To move it 1 to the left, we make x into (x+1), so we have (x+1)². Conversely, if we wanted to move it to the right, we'd subtract 1 from x. Next, we have to vertically stretch by a factor of 3, meaning that we have to multiply the whole thing (at the current point) by 3, turning our equation into 3(x+1)². Lastly, we must reflect over the x axis, which is the line g(x)=0. If we want to reflect over g(x), we essentially multiply g(x) by -1, making -g(x)=3(x+1)². However, we want to solve for g(x), not -g(x), so we multiply both sides by -1 to end up with -3(x+1)²
Answer:
1) 2x = x + 15
Step-by-step explanation:
The two parallel lines and one bisecting line makes these two angles equal so you can set the values equal to each other to solve for x
Answer:
1/2
Step-by-step explanation:
the dilation factor should be 1/2
- if u count the dots on the sides of the preimage there are 2 dots that's the length
- if u count the dots on the real image it's 4
- therefore 2/4 to it's lowest term is 1/2
- so 1/2 is the scale factor
Answer:
19.6 cubic centimeters
Step-by-step explanation:
The ratio of two similar 3D figures' volumes is equivalent to the ratio of their corresponding lengths (whether it's width, height, length, radius, etc) cubed.
Here, we know the cones are similar, and we know the smaller radius is 2 and the larger radius is 3. Then the ratio of the volume of the smaller one to the volume of the larger one is
.
We also know the actual volume of the larger cone is 66. So, if x is the volume of the smaller cone, we have the proportion:
x / 66 = 8 / 27
Cross-multiply:
27x = 66 * 8 = 528
Divide by 27:
x = 528/27 ≈ 19.6
The answer is thus 19.6 cubic centimeters.
<em>~ an aesthetics lover</em>
Answer:
The quadratic equation
has no real solution.
Step-by-step explanation:
Rewrite the quadratic equation
in the standard form
:
, for which:
The quadratic discriminant of
is
. The quadratic discriminant of
would be:
.
Since the quadratic discriminant of this equation is negative, this quadratic equation has no real solution.