Answer:
Standard form of the line with point (4,-8) and slope of 1/4 is
-x + 4 y = -36.
Step-by-step explanation:
The slope of the line equation = 1/4
The point is given as (4,-8).
Now, by POINT SLOPE formula,
The line equation with slope m nad point (x0,y0) is given as:
(y - y0) = m (x -x0)
So, the line equation here is given as
Now, the standard form of line equation is Ax + By = C
Here, 4y = x - 36 ⇒ 4y - x = -36
or, -x + 4y = -36 is the standard form.
Hence,standard form of the line with point (4,-8) and slope of 1/4
is -x + 4y = -36.
Answer:
The solution of the linear equation is: (6,7)
Step-by-step explanation:
This being that:
x + y = 13
1/2x + y = 10
What you do in order to find the solution is either (2 ways):
- Substitution
- Elimination
I'm sure that either way, you'll get the same thing. I used: Substitution.
To do this choose either if you want to find [x] or [y] first, then substitute it in. I will choose to find [x] first.
<h2>x + y = 13</h2><h2><u> - y </u> </h2><h2>x = 13 - y</h2>
Now substitute it into:
1/2x + y = 10
1/2(13 - y) + y = 10
1/2(13 -y) + y= 10
<h2>Then to get rid of fraction, instead of dividing, you multiply with reciprocal</h2><h2>1/2 · 2/1 (They cancel out) Leaving you with:</h2><h3 /><h3>(13 - y) 2(y) = 2(10)</h3><h3>(Everything is multiplied, except for 13 - y, because it had parenthesis to protect it.)</h3><h3>13 - y + 2y = 20</h3><h3 /><h2>13 + y = 20</h2><h2><u>- 13 - 13</u></h2><h2> <u>y = 7</u></h2><h2 /><h2>You now have your [y] for your coordinate.</h2><h2>(x, 7), now time to find your [x]</h2><h2 />
Now you substitute your [y] into your equation:
1/2x + (7) = 10
<h2>
1/2x + 7 = 10</h2><h2><u>
-7 = -7</u></h2><h2>
1/2x = 3</h2><h2>
(To get rid of fraction, multiply on both sides with reciprocal)</h2><h2>
1/2 cancels out with 2/1</h2><h2>
x = 2(3)</h2><h2>
x = 6</h2><h2>You now have your [x] coordinate.</h2><h2 /><h2>This is your coordinate: </h2><h2>(6,7)</h2><h2>
</h2>
Answer:
d. The equation has one solution and there is not enough information to determine the direction of the parabola.
Step-by-step explanation:
For a general quadratic equation
y = ax² +bx +c
the solution is
The discriminant (D) is the part of the quadratic formula underneath the radical: b² - 4ac.
D tells us whether there are
- two different real solutions
- two identical real solutions ("one solution")
- two complex solutions.
If D= 0,
and there are two identical solutions ("one solution").
The direction of the parabola depends on the sign of a.
That information is not given, so we cannot determine the direction of the parabola.
I think it’s what ever you have left after paying, I’m sorry if this is wrong.
