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Semenov [28]
3 years ago
12

1.What is the shape of the graph of any quadratic function?

Mathematics
1 answer:
likoan [24]3 years ago
7 0

Answer:

Inverted parabola

Two complex solution

Step-by-step explanation:

any quadratic equation can be expressed in terms of ax^2 + bx + c = 0

It has two solutions which can be found using formula X =( -b + \sqrt{b^2 -4ac} )/2a \\or  \ ( -b - \sqrt{b^2 -4ac} )/2a

We know that  for any value inside the square root function

if it is positive its solution will be real number

for example  \sqrt{9} we can have two real solution -3 and 3

if it is negative its solution will be complex number

for example  \sqrt{-9}we can have two complex solution

expressed in term of a + ib or a - ib

------------------------------------------------------------------------------------------

Given in the problem

we have  ax^2 - bx + c

so its solution will be

X =( -(-b) + \sqrt{b^2 -4ac} )/2a \\or  \ ( -(-b) - \sqrt{b^2 -4ac} )/2a\\\\X =( b + \sqrt{b^2 -4ac} )/2a \\or  \ ( b - \sqrt{b^2 -4ac} )/2a\\

Since in this expression it is given in problem statement that b^2 - 4ac < 0 which will be a negative number and for negative number, its square root is complex number.

also X has two values as given above it will have two solution

hence it will have two complex solution based on above discussion.

Also for any quadratic equation shape of its curve if plotted on coordinate plane is parabolic.

If it has complex solution then curve of such expression  will not pass through X axis

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Marta_Voda [28]

Answer:

£631.07

Step-by-step explanation:

Increasing a value by 3% is the same as taking 103% of it - you have the original price (100%) plus an additional 3% of it. Let's call the original price here p. We're told that after a 3% increase, the price goes up to £650. Put another way: 103% of p is £650. In equation form:

1.03p=650

To solve for p, we can simply divide both sides of our equation by 1.03 to get

p=650/1.03\approx631.07

So our orignal amount, to the nearest penny, was £631.07

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2 years ago
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adoni [48]
Add the whole numbers, including the decimals, then the variables like y and x.
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3 years ago
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Information about the proportion of a sample that agrees with a certain statement is given below. Use StatKey or other technolog
lorasvet [3.4K]

Answer:

a) Standard Error = 0.010

b) 95% Confidence Interval = (0.0924 , 0.1316)

Step-by-step explanation:

a) The formula for Standard Error = √Sample Proportion (1 - sample proportion)/n

Standard Error = √p (1 - p)/n

We are told in the question that:

In a random sample of 400 people, 112 agree and 288 disagree. Estimate the standard error using 1000 samples

p = x/n

n = 1000 because we were told to use it instead of 400

x = number for people that agree = 112

p = 112/1000

p = 0.112

Standard Error = √p (1 - p)/n

= √0.112 (1 - 0.112)/1000

= √0.112 × 0.888/1000

= √0.099456 /1000

= √0.000099456

= 0.0099727629

Approximately to 3 decimal places = 0.010

Therefore, the standard error is 0.010

b) The Question above also asked that we solve for the 95% Confidence Interval

The formula =

p ± z × Standard Error

p = 0.112

z score for 95% confidence interval = 1.96

Standard Error = 0.010

Confidence Interval =

0.112 ± 1.96 × 0.010

= 0.112 ± 0.0196

0.112 - 0.0196

= 0.0924

0.112 + 0.0196

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Therefore, the 95% confidence interval = (0.0924 , 0.1316)

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3 years ago
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Does anyone know the answer???
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Answer:

<h2>3,600 m²</h2>

Step-by-step explanation:

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SA=4\pi R^2

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<em />

We have <em>R = 30m</em>.

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24 · 3 = 72

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