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2 years ago

Help me pls thank you alot!

Mathematics

2 answers:

damaskus [11]2 years ago

4 0

Your answer will be -1/7

Rainbow [258]2 years ago

4 0

Answer -1/7..........

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The line through (-1/2, -7/2) and (2, 14) in slope intercept form??

icang [17]

To find the equation of a line in slope-intercept form given two points, we must arrange the points this way to find the slope ( $m$ ):

$m = \frac{y_{2}-y _{1}}{x_{2}-x_{1}}$

We can replace the variables in this equation with the values from the points we have been given, ( $\frac{-1}{2}, \frac{-7}{2}$ ) and (2, 14). We know that the x-values always come first in an ordered pair, so we can put those in our equation first.
It doesn't really matter which x-value goes in which x-value slot in the equation as long as you match up the y-values in the same fashion. But for the sake of convenience, we will call the 2 in the second ordered pair $x_{2}$ and the $\frac{-1}{2}$ in the first ordered pair $x_{1}$ .
Now, we can match these values in our equation, and while we're at it, we can substitute the appropriate y-values into their places as well.

$m = \frac{y_{2}-y _{1}}{x_{2}-x_{1}}$

$m = \frac{14 - \frac{-7}{2} }{2 - \frac{-1}{2} }$

Now, we can see that we are subtracting negatives in this equation. Remember that whenever you subtract a negative, it is the same as adding a positive. So, this equation could be rewritten as

$m = \frac{14 + \frac{7}{2} }{2 + \frac{1}{2} }$

and we can change the improper fraction in the numerator into a mixed number for ease of addition.

$m = \frac{14 + 3 \frac{1}{2} }{2+ \frac{1}{2} }$

And here, we can add, since it's made simple for us.

$m = \frac{17 \frac{1}{2} }{2 \frac{1}{2} }$

Finally, to get the slope we can complete the fraction by dividing.

$17.5 ÷ 2.5 = 7$

The slope of this equation, $m$ , is 7, and so far, our equation looks like this:

$y = 7m + b$

Now, to find y-intercept.

To do this, we simply have to substitute one of the ordered pairs in for the appropriate x- and y-values and solve. To make it easier on ourselves, we can use (2, 14) so we don't have to deal with negative numbers or fractions.

$y = 7x + b$

Let us substitute in our values.

$14=7(2)+b$

Now, we can solve by multiplying the 7 and 2.

$14=14+b$

Here, we can subtract 14 from both sides, since it is added to both in the equation, and we are left with

$0 = b$

which can be flipped around to show

$b=0$

The y-intercept of this line is 0.

Now, we can make this known in our equation like this:

$y=7x+0$

Or, for neatness' sake, we can just say

$y=7x$

which is your final equation.

The line through ( $\frac{-1}{2}, \frac{-7}{2}$ ) and (2, 14) in slope-intercept form is <span> $y=7x$ .
Hope that helped! =) </span>

7 0

3 years ago

Oscar wants to put $1000 in a bank account that

Feliz [49]

Answer:

he would end up with 3000$ in 10 years with simple interest

Step-by-step explanation:

8 0

3 years ago

Find the angle between u =the square root of 5i-8j and v =the square root of 5i+j.

fenix001 [56]

Answer:

The angle between vector $\vec{u} = 5\, \vec{i} - 8\, \vec{j}$ and $\vec{v} = 5\, \vec{i} + \, \vec{j}$ is approximately $1.21$ radians, which is equivalent to approximately $69.3^\circ$ .

Step-by-step explanation:

The angle between two vectors can be found from the ratio between:

their dot products, and
the product of their lengths.

To be precise, if $\theta$ denotes the angle between $\vec{u}$ and $\vec{v}$ (assume that $0^\circ \le \theta < 180^\circ$ or equivalently $0 \le \theta < \pi$ ,) then:

$\displaystyle \cos(\theta) = \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|}$ .

<h3>Dot product of the two vectors</h3>

The first component of $\vec{u}$ is $5$ and the first component of $\vec{v}$ is also

The second component of $\vec{u}$ is $(-8)$ while the second component of $\vec{v}$ is $1$ . The product of these two second components is $(-8) \times 1= (-8)$ .

The dot product of $\vec{u}$ and $\vec{v}$ will thus be:

$\begin{aligned} \vec{u} \cdot \vec{v} = 5 \times 5 + (-8) \times1 = 17 \end{aligned}$ .

<h3>Lengths of the two vectors</h3>

Apply the Pythagorean Theorem to both $\vec{u}$ and $\vec{v}$ :

$\| u \| = \sqrt{5^2 + (-8)^2} = \sqrt{89}$ .
$\| v \| = \sqrt{5^2 + 1^2} = \sqrt{26}$ .

<h3>Angle between the two vectors</h3>

Let $\theta$ represent the angle between $\vec{u}$ and $\vec{v}$ . Apply the formula $\displaystyle \cos(\theta) = \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|}$ to find the cosine of this angle:

$\begin{aligned} \cos(\theta)&= \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|} = \frac{17}{\sqrt{89}\cdot \sqrt{26}}\end{aligned}$ .

Since $\theta$ is the angle between two vectors, its value should be between $0\; \rm radians$ and $\pi \; \rm radians$ ( $0^\circ$ and $180^\circ$ .) That is: $0 \le \theta < \pi$ and $0^\circ \le \theta < 180^\circ$ . Apply the arccosine function (the inverse of the cosine function) to find the value of $\theta$ :