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3 years ago

Which quadratic equation is equivalent to (x+2)2+5(x+2)-6=0

Mathematics

1 answer:

professor190 [17]3 years ago

6 0

$(x+2)^2+5(x+2)-6=0\\\\x^2+2\cdot x\cdot2+2^2+5\cdot x+5\cdot2-6=0\\\\x^2+4x+4+5x+4-6=0\\\\x^2+9x+2=0$

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3+ 4×12 Word problem

Rudiy27

Three plus four times twelve

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3 years ago

Read 2 more answers

1.) Determine the type of solutions for the function (Picture 1)

NNADVOKAT [17]

Answer:

1) 2 nonreal complex roots

2) 1 Real Solution

3) 16

4) Reflected, narrower by a factor of 2/5, slides right 4 units and slides up 6 (units)

Step-by-step explanation:

1) The graph does not intercept the x-axis, therefore, there are no real solutions at the point y = 0

We get;

y = a·x² + b·x + c

At y = 6, x = -2

Therefore;

6 = a·(-2)² - 2·b + c = 4·a - 2·b + c

6 = 4·a - 2·b + c...(1)

At y = 8, x = 0

8 = a·(0)² + b·0 + c

∴ c = 8...(2)

Similarly, we have;

At y = 8, x = -4

8 = a·(-4)² - 4·b + c = 16·a - 4·b + 8

16·a - 4·b = 0

∴ b = 16·a/4 = 4·a

b = 4·a...(3)

From equation (1), (2) and (3), we have;

6 = 4·a - 2·b + c

∴ 6 = b - 2·b + 8 = -b + 8

6 - 8 = -b

∴ -b = -2

b = 2

b = 4·a

∴ a = b/4 = 2/4 = 1/2

The equation is therefor;

y = (1/2)·x² + 2·x + 8

Solving we get;

x = (-2 ± √(2² - 4 × (1/2) × 8))/(2 × (1/2))

x =( -2 ± √(-12))/1 = -2 ± √(-12)

Therefore, we have;

2 nonreal complex roots

2) Give that the graph of the function touches the x-axis once, we have;

1 Real Solution

3) The given function is f(x) = 2·x² + 8·x + 6

The general form of the quadratic function is f(x) = a·x² + b·x + c

Comparing, we have;

a = 2, b = 8, c = 6

The discriminant of the function, D = b² - 4·a·c, therefore, for the function, we have;

D = 8² - 4 × 2 × 6 = 16

The discriminant of the function, D = 16

4.) The given function is g(x) = (-2/5)·(x - 4)² + 6

The parent function of a quadratic equation is y = x²

A vertical translation is given by the following equation;

y = f(x) + b

A horizontal to the right by 'a' translation is given by an equation of the form; y = f(x - a)

A vertical reflection is given by an equation of the form; y = -f(x) = -x²

A narrowing is given by an equation of the form; y = b·f(x), where b < 1

Therefore, the transformations of g(x) from the parent function are;

g(x) is a reflection of the parent function, with the graph of g(x) being narrower by 2/5 than the graph of the parent function. The graph of g(x) is shifted right by 4 units and is then slides up by 6 units.

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3 years ago

SAT scores have a mean of 1026 and a standard deviation of 209. ACT scores have a mean of 20.8 and a standard deviation of 4.8.

Y_Kistochka [10]

Answer:

The z-score for SAT exam of junior is much small than his ACT score. This means he performed well in his ACT exam and performed poor in his SAT exam.

Step-by-step explanation:

Mean SAT scores = 1026

Standard Deviation = 209

Mean ACT score = 20.8

Standard Deviation = 4.8

We are given SAT and ACT scores of a student and we have to compare them. We cannot compare them directly so we have to Normalize them i.e. convert them into such a form that we can compare the numbers in a meaningful manner. The best way out is to convert both the values into their equivalent z-scores and then do the comparison. Comparison of equivalent z-scores will tell us which score is higher and which is lower.

The formula to calculate the z-score is:

$z=\frac{x-\mu}{\sigma}$

Here, μ is the mean and σ is the standard deviation. x is the value we want to convert to z score.

z-score for junior scoring 860 in SAT exam will be:

$z=\frac{860-1026}{209}=-7.59$

z-score for junior scoring 16 in ACT exam will be:

$z=\frac{16-20.8}{4.8}=-1$

The z-score for SAT exam of junior is much small than his ACT score. This means he performed well in his ACT exam and performed poor in his SAT exam.

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The x variable represents the number of days or the daily rental fee.

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3 years ago

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Answer:

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Step-by-step explanation:

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