The greatest common factor for 162, 378, and 414 is 18. k
Answer:
Step-by-step explanation:
Since we are finding the x-intercepts, that implies that this is a parabola that opens either up or down as opposed to right or left. It would benefit us to know the equation of the parabola so we could factor it to find the roots (which are also known as the x-intercepts).
Here's what we know:
h = 1, k = 20, x = 0, and y = 20. Filling in the vertex form of a parabola is already halfway to factored, so we'll use that format as opposed to the standard form, which is
. The vertex form is
and filling in our values from above:
and
and
-4 = a. So the equation for the parabola is
. Now set it equal to 0 and factor.
and divide both sides by -4 to get:
and take the square root of both sides to get
±
and then add 1 to both sides to get the x-intercepts (or roots or solutions or zeros...they're all the same).
x = 1 ±√5 and you're done!
Dy/dx = dy/dt * dt/dx
xy = 4
y + x(dy/dx) = 0 by implicit differentiation.
x(dy/dx) = -y
dy/dx = -y/x
<span>dy/dx = dy/dt * dt/dx dy/dt = -2
</span>
<span>-y/x = -2 * dt/dx
</span>
y/(2x) = dt/dx
dt/dx = y/(2x)
dx/dt = 2x/y
When x = -3, xy = 4, y = 4/x = 4/-3 = -4/3
dx/dt = 2*-3/(-4/3) = -6 *-3/4 = 18/4 = 9/2 = 4.5
dx/dt = 4.5
Answer: Ayesha = 9. Bennie = 16. Chloe = 32
Explanation: (A stands for Ayesha, B stands for Bennie and C stands for Chloe) B = A + 7
C = 2(A + 7)
A + A + 7 + 2(A+7) = 57
A + A + 7 + 2A + 14 = 57
4A + 21 = 57
4A = 36
A= 9
hope that helps if you have any questions let me know!!
Answer: y = 2/3x + 3
Step-by-step explanation:
To write the equation in y = mx + b, or slope-intercept form, we first need to find the y-intercept.
To do that, we will need to plug our numbers into y = mx + b. <em>y </em>is the y-coordinate, <em>m</em> is the slope, <em>x </em>is the x-coordinate, and <em>b</em> is the y-intercept.
It should look something like this:
5 = 2/3(3) + b
Now we simplify.
5 = 2 + b
Subtract 2 from both sides.
5 - 2 = 2 - 2 + b
Simplify.
3 = b
Our y-intercept is 3.
Now, we can form our equation
y = 2/3x + 3
