A quadratic equation is shown:x2 - 14x + 41 = 0
Which of the following is the first correct step to write the above equation in the form (x - p)2 = 9, where p and q are integers?
x2 - 14x + 41 + 8 = 0 + 8
x2 - 14x + 41 + 9 = 0 + 9
x2 - 14x + 41 - 8 = 0 - 8
x2 – 14x + 41 - 9 = 0 - 9

Answers

Answer 1
Answer:

Answer:

The correct answer is the first option

Step-by-step explanation:

Quadratic Equation

The standard form of a quadratic equation is

ax^2+bx+c=0

Sometimes we need to change the expression of the same equation to the form

(x-p)^2=q

To accomplish that change, we usually modify the left-hand expression to make it look like the square of a binomial.

The given quadratic equation is

x^2-14x+41=0

Recall the square of a binomial is

(x-p)^2=x^2-2px+p^2

The first term is already present. The second term gives us the value of p:

-2px=-14x

Solving

p=7

Now we need to produce the third term p^2=49. We only have 41, thus we need to add 8 to both sides of the equation:

x^2-14x+41+8=0+8

The correct answer is the first option


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Answers

Answer: 56 times

Pls mark brainleist i really need it

Find the slope (m) and the y-intercept (b) of the given line on the graph. pls show work/explanation!

Answers

Answer:

m= 1/2

b= (0,6)

Step-by-step explanation:

Slope is rise over run

The y intercept is when x=o or just look at the vertical line

A portrait without its frame has a height 1.5 times its width w, in inches. The width of the frame is 3 inches. Which of the following is an expression for the area of the framed portrait in terms of w

Answers

Answer:

Area = 1.5w^2+15w+36

Step-by-step explanation:

Let the width of portrait be 'w'

Given:

Height of portrait without frame (h) = 1.5 times its width =1.5w

Width of the frame is 3 inches on all sides.

Area of the framed portrait is the total area of the portrait plus the area of the frame.

The figure representing the above scenario is shown below.

From the figure, area of rectangle ABCD is the area of the framed portrait.

From the figure,

AB = 3 + w + 3 = w + 6

BC = 3 + h + 3 = h + 6 = 1.5w + 6

Now, area of the rectangle ABCD is given as the product of the length AB and width BC. Therefore,

Area=AB* BC\n\nArea=(w+6)(1.5w+6)\n\nArea=(w* 1.5w)+(w* 6)+(6* 1.5w)+(6* 6)\n\nArea=1.5w^2+6w+9w+36\n\nArea=1.5w^2+15w+36

Therefore, the expression for the area of the framed portrait in terms of the width 'w' is given as:

Area = 1.5w^2+15w+36

The area of the portrait without the frame will be A=13.5=1.5w^2.

Given information:

A portrait without its frame has a height 1.5 times its width w, in inches.

The width of the frame is 3 inches.

Length of the frame will be,

l=1.5w\nl=1.5* 3\nl=4.5

So, the area of portrait without frame will be,

A=l* w\nA=1.5w* w\nA=1.5w^2\nA=1.5* 9=13.5=1.5w^2

Therefore, the area of the portrait without the frame will be A=13.5=1.5w^2.

For more details, refer to the link:

brainly.com/question/15218510

It is known that the variance of a population equals 1,936. A random sample of 121 has been taken from the population. There is a .95 probability that the sample mean will provide a margin of error of a. 7.84 b. 31.36 c. 344.96 d. 1,936

Answers

There is a 0.95 probability that the sample mean will provide a margin of error of 7.84.

What is mean by Probability?

The term probability refers to the likelihood of an event occurring.

Given that;

The variance of a population = 1,936

And, A random sample of 121 has been taken from the population.

Now,

Since, Standard deviation = √ Variance

                                        = √1,936

                                        = 44

Hence, The standard error = 44 / √121

                                         = 44 /11

                                         = 4

We know that;

The critical z factor for a confident interval of 0.95 = ± 1.96

Thus, The sample mean will provide a margin of error = 4 × 1.96

                                                                                    = 7.84

Learn more about the probability visit:

brainly.com/question/13604758

#SPJ5

Answer:

It is known that the variance of a popualtion equals 1,936.

Step-by-step explanation:

That should be correct!!!

Is this one correct?​

Answers

Answer:

do you expect me to flip sideways just to help you cheat on ur homework

Step-by-step explanation:

It’s f .................

In Exercise, expand the logarithmic expression.
ln(x + 1)2

Answers

Answer:

In(x^2+2x+1)

Step-by-step explanation:

In(x+1)^2 = In(x+1)(x+1) = In(x^2+x+x+1) = In(x^2+2x+1)

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