What is the value of x? 3(-9 - 4x) - 4= 8x - 9(x + 12)

Mathematics

2 answers:

Snowcat [4.5K]2 years ago

6 0

Answer:

x=7

Step-by-step explanation:

3(-9 - 4x) - 4= 8x - 9(x + 12)

distribute

-27-12x-4=8x-9x-108

combine like terms

-31-12x=-x-108

add x to both sides

-31-12x+x-108

add 31 to both sides

-12x+x=-108+31

combine like terms

-11x=-77

divide both sides by -11

x=7

Gemiola [76]2 years ago

5 0

Answer:

x=7

Step-by-step explanation:

uhhh yes

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Which description of the vector shown is correct ?

BartSMP [9]

Answer:

(B) The magnitude is 7sqrt2, and the direction angle is approximately 135 degrees.

Step-by-step explanation:

From the figure, the coordinate of the tail of the vector,

$(x_1,y_1)=(3,-6).$

The coordinate of the head of the vector,

$(x_2,y_2)=(-4,1).$

The magnitude of a vector is the length between the head and tail of the vector.

By using the distance formula,

the magnitude of the vector $= \sqrt{(1-(-6))^2+(-4-3)^2}$

$=\sqrt{(7^2+(-7)^2}\\\\=\sqrt{98}\\\\=7\sqrt{2}$

Now, let $\theta$ be the angle made by the vector with the positive direction of the x-axis, so

$\tan\theta = \frac{y_2-y_1}{x_2-x_1}\\\\\Rightarrow \tan\theta = \frac{1-(-6)}{-4-3}=\frac{7}{-7}=-1 \\\\\Rightarrow \theta = \tan^{-1}(-1) \\\\\Rightarrow \theta =\pi- \tan^{-1}1 \\\\\Rightarrow \theta = \pi-\frac{\pi}{4} \\\\\Rightarrow \theta =\frac{3\pi}{4} \\\\\Rightarrow \theta = 135 ^{\circ}.$