Solve the simultaneous equations y-2x=6 y+2x=0

1 answer:

5 0

Y-2x=6 => y=6+2x
Y+2x=0
(6+2x) + 2x = 0
6 + 4x = 0
4x= 6
X=6/4
X= 3/2
Y=6+2x
Y=6+2. 3/2
Y= 6 + 3
Y=9
Check: y-2x=6
9-2. 3/2 = 6
9 - 3 = 6

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70 POINTSS!!!! URGETT PLS HELP!! Vectors t = −5i + 2j, u = −3i + 7j, and v = 8i + 20j are given.

LUCKY_DIMON [66]

The angle between the vectors t and u is 45°. And the vector t and vector w are orthogonal to each other.

<h3>What is a vector?</h3>

The quantity which has magnitude, direction and follows the law of vector addition is called a vector.

The vectors are given below.

t = −5i + 2j, u = −3i + 7j, and v = 8i + 20j

Part A: Then the angle between vectors t and u will be

$\cos \theta = \dfrac{\overrightarrow{a} \cdot \overrightarrow{b}}{|\overrightarrow{a}| + |\overrightarrow{b}|}$

Then we have

cos θ = [(−5i + 2j)(−3i + 7j)] / [√{(-5²) + 2²} + √{(-3)² + 7²}]

cos θ = 1 / √2

θ = 45°

Part B: c is a scalar

If $\rm \overrightarrow{\rm v} = (a, b)$ , then $\rm c\overrightarrow{\rm v} = c(ca, cb)$

Let c = 2, then we have

$\overrightarrow{\rm w} = c\overrightarrow{v}\\\\\overrightarrow{\rm w} = (2*8, 2*20)\\\\\overrightarrow{\rm w} = (16, 40)$

Part C: Use the dot product to determine if t and w are parallel or orthogonal.

$\overrightarrow{\rm t} \cdot \overrightarrow{\rm w} = (-5, 2)(16, 40)\\\\ \overrightarrow{\rm t} \cdot \overrightarrow{\rm w} = -5*16+ 2*40\\\\ \overrightarrow{\rm t} \cdot \overrightarrow{\rm w} = -80+ 80\\\\ \overrightarrow{\rm t} \cdot \overrightarrow{\rm w} = 0$