Use the quadratic formula to solve x - 5x+3 = 0.
1 answer:
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Answer:
Since a/2⁽ⁿ ⁺ ¹⁾b < a/2ⁿb, we cannot find a smallest positive rational number because there would always be a number smaller than that number if it were divided by half.
Step-by-step explanation:
Let a/b be the rational number in its simplest form. If we divide a/b by 2, we get another rational number a/2b. a/2b < a/b. If we divide a/2b we have a/2b ÷ 2 = a/4b = a/2²b. So, for a given rational number a/b divided by 2, n times, we have our new number c = a/2ⁿb where n ≥ 1
Since = a/(2^∞)b = a/b × 1/∞ = a/b × 0 = 0, the sequence converges.
Now for each successive division by 2, a/2⁽ⁿ ⁺ ¹⁾b < a/2ⁿb and
a/2⁽ⁿ ⁺ ¹⁾b/a/2ⁿb = 1/2, so the next number is always half the previous number.
So, we cannot find a smallest positive rational number because there would always be a number smaller than that number if it were divided by half.
Answer:
Step-by-step explanation:
This is written in the standard form of a quadratic function:
where:
- ax² → quadratic term
- bx → linear term
- c → constant
You need to convert this to vertex form:
where:
- (h,k) → vertex
To find the vertex form, you need to find the vertex. For this, use the equation for axis of symmetry, since this line passes through the vertex:
Using your original equation, identify the a, b, and c terms:
Insert the known values into the equation:
Simplify. Two negatives make a positive:
X is equal to 3 (3,y). Insert the value of x into the standard form equation and solve for y:
Simplify using PEMDAS:
The value of y is -6 (3,-6). Insert these values into the vertex form:
Insert the value of a and simplify:
:Done