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3 years ago

Solve w^2+13w+42=0 by factoring.

Mathematics

2 answers:

Bingel [31]3 years ago

4 0

Move all terms to the left side and set equal to zero. Then set each factor equal to zero.
w = -6, -7
Hope this helps! :)

andre [41]3 years ago

3 0

The answer is therefore (w+7)(w+6), meaning the zeros are -7 and -6
Hope this helps

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Find a vector equation and parametric equations for the line segment that joins p to q.P(0, - 1, 1), Q(1/2, 1/3, 1/4)

lakkis [162]

Answer:

vector equation:

$\overrightarrow{PQ}=\begin{bmatrix}1/2}\\4/3\\-3/4\end{bmatrix}$

parametric equations:

$r_x = \dfrac{1}{2}t\\r_y = -1 +\dfrac{4}{3}t\\r_z = 1=\dfrac{3}{4}t$

Step-by-step explanation:

The coordinates of the points are given as:

P(0,-1,1) and Q(1/2,1/3,1/4)

the coordinates of any points are also position vectors (vectors starting from the origin to that point), and can be represented as:

$\overrightarrow{OP} = 0\hat{i}-1\hat{j}+1\hat{k}$

$\overrightarrow{OP} = \begin{bmatrix}0\\-1\\1\end{bmatrix}$

similarly,

$\overrightarrow{OQ} =\dfrac{1}{2}\hat{i}+\dfrac{1}{3}\hat{j}+\dfrac{1}{4}\hat{k}$

$\overrightarrow{OQ} = \begin{bmatrix}1/2}\\1/3\\1/4\end{bmatrix}$

the vector PQ can be described as:

$\overrightarrow{PQ}=\overrightarrow{OQ}-\overrightarrow{OP}$

$\overrightarrow{PQ}=\begin{bmatrix}1/2}\\1/3\\1/4\end{bmatrix}-\begin{bmatrix}0\\-1\\1\end{bmatrix}$

$\overrightarrow{PQ}=\begin{bmatrix}1/2}\\4/3\\-3/4\end{bmatrix}$

this is the vector equation of the line segment from P to Q.

to make the parametric equations:

we know that the general equation of a line is represented as:

$\overrightarrow{r} = \overrightarrow{r_0} + t\overrightarrow{d}$

here, $\overrightarrow{r_0}$ : is the initial position or the starting point. in our case it is the position vector of P

and $\overrightarrow{d}$ : is the direction vector or the direction of the line. in our case that's PQ vector.

$\overrightarrow{r} = \begin{bmatrix}0\\-1\\1\end{bmatrix} + t\begin{bmatrix}1/2}\\4/3\\-3/4\end{bmatrix}$

that parametric equations can now be easily formed:

$\begin{bmatrix}r_x\\r_y\\r_z\end{bmatrix} = \begin{bmatrix}0\\-1\\1\end{bmatrix} + t\begin{bmatrix}1/2}\\4/3\\-3/4\end{bmatrix}$

$r_x = \dfrac{1}{2}t\\r_y = -1 +\dfrac{4}{3}t\\r_z = 1=\dfrac{3}{4}t$

these are the parametric equations of the line PQ

4 0

3 years ago

WRITE THE EQUATION THAT DESCRIBES THIS FUNCTION:

uranmaximum [27]

Y=-2+-1x

I hope this helps!

6 0

3 years ago

A Chemist needs to mix a 20% acid solution with a 50% acid solution to obtain 15 liters of a 34% acid solution. How many liters

Nuetrik [128]

8 litres (amount of 20% solution needed) and 7 litres for (amount of 50% solution needed)

<u>Step-by-step explanation:</u>

Let consider ‘x’ for 20% acid solution and (15 – x) for 50% acid solution. And so, the equation would be as below,

20% in x + 50% in (15 – x) = 15 litres of 34%

Convert percentage values, we get

0.20(x) + 0.50 (15 – x) = 15 (0.34)

0.20 x + 7.5 – 0.50 x = 5.1

-0.3 x + 7.5 = 5.1

0.3 x = 7.5 – 5.1

0.3 x = 2.4

$x = \frac{2.4}{0.3} = 8 litres (amount of 20 \% solution needed)$

Apply ‘x = 8’ value in (15 – x) we get,

15 – 8 = 7 litres

The value of 7 litres for (amount of 50% solution needed)

8 0

3 years ago

I need help pweaseee

torisob [31]

Answer:

Its c. there is no solution :)

Step-by-step explanation:

8 0

3 years ago

36 divided by 10 = ?

Fittoniya [83]

It's 3.6 hope this helps

4 0

3 years ago

Read 2 more answers