Use factoring to solve the quadratic equation. Check by substitution or by using a graphing utility and identifying x-intercepts
1 answer:
9514 1404 393
Answer:
x = -1/2, x = 7
Step-by-step explanation:
Written in standard form, the equation is ...
2x² -13x -7 = 0
We observe that factors of (2)(-7) that have a sum of -13 are -14 and +1. Rewriting the middle term using these numbers, we have ...
2x² -14x +x -7 = 0
2x(x -7) +1(x -7) = 0 . . . . . factor pairs of terms
(2x +1)(x -7) = 0 . . . . . . . . factored form
The solutions are the values of x that make these factors zero.
2x +1 = 0 ⇒ x = -1/2
x -7 = 0 ⇒ x = 7
The solutions to the quadratic are x = -1/2 and x = 7.
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Answer: 972π in³
Step-by-step explanation:
We will use the proper formula to solve for the volume of the sphere.
-> The radius (r) is half the diameter. 18 in / 2 = 9 in
V = πr³
V = π(9)³
V = * (9)³ * π
V = 972π in³
The volume is 972π in³
Answer:
The area of the shaded figure is:
- <u>20 units^2</u>
Step-by-step explanation:
To obtain the area of the shaded figure, first, you must calculate this as a rectangle, with the measurements: wide (4 units), and long (6 units):
- Area of a rectangle = long * wide
- Area of a rectangle = 6 * 4
- Area of a rectangle = 24 units^2
How the figure isn't a rectangle, you must subtract the triangle on the top, so, now we calculate the area of that triangle with measurements: wide (4 units), and height (2 units):
- Area of a triangle =
- Area of a triangle =
- Area of a triangle =
- Area of a triangle = 4 units^2
In the end, you subtract the area of the triangle to the area of the rectangle, to obtain the area of the shaded figure:
- Area of the shaded figure = Area of the rectangle - Area of the triangle
- Area of the shaded figure = 24 units^2 - 4 units^2
- <u>Area of the shaded figure = 20 units^2</u>
I use the name "units" because the exercise doesn't say if they are feet, inches, or another, but you can replace this in case you need it.