Your answer is 7. I hope this helps you out.
Answer:
x = 1 +√5
Step-by-step explanation:
There are different formulas for the area of a triangle available, depending on the given information.
<h3>Formulas</h3>
When two sides and the angle between them are given, the relevant area formula is ...
Area = 1/2(ab)sin(C)
When the base and height of a triangle are given, the relevant area formula is ...
Area = 1/2bh
<h3>Equal Areas</h3>
The problem statement tells us the two triangles shown have equal areas. That means the two formulas will give the same result.
Area from angle = Area from base/height
1/2(x·x)sin(30°) = 1/2(x-2)(x+1)
x² = 2(x² -x -2) . . . . . . . . . . . use sin(30°) = 1/2, multiply by 4
x² -2x -4 = 0 . . . . . . . . subtract x², eliminate parentheses
(x -1)² = 5 . . . . . . . . . add 4+1 to complete the square
<h3>Value of x</h3>
x = 1 ± √5 . . . . . . take the square root, add 1
The value of x must be greater than 2 in order for the triangle side lengths to be positive. (x-2 > 0) This means x = 1-√5 is an extraneous solution.
The value of x is 1 +√5.
Answer: See each part below.
1) A, B, and C are the coefficients in order when it equals 0. Move over the 4 and you have 5, 9, -4 or Choice B.
3) If you graph the equation, it will be above the x-axis. Therefore, it has no roots. Choice D
4) Choice A is correct. Use the coefficients: A = 4, B = 3, C = -10. Simply plug those into the quadratic equation and you will get -2 and 1.25.
A= 1/2 bh that is the formula
Answer:
Step-by-step explanation:
The formula for determining the area of a rectangle is expressed as
Area = length × width
Their backyard is rectangular, with a length of 3x – 5 feet and a width of 4x – 10 feet. This means that the area of the backyard is
(3x - 5)(4x - 10)
= 12x² - 30x - 20x + 15
= (12x² - 50x + 15) square feet
Their rectangular swimming pool, along with its surrounding patio, has dimensions of x + 8 by x – 2 feet. This means that the area occupied by the swimming pool and its surrounding patio is
(x + 8)(x - 2)
= x² - 2x + 8x - 16
= x² + 6x - 16
Assuming the swimming pool and its surrounding patio will not be covered with new grass, then the area of the region of the yard that they want to cover with new grass is
12x² - 50x + 15 - (x² + 6x - 16)
= 12x² - 50x + 15 - x² - 6x + 16
= 12x² - x² - 50x - 6x + 15 + 16
= 11x² - 56x + 31 square feet
