Solve the following problem for the roots by completing the square

3x^2 -12x = 9

Answers

Answer 1

3(x^2+3) is the answer you are looking for. :)

Answer 2

3x^2 - 12x = 9
Divide both sides by 3
x^2 - 4x = 3
To make a square with "x^2 - 4x", you need to have a "+ 4" after it so it can be simplified as (x-2)^2. So add 4 to both sides.
x^2 - 4x + 4 = 7
(x-2)^2 = 7
x - 2 = (square root) of 7
x = 2 (+/-) (square root) of 7.
x = {-0.65, 4.65}

The solutions are -0.65 and 4.65.

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Related Questions

Suppose that you have he option to buy an item with either cash or credit. Under which condition would you use credit?

Answers

if they didn't take cash

Answer:

If you want to build a good credit history

Step-by-step explanation:

Buying something in order to build a good credit history does not benefit in the short run such as any financial or non-financial benefit.

However, when need arises to make request for a large sum of loan in the long run (such as buying house, purchasing vehicle or capital for investing in business) from the financial institution or any other credit providers, then the good credit history would be winning key factor for obtaining the loan.

Sue receives a base salary of $90 weekly plus a 12% commission on all sales. sue had $3,000 in sales this week. how much did she make total?

Answers

$90+12/100x = y

Where x is sales made and y is total money made

$90 + 12/100 x 3000 = y

Y = 450

She made $450

Her gross pay was the amount of $450 for last week.

What is the commission?

The commission is determined by the product of the commission rate and the total sales.

Commission = Commission rate x Total sales

As per the question, we have data :

Commission rate = 12 %

Total sales = $3,000

The base salary = $90

We know that,

Commission = Commission rate x Total sales

= 12% x $3,000

= 0.12 x $3,000

= $360

The total pay is then the base salary increased by the commission:

Total pay = base salary + Commission

Total pay = $90+ $360

Total pay = $450

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Amy leaves a rest stop at 2 PM traveling west, at 45 miles per hour. Sarah leaves 2 hours later, also traveling west, but at 55 miles per hour. At what time will Sarah catch up with Amy?

Answers

55(t-2) =45t

55t-110 = 45t

-110 = -10t

t = 11 hours

2 pm plus 11 hours = 1 am

Answer: mathematics, central tendency is the tendency of data values to cluster around some central value. What does a measure of variability tell you about the central tendency of a set of data? ... If the range and IQR are small, the values are clustering around some central value.

Step-by-step explanation:

-3x+2y=-10, -2x+y=-6 solve by substitution

Answers

-2x+y=-6 (this equation is easier since you can get y=something easily.)
y = -6+2x
So, you can substitute y in the other equation.
-3x+2(-6+2x)=-10
-3x-12+4x=-10
x-12=-10
x=2
You can get y value by substituting too.
y=-6+2(2)=-2

Solve the literal equation 2a-b=8b-4a for a

Answers

a = 1.5b
Have a great day!

firs you need to look for the like terms (look at the a terms) then you will need to look for any other like terms in this case look at the b and the 8b it would probably be easier to add or subtract the smallest number. then if you answer turns out to be 2/3 your correct. HOPE IT HELPS SORRY IF YOU DONT GET IT.

Which expression represents the phrase, "one third the sum of 12 and a number"?

Answers

1/3(12 + x) is your answer

you must get the sum first before you can one third it

hope this helps

Let

x--------> the number

we know that

1) the phrase, "the sum of 12 and a number"

represent the expression --------> [tex](12+x)[/tex]

and

2) the complete phrase, "one third the sum of 12 and a number"

represent the expression --------> [tex]\frac{1}{3}(12+x)[/tex]

therefore

the answer is

[tex]\frac{1}{3}(12+x)[/tex]

Twice a number is added to the number and the answer is 90. find the number

Answers

let the first number be x
so the pther number becomes 2x

According to question
x+ 2x = 90
3x = 90
x = 30

so, the first number = 30
and the other one is 2x = 2 (30) = 60.

Write the polynomial in standard form. identify the degree and leading coefficient of the polynomial. then classify the polynomial by the number of terms

Answers

You'll need to post the polynomial itself. The degree will be the highest exponent, the leading coefficient will be the number in front of the variable of the term with the highest exponent, then count the number of terms separated by + and - signs.

The Standard Form: -w¹² + 4w¹¹,

Degree: 12 degree

Leading Coefficient: -1

What is polynomial?

Polynomial is formed composed of the phrases Nominal, which means "terms," and Poly, which means "many." An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

Given equation

4w¹¹ - w¹²

Standard form of polynomial,

List the exponents in decreasing order of importance.

-w¹² + 4w¹¹

Degree of polynomial,

The degree, or the exponent in the first term, if it is in standard form, is the biggest exponent.

degree is 12.

Leading coefficient,

the first term's standard form coefficient Before the w in the first phrase, there is and understood 1.

for equation coefficient is -1,

Hence degree = 12, and leading coefficient is -1.

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The complete Question is

Write the polynomial in standard form. Identify the degree and leading coefficient of the polynomial.

Then classify the polynomial by the number of terms.

4w11 - w12

standard form

degree

leading coefficient.

Claire made 1⁄2 pound of trail mix. If she puts 1⁄4 pound of trail mix into each bag, how many bags are filled?

Answers

There's 2 bags filled. 1/2 is equal to 2/4. If Claire does put 1/4 pound of trail mix into each bag, like the problem said, then she fills 2 bags.

Subtract the polynomials: (3x2 + 2x + 4) - (x2 + 2x + 1). Enter your answer as a polynomial in descending order below, and use the caret (^) for exponents. For example, you would write as 4x^2.

Answers

Line up the like terms like so

3x^2 + 2x + 4
x^2 + 2x + 1

Now subtract straight down
3x^2 - x^2 = 3x^2 - 1x^2 = 2x^2
2x - 2x = 0x = 0
4 - 1 = 3

The results of 2x^2, 0 and 3 are added up to get 2x^2 + 0 + 3 and that turns into 2x^2 + 3

Answer: 2x^2 + 3

What is 7,130 divided by 86?

Answers

the answer is 82.906

4 pieces of wood each 11 and a half inches long are required to build a cabinet. If all four pieces are cut from one board and 1 inch is allowed for waste in cutting each piece, how long should the board be?

Answers

ok first we calculate the length of board without losses:
4 * 11.5 = 46 inches
then, we have 1 inch of waste allowed fir each piece, so the total waste is 4*1 = 4 inches

finally, we will add the length of the waste to the desired length to get the total length of the board as follows:
total length of board = 46+4 = 50 inches

what is the area of a circular mirror with a radius of 10 cm?

Answers

area=pi r squared
area=3.14 x 10squared
area= 314
the answer is 314

Final answer:

The area of a circular mirror with a radius of 10 cm is calculated using the formula πr², which results in an area of 314.16 cm².

Explanation:

The area of a circular mirror can be calculated using the formula πr², where π (pi) is approximately 3.1416 and r is the radius of the circle. Given the radius of the circular mirror as 10 cm, we can substitute this value into the formula to find the area.

Area = π × (10 cm)²
A = 3.1416 × 100 cm²
A = 314.16 cm²

Therefore, the area of the circular mirror is 314.16 cm².

if you live in Dallas then you live in Texas what is the biconditional of this

Answers

you live in Dallas, if and only if you live in Texas

Final answer:

The biconditional of the statement 'If you live in Dallas then you live in Texas' is 'You live in Dallas if and only if you live in Texas'. This means that living in Dallas is both necessary and sufficient for living in Texas.

Explanation:

The biconditional of the statement 'If you live in Dallas then you live in Texas' would be 'You live in Dallas if and only if you live in Texas'. In other words, living in Dallas is both necessary and sufficient for living in Texas. This means that if one condition is true, then the other must also be true. Similarly, if one condition is false, then the other must also be false. A biconditional statement essentially equates the truth of two conditions.

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Laura drove to the mountains last weekend. there was heavy traffic on the way there, and the trip took 8 hours. when laura drove home, there was no traffic and the trip only took 6 hours. if her average rate was 16 miles per hour faster on the trip home, how far away does laura live from the mountains

Answers

Final answer:

To find the distance Laura lives from the mountains, calculate her average speed when driving to the mountains and use the time taken during the trip. With the given speeds and travel times, the distance can be determined using a simple equation.

Explanation:

To find the distance Laura lives from the mountains:

Let x be Laura's average speed when driving to the mountains.Since Laura drove 16 mph faster on the way home, her speed returning was x+16 mph.Distance to mountains = x * 8 (hours) and distance from mountains = (x+16) * 6 (hours).Set up the equation: x * 8 = (x+16) * 6 to solve for x.Once x is found, the distance Laura lives from the mountains can be calculated as x * 8.

the perimeter of a square picture frame is 48 inches. one side length of the frame is 30.48 centimeters. how many centimeters are in an inch?
The answer is 2.54 centimeters but i need help with my work

Answers

Since the perimeter is 4 times a side in a square, we get 48/4=12 inches per side, and 12 in= 30.48 cm. Dividing both sides by 12,we get 1in= 2.54 cm

Three sides of a fence and an existing wall form a rectangular enclosure. the total length of fence used for three sides is 240 ft. write the area function in terms of one variable, then find the domain of that function

Answers

Let the length of the side opposite the wall be x, and the lengths of the other 2 sides be y.

x+2y=240 ft

then

2y=240-x
y=(240-x)/2=120-x/2

The area of the rectangular enclosure is determined by the function
[tex]A(x)=x \cdot y =x \cdot (120-x/2)[/tex] (square feet)

both width and length must be >0,

so we must have:

i) x>0
ii) 120-x/2>0 (at the same time)

solving the second inequation:

120-x/2>0

120>x/2

240>x

so x must be smaller than 240, but also larger than 0.

Thus the domain is (0, 240)

Answer: Domain: (0, 240)

Jana is thinking of a number. If she divides her number by 12 and then multiplies the quotient by 8, the result is 520. What number is Jana thinking of?

Answers

You would do the reverse of what was done so you would do 520/8 and then multiply that by 12 so you get 780

What is 7 more than five times the number 9 divided by 15?

Answers

Answer:

7 more than five times the number 9 divided by 15 is, 10

Step-by-step explanation:

As per the statement:

7 more than five times the number 9 divided by 15

"five times the number 9" translated to [tex]5 \times 9 = 45[/tex]

"five times the number 9 divided by 15" translated to [tex]\frac{45}{15} = 3[/tex]

then;

"7 more than five times the number 9" divided by 15 means 7 + 3 = 10

Therefore, 7 more than five times the number 9 divided by 15 is, 10

Answer:

Step-by-step explanation:

Hope this helps!

Write an equation that represents degrees fahrenheit in terms of degrees celsius. let xx represent the temperature in degrees celsius and let yy represent the temperature in degrees fahrenheit.

Answers

As we know Conversion from fahrenheit to celsius is
[tex]F - 32 = \frac{9C}{5} [/tex]

We can write it also as

[tex]F = \frac{9C}{5}+32 [/tex]

F as y and C as x then we can write it as

[tex]y = \frac{9x}{5} + 32 [/tex]

An equation is formed of two equal expressions. An equation that represents degrees Fahrenheit in terms of degrees celsius is y=(9/5)x+32.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The equation to covert degrees fahrenheit to degrees celsius is given as,

(C × 9/5) + 32 = F

where C represents temperature in degrees Celcius and F represents the temperature in degrees Fahrenheit.

Now, we need to represent the degree Celcius by x, while the degree Fahrenheit by y. Therefore, the above equation can be rewritten as,

y = (x × 9/5) + 32

y = (9/5)x + 32

Hence, an equation that represents degrees Fahrenheit in terms of degrees celsius is y=(9/5)x+32.

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Need help finishing problem 27.

Answers

It looks as though the formula is right there.
Total = 1,000 * (1 +[.0925/12])^12*42
Total = 1,000 * (1.00770833333333)^504
Total = 1,000 * 47.9473276233
Total = 47,947.33

I've never even seen a box and whiskers plot before!! Should be pretty straight forward though. Thanks!

Answers

For a box and whispers plot, each section represents 25% of the data. Therefore, the area from 85-99 represents 25% of the data.

25% of 24 students= 6 students
Final answer: 6 students

So a box and whiskers plot is relatively simple if you know how to do it.

The left whisker ending, which is at 35, signifies the minimum.

The right whisker ending, which is at 99, signifies the maximum.

The middle line, at 68, is the median.

And the edge of the box on the left, at 50, is the First Quartile. (If you don't know what that is, basically the marker in between the first quarter and the second quarter)

And the edge of the box on the right is the Third Quartile, (Same thing except in between the third quarter and fourth)

So since the question is asking how many students scored better than an 85, and we know that 85 is the third quartile here, we know that 1/4 of the students scored better than an 85.

(So basically each section is 1/4 of the data set)

And 1/4 of 24 is 6.

So 6 students scored better than an 85.

What is767,074 rounded to the nearest hundred thousand

Answers

800,000 is the answer

800,000 is the rounded answer.

The cruise control function on Georgina's car should keep the speed of the car within 3 miles per hour of the set speed. The set speed is 55 miles per hour. Write a compound inequality to show the leaves that are within each range. Then graph the solutions.

Answers

This should help. Sorry I had to make this rn.

Answer:

Given,

Set speed of car = 55,

∵ The speed of the car within 3 miles per hour of the set speed.

So, the maximum speed of car = 55 + 3,

And, the minimum speed of car = 55 - 3

Let x shows the current speed of car,

x ≤ 55 + 3 or x ≥ 55 - 3

x - 55 ≤ 3 or x - 55 ≥ - 3

x - 55 ≤ 3 or -(x-55) ≤ 3

⇒ | x-55 | ≤ 3

Which is the required compound inequality,

Now, 55 - 3 ≤ x ≤ 55 + 3

52 ≤ x ≤ 58

⇒ [52, 58]

Which is the solution of the above compound inequality.

Also, the graph is shown below.

How many n's are there in an atom of p-33?

Answers

There are 2 n's in the atom of p-33.

The penny size d is given by the literal equation d = 4n - 2, solve for n

Answers

Thanks for your question!

d = 4n -2
d + 2 = 4n
(d+2)/4 = n

Hope this helped!

Over the past ten years, the town's population doubled in size. The population is currently 12,000. What was the population ten years ago?

Which of the following represents the given word problem if "P" represents the population ten years ago?

Answers

I think the answer is 2P = 12,000 but I might be wrong

Help In Math Please!!
The graphic shows the average number of points scored per game for ten players in the NBA.

What is the interquartile range (IQR) of the data set.
A) 1.1
B) 4.9
C) 6.9
D) 9.8

Answers

To calculate the interquartile range of a dataset, we first arrange the dataset in order:

Since the given dataset is already arranged in order.

We obtain the Q1 and the Q3 data values.

The Q1 value is the value for which 25% of the datavalues lie below it. For the given dataset, the Q1 value is 24.

Similarly, the Q3 value is the value for which 25% of the datavalues lie above it. For the given dataset, the Q1 value is 28.9.

The interquartile range is given by

IQR = Q3 - Q1 = 28.9 - 24 = 4.9

Therefore, the interquartile range (IQR) of the data set is 4.9.

Answer:

The other answer for USA TP is 26.25

Step-by-step explanation:

The mean is the average of the numbers.

29.8 + 29.6 + 28.9 + 27.1 + 26.4 + 25.5 + 24.5 + 24.0 + 23.8 + 22.9

= 26.25

Determine the 3-day sma for the ten consecutive day closing prices of sprint nextel corp listed below. $7.78, $8.08, $7.99, $8.02, $7.89, $8.72, $9.19, $9.16, $8.98, $9.38

Answers

The 3-day moving average is the average 3 number moiving one place each time.

The 3-day sma for the ten consecutive day closing prices is given by of sprint nextel corp:

(1st day price + 2nd day price + 3rd day price) / 3 = ($7.78 + $8.08 + $7.99) / 3 = $23.85 / 3 = $7.95

(2nd day price + 3rd day price + 4th day price) / 3 = ($8.08 + $7.99 + $8.02) / 3 = $24.09 / 3 = $8.03

(3rd day price + 4th day price + 5th day price) / 3 = ($7.99 + $8.02 + $7.89) / 3 = $23.90 / 3 = $7.97

(4th day price + 5th day price + 6th day price) / 3 = ($8.02 + $7.89 + $8.72) / 3 = $24.63 / 3 = $8.21

(5th day price + 6th day price + 7th day price) / 3 = ($7.89 + $8.72 + $9.19) / 3 = $25.80 / 3 = $8.60

(6th day price + 7th day price + 8th day price) / 3 = ($8.72 + $9.19 + $9.16) / 3 = $25.80 / 3 = $27.07 / 3 = $9.02

(7th day price + 8th day price + 9th day price) / 3 = ($9.19 + $9.16 + $8.98) / 3 = $27.33 / 3 = $27.33 / 3 = $9.11

(8th day price + 9th day price + 10th day price) / 3 = ($9.16 + $8.98 + $9.38) / 3 = $27.33 / 3 = $27.52 / 3 = $9.17

Therefore, the 3-day sma for the ten consecutive day closing prices of sprint nextel corp are $7.95, $8.03, $7.97, $8.21, $8.60, $9.02, $9.11, $9.17

Answer:

Step-by-step explanation:

The 3-day moving average is the average 3 number moiving one place each time.

The 3-day sma for the ten consecutive day closing prices is given by of sprint nextel corp:

(1st day price + 2nd day price + 3rd day price) / 3 = ($7.78 + $8.08 + $7.99) / 3 = $23.85 / 3 = $7.95

(2nd day price + 3rd day price + 4th day price) / 3 = ($8.08 + $7.99 + $8.02) / 3 = $24.09 / 3 = $8.03

(3rd day price + 4th day price + 5th day price) / 3 = ($7.99 + $8.02 + $7.89) / 3 = $23.90 / 3 = $7.97

(4th day price + 5th day price + 6th day price) / 3 = ($8.02 + $7.89 + $8.72) / 3 = $24.63 / 3 = $8.21

(5th day price + 6th day price + 7th day price) / 3 = ($7.89 + $8.72 + $9.19) / 3 = $25.80 / 3 = $8.60

(6th day price + 7th day price + 8th day price) / 3 = ($8.72 + $9.19 + $9.16) / 3 = $25.80 / 3 = $27.07 / 3 = $9.02

(7th day price + 8th day price + 9th day price) / 3 = ($9.19 + $9.16 + $8.98) / 3 = $27.33 / 3 = $27.33 / 3 = $9.11

(8th day price + 9th day price + 10th day price) / 3 = ($9.16 + $8.98 + $9.38) / 3 = $27.33 / 3 = $27.52 / 3 = $9.17

Therefore, the 3-day sma for the ten consecutive day closing prices of sprint nextel corp are $7.95, $8.03, $7.97, $8.21, $8.60, $9.02, $9.11, $9.17

Find the perimeter of the polygon with the vertices g(2, 4), h(2,−3), j(−2,−3), g(2, 4), h(2,−3), j(−2,−3), and k(−2, 4)k(−2, 4).

Answers

The distance between g and h is sqrt[(2-2)^2+(4+3)^2]=7 The distance between h and j is sqrt[(2+2)^2+(-3+3)^2]=4 The distance between j and k is sqrt[(-2+2)^2+(-3-4)^2]=7 The distance between k and g is sqrt[(-2-2)^2+(4-4)^2]=4 The perimeter of the polygon is 7+4+7+4=22

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Solve the following problem for the roots by completing the square 3x^2 -12x = 9

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Solve the following problem for the roots by completing the square

3x^2 -12x = 9