = 150^\circ$

Now,

$u_x=|u|\cos \theta=10\cos 45^\circ=7.071$

$u_y=|u|\sin \theta=u_y=10\sin 45^\circ=7.071$

$v_x=|v|\cos \phi=13\cos 150^\circ=-11.25833$

$v_y=|v|\sin \phi=u_y=13\sin 150^\circ=6.5$

Using these information, we get

$R_x=u_x+v_x=7.071-11.25833=-4.18733$

$R_y=u_y+v_y=7.071+6.5=13.571$

$\text{Direction angle}=\tan^{-1}(\dfrac{R_y}{R_x})$

$\text{Direction angle}=\tan^{-1}(\dfrac{13.571}{-4.18733})$

$\text{Direction angle}=-72.8239$

$\text{Direction angle}=107.1476$

$\text{Direction angle}\approx 107.1$

Now,

$|w|=\sqrt{(|u|\cos \theta +|v|\cos \phi)^2+(|u|\sin \theta +|v|\sin \phi)^2}$

$|w|=\sqrt{(10\cos(45)+13\cos 150)^2+(10\sin(45)+13\sin 150)^2}$

$|w|=\sqrt{(10(\dfrac{1}{\sqrt{2}})+13(-\dfrac{\sqrt{3}}{2}))^2+(10(\dfrac{1}{\sqrt{2}})+13(\dfrac{1}{2}))^2}$

$|w|=14.20236$

$|w|\approx 14.20236$

Therefore, the correct option is D.

4 0

3 years ago

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snow_tiger [21]

Answer:

$123.62

Step-by-step explanation:

85.10 + 23.95 + 8.47 = 117.52

117.52 + 100 + 2.50 = 220.02

$343.64 - $220.02 = $123.62

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3 years ago

Two-step equations

cupoosta [38]

Answer: K = 44

Explanation:

K + 12 = 56

K = 56 - 12

K = 44

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3 years ago

What are the equations for the asymptotes of this hyperbola

Fofino [41]

Answer:

its d

Step-by-step explanation:

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3 years ago

A prism is completely filled with 2304 cubes that have edge length of 1/4 cm what is the volume of the prism

Tomtit [17]

Since the prism completely filled with 2304 cubs

Since the edge of the cube is 1/4 cm

Since the volume of the cube = edge x edge x edge

Then find the volume of 1 cube, then multiply it by the number of cubes to find the volume of the prism

$V_c=\frac{1}{4}\times\frac{1}{4}\times\frac{1}{4}=\frac{1}{64}cm^3$

Multiply it by 2304

$V_P=2304\times\frac{1}{64}=36cm^3$

The volume of the prism is 36 cm^3

3 0

1 year ago