Determine the vertex form of g(x) = x2 + 2x – 1

1 answer:

3 0

$The\ vertex\ form:f(x)=a(x-h)^2+k\\\\g(x)=x^2+2x-1=\underbrace{x^2+2x\cdot1+1^2}_{use\ (*)}-1^2-1\\\\\boxed{f(x)=(x+1)^2-2}\\\\(*)\ (a+b)^2=a^2+2ab+b^2$

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Which irrational number can be added to pi to get a sum that is rational?

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The irrational number that can be added to pi to get a rational sum is PI.

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4 years ago

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Please help for a cookie

olasank [31]

Answer:

Step-by-step explanation:

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3 years ago

I need help asap pls and thank you ;)

olga55 [171]

Answer:

$\text{Length of AB is }\frac{ah}{a+h}$

Step-by-step explanation:

Given △KMN, ABCD is a square where KN=a, MP⊥KN, MP=h.

we have to find the length of AB.

Let the side of square i.e AB is x units.

As ADCB is a square ⇒ ∠CDN=90°⇒∠CDP=90°

⇒ CP||MP||AB

In ΔMNP and ΔCND

∠NCD=∠NMP (∵ corresponding angles)

∠NDC=∠NPM (∵ corresponding angles)

By AA similarity rule, ΔMNP~ΔCND

Also, ΔKAP~ΔKPM by similarity rule as above.

Hence, corresponding sides are in proportion

$\frac{ND}{NP}=\frac{CD}{MP} \thinspace\thinspace and\thinspace\thinspace \frac{KA}{KP}=\frac{AB}{PM} \\\\\frac{ND}{NP}=\frac{x}{h} \thinspace\thinspace and\thinspace\thinspace \frac{KA}{KP}=\frac{x}{h}\\\\\frac{NP}{ND}=\frac{h}{x} \thinspace\thinspace and\thinspace\thinspace \frac{KP}{KA}=\frac{h}{x}\\\\\frac{PD}{ND}=\frac{h}{x}-1 \thinspace\thinspace and\thinspace\thinspace \frac{AP}{KA}=\frac{h}{x}-1\\$