The sum of half of a number and three-fourths is at least five and one quarter.
It's all about making sense of an English statement. "half the sum" and "the sum of half" are two distinct expressions.
Additionally, "at least" and "not less than" have equivalent meanings, as do "not more than" and "at most."
It is an issue of matching the thoughts conveyed because all of the expressions are verbally expressed. That is a reading comprehension issue, not a math issue.
"A number is at least five and one quarter when divided by half and three-fourths."
In mathematics, a statement with unequal sides is referred to as an inequality. When a link leads to a non-equal comparison between two expressions or two numbers, it is referred to as an inequality in mathematics.
In this case, the equal sign "=" is replaced with any of the inequality symbols, such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), or not equal to symbol (≠). There are numerous types of inequalities that can exist in mathematics, including absolute value inequality, rational inequality, and polynomial inequality.
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The function is (-x+3)/ (3x-2) and we get f(1)=1 and differentiation is f'(x)=-7/ (9x²- 12x+4).
Given that,
The function is (-x+3)/ (3x-2)
We have to find f(1) and f'(x).
Take the function expression
f(x)= (-x+3)/ (3x-2)
Taking x as 1 value
f(1)= (-1+3)/(3(1)-2)
f(1)=2/1
f(1)=1
Now, to get f'(x)
With regard to x, we must differentiate.
f(x) is in u/v
We know
u/v=(vu'-uv')/ v² (formula)
f'(x)= ((3x-2)(-1)- (-x+3)(3))/ (3x-2)²
f'(x)= ((-3x+2)-(-3x+9))/ 9x²- 12x+4
f'(x)=(-3x+2+3x-9)/ 9x²- 12x+4
f'(x)=2-9/ (9x²- 12x+4)
f'(x)=-7/ (9x²- 12x+4)
Therefore, The function is (-x+3)/ (3x-2) and we get f(1)=1 and differentiation is f'(x)=-7/ (9x²- 12x+4).
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Answer:
16x / 15
Step-by-step explanation:
2/5x + 2x/3
6x - 10x /15
16x / 15
