Answer:
We were given the equation of a rainbow, which follows a parabolic path, which is
By comparing to the vertex form,
We have the vertex at (h,k)=(1,6)
Since a=-0.1<0, the parabola opens down.
At y-intercept, x=0.
Step-by-step explanation:
Answer:
(x - 3)² + (y - 3)² = 4
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Here (h, k) = (3, 3) and r = 2, thus
(x - 3)² + (y - 3)² = 4
Answer: the second choice: (0, - 2) and (1, 0).
Explanation:
1) The solution of a graphed system of equations is the points of intersection of the equations.
2) Hence, this method requires to graph each function in one Cartesian coordinate system.
3) To graph the function y = x² + x - 2, you can follow these steps
- draw the perpendicular x(horizontal)-axis, and y(vertical)- axis
- mark the divisions in each axis (1 unit is a good scale for this case)
- notice that y = x² + x - 2 is a parabola
- write y = x² + x - 2 in its vertex form following these steps:
y = (x² + x) - 2
y + 1/4 = (x² + x + 1/4) - 2
y + 1/4 = (x + 1/2)² - 2
y = (x + 1/2)² - 2 - 1/4
y = (x + 1/2)² - 9/4
Compare with the vertex form y = (x + h)² + k, where the coordinates of the vertex are (h,k). Therefore, the vertex is (1/2, - 9/4).
- The parabola open upwards (because the coefficient of the quadratic term is positive).
- Find the y-intercept (x =0) and x-intercepts (y = 0), and write a table with some values:
4) To graph the function y = 2x - 2, you can follow these steps:
- Use the same Cartesian coordinate system
- Notice it is a line
- The slope is 2 (the coefficient of x)
- The y-intercept is - 2( the constant term)
- Build a table (use the same x-values used for the first graph)
- x y = 2x - 2
- -2 - 6
- -1 - 4
- -1/2 - 3
- 0 - 2
- 1/2 - 1
- 1 0
- 2 2
The tables show that these points are common to the two functions: (0, - 2) and (1,0).
The graphs are shown in the figure attached.
You can see that the parabola (blue curve) and the line (purple line) intercept each other at those two points ( 0, - 2) and (1,0).
Answer:
v=68
Step-by-step explanation:
The volume of the rectangle in the middle is 56.
You use the Pythagorean theorem to find the side lengths of the triangle and us them along with the other numbers to find the volume of the triangles.
The volume of each triangle is 6.
6*2+56=68
To divide fractions, you multiply by the reciprocal.
a.k.a., *
This gives you