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2 years ago

What is an equation of the line that passes through the points (3, 1)(3,1) and (-3, -7)(−3,−7)?

Mathematics

1 answer:

rusak2 [61]2 years ago

3 0

Answer:

y = (4/3)x - 3

Step-by-step explanation:

What is an equation of the line that passes through the points (3, 1) and (-3, -7)? (Do not repeat the coordinates of the points.)

First we need to find the slope of the line through these two points. From (-3, -7) to (3, 1), x increases by 6 (which is the 'run') and y increases from -7 to 1 ( a 'rise' of 8). Thus, the slope of this line is m = rise/run = 8/6, or m = 4/3.

Using the point-slope formula as our starting point, we insert the known values m = 4/3 and point (3, 1):

y - k = m(x - h) becomes y - 1 = (4/3)(x - 3). This in itself is a satisfactory answer. We could also write this equation in slope-intercept form, as follows:

y = 1 + (4/3)x - 4, or

y = (4/3)x - 3

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Write an equation for a parabola in which the set of all points in the plane are equidistant from the focus and line F(-6,0); x=

Bogdan [553]

Step-by-step explanation:

Since we have a vertical directrix, the equation of the parabola is

$(y - k) {}^{2} = 4p(x - h)$

Where p is the distance from the vertex to the directrix.

or the distance from the vertex to the focus.

Since we have a sideways parabola, let use the point for the directrix is (-6,0). So let find the midpoint of (-6,0) and (6,0). That would be our vertex.

$\frac{ - 6 + 6)}{2} = 0$

$\frac{0 + 0}{2} = 0$

So our vertex is (0,0).

So our equation become

${y}^{2} = 4px$

The distance from the focus and directrix is 6.

So p=6.

${y}^{2} = 24x$

So p is 6.

Since p is 6,

$\frac{ {y}^{2} }{24} = x$

3 0

1 year ago

How am I supposed to figure this out if csc Theta(0) has a radical number on the top?

Harman [31]

$\bf csc(\theta)=\cfrac{hypotenuse}{opposite}\implies csc(\theta)=\cfrac{\sqrt{7}}{2}\cfrac{\leftarrow hypotenuse=c}{\leftarrow opposite=b}\\\\
-----------------------------\\\\
\textit{so hmm using the pythagorean theorem, we can say that}\\\\
c^2=a^2+b^2\implies \pm \sqrt{c^2-b^2}=a\qquad 
\begin{cases}
c=hypotenuse\\
b=opposite\\
a=adjacent
\end{cases}\\\\
\textit{we'll assume is the + of the root, since you're not}\\
\textit{given further info on it, that means the I quadrant}\\\\
$

$\bf -----------------------------\\\\
cos(\theta)=\cfrac{a}{c}\qquad sec(\theta)=\cfrac{c}{a}\qquad tan(\theta)=\cfrac{b}{a}\qquad cot(\theta)\cfrac{a}{b}
$

so just find the "adjacent" side, using the pythagorean theorem, and even though the square root can give you +/-, use the positive one, assuming the angle is in the 1st quadrant

keeping in mind, that the 2nd quadrant is feasible as well, since the opposite side of +2 can also be in the 2nd quadrant

but anyhow, use the I quadrant

7 0

2 years ago

Pleas e help ; ^ (((

Yuri [45]

Answer:

$535.25

Step-by-step explanation:

withdrawal means to take out (subtract)

$539.50- $35.50= $504

$504- 23.75= $480.25

deposit means to put in (addition)

$480.25+ $55.00 = $535.25

8 0

2 years ago

What is 3a² bc<br> ² if a= 2 b =3 c =4

RSB [31]

Answer:

If a=2, b=3, c=4,

3a²bc = 3(2)²(3)(4)

= 3×4×3×4

= 12²

= 144

4 0

1 year ago

Read 2 more answers

Find the y intercept

STALIN [3.7K]

Answer:

its -5. The y intercept is where the line touches the y axis

8 0

2 years ago