Answer:
(8x-5y) (8x+5y)
Step-by-step explanation:
64x^2−25y^2
This is the difference of squares
a^2 - b^2 = (a-b) (a+b)
Let 64 x^2 = a^2 Then a = 8x
Let 25 y^2 = b^2 then b = 5y
64x^2−25y^2 = (8x-5y) (8x+5y)
Answer: 6 cm, V=48π or V=150.8 cm³
It appears the question is asking for the radius, but below I have shown how to find the volume.
Step-by-step explanation:
The radius is half of the diameter. The diameter of the cone of 12 cm. Half of 12 is 6. Therefore, the radius is 6 cm.
The formula to find the volume of a cone is . Now that we have the radius from above, we can use that to plug into the equation along with the given height.
[expand the exponent]
[combine like terms]
or
Step-by-step explanation:
the slope-intercept form is
y = ax + b
"a" is the slope (the slope is in all forms the factor of x). and "b" is the y-intercept (the y value when x = 0).
so the first equation is
y = -5x + b
b we get by using the point coordinates :
-22 = -5×5 + b = -25 + b
b = 3
so, the full equation is
y = -5x + 3
for the second equation we need to calculate the slope first. remember, it is the ratio "y coordinate change / x coordinate change" :
x changes by +1 (from -4 to -3).
y changes by +7 (from -2 to 5).
the slope is +7/+1 = 7/1 = 7.
the equation looks like
y = 7x + b
again, we use the coordinates of a point to get b. I picked (-4, -2) :
-2 = 7×-4 + b = -28 + b
b = 26
and the full equation is
y = 7x + 26
Answer:
<em>(-8,4)</em>
Step-by-step explanation:
<u>System of Equations:</u>
Solve the following system of equations by the substitution method:
5x - 6y = -64 [1]
y = 20 + 2x [2]
Substituting y from [2] in [1]:
5x - 6(20 + 2x) = -64
Operating:
5x - 120 - 12x = -64
Simplifying:
-7x - 120 = -64
Adding 120:
-7x = -64 + 120 = 56
x = 56/(-7) = -8
x = -8
From [2]:
y = 20 + 2(-8) = 4
Solution (-8,4)