Ettiene solved a quadratic equation. His work is shown below.

In which step did Ettiene make an error?

Answers

Answer 1

The Step 2 shows the mistake done by Ettiene.

What is Quadratic Equation?

A quadratic equation is a second-order polynomial equation in a single variable x, ax²+bx+c=0. with a ≠ 0 .

It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem.

Given:

The given equation is x(x+4)=117.

Step1:  x²+4x=117

Now, b/2 =4/2 =2

Then, add 2² to both the sides of an equation, we get

x²+4x+2²=117+2²

x²+4x+4=117+4

(x+2)²=121

x+2=±√121

x+2=±11

x=±11-2

x=11-2=9 and x=-11-2=-13

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Ettiene Solved A Quadratic Equation. His Work Is Shown Below.In Which Step Did Ettiene Make An Error?

Related Questions

WILL GIVE BRAINLIEST!
Deanna collected data on the favorite sports of the students of two grades. The table shows the relative frequencies of rows for the data collected:


Favorite Sport
Swimming Running Volleyball Row totals
Grade 8 0.14 0.18 0.22 0.54
Grade 9 0.17 0.24 0.05 0.46
Column totals 0.31 0.42 0.27 1


Based on the data, which statement is most likely correct?
A) In Grade 8, 14 students liked swimming.
B) In Grade 9, 31% of students liked swimming.
C) In Grade 8, 22% of students liked volleyball.
D) In Grade 9, 5 students liked volleyball.

Answers

I think the answer is C I’m not sure tho but try it it’s a 50/50

Answer:

In Grade 8, 22% of students liked volleyball.

Step-by-step explanation:

I toke the exam

A rectangular prism is shown below:



What is the volume of the prism?


Question 2 options:




140 in3





104 in3





186 in3





168 in3

Answers

um can you please attach a picture? i’m willing to help you if you do!

Answer:168

Step-by-step explanation:

Which transformation did NOT take place?

Answers

Answer:

C

Step-by-step explanation:

The area of a kite ABCD is 72cm2 and one diagonal is 18cm long. Find the length of the other diagonal.​

Answers

Answer:

8cm

Step-by-step explanation:

1/2 × 18b = 72

9b = 72

b = 72/9

b = 8

Answer:

Answer:

8 cm

Step-by-step explanation:

1/2 × 18 b = 72

9 b = 72

b = 72/9

b = 8

How many one-third cubes are needed to fill the gap in the prism shown below?


A prism has a length of 4 and two-thirds, height of 2, and width of 4. 16 blocks are inside of the prism.

4

8

16

24

Answers

Answer:

The answer is 16 I've seen this before so I would know. and your welcome

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

Which detail explains why police
suspected the thief worked at the
museum?
HELP QUICK

Answers

Answer:

C. The alarm and security cameras were off when the theft took place

Step-by-step explanation:

Answer:

C is the correct answer

Step-by-step explanation:

Write log8 16= 4/3
in exponential form
Can I just get the formula? I don’t remember it

Answers

Answer:

16 = [tex]8^{\frac{4}{3} }[/tex]

Step-by-step explanation:

Using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]

Given

[tex]log_{8}[/tex] 16 = [tex]\frac{4}{3}[/tex], then

16 = [tex]8^{\frac{4}{3} }[/tex] ← in exponential form

Is (-4,4) the solution of the system. 4x+5y>-6 and -2x+7y>20

Answers

Answer:

  It is a solution, one of an infinite number of solutions.

Step-by-step explanation:

You can check to see if the given point is in the solution set:

  4(-4) +5(4) = -16 +20 = 4 > -6 . . . . yes

  -2(-4) +7(4) = 8 +28 = 36 > 20 . . . yes

The offered point satisfies both inequalities, so is in the solution set. It is not the solution, but is one of an infinite number of solutions.

What is the period of this graph?

Answers

Answer:

Period is time between the two peaks.

Period = 4.114 - 1.870

Period = 2.244 seconds

Step-by-step explanation:

Answer:

p=2.244 and b = 2.8

Step-by-step explanation:

edge 2023

The box plots below show the average daily temperatures in January and December for a U.S.city:
January
December
What can you tell about the means for these two months? (1 point)

Answers

Answer:

There is no way of telling what the means

Step-by-step explanation:

I think your question missed key information, allow me to add in and hope it will fit the orginal one. Please have a look at the attached photo

My answer:

There is no way of telling what the means are because we do not the exactly number of the average daily temperatures even the narrow IQR for January  is but we can not make sure it is lower than the  IQR for December when having no real number.

Hope it will find you well.

A restaurant noted what type of food its customers purchased last week. Here are the results:

Burger

Fries

15%

55%

10%

20%

In this sample, are the events "burger" and "fries" mutually exclusive?

Answers

Answer:

No, they are not mutually exclusive because a customer can purchase a burger and fries together.

Step-by-step explanation:

Mutually exclusive events are events that cannot occur at the same time, e.g. I cannot sleep while running. In the case of a restaurant, you could consider purchasing pizza and burgers as mutually exclusive since most people would only purchase one of them (unless they eat a lot). But burgers and fries are not mutually exclusive because people can purchase them together.

convert 3.5 gallons to litres

Answers

Answer:    13.2489 Liters

Step-by-step explanation:

Answer:

[tex]13.2489l[/tex]

Use trianglePQR to write the trigonometric ratio as a decimal. round to four decimal places.

Answers

I hope this answer helps, it’s kinda messy, but it’s still understandable (I guess)

need answer 1-4 please worth 30!

Answers

I don’t know the actual answer but there are answer keys all over the internet love. type in the top corner of the page along with one of the questions and the full key should pop up

26 out of 48 books are small. What percentage of the books are small?

Answers

Answer:

54.16%

Step-by-step explanation:

The percentage of books that are some is 54.16 %

In order to find that answer you would have to calculate the total number of small books (26) over the total number of all of the books (48).

The equation would be 26/48=0.5416 however Multiply that answer by 100 and you would get 54.16% and if you want to round to the nearest whole number it would just be 54%

Can someone please help

Answers

Answer:

C

Step-by-step explanation:

We need to use the distance formula, which says that for two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], the distance between them is:

d = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Here, the two points are (-2.5, 4.5) and (4.75, 4.5), so:

d = [tex]\sqrt{(4.75-(-2.5))^2+(4.5-4.5)^2}=\sqrt{(7.25)^2+(0)^2}=7.25[/tex] = 7 1/4

The answer is C.

Answer:

7¼ units

Step-by-step explanation:

Since the y-coordinate is the same, the two points lie on the same horizontal line

No vertical distance

Only horizontal distance of:

4¾ - (-2½)

4.75 + 2.5

7.25 units

Or

7¼ units

How do I find x???????​

Answers

Answer:

Step-by-step explanation:

x=30

Right traingles angles add up to 90 degrees so 30+60=90

I dont understand what the 14 is up there for though

I am very late for this question ;w;

Nara got two new plants for her apartment. Each plant grew at a constant rate.

The height (in centimeters) of the first plant as a function of time (in days since Nara got it) is given by the following table of values:

Time\text{Time}Timestart text, T, i, m, e, end text (days) Height\text{Height}Heightstart text, H, e, i, g, h, t, end text (centimeters)

10 34

15 36

20 38

The graph of the height (in centimeters) of the second plant as a function of time (in days since Nara got it) is shown below.

Which plant was taller when Nara got the plants?

Choose 1 answer:

Choose 1 answer:


(Choice A)

A

The first plant

(Choice B)

B

The second plant

(Choice C)

C

They were equally tall


Which plant grew faster?

Choose 1 answer:

Choose 1 answer:


(Choice A)

A

The first plant

(Choice B)

B

The second plant

(Choice C, Checked)

C

They both grew at the same rate

Answers

Answer:

Which plant was taller when Nara got the plants? C. They were equally tall

Which plant grew faster?  B. The second plant

Step-by-step explanation:

Slope of the first plant :

m = (y2 - y1)/(x2- x1)

m = (36 - 34)/(15 - 10) = 0.4

y-intercept of the first plant :

y = m*x + b

b = y1 - m*x1

b = 34 - 0.4*10 = 30

From the picture we can see that the y-intercept of the second plant is 30 cm

Y-intercept represents plant heights when Nara got the plants; then they were equally tall

From the picture we can see that second plant grew 2 cm in 2 days; then its slope is 2/2 = 1

Slope measures how fast each plant grew; then the second plant grew faster

Matt has $900 in a checking account, has $15,000 in investments, owns an
$8000 car, and owns a $30,000 house. What is the total value of his large
assets

Answers

Final answer:

The total value of Matt's large assets, which include his investments, car, and house, adds up to $53,000.

Explanation:

The student is asking about calculating the total value of large assets that Matt owns. To find this, we add up the value of the investment, car, and house as these are considered large assets. The checking account is generally not included in large assets, as it is considered liquid cash rather than an asset of substantial value like property or investments.

Investments: $15,000Car: $8,000House: $30,000

We calculate the sum of these amounts to get the total value of Matt's large assets:

$15,000 + $8,000 + $30,000 = $53,000

Therefore, the total value of Matt's large assets is $53,000.

1.) What four-digit number has a digit 2 smaller than digit 4 which is two thirds of digit 1 which is two thirds of digit 3 which is three times digit 2?

2.) What number comes next in this sequence:
917452; 97452; 9745; 975; _ ; _ ?

Answers

Answer:

i dont know the first one but the second one is 97

Step-by-step explanation:

the lowest digit gets dropped

Answer:

1) 6394

2) 97, 9

Step-by-step explanation:

1)

WXYZ

X < Z

Z = ⅔W

W = ⅔Y

Y = 3X

W = ⅔(3X) = 2X

Z = ⅔(2X) = (4/3)X

X has to be a multiple of 3

If X = 3,

Y = 9

Z = 4

W = 6

WXYZ

6394

2)

917452; 97452; 9745; 975; _ ; _ ?

Just remove the smallest digit to get the next terms

97, 9

Expand
3m (m +1)
???????????????

Answers

Answer:

3m^2+3

Step-by-step explanation:

Step 1:  First you have your equation or something.

3m (m+1)

Step 2: You multiply the parenthesis with the number.

Step 3: Then 3m to the parenthesis if you have 3m and m will convert to m^2.

Step 4: Your answer would be 3m^2+3

Answer:

So you solve it .... 3m^2+ 3m

Step-by-step explanation:

Which type of graph would you choose to show the test scores for a whole class arranged in Intervals?
bar graph
Circle graph
histogram
line graph

Answers

i'd go with a bar graph, it just seems the most logical way to organize test scores

Answer:

---------bar graph

Step-by-step explanation:

What effect will multiplying by 3 have on f(x)?

Answers

Answer:For a positive value k, the graph of y=kf(x) is obtained from the graph of y=f(x) by scaling in the vertical direction. In coordinates, if (x0,y0) is on the graph of y=f(x), then that point moves to (x0,ky0) on the graph of y=kf(x). Any point on the x-axis remains fixed (as then y=0). When k>1, the graph is stretched vertically (away from the x-axis), while if 0<k<1, the graph is compressed vertically (toward the x-axis).

Another way to think about this: The graph of y=kf(x) is exactly the same as the graph of y=f(x) if the y-axis is scaled so that 1 is relabeled k, 2↦2k, −1↦−k, etc.

Step-by-step explanation:

The table below shows the ages of houses to the nearest year in a neighborhood. Using the age of the houses as the random variable, X, which graph shows the probability distribution, PX(x), of a randomly chosen house? HURRYYYYYYY!!!!!

Answers

Answer:

Find the probability distribution by dividing the number of houses in each category by the total number of houses. We find that Graph A most accurately shows the distribution.

Step-by-step explanation:

Let's start by finding the probability of randomly selecting a house in each category. To find the probability, divide the number of houses in the category by the total number of houses.

The total number of houses is 15 + 20 + 25 + 30 = 90. The number of 1 y/o houses is 15. Dividing these two numbers, we get 15/90 = 0.167

Make the same calculation for the other ages:

2 y/o: 20/90 = 0.222

3 y/0: 25/90 = 0.278

4 y/o: 30/90 = 0.333

Now, look at the graphs to determine which most closely matches these calculations. (Note: make sure to look closely at the axis.) That graph is A.

Find the equation of the line that has slope of 7 and passes through the point (-9,2).

Answers

Answer:

y=7x+65

Step-by-step explanation:

You want to find the equation for a line that passes through the point (-9,2) and has a slope of 7.

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

To start, you know what m is; it's just the slope, which you said was 7. So you can right away fill in the equation for a line somewhat to read:

y=7x+b.

Now, what about b, the y-intercept?

To find b, think about what your (x,y) point means:

(-9,2). When x of the line is -9, y of the line must be 2.

Because you said the line passes through this point, right?

Now, look at our line's equation so far: . b is what we want, the 7 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the the point (-9,2).

So, why not plug in for x the number -9 and for y the number 2? This will allow us to solve for b for the particular line that passes through the point you gave!.

(-9,2). y=mx+b or 2=7 × -9+b, or solving for b: b=2-(7)(-9). b=65.

The equation of the line that passes through the point (-9,2) with a slope of 7

is

y=7x+65

Have a nice day!

If another 10-year old were to join the baseball team shown in the scatter plot below, what is the best estimate for his height?

A.) 55 in
B.) 64 in
C.) 58 in
D.) 60 in

Answers

Answer:

55

Step-by-step explanation:

Answer:

55

Step-by-step explanation:

ANSWER QUICKLY ASAP. ​

Answers

(4,4) and (8,8), I hope this helps you!!!
I think the answer is

(4, 4) and (8, 8)

:D

Which of the following is an expression for” twice a number n divided by 3” A. 2/3n B. 2n/3 C. 2+n/3 D. n2/3

Answers

Answer:

B) 2n/3

Step-by-step explanation:

twice a number n = 2 * n = 2n

divided by 3 = 2n/3

Answer:

d

Step-by-step explanation:

The graph of a polynomial function is shown here.
Which statement about the polynomial function is true?
es
A)
It is of odd degree and has 3 real zeroes.
B)
It is of odd degree and has 2 real zeroes.
C)
It is of even degree and has 2 real zeroes.
D
It is of even degree and has 3 real zeroes.

Answers

Answer:

B

Step-by-step explanation:

Final answer:

The polynomial function shown in the graph is of even degree and has 2 real zeroes.

Explanation:

The polynomial function shown in the graph appears to have 2 real zeroes. Since the degree of the polynomial cannot be determined from the graph alone, we cannot determine if it is of odd or even degree. Therefore, option A) and B) can be eliminated. Thus, the correct answer is C) It is of even degree and has 2 real zeroes.

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According to a recent New York Times poll, 25% of the public have responded to a telephone call-in
poll. Based upon this information, what is the probability that exactly two people out of a randomly
chosen group of five people have responded to a telephone call-in poll? Round your answer to the
nearest thousandth (3 decimal places).

Answers

Answer:

Probability that exactly two people out of a randomly  chosen group of five people have responded to a telephone call-in poll is 0.264.

Step-by-step explanation:

We are given that according to a recent New York Times poll, 25% of the public have responded to a telephone call-in  poll.

Also, five people have people have been randomly selected.

The above situation can be represented through binomial distribution;

[tex]P(X = r) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r};x=0,1,2,3,.......[/tex]

where, n = number trials (samples) taken = 5 people

           r = number of success = exactly two

           p = probability of success which in our question is probability that

                 public have responded to a telephone call-in  poll, i.e; p = 25%

Let X = Number of people who have responded to a telephone call-in  poll

So, X ~ Binom(n = 5, p = 0.25)

Now, probability that exactly two people out of group of five people have responded to a telephone call-in poll is given by = P(X = 2)

                P(X = 2)  =  [tex]\binom{5}{2} \times 0.25^{2} \times (1-0.25)^{5-2}[/tex]

                               =  [tex]10 \times 0.25^{2} \times 0.75^{3}[/tex]

                               =  0.264

Therefore, the probability that exactly two people out of a randomly  chosen group of five people have responded to a telephone call-in poll is 0.264.

Final answer:

The probability of exactly two people responding is 0.262 in this case.

Explanation:

To calculate the probability that exactly two people out of a randomly chosen group of five people have responded to a telephone call-in poll, we need to use the binomial distribution formula. The formula is: P(X=k) = C(n, k) * p^k * (1-p)^(n-k), where P(X=k) is the probability that k people responded, C(n, k) is the number of ways to choose k people out of n, p is the probability of success (25% in this case), and n is the number of trials (5 in this case).

Plugging in the values: P(X=2) = C(5, 2) * (0.25)^2 * (0.75)^(5-2)

Simplifying and calculating, we get: P(X=2) = 10 * 0.0625 * 0.421875 = 0.26172

Rounding to the nearest thousandth, the probability that exactly two people out of a randomly chosen group of five people have responded to a telephone call-in poll is approximately 0.262.

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