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3 years ago

10

One point on a line is (4, 6). The slope of the line is 3/4. Choose all of the following that could be another point on the line

.
a. (0, 3)
b. (-8, -3)
c. (0, -3)
d. (-8, -1)
e. (12, 12)

1 answer:

Crank3 years ago

8 0

The answer is d. I believe it was for mine

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Factor each expression completely.<br> 5x^2 + 10x<br><br> SHOW YOUR WORK!!!

Snowcat [4.5K]

5x^2+10x

factorise 5 and 10 first
then factorise the x

so 5x(x+2)
completed :))

hope this helped :)

8 0

3 years ago

The price of a technology stock was $9.64 yesterday. Today, the price rose to $9.77 . Find the percentage increase. Round your a

belka [17]

9.64/9.77-1 x-1= 0.01330603889 round to the nearest tenth 1.3%

3 0

4 years ago

Read 2 more answers

Let U = {1,2,3,4,5,6,7,8,9,10}, A = {1,3,5,7,9}, B = {2,4,6,8,10} and C = {1,2,3,4} find (i) U' ii) A∩A' iii) A – ( B U C) iv) A

Artyom0805 [142]

Answer:

(i) U' = Φ

(ii) A∩A' = Φ

(iii) A – ( B U C) = {5,7,9}

(iv) A' U ( B U C ) = {2,4,6,8,10}

(v) A' U ( B' ∩ C') = {2,4,5,6,7,8,9,10}

Step-by-step explanation:

8 0

3 years ago

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

A cube has an edge of 2 feet. The edge is increasing at the rate of 3 feet per minute. Express the volume of the cube as a funct

Harrizon [31]

Answer:

36 ft³/min

Step-by-step explanation:

Given that:

Let assume that length of the cube = m

Then;

m = 2 feet &;

$\dfrac{dm}{dt}= 3 \ ft/ min$

The volume (V) = m³

By differentiating with respect to t, we get

$\dfrac{dV}{dt} = 3m^2 \dfrac{dm}{dt}$

$\dfrac{dV}{dt} = 3(2)^2 \times 3$

$\dfrac{dV}{dt} = 12 \times 3$

= 36 ft³/min

4 0

3 years ago