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Anna [14]
3 years ago
14

A) Show that 4x² -6x+9 is positive for all values real numbers x.

Mathematics
1 answer:
wolverine [178]3 years ago
7 0

Answer:

(4x² -6x+1.5²) +9-1.5²= (2x-1.5)²+9-2.25= (2x-1.5)²+6.75

(2x-1.5)² is greater or equal to 0 , 6.75>0 so expression is positive for all real numbers x

Step-by-step explanation:

a) Use the formula a²-2ab+b²= (a-b)² (You need to make squared expression because it is always positive)

Consider 4x² as a² and -6x=-2ab

4x²=a² a=2x  ab=3x 2x*b=3x

b=1.5

Express 4x² -6x+9= (4x² -6x+1.5²) +9-1.5²= (2x-1.5)²+9-2.25= (2x-1.5)²+6.75

(2x-1.5)² is greater or equal to 0 , 6.75>0 so expression is positive for all real numbers x

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<u><em>You want to leave a 18% tip on a meal that cost $150.</em></u>

<u><em>First, convert the 18% to an actual number that can be used in a calculation. For percents,this is always done by simply dividing the percent (in this case 18%) by 100%.So, the conversational term "18%" becomes 18% / 100% = 0.18 in terms of a real mathematical number.</em></u>

<u><em>Second, you need to find out what 18% of your $150 meal cost is.This is always done by multiplying 0.18 by $150.00, or</em></u>

<u><em></em></u>

<u><em>0.18 x $150.00=$27.00.</em></u>

<u><em>So, the amount of tip you are going to leave is $27.00.</em></u>

<u><em></em></u>

<u><em>This makes the total cost of your meal (to write on your charge slip or other payment)</em></u>

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8 0
2 years ago
The following information is obtained from two independent samples selected from two normally distributed populations.
AysviL [449]

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μ1 − μ2 = 1.83

 

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Confidence interval = (x1 –x2) ± z σ

where z is a value taken from the standard distribution tables at 99% confidence interval, z = 2.58

and σ is calculated using the formula:

σ = sqrt [(σ1^2 / n1) + (σ2^2 / n2)]

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3 years ago
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inna [77]

t N.

In the figure shown below

Answer:

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∠J N M =(5x+2)°

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8 0
3 years ago
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Contact [7]

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