- Quadratic Formula:
, with a = x^2 coefficient, b = x coefficient, and c = constant.
Firstly, starting with the y-intercept. To find the y-intercept, set the x variable to zero and solve as such:
<u>Your y-intercept is (0,-51).</u>
Next, using our equation plug the appropriate values into the quadratic formula:
Next, solve the multiplications and exponent:
Next, solve the addition:
Now, simplify the radical using the product rule of radicals as such:
- Product Rule of Radicals: √ab = √a × √b
√1224 = √12 × √102 = √2 × √6 × √6 × √17 = 6 × √2 × √17 = 6√34
Next, divide:
<u>The exact values of your x-intercepts are (-4 + √34, 0) and (-4 - √34, 0).</u>
Now to find the approximate values, solve this twice: once with the + symbol and once with the - symbol:
<u>The approximate values of your x-intercepts (rounded to the hundredths) are (1.83,0) and (-9.83,0).</u>
Check the picture below.
recall that in a square, all sides are equal, so if we make b = a, then we get that for one side, also recall that the area of a rectangle is length*width, so in this case,
x = 20 is the answer.
<u>Step-by-step explanation:</u>
When a parallel lines cut by a transversal, then the alternate exterior angles are congruent.
So the given 2 angles add up to 180 degrees.
5x+ 9 + 3x+ 11 = 180
8x + 20 = 180
8x = 180 - 20 = 160
x = 160/8 = 20
Two expressions for the perimeter of a square are:
4a
- a represents one side of the square
a + a + a + a
- a representa one side of the square
the first expression does not include any addition. But the two expressions are actually equivalent.
Let the two numbers be x and y.
Let m = the fraction (or percentage) for increasing the numbers.
Increase x by 5, multiply (x+5) by (1+m), and set it qual to 36.
(x + 5)*(1 + m) = 36
Increase y by 5, multiply (y+5) by (1+m), and set it equal to 36.
(y+5)*(1+m) = 36
Therefore
(x+5)*(1+m) = (y+5)*(1+m)
x + 5 = y + 5
x = y
x - y = 0
Answer: 0.
The difference between the two numbers is zero.
