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2 years ago

Solve the system of linear equations. 3x−2y=1 9x−6y=3

1 answer:

8 0

Get the y by itself

-2y= -3x + 1

Divide -2 to everything

y= 3/2x - 1/2

Other equation (get y by itself)

-6y= -9x + 3
y=3/2x - 1/2

Use substitution

3/2x-1/2=3/2-1/2

0=0

All real numbers (any value of x makes the equation true)

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Let u = (1, k) and v = (2, 1). Find k such that The distance between u and v is 1 u and v are orthogonal The angle between u and

SVETLANKA909090 [29]

Answer:k=1,k=-2,k= $8\pm 5\sqrt{3}$

Step-by-step explanation:

Given two vectors

$u=1\hat{i}+k\hat{j}$

$v=2\hat{i}+1\hat{j}$

$\left ( i\right )$ Distance between them is given by

$|u-v|=\sqrt{\left ( 2-1\right )^2+\left ( 1-k\right )^2}=1$

squaring both side

$1^{2}+\left ( 1-k\right )^2=1$

$k^2-2k+1=0$

$\left ( k-1\right )^2=0$

k=1

$\left ( ii\right )$

angle between u and v is 90 i.e. orthogonal

$u\dot v=0$

$\left ( 1\hat{i}+k\hat{j}\right )\dot \left ( 2\hat{i}+1\hat{j}\right )$ =0

2+k=0

k=-2

$\left ( iii\right )$

angle between u & v is $\frac{\pi }{3}$

$u\dot v=|u||v|cos\left (\frac{\pi }{3}\right )$

$|u|=\sqrt{1^2+k^2}$

$|v|=\sqrt{2^2+1^2}$

$2+k=\left ( \sqrt{1+k^2}\right )\left ( \sqrt{5}\right )cos\left ( \frac{\pi }{3}\right )$

$\left ( 4+2\right )^2=\left ( 1+k^2\right )5$

$k^2-16k-11$ =0

k= $8\pm 5\sqrt{3}$

7 0

2 years ago

Graph a line with a slope of - 3/4 that contains the point (2 3)

Savatey [412]

Answer:

Step-by-step explanation:

1. Graph point (2, 3)

2. Go down 3, 4 to the right or up 3 and 4 to the left

3. Repeat until you have about 3 to 4 points

4. Create a line

6 0

3 years ago

X^2-6x+5=0 solve with quadratic formula

Yuliya22 [10]

Answer: x1 = 5

x2 = 1

Step-by-step explanation:

1. Identify the coefficients

2. Move the constant to the right side of the equation and combine

3. Complete the square

4. Solve for x

7 0

1 year ago

Read 2 more answers

How to work out 12.5% of a number

mario62 [17]

Step-by-step explanation:

12.5÷100 × 5

=0.125×5

=0.625

4 0

2 years ago

How many solutions does the following system have 2x+3y=12 2x+3y=18

Alika [10]

Answer:

Mmm

Step-by-step explanation:

wait I tell the answer

4 0

2 years ago