Please use " ^ " to indicate exponentiation: x^2 + 3x - 4 = 0
Here, a = 1, b = 3 and c = -4.
The formula for the discriminant is b^2 - 4(a)(c).
Substituting the given values of a, b and c, we get:
(3)^2 - 4(1)(-4)
Evaluating this, we get 9 + 16 = 25.
The discriminant is 25.
-3 plus or minus √25
Taking this further, x = ------------------------------------
2
-3 plus or minus 5
or: x = -------------------------------- => {-4, 1} (solutions)
2
1) y=(7/2)x-2.
Slope is the coefficient of x, that is 7/2
Intercept x is the value of x when y = 0 ==> 0=(7/2) X - 2==> 7/2x=2 &x=4/7
so intercept x, (4/7,0)
Intercept y is the value of y when x=0 ==> y= (7/2).(0) - 2 ==> y = 2
and so intercept y, (0,-2)
Now you will follow the same logic to find the are same questions
2) y= -6x + 3 ==>Slope= -6, Intercept x =1/2 & intercept y=3
3) y=-5 has a slope 0 (it doesn't exist). The graph is a line // to x-axis at y=-5
4)y=(6/5)x + 1:==>Slope= -5/6, Intercept x =-5/6 & intercept y=1
5) y=(1/4)x + 2 ==>Slope= 1/4, Intercept x =-8 & intercept y=2
6) x=5, this ligne is // to y axis at x=-5
The number 12,300 is written 1.23 x 10⁴ as a scientific notation. It's coefficient is 1.23; base is 10⁴ in exponent form.
Scientific notation is a method developed by scientists to shorten the number that expresses a very large number. The scientific notation is based on powers of the base number 10.
Scientific notation has two numbers: coefficient and base. The coefficient must be greater than or equal to 1 and less than 10. The base is always 10 written in exponent form.
12,300 as coefficient in standard form in scientific notation.
1) put decimal after the first digit and drop the zeros. from 12,300 to 1.23 this is the coefficient.
2) to find the exponent, count the number of places from decimal to the end of the number.
1.2300 ; there are 4 places
So the scientific notation is 1.23 x 10⁴
Answer:
(x - 1) (x + 1) (x - 4) (x + 4)
Step-by-step explanation:
actor the following:
x^4 - 17 x^2 + 16
x^4 - 17 x^2 + 16 = (x^2)^2 - 17 x^2 + 16:
(x^2)^2 - 17 x^2 + 16
The factors of 16 that sum to -17 are -1 and -16. So, (x^2)^2 - 17 x^2 + 16 = (x^2 - 1) (x^2 - 16):
(x^2 - 1) (x^2 - 16)
x^2 - 16 = x^2 - 4^2:
(x^2 - 1) (x^2 - 4^2)
Factor the difference of two squares. x^2 - 4^2 = (x - 4) (x + 4):
(x - 4) (x + 4) (x^2 - 1)
x^2 - 1 = x^2 - 1^2:
(x^2 - 1^2) (x - 4) (x + 4)
Factor the difference of two squares. x^2 - 1^2 = (x - 1) (x + 1):
Answer: (x - 1) (x + 1) (x - 4) (x + 4)
Answer: ![(-9, 16]](https://tex.z-dn.net/?f=%28-9%2C%2016%5D)
This is the interval from -9 to 16. Exclude -9 but include 16.
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Work Shown:
The idea is to multiply all sides by 5, then add 1 to all sides
This converts to the interval notation
note: a curved parenthesis means "do not include this value in the solution set"; while a square bracket has us include the value. So we exclude -9 and include 16.
