Use the method of completing the square to transform the quadratic equation into the equation form (x + p)2 = q. 3 + x - 3x2 = 9

Answers

Answer 1

[tex]x-3x^2=9\\\\3x^2-x=-9\ \ \ \ |:3\\\\x^2-\dfrac{1}{3}x=-3\\\\x^2-2\cdot x\cdot\dfrac{1}{6}+\left(\dfrac{1}{6}\right)^2=-3+\left(\dfrac{1}{6}\right)^2\ \ \ \ |use:\ (a-b)^2=a^2-2ab+b^2\\\\\left(x-\dfrac{1}{6}\right)^2=-3+\dfrac{1}{36}\\\\\left(x-\dfrac{1}{6}\right)^2=-2\dfrac{35}{36}[/tex]

Answer: No solution.

Related Questions

find the difference. express your answer in simplest form. (4r/s) - (r/s)

Answers

your answer would be 4 because r/s - r/s would be 0 so you have 4 left hope this helps you!!!!

For this case we have the following expression:
(4r / s) - (r / s)
We observe that we have the term r / s in the whole expression.
Therefore, we can draw common factor.
Rewriting we have:
(r / s) * (4-1)
(r / s) * (3)
3 (r / s)
Answer:
the difference is:
3 (r / s)

kendra flips a coin 3 times what is the probability that she flips tails all 3 times

Answers

If Kendra were to flip the coin only once, she'd have a fifty fifty chance (1/2). Two times for tails would be (1/2) again, since (1/4+1/4=1/2). Now, three times would be (1/6+1/6+1/6). This equals (1/2), so she remains at a 50% chance of flipping the coin three times.

To find the probability of flipping tails all three times, we need to consider that each flip of a fair coin has a probability of 0.5 of landing on tails.

Since the coin flips are independent events (the outcome of one flip doesn't affect the outcome of another flip), we can simply multiply the probability of each individual flip.

So, the probability of flipping tails three times in a row is:

P(Tails, Tails, Tails) = P(Tails) × P(Tails) × P(Tails)

P(Tails, Tails, Tails) = 0.5 × 0.5 × 0.5

P(Tails, Tails, Tails) = 0.5³

P(Tails, Tails, Tails) = 0.125

So, the probability that Kendra flips tails all three times is 0.125 or18.

The probability of flipping tails on a fair coin is 0.5 (or 1/2) since there are two equally likely outcomes, heads or tails. When flipping a coin three times, each flip is independent, meaning the outcome of one flip doesn't affect the outcome of another.

To find the probability of flipping tails all three times, we multiply the probability of each individual flip.

So, 0.5 (tails on the first flip) times 0.5 (tails on the second flip) times 0.5 (tails on the third flip) equals 0.5³ = 0.125.

Therefore, the probability that Kendra flips tails all three times is 0.125 or 1/8.

Complete Question:

Kendra flips a coin 3 times what is the probability that she flips tails all 3 times.

Need help please, pt 4 Thanks!

Answers

Hello,
Please, see the attached files.
Thanks.

556 multiplied by 34

Answers

556 x 34 = 18,904
Mark brainliest if this helped :D

The answer to 556 * 34 is 18,904.

major help and if you can, please explain how you got your answer

Answers

The correct answer is: [A]: " 384 in² " .
_______________________________________________________

Explanation:
______________________________________________________
The formula for the surface area of a cube is:
______________________________________________________

→ A = 6a² ;
______________________________________________________ → in which:
______________________________________________________
  A = surface area of the cube— for which we shall solve ;
(in "square units" ; or, " in² " ; in our case) ;

a = side length = " 8 in " (given);

→ Note: A cube has all equal side lengths.

→ The "6" in the formula accounts for "6 sides" of a cube.

_______________________________________________________

→ To solve for the surface area of the cube; plug in our known value(s);
& solve; as follows:
_______________________________________________________
  → A = 6 a² ;

= 6 * (8 in)² ;

= 6 * 8² * in² ;

= 6 * 8 * 8 * in² ;

= 48 * 8 * in² ;

= 384 in² ;
_______________________________________________________
The answer is: " 384 in² " ;

→ which is: Answer choice: [A]: " 384 in² " .
_______________________________________________________

Emilio borrows $1200 from a bank with 8% simple interest per year. How much interest will he have to pay back in 2 years?

Answers

Simple Interest equation is I=p×r×t
P= is the principal amount (1200)
R= is the interest rate per year (8% or 0.08)
T= time in years (2)

I= 1200 × 0.08 × 2= 192.00

Interest is 192.00

The interest per year on the amount of money that Emillio borrowed from the bank at the rate of 8% interest is $192

Interest can be regarded as the charges that is added to the principal, usually some percentage of the principal.Principal is the amount of money that is been lent out.Rate can be regarded as the percentage increase of the principal.Time (t) can be regarded as the period that is needed to pay the money that was lent out back.

were were given rate (r) as[tex]8% = 0.08[/tex]%with[tex]interest (I)[/tex]as ?[tex]principal (P)= $1200[/tex]

From the the formula for expressing

[tex]simple interest [ I= prt][/tex]

[tex]P= principal \\ I= interest\\ r= rate[/tex]Then substitute into the formula[tex]I= (1200 * 0.08 * 2)[/tex]

[tex]= 192.00[/tex]

Therefore, the interest on the money is $192

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Isabella and Mateo each collect beautifully polished rocks. The weights, in ounces, of their rocks are listed below.

Which statistical measure could be used to support the claim that Mateo’s rocks generally weigh more than Isabella’s rocks?

Question 7 options:

A) mean

B) median

C) mode

D) range

Answers

In order to answer this question we have to find all the 4 measure, Mean, Median, Mode and Range of both data sets.

1) For the Rocks of Isabella:

Mean = (Sum of all numbers)/Total numbers
So, Mean weight of Isabella's Rocks = 7.64

Median is the central value.
So, Median weight of Isabella's Rocks = 6

Mode is the most frequently occurring value.
So, Mode weight of Isabella's Rocks = 8.75

Range = Maximum - Minimum
So, Range weight of Isabella's rocks = 13.75

2) For Mateo's Rocks:

Mean = 8
Median = 6
Mode = 8
Range = 14.75

From the above data, we can see that the Range of Mateo's Rocks is more as compared to the Isabella's Rocks.

Thus, Range can be used be used to support the claim that Mateo’s rocks generally weigh more than Isabella’s rocks.

So option D is the correct option

(3.) Would you be able to tell how much temperature rose since 6 A.M? Why or why not?

Answers

hmm since it only rose one degree then went down 6 id say around -5* (star is supposivly the degree sign)

10. Write an inverse variation to model the situation and answer the question. Two rectangular fields have the same area. One measures 75 yd by 60 yd. If the other has a length of 72 yd, what is its width?. show your work.

Answers

Answer:
equation is: width = area / length
width = 62.5 yd

Explanation:
For the first rectangle:
We have:
length = 75 yd and width = 60 yd
Therefore:
area = length * width
area = 75 * 60
area = 4500 yd²

For the second rectangle:
We have:
area = area of first rectangle = 4500 yd²
length = 72 yd
area = length * width
width = area / length ............> The required equation
width = 4500 / 72
width = 62.5 yd

Hope this helps :)

The vertices of a triangle are A(4,5), B(7,1), and (9,6). After reflecting over the line x = 5, what are the new coordinates? A) A'(5,6), B'(1,3), C'(6,1) B) A'(6,5), B'(3,1), C'(1,6) C) A'(5,5), B'(5,1), C'(5,6) D) A'(5,4), B'(5,7), C'(5,6)

Answers

the answer is B i just did it

Answer:

The answer is B.

Step-by-step explanation:

I took the benchmark too.

Martina chose a random sample of 10 bags of candy from two different Brands, A and B. All bags in the sample are the same size. Martina counts the number of candy pieces in each bag and plots the results on two dot plots.
(see photo)

Based on the plots, which statement is a valid comparison of the number of candies in the bags of the two Brands?

A. The number of candies in the bags from Brand B is greater and more consistent than the number of candies in the bags from Brand A.
B. The number of candies in the bags from Brand B is greater and less consistent than the number of candies in the bags from Brand A.
C. The number of candies in the bags from Brand B is fewer and more consistent than the number of candies in the bags from Brand A.
D. The number of candies in the bags from brand B is fewer and less consistent than the number of candies in the bags from brand A.

Answers

I think the answer is A.

The answer is:
The number of candies in the bags from brand B is fewer and less consistent than the number of candies in the bags from brand A.

How does the volume of a cylinder change when its diameter is quadrupled?

Answers

If the radius of a cylinder is x, and the height is y, then the volume of the cylinder will be x²yπ. If every thing is quadrupled then it will be 4x and 4y, Therefore it will become (4x)²4yπ. This simplifies to 16x²4yπ, and then even further to 64x²yπ. Excluding the 64, that is the same as the original equation, so we now know that the coefficient of volume increase is 64, so the volume is 64 times greater. By the way, if you know the scale factor of change, the volume change will always be the scale factor change cubed. For area, or surface area it will be the scale factor squared. I hope this helps.

When the diameter of a cylinder is quadrupled, its volume increases by a factor of 4 because the volume is directly proportional to the square of the radius.

When the diameter of a cylinder is quadrupled, it means the diameter is multiplied by 4.

The formula for the volume of a cylinder is [tex]$V = \pi r^2 h$[/tex], where r is the radius and h is the height.

If the diameter is quadrupled, the radius would be doubled because the radius is half the diameter.

Let's denote the original radius as r and the new radius after quadrupling the diameter as 2r.

Substituting the new radius into the volume formula, we get:

Original Volume: [tex]$V_1 = \pi r^2 h$[/tex]

New Volume: [tex]$V_2 = \pi (2r)^2 h = \pi (4r^2) h$[/tex]

We can see that the new volume is 4 times the original volume [tex]($V_2 = 4V_1$)[/tex].

So, when the diameter of a cylinder is quadrupled, its volume increases by a factor of 4.

7r. r represents a fraction which value of r makes the expression equal a number less than 7? 4/4 or 4/3 or 4/5 or 4/1

Answers

Multiply 7 by each of the fractions to find the solution that is less than 7

= 7 * 4/4
= (7*4)/4
= 28/4
= 7

= 7 * 4/3
= (7*4)/3
= 28/3
= 9 1/3

= 7 * 4/5
= (7*4)/5
= 28/5
= 5 3/5

= 7 * 4/1
= (7*4)/1
= 28/1
= 28

ANSWER: The fraction that gives a solution less than 7 is 4/5. 4/5 multiplied by 7 is 5 3/5.

Hope this helps! :)

The value of r that makes the expression 7r less than 7 is 4/5, as multiplying 7 by 4/5 results in 5.6, which is less than 7.

The question asks which value of r makes the expression 7r equal a number less than 7, given the choices of 4/4, 4/3, 4/5, or 4/1. To find the solution, we simply multiply 7 by each fraction option and see which results in a number less than 7.

For 4/4 (or 1): 7 * 1 = 7For 4/3: 7 * (4/3) > 7For 4/5: 7 * (4/5) = 5.6, which is less than 7For 4/1 (or 4): 7 * 4 > 7

Thus, the value of r that makes the expression 7r result in a number less than 7 is 4/5.

Mrs. Thomas is preparing a lunch for a group of students.

A can of juice has a radius of 4 cm and a height of 11 cm.
Mrs. Thomas knows she needs at least 5,100 Cm^3 of juice.

How many cans of juice will Mrs. Thomas need to buy?

Answers

Volume for a cylinder- V= πr^2h (pi multiplied by r squared times h)

V=π4^2(11)
V= (approximately) 552.92 cm cubed

5100/552.92= (approximately) 9.2 cans

To determine the number of cans of juice Mrs. Thomas needs to buy, calculate the volume of juice in one can and then divide the total required volume by the volume of one can. Mrs. Thomas will need to purchase at least 10 cans of juice.

To find out how many cans of juice Mrs. Thomas needs to buy, we need to calculate the volume of juice in one can first.

We use the formula for the volume of a cylinder: V = πr²h, where r is the radius and h is the height.Calculate the volume of one can: V = 3.142 x (4 cm)² x 11 cm = 554.632 cm³.Divide the total volume needed by the volume of one can: Number of cans = 5,100 cm³ / 554.632 cm³ = 9.19.

Since you can't buy a fraction of a can, Mrs. Thomas will need to buy at least 10 cans of juice.

Please help ASAP! And please show steps or explain!

Answers

first put 3 out of the way then divide 100 by 16.666666 then you should get around 3 1/6

There is one repeating digit, so we effectively multiply and divide by 10^1 -1 = 9. (The exponent of 10 here is the number of repeating digits.)

[tex]10 \times 3.1\overline{6} - 3.1\overline{6} = 31.6\overline{6} -3.1\overline{6} = 28.5 = 9 \times 3.1\overline{6}[/tex]

Then you have
[tex]3.1\overline{6} = \dfrac{28.5}{9} = \dfrac{285}{90} = \dfrac{19}{6}[/tex]

The equivalent fraction is 19/6.

how do you do application of linear equations

Answers

You can use linear equations if something is being raised or decreased with the same linear function. Such as temperature or the amount of books that get sold.

Given the figure below, find the values of x and z.

Answers

[tex](13x-85)^o=97^o\\\\13x-85=97\ \ \ |+85\\\\13x=182\ \ \ |:13\\\\x=14[/tex]

[tex]z^o+97^o=180^o\ \ \ |-97^o\\\\z^o=83^o[/tex]

Answer: x = 14; z = 83

Answer:

x = 14; z = 83 hope this helps u

Nick gets out of school at 2:25pm he has a 16 minute ride home on the bus next he goes on s 30 minute bike ride then he spends 55 minutes doing homework at what time does nick finish his homework

Answers

Hi there! The answer is 4:06 pm.

Nick gets out of school at 2:25 pm.
He has a 16 minute ride home on the bus, so he'll arrive at home at 2:41 pm.

Next, he goes on a 30 minute bike ride, which will start at 2:41 pm. and thus and at 3:11 pm.

Then he spends 55 minutes doing homework, which starts at 3:11 pm. and will end at 4:06 pm.

The answer is 4:06 pm.
~Hope this helps you!

Find the value of x in each of the following:
[tex] \sqrt[3]{27} = \: x[/tex]

[tex] \sqrt[3]{x} = \frac{1}{4} [/tex]

[tex] \sqrt[3]{ \frac{1}{512} } = \: x[/tex]

[tex] \sqrt[3]{x} = 11[/tex]

Please explain how you got your answer(s), thanks!

Answers

the first one: x is 3 because 3 x 3 x 3 is 27
the second one: x is 1/64 because the denominator, 4, to the power of 3 is 64. Anything rad 1 will always be 1, ∛64 is 4.
the third one: x is 1/8 because 8 x 8 x 8 which is the same thing as 8^3 is 512.
∛1/512 (1 divided or multiplied by 1 is always going to be 1)
the fourth one: x is 1331, I know this because I did, 11 x 11 x 11 to get 1331.
Let me know if this doesn't make sense

which is a value of x, when 3x²+4=40

Answers

3x^2+4=40
3x^2=36
x^2=12
x=+or-sqrt(12)

:)

Hey there!

Let's solve the equation step by step!
[tex]3 x^{2} + 4 = 40[/tex]

Subtract 4 from both sides.
[tex]3 x^{2} = 36[/tex]

Divide both sides by 3.
[tex] x^{2} = 12[/tex]

Solve the equation by taking the positive and negative root of 12.
[tex]x = \sqrt{12} = 2 \sqrt{3} = 3.46... \\or\\ x = - \sqrt{12} = -2 \sqrt{3} =3.46...[/tex]

The exact answer includes the roots, the other answer is the answer in two decimals.
~Hope this helps you!

The lowest altitude of an altocumulus cloud is about 3 8 feet. The highest altitude of an altocumulus cloud is about 3 times the lowest altitude. What is the highest altitude of an altocumulus cloud? Write your answer as a power

Answers

[tex]3(3^8)[/tex] equals [tex]9^8[/tex] feet. hope this helps

It is given The lowest altitude of an alto cumulus cloud is about [tex]3^{8}[/tex] feet.The highest altitude of an alto cumulus cloud is about 3 times the lowest altitude . The question is asking us to find the highest altitude of an alto cumulus cloud.

The the highest altitude of an alto cumulus cloud = [tex]3 .(3^{2}) =3^{1+2}=3^{9}.feet.[/tex].

Which is not a factor of 56? A. 4 B. 8 C. 14 D. 26

Answers

Divide each by 56. If you get a number with a decimal that’s your answer

26 is not a factor of 56

The circle has a radius of 3 cm. What is the area of the circle?
A. 9.42 cm2
B. 56.52 cm2
C. 18.84 cm2
D. 28.26 cm2

Answers

you would do
3.14*r^2
which is 3
r=3
what you do is
3.14*3*3 which is 28.26cm^2 which is D

Answer:

D: 28.26

Step-by-step explanation:

the ratio of boy to girls in 8th grade is 5 to 3 ,how many girls are there in 8th grade if there are 80 students in 8th grade

Answers

boys 5
------- = --- Note that 5+3 = 8. Thus, (5/8) of the 80 students are boys and
girls 3 (3/8) of the 80 students are girls. This comes out to 30 girls (and 50 boys) Note that 30+50=80 (students)

. Thus, the number of girls =30.

Let's denote the number of boys as 5x and the number of girls as 3x. According to the problem, the total number of students is the sum of both boys and girls:

5x + 3x = 80

Combining the terms, we get:

8x = 80

Now, solving for x:

x = 80 / 8

x = 10

Now that we know the value of x, we can find the number of girls:

Number of girls = 3x = 3 * 10 = 30

Therefore, there are 30 girls in the 8th grade.

genna painted a table top that is shaped like a circle . the circumferance of the tabletop is 6 feet which measurement is closest to the area of the tabletop in square feet?

Answers

To solve this problem you must apply the proccedure shown below:

1. You must apply the formula for calculate the area of a circle, which is:

A=πr^2

Where A is the area of the circle and r is the radius of the circle.

2. You have that the diameter is 6 feet, then the radius is:

r=D/2
r=3 feet

3. When you apply the formula shown above, you obtain:

A=9π feet^2
A=28.27 feet^2

The answer is: 28.27 feet^2

circumference = 6 ft

circumference = 2*pi*r = 6

solve for r:
r = 6/(2*pi) = 0.9554 ft

area = pi*r^2 = 0.9554*0.9554 * 3.14 = 2.866 sq. ft

Kim spent $26 on a magazine and 6 notepads have the magazines cost $2 then how much was each Notepad

Answers

The answer is $4 per notepad.

First you subtract the $2 from the total of $26 to get $24 for all the Notepads together, then you divide the $24 by the number of notepads. 24 divided by 6 equals 4. So each notepad cost $4.

the cost of running an appliance varies jointly as the number of watts used, the hours of operation, and the cost per kilo-watt hour. A 6000 watt convection oven operates for 10 minutes for 15 cents at a cost of 7.5 cents per kilo-watt hour. what is the cost of cooking two meals if each meal takes 70 minutes to make?

Answers

Final answer:

The cost of cooking two 70-minute meals on a 6000-watt appliance with a kilo-watt rate of 7.5 cents will be roughly $1.05.

Explanation:

Your question relates to the calculation of the cost of running an appliance based on its power, time of use, and the cost per kilo-watt hour. When evaluating power and energy consumption, we use an equation for energy, which states that E = Pt, where E is the energy (in kilo-watt hours), P is the power (in kilo-watts), and t is the time (in hours).

First, to find the cost, we need to convert everything to respective units. The 6000 watts is equivalent to 6 kilowatts (kw), and 10 minutes is equivalent to 10/60 or approximately 0.167 hours. The cost per kilo-watt hour is 7.5 cents.

The energy consumed would thus be E = Pt = (6kw)(0.167 hr)= 1kwh. The cost of running the appliance for 10 mins is (1kwh)(7.5 cent/kwh) = 7.5 cents.

To cook one meal, with a time of 70 minutes (or approximately 1.167 hours), we will have E = Pt = (6kw)(1.167 hr)= 7kwh. The cost of cooking one meal therefore would be (7kwh)(7.5 cent/kwh) = 52.5 cents.

Finally, to cook two meals, you would just double this cost, resulting in 2 * 52.5 cents = 105 cents or $1.05.

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a trapezoid with an area of 166.75 in has bases that measure 21 in and 8 in find the height of the trapezoid

Answers

The usual equation for a trapezoid is base1+base2/2 * height. For this, 21+8/2 equals to 166.75. Use division, and your height is 11.5

The area of trapezoid is calculated as -

Area of trapezoid = [tex] \frac{a + b}{2} X height [/tex]

Here, a = base 1

b = base 2

Height is the height of trapezoid.

It is given that,

Area of trapezoid = 166.75 in

Base 1, a = 21 in

Base 2, b = 8 in

Area of trapezoid = [tex] \frac{a + b}{2} X height [/tex]

166.75 in = [tex] \frac{21 in + 8 in}{2} X height [/tex]

Height = [tex] \frac{ 166.75 in}{14.5}

Height = 11.5 in

Thus, height of trapezoid = 11.5 In

use (r,16) to solve y=2x-4

Answers

(x,y) = (r,16)

With this knowledge, plug in r for x, and 16 for y

16 = 2(r) - 4

Isolate the r, add 4 to both sides

16 (+4) = 2r - 4 (+4)

20 = 2r

Divide 2 from both sides

20/2 = 2r/2

r = 20/2

r = 10

hope this helps

what is the position of D on the number line below?

write your answer a fraction or mixed number

Answers

The position 'D' on a number line, based on the information given, is approximately one and two-thirds units, or 1 2/3, to the right of the center bottom perpendicular hash mark, often representing zero.

The position of 'D' on the number line represents the location of a particular point labeled as 'D.'

According to the provided reference, the fifth dot, presumably 'D', is about one and two-third perpendicular hash marks to the right of the center bottom perpendicular hash mark.

On a typical number line, the center bottom perpendicular hash mark often represents zero.

If each perpendicular hash mark to the right of zero denotes one unit, then 'D' would be located at 1 2/3 or 1.67 on the number line. However, without the actual number line, this remains an estimated position.

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The probable question may be:

What is the position of D below?

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