Answer:
Step-by-step explanation:
This is right triangle trig. The side opposite the x is 8, and the side adjacent to the x is 5. The tangent ratio uses those sides. We need to find what angle has a tangent of 8/5. To do this, make sure your calculator is in degree mode. Then hit "2nd" then tan and you will see tan with a little -1 and a parenthesis. Enter 8/5 and hit "enter" and you will get an angle measure of 57.9946. Rounded to the nearest degree this is 58 degrees. That's your answer!
Answer:
x=1
y=-4
Step-by-step explanation:
4x+y=0 -> y= -4x
2(-4x)+x=-7
-8x+ x=-7
-7x=-7
x=-7/-7=1
y=-4 . 1 = -4
We have that
f(x) = –4x²<span> + 24x + 13
</span>
we know that
The vertex form for a parabola that opens up or down is:
f(x) = a(x - h)^2 + k
in the given equation, <span>a=-4</span><span>, therefore we add zero to the original equation in the form of </span><span>4h</span>²<span>−4h</span>²
f(x) = –4x² + 24x + 4h²−4h² +13
<span>Factor 4 out of the first 3 terms and group them
</span>f(x) = –4*(x² -6x +h²) +4h² +13
<span>We can find the value of h by setting the middle term equal to -2hx
</span>−2hx=−6x
<span>h=3</span><span> and </span><span>4h</span>²<span>=<span>36
</span></span>f(x) = –4*(x² -6x +9) +36 +13
we know that the term (x² -6x +9) is equals to------> (x-3)²
so
f(x) = –4*(x-3)² +49
the answer isf(x) = –4*(x-3)² +49
Answer:
Step-by-step explanation:
The center of the circle is the midpoint of the two end points of the diameter.
Formula
Center = (x2 + x1)/2 , (y2 + y1)/2
Givens
x2 = 4
x1 = - 10
y2 = 6
y1 = - 2
Solution
Center = (4 - 10)/2, (6 - 2)/2
Center = -6/2 , 4/2
Center = - 3 , 2
So far what you have is
(x+3)^2 + (y - 2)^2 = r^2
Now you have to find the radius.
You can use either of the endpoints to find the radius.
find the distance from (4,6) to (-3,2)
r^2 = ( (x2 - x1)^2 + (y2 - y1)^2 )
x2 = 4
x1 = -3
y2 = 6
y1 = 2
r^2 = ( (4 - -3)^2 + (6 - 2)^2 )
r^2 = ( (7)^2 + 4^2)
r^2 = ( 49 + 16)
r^2 = 65
Ultimate formula is
(x+3)^2 + (y - 2)^2 = 65
The radius is √65 = 8.06
