Answer:
a) x > − 24
b) x < − 3
c) q < 56
Step-by-step explanation:
a) −2/5x−9<9/10
<=> 2/5x + 9 > − 9/10
<=> 2/5x > − 9/10 − 9
<=> 2×2/2×5x > − 9/10 − 9×10/10
<=> 4/10x > − 99/10
<=> x > − 99/4
<=> x > − 24
b) 4x+6<−6
<=> 4x < − 6 − 6
<=> 4x < − 12
<=> x < − 12/4
<=> x < − 3
c) q+12−2(q−22)>0
<=> q+12−2q −2×(−22)>0
<=> (q−2q) + (12+ 44) >0
<=> −q + 56 >0
<=> q < 56
Answer:
B. y=1/3x+4
Step-by-step explanation:
Hi there!
We are given the line PQ and we want to find the line that is perpendicular to it
Perpendicular lines have slopes that are negative and reciprocal. When they are multiplied together, the result is -1
So first, let's find the slope of the line PQ
The point P is given as (-8, 7) and the point Q is given as (-4, -5)
The formula for the slope calculated from two points is where (
) and (
,
) are points
We have the needed information for the slope, but let's label the values of the points to avoid any confusion
x1=-8
y1=7
x2=-4
y2=-5
Now substitute into the formula (m is the slope, and remember: the formula contains SUBTRACTION):
m=
simplify
m=
add
m=-12/4
divide
m=-3
So the slope of the line PQ is -3
As said above, perpendicular lines have slopes that have a product of -1
So to find the slope of the line perpendicular to PQ, use this formula:
-3m=-1
divide both sides by -3
m=1/3
The only line that has a slope of 1/3 is B (y=1/3x+4), so B is the answer.
Hope this helps!
Answer:
4 cm
Step-by-step explanation:
The equation of a parabola with its vertex at the origin can be written as ...
y = 1/(4p)x^2
The problem statement tells us that one point on the parabola is (x, y) = (12, 9). We can put these values into the equation and solve for p, the distance from the focus to the vertex.
9 = 1/(4p)(12^2)
9×4/144 = 1/p = 1/4 . . . . . . . . multiply by the inverse of the coefficient of 1/p
Then p = 4, and the bulb is 4 cm from the vertex.
