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3 years ago

X^2 + 4x + 4 = 10please help!! I missed class! show steps!

Mathematics

1 answer:

lina2011 [118]3 years ago

3 0

Answer:

x = √(10) - 2, -√(10) - 2

Step-by-step explanation:

x² + 4x + 4 = 10

factor:

(x + 2)² = 10

take square root of both sides:

x + 2 = ±√(10)

split into 2 equations:

x + 2 = √(10) x + 2 = -√(10)

solve both equations and collect solutions:

x = √(10) - 2, -√(10) - 2

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A bank offers all savings accounts 5% interest compounded annually. If one account has a principal of $100 and another

arsen [322]

Answer:

From the calculation for both the accounts, it is clear that both the account double in the same time period of 14 years 26 days .

Step-by-step explanation:

Given as :

The principal for the first account = p = $100

The rate of interest = r = 5% compounded annually

The account gets double , so, Amount = A = $200

Let the time after which account gets double = t years

So, From Compound Interest method

Amount = Principal × $(1+\dfrac{\trxtrm rate}{100})^{\textrm time}$

As amount is double its principal

So, A = 2 × $100 = $200

Or, A = p × $(1+\dfrac{\trxtrm r}{100})^{\textrm t}$

Or, $200 = $100 × $(1+\dfrac{\trxtrm 5}{100})^{\textrm t}$

Or, $\dfrac{200}{100}$ = $(1.05)^{\textrm t}$

Or, 2 = $(1.05)^{\textrm t}$

Taking Log both side

$Log_{10}2$ = $Log_{10}(1.05)^{t}$

Or, 0.3010 = t $Log_{10}1.05$

Or, 0.3010 = t × 0.0211

∴ t = $\dfrac{0.3010}{0.0211}$

I.e t = 14.26

So, The time period to get account double is 14 years 26 days

Again

Amount = Principal × $(1+\dfrac{\trxtrm rate}{100})^{\textrm time}$

Or, A = p × $(1+\dfrac{\trxtrm r}{100})^{\textrm t}$

As amount is double its principal

So, A = 2 × $1000 = $2000

Or, $2000 = $1000 × $(1+\dfrac{\trxtrm 5}{100})^{\textrm t}$

Or, $\dfrac{2000}{1000}$ = $(1.05)^{\textrm t}$

Or, 2 = $(1.05)^{\textrm t}$

Taking Log both side

$Log_{10}2$ = $Log_{10}(1.05)^{t}$

Or, 0.3010 = t $Log_{10}1.05$

Or, 0.3010 = t × 0.0211

∴ t = $\dfrac{0.3010}{0.0211}$

I.e t = 14.26

So, The time period to get account double is 14 years 26 days

Hence From the calculation for both the accounts, it is clear that both the account double in the same time period of 14 years 26 days . Answer

7 0

3 years ago

Martin thinks of two numbers. He says "The Highest Common Factor (HCF) of my two numbers is 8 The Lowest Common Multiple (LCM) o

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Answer:

30, 42

Step-by-step explanation:

the highest common factor of the 2 numbers in 6 the only factors the 2 numbers have in common are 2 and 3. each number must have 2 and 3 as factors.

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3 years ago

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lisov135 [29]

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3 years ago

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stira [4]

Step-by-step explanation:

By Intersecting Chords Theorem,

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3 years ago

Read 2 more answers

Which of the following is a which of the following is a rational number?

Nastasia [14]

Answer:

A. √25

General Formulas and Concepts:

Math

Rational Numbers - numbers that can be written as integers, terminating decimals, or fractions
Irrational Numbers - numbers that have non-terminating decimals i.e infinite decimals and cannot be written into a fraction

Step-by-step explanation:

Step 1: Define

A. √25

B. √123

C. √20

D. π

Step 2: Identify

A. √25 = 5; Rational

B. √123 ≈ 11.0905...; Irrational

C. √20 = 2√5 ≈ 4.47214...; Irrational

D. π ≈ 3.1415926535897932384626433832795...; Irrational

Therefore, our answer choice is A.

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3 years ago

X^2 + 4x + 4 = 10please help!! I missed class! show steps!​

X^2 + 4x + 4 = 10please help!! I missed class! show steps!