Answer:
y = 2/3x + 7/3
Step-by-step explanation:
We know
The line pass through the point (4,5)
The equation is: y = 2/3x - 4
m = 2/3
To solve this, we can use the fact that parallel lines have the same slope. Since the parallel line we're looking for has the same slope, we can use the point-slope form of a linear equation to find its equation:
y - y1 = m(x - x1)
y - 5 = 2/3(x - 4)
y - 5 = 2/3x - 8/3
y = 2/3x + 7/3
So, the answer is y = 2/3x + 7/3
(B) f(t) = 4(t − 1)2 + 3; the minimum height of the roller coaster is 1 meter from the ground
(C) f(t) = 4(t − 1)2 + 2; the minimum height of the roller coaster is 2 meters from the ground
(D) f(t) = 4(t − 1)2 + 2; the minimum height of the roller coaster is 1 meter from the ground
The function is a parabola, and the problem asks to transform the equation into f(t)=a(x-h)2 + k
Given f(t) = 4t2 -8t +7
= (4t2 - 8t + 4) + 7 - 4
=4 (t2 - 2t + 1) + 3
= 4 (t-1) 2 +3
This removes C and D from the viable choices.
Differentiating the f(t),
f’(t) = 8t – 8, the maximum/minimum value occurs at f’(t) = 0
0 = 8t – 8
t = 1
determining if maximum or minimum, f”(t) > 0 if minimum, f”(t) < 0 maximum
f”(t) = 8 > 0, therefore minimum
f(1) =4(1)^2 – 8(1) +7
= 3
Therefore, minimum height is 3.
Answer:
T= 4 s (second option).
Answer:
The answer is B
Step-by-step explanation:
or the triangle should be on the positive side of the x-axis.
How would you "undo" each of those operations
Which operation should you "undo" first why?? Please I need help
x = 39
x = 29
y = 61
y = 29
z = 61
z = 29
answer:
x = 29
y = 29
z = 61
step-by-step explanation:
all angles in a triangle must equal 180 degrees.
we were already given the angle degree of 61 degrees so we must include that in our formula to determine the degree of y.
the line in the middle already gives us two more angles because they both are 90 degrees for being a perfect quarter turn.
so to figure out y,
we must add 61+90 and then subtract the sum of that from 180.
so, 61+90 = 150 and 180-151 = 29
therefore,
we can conclude that y = 29
now, to determine the degrees of x and z we do the same thing.
we already know one angle equals 90 degrees.
180-90 = 90
that concludes that x and z must have a sum of 90.
if we use our choices,
39+61 = 100 (no)
39+29 = 68 (no)
29+61 = 90 (CORRECT)
29+29 = 28 (no)
therefore, x = 29 and z = 61
so, in total :
x = 29
y = 29
z = 61
hope this helps :)
-audrey <3
Which of the following completes the proof? (6 points)
By the midpoint formula
By definition of congruence
Given
By construction