Answer:
LB = 12ft
Step-by-step explanation:
m< CAB = 60 because of the triangle sum theorem
We can use triangle sum theorem to find the measure of all the angles in triangle CLA.
m< CAL = 60/2 = 30, because AL is a angle bisector
The m<CLA = 60 because of the triangle sun theorem
Then we can use properties of a 30 - 60 - 90 triangle.
LA = 12
Then, we also know that m< ALC = 30 because that is what is reamining of that angle.
So, we can see that triangle ALB is a isosceles triangle.
Then LA would equal LB by the definition of a Isosceles triangle, so LB would be 12 as well.
Answer:
y = 2
Step-by-step explanation:
from the question which says that y is directly proportional to the positive square root of x can be expressed mathematically by saying
y ∝ √x
y = k√x..................................................... where k is the constant of proportionality.
y = 12, x = 9 , k = ?
from
y = k√x
12 = k√9
12 =3k
divide both sides by the coefficient of k which is 3
12/3 = 3k/3
4 = k
therefore K = 3
now, to find the value of y when x = 1/4
from y = k√x
y = 4√1/4
y = 4 × 1/2
y = 2
therefore the value of y when x = 1/4 in this expression y = k√x is 2
<u>Answer-</u>
<u>Solution-</u>
Given,
the parabola has vertex at (3,5) and focus at (3,9)
It can be easily noticed that focus and vertex lie on the same vertical line,
Hence, the axis of symmetry is a vertical line ( a line perpendicular to x-axis). Also, the focus lies to the top of the vertex so the parabola will open up upwards.
General form of parabola vertex at (h, k)and vertical line of symmetry is,
Putting the values,
We can find the value of 'a' which is distance between vertex and focus by using distance formula,
Taking only +ve value, as the parabola opens upwards.
then the equation becomes,
Compatible numbers are numbers in a problem that are easy to conpute mentally
Answer:
5x -3y = 15
Step-by-step explanation:
First find the slope of the line through ( -3,2) and (2,-1)
m = (y2-y1)/(x2-x1)
=( -1-2)/(2--3)
= -3/(2+3)
= -3/5
We want a line that is perpendicular so the slopes will multiply to -1
m * -3/5 = -1
Multiply each side by -5/3
m * -3/5 * -5/3 = -1 *-5/3
m = 5/3
The slope of the perpendicular line is 5/3
We have a slope and a point
Using point slope form
y-y1 = m(x-x1)
y-0 = 5/3( x-3)
y = 5/3( x-3)
Distribute
y = 5/3x -5
Multiply each side by 3
3*y = 3(5/3x -5)
3y = 5x - 15
Subtract 5x from each side
-5x+3y = -15
Multiply each side by -1
5x -3y = 15
