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2 years ago

All three please 10 points

Mathematics

1 answer:

GaryK [48]2 years ago

5 0

Answer:

A) x = 3 or -1

B) x = -7

C)x = -7

Step-by-step explanation:

A) x² + 2x + 1 = 2x² - 2

Rearranging, we have;

2x² - x² - 2x - 2 - 1 = 0

x² - 2x - 3 = 0

Using quadratic formula, we have;

x = [-(-2) ± √((-2)² - 4(1 × -3))]/(2 × 1)

x = (2 ± √16)/2

x = (2 + 4)/2 or (2 - 4)/2

x = 6/2 or -2/2

x = 3 or -1

B) ((x + 2)/3) - 2/15 = (x - 2)/5

Multiply through by 15 to get;

5(x + 2) - 2 = 3(x - 2)

5x + 10 - 2 = 3x - 6

5x - 3x = -6 - 10 + 2

2x = -14

x = -14/2

x = -7

C) log(2x + 3) = 2log x

From log derivations, 2 log x is same as log x²

Thus;

log(2x + 3) = logx²

Log will cancel out to give;

2x + 3 = x²

x² - 2x - 3 = 0

Using quadratic formula, we have;

x = [-(-2) ± √((-2)² - 4(1 × -3))]/(2 × 1)

x = (2 ± √16)/2

x = (2 + 4)/2 or (2 - 4)/2

x = 6/2 or -2/2

x = 3 or -1

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Find the measure of the missing angle

Leokris [45]

Answer:

z = 69°

Step-by-step explanation:

The sum of all interior angles in a quadrilateral is 360°, and a right angle is worth 90°. We're given the values of the interior angles as 90, 122, 79, and z degrees.

We can solve this question algebraically with the equation $90 + 122 + 79 + z = 360$

Step 1: Combine like terms.

$(90+122+79)+z=360$
$z + 291 = 360$

Step 2: Subtract 291 from both sides.

$z + 291 - 291 = 360 - 291$
$z = 69$

Step 3: Check if solution is correct.

$(69) + 261=360$
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Therefore, z = 69°.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

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1 year ago

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LenaWriter [7]

Answer:

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2 years ago

What is the total cost on an easy-access loan of $2000 with a monthly fee of 20% for 30 days?

kolezko [41]

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2 years ago

In what time will a sum of money double itself at 5 parcent compound interest payable half yearly

ella [17]

Answer:

The Time in which sum of money double itself is 14 years .

Step-by-step explanation:

Given as :

The principal money = P

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The Amount = Double of principal

Let The time in which sum become double = t years

I.e A = 2 P

<u>From Compounded method</u>

Amount = principal × $(1+\dfrac{\textrm rate}{2\times 100})^{2\times \textrm time}$

or, 2 P = P × $(1+\dfrac{\textrm 5}{2\times 100})^{2\times \textrm t}$

Or, 2 = $(1.025)^{2 t}$

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So, $Log_{10}$ 2 = $Log_{10}$ $(1.025)^{2 t}$

or, 0.3010 = 2 t × $Log_{10}$ 1.025

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I.e t = 14.03 years ≈ 14 years

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Hence The Time in which sum of money double itself is 14 years . Answer

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2 years ago

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3 years ago