Select the correct answer.

A line passes through the points (–6, 4) and (–2, 2). Which is the equation of the line?

insens350 [35]

Answer:

y=-1/2x+1

Step-by-step explanation:

We can use the points to find the slope of the line.

Equation: y₂-y₁/x₂-x₁

2-4/-2-(-6)

2-4/-2+6

-2/4

-1/2 is the slope of the line

So the equation is y=-1/2x+b

We can substitute one of the x-coordinates and the matching y-coordinate into this equation:

2=-1/2*(-2)+b

2=1+b

1=b

b=1

Therefore, the equation is y=-1/2x+1

5 0

3 years ago

Luis bought a box of 84 nails.He used 3/4 the nails in the box.How many nails did he use?

Taya2010 [7]

Answer: 63

Step By Step: Put 84 over a 1 to make this easier. One in the format, multiply 84/1 by 3/4. You should get 252/4. One you simply this you should get 63.

6 0

3 years ago

If a polygon has a vertex at (161, -329) and it is translated 168 units to the right, what are the coordinates of that vertex's

bearhunter [10]

Vertex of the polygon is (161, -329)

The new vertex is shifted 168 units to the right. A horizontal shift can be achieved be adding or subtracting the number from the x-coordinate. A change in the y coordinate brings the vertical shift. So in this case the x-component will change only and y component will be the same.

A shift towards right means, the value of x component is increase as x gets larger as we move towards right on the graph. So moving 168 units to the right, we will get the following vertex (329 , -329)

Thus, the new vertex of the polygon will be at the point (329, -329)

5 0

3 years ago

LINEAR ALGEBRA

kenny6666 [7]

Answer:

The value of the constant $k$ so that $\vec u_{3}$ is a linear combination of $\vec u_{1}$ and $\vec u_{2}$ is $\frac{7}{10}$ .

Step-by-step explanation:

Let be $\vec u_{1} = [2,3,1]$ , $\vec u_{2} = [4,1,0]$ and $\vec u_{3} = [1, 2,k]$ , $\vec u_{3}$ is a linear combination of $\vec u_{1}$ and $\vec u_{3}$ if and only if:

$\alpha_{1} \cdot \vec u_{1} + \alpha_{2} \cdot \vec u_{2} +\alpha_{3}\cdot \vec u_{3} = \vec O$ (Eq. 1)

Where:

$\alpha_{1}$ , $\alpha_{2}$ , $\alpha_{3}$ - Scalar coefficients of linear combination, dimensionless.

By dividing each term by $\alpha_{3}$ :

$\lambda_{1}\cdot \vec u_{1} + \lambda_{2}\cdot \vec u_{3} = -\vec u_{3}$

$\vec u_{3}=-\lambda_{1}\cdot \vec u_{1}-\lambda_{2}\cdot \vec u_{2}$ (Eq. 2)

$\vec O$ - Zero vector, dimensionless.

And all vectors are linearly independent, meaning that at least one coefficient must be different from zero. Now we expand (Eq. 2) by direct substitution and simplify the resulting expression:

$[1,2,k] = -\lambda_{1}\cdot [2,3,1]-\lambda_{2}\cdot [4,1,0]$

$[1,2,k] = [-2\cdot\lambda_{1},-3\cdot \lambda_{1},-\lambda_{1}]+[-4\cdot \lambda_{2},-\lambda_{2},0]$

$[0,0,0] = [-2\cdot \lambda_{1},-3\cdot \lambda_{1},-\lambda_{1}]+[-4\cdot \lambda_{2},-\lambda_{2},0]+[-1,-2,-k]$

$[-2\cdot \lambda_{1}-4\cdot \lambda_{2}-1,-3\cdot \lambda_{1}-\lambda_{2}-2,-\lambda_{1}-k] =[0,0,0]$

The following system of linear equations is obtained:

$-2\cdot \lambda_{1}-4\cdot \lambda_{2}= 1$ (Eq. 3)

$-3\cdot \lambda_{1}-\lambda_{2}= 2$ (Eq. 4)

$-\lambda_{1}-k = 0$ (Eq. 5)

The solution of this system is:

$\lambda_{1} = -\frac{7}{10}$ , $\lambda_{2} = \frac{1}{10}$ , $k = \frac{7}{10}$

The value of the constant $k$ so that $\vec u_{3}$ is a linear combination of $\vec u_{1}$ and $\vec u_{2}$ is $\frac{7}{10}$ .

4 0

4 years ago

CAN SOMEONE HELP ME DO THIS PROBLEM QUICK ILL GIVE BRAINLIEST<br><br><br> <img src="https://tex.z-dn.net/?f=%5Csqrt%5B3%5D8%2F%7

insens350 [35]

Cube root of 8=2 so the fraction simplifies to 2/27 (in decimal form it’s .074 repeating)

4 0

3 years ago