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Mathematics

2 answers:

Andreyy892 years ago

4 0

$\tt \dfrac{1}{4}+\dfrac{2}{4}+\dfrac{3}{4}+1+\dfrac{5}{4}=\dfrac{15}{4}$

ryzh [129]2 years ago

3 0

Answer:

5/4 ounces.

Step-by-step explanation:

There are 4 marks. So 1/4 is the smallest one. There are 5 of them. 5x1/4 is 5/4 or 1 1/4

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Step-by-step explanation:

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Read 2 more answers

What’s the vertex form of F(x)=x^2+2x-3

kupik [55]

Answer:

$\large\boxed{f(x)=(x+1)^2-4}$

Step-by-step explanation:

$\text{The vertex form of a quadratic equation}\ f(x)=ax^2+bx+c:\\\\f(x)=a(x-h)^2+k\\\\(h,\ k)-\text{vertex}\\=====================================$

$\bold{METHOD\ 1:}\\\\\text{convert to the perfect square}\ (a+b)^2=a^2+2ab+b^2\qquad(*)\\\\f(x)=x^2+2x-3=\underbrace{x^2+2(x)(1)+1^2}_{(*)}-1^2-3\\\\f(x)=(x+1)^2-4\\==============================$

$\bold{METHOD\ 2:}\\\\\text{Use the formulas:}\ h=\dfrac{-b}{2a},\ k=f(k)\\\\f(x)=x^2+2x-3\to a=1,\ b=2,\ c=-3\\\\h=\dfrac{-2}{2(1)}=\dfrac{-2}{2}=-1\\\\k=f(-1)=(-1)^2+2(-1)-3=1-2-3=-4\\\\f(x)=(x-(-1))^2-4=(x+1)^2-4$