Use the method of completing the square to transform the quadratic equation into the equation form (x + p)2 = q. 3 + x - 3x2 = 9 A) (x - 1 6 )2 = 71 36 B) (x - 1 3 )2 = 71 36 C) (x - 1 6 )2 = - 71 36 Eliminate D) (x - 1 3 )2 = - 71 36

Answers

Answer 1

To transform the quadratic equation into the equation form (x + p)2 = q we shall proceed as follows:
3+x-3x^2=9
putting like terms together we have:
-3x^2+x=6
dividing through by -3 we get:
x^2-x/3=-2
but
c=(b/2a)^2
c=(-1/6)^2=1/36
thus the expression will be:
x^2-x/3+1/36=-2+1/36
1/36(6x-1)²=-71/36

the answer is:
1/36(6x-1)²=-71/36

Related Questions

6. Food Express is running a special promotion in which customers can win a free gallon of milk with their food purchase if there is a star on their receipt. So far, 147 of the first 156 customers have not received a star on their receipts. What is experimental probability of winning a free gallon of milk?

A. 11/156
B. 49/52
C. 2/39
D. 3/52*****?

Answers

if you take 156 and subtract 147 you get nine and 9/156 simplifies down to 3/52

The experimental probability of winning a free gallon of milk will be calculated as under -

It is given that, total number of outcomes = 156

Non-winning customers = 147 (it is given in the question)

Thus, the winning customers will be = Total outcomes - Non-winning customers

Expected winning customers = 156 - 147 = 9

The probability is calculated as -

Probability (Winning customer) = [tex] \frac{Winning Customers}{Total Customers} [/tex]

Probability (Winning customer) = [tex] \frac{9}{156} [/tex] = [tex] \frac{3}{52} [/tex]

plz help me!!!!!!!

Instructions: Select the correct answer from each drop-down menu. When p2 – 4p is subtracted from p2 + p – 6, the result is . To get p – 9, subtract from this result.

-3p-6. 4p+3
5p-6 4p-15
4p+6. 4p+12

Answers

When p2 – 4p is subtracted from p2 + p – 6, the result is:
p2+p-6-(p2-4p)=p2+p-6-p2+4p=5p-6

To get p – 9, subtract from this result x:
5p-6-x=p-9
Solving for x:
5p-6-x+x-p+9=p-9+x-p+9
4p+3=x
x=4p+3

Answer:
1) When p2 – 4p is subtracted from p2 + p – 6, the result is 5p-6
2) To get p – 9, subtract from this result 4p+3

I need step by step instructions on how to get the y-intercept for the following function:

f(x)=x^3-18x^2+107x-210.

Answers

luktdkilfdiykfg;oizxkuilouyk7it8rl,kvkuc kugc ulv lug

For the triangle above, find sin A. a. 36° c. 0.9323 b. 50° d. 0.385

Answers

the picture in the attached figure

we know that
in the right triangle ABC
sin A=opposite side angle A/hypotenuse

in this problem
opposite side angle A=BC-----> 10
hypotenuse=AB-----> 26
so
sin A=10/36------> sin A=0.3846------> sin A=0.385

the answer is
the option d. 0.385

Choose an example of a fixed expense and an example of a variable expense, and explain why they are classified that way.

Answers

Fixed costs are those that do not depend on the level of production of a company and whose only way to avoid them is to close the company. For example, the cost of renting the plant or machinery.
Variable costs are those that depend on the level of production of the company. For example, the cost of raw material. In a company that produces juices, the bottles will be part of the cost of raw material, and the amount of bottles to use depends on the amount of juice to produce, if this amount increases the cost of raw material will also increase. On the other hand, the rental cost of the place where the juices are produced will be the same regardless of the amount of juices that are produced, for this reason it is considered a fixed cost.

Final answer:

Fixed costs, such as rent, remain constant regardless of production levels, while variable costs, like raw material expenses, will fluctuate based on the level of production.

Explanation:

Firms classify their costs into two categories: fixed costs and variable costs. Fixed costs are expenses that do not change regardless of the level of production. For instance, a lease on a retail space would be considered a fixed cost as it remains the same whether you sell a lot or a little. On the other hand, variable costs are directly tied to the level of production. For example, the cost of buying materials to produce a product tends to rise as the level of production increases. It's variable because the more you produce, the more materials you would need, and therefore the cost varies with the level of output.

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PLLLLLLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Find the value of n.

Answers

The answer to this question is 23. How you get this is by adding all the sides like this: 2n+6+135+151+140+63=540. Then you just solve the equation.

Which expression is equivalent to 2m(3/2m+1)+3(5/3m-2)?

Answers

c is the answer. Distribute the terms and combine like terms.

The expression is equivalent to [tex]\rm 3m^2+7m-6[/tex].

Given

Expression; [tex]\rm 2m \left (\dfrac{3}{2}m+1 \right )+3\left ( \dfrac{5}{3}m-2\right )[/tex]

How to find the equivalent expression to the given expression?

To find the equivalent expression first multiply by term then combine like terms and simplify.

Therefore,

The expression is equivalent to;

[tex]\rm =2m \left (\dfrac{3}{2}m+1 \right )+3\left ( \dfrac{5}{3}m-2\right )\\\\=2m \times 3m + 1\times 2m + 5m \times 1-3\times 2\\\\=3m^2+2m+5m-6\\\\= 3m^2+7m-6[/tex]

Hence, the expression is equivalent to [tex]\rm 3m^2+7m-6[/tex].

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Which is the correct form of the quadratic formula? A) x = b ± b2 - 4ac a B) x = b ± b2 - 4ac 2a C) x = - b ± b2 - 4ac a D) x = - b ± b2 - 4ac 2a

Answers

Hello!

The quadratic formula is

[tex]x = \frac{-b +- \sqrt{ b^{2}-4ac } }{2a} [/tex]

So the answer is D

Hope this helps!

The correct form of the quadratic formula is x = (-b±√(b² - 4ac)) / (2a).

Hence, option D) is the correct answer.

What is a Quadratic Equation?

Quadratic equation is simply an algebraic expression of the second degree in x. Quadratic equation in its standard form is;

ax² + bx + c = 0

Where x is the unknown

To solve for x using the quadratic formula;

x = (-b±√(b² - 4ac)) / (2a)

The correct form of the quadratic formula is x = (-b±√(b² - 4ac)) / (2a).

Hence, option D) is the correct answer.

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Make a box and whisker plot of the data.

24, 18, 29, 21, 16, 23, 13, 11

Answers

To make a box and whisker plot you must first order the data:

11, 13, 16, 18, 21, 23, 24, 29

Then find the median:

19.5

Then split the data into two sections by the median:

11, 13, 16, 18 and 21, 23, 24, 29

Now find the medians of those sets

14.5 and 23.5

With this information we can conclude Option C is the correct plot

Hope this helps!

none of those are correct.
minimum-11
lower quartile-17
median-23.5
upper quartile-26.5
maximum-29

PLS HELP ME ASAP WITH 1!

BRAINLIEST WILL BE GIVEN HOPEFULLY

Do question 2 if u can, if u can’t it’s fine

(Random answers gets moderated)

Answers

All of these make use of the expansion
(a + b)² = a² + 2ab + b²
You would do well to memorize this "formula." Of course, it also helps to be able to double (or halve) a number, and to know the squares of small integers.

1.
x² +2x +1
x² -6x +9
x² +12x +36
x² -0.4x +0.04
4x² +28x +49
9x² +30x +25

2.
(x + 4)²
(x + 3)²
(x - 9)²
(x - 5)²

3. (12/2)² = 36

4. ±2√49 = ±14

PLEASE HELP ME!! How much greater is the median number of employees at Restaurant A than the median number of employers at Restaurant B?

Answers

The median is visually the vertical line inside the box (of the box and whisker plot).

Median of Restaurant A is 35
Median of Restaurant B is 25
Subtract the values: 35-25 = 10

Answer: 10

What is the standard deviation of the data set? 29, 36, 41, 53, 45, 30, 60

Answers

The standard deviation for the set of number will be found as follows:
mean=( 29 + 36 + 41 + 53 + 45 + 30 + 60)/5=294/7=42
next:
sum of (x-mean)^2=[(29-42)^2+(36-42)^2+(41-42)^2+(53-42)^2+(45-42)^2+(30-42)^2+(60-42)^2]
=804
thus the variance will be:
var=(804)/(7-1)=134
thus the standard deviation will be:
σ=√134=11.576

How much of a 14% iodine solution should be added to 89 ounces of a 47% iodine solution to get a 29% solution

Answers

whatever% of anything is just (whatever/100) * anything.

x = ounces of 14% iodine.

y = ounces of 29% iodine.

we know that in a 14% iodine solution, 14% is iodine and the rest is something else, we also know that "x" ounces of the solution have 14% of iodine, how much is that? (14/100) * x, or 0.14x.

likewise, in the 89 ounces of 47% solution there is (47/100) * 89 of iodine.

and likewise as well, in "y" ounces of 29% iodine there is (29/100) * y, or 0.29y of iodine.

bearing in mind that, whatever "x" and "y" may be, x + 89 = y, and that the sum of the iodine amounts also will equate 0.29y.

[tex]\bf \begin{array}{lccclll} &\stackrel{ounces}{amount}&\stackrel{\%~of~iodine}{quantity}&\stackrel{iodine~oz}{amount}\\ &------&------&------\\ \textit{14\% solution}&x&0.14&0.14x\\ \textit{47\% solution}&89&0.47&41.83\\ ------&------&------&------\\ mixture&y&0.29&0.29y \end{array} \\\\\\ \begin{cases} x+89=\boxed{y}\\ 0.14x+41.83=0.29y\\ --------------\\ 0.14x+41.83=0.29\left( \boxed{x+89} \right) \end{cases} \\\\\\ 0.14x+41.83=0.29x+25.81\implies 16.02=0.15x \\\\\\ \cfrac{16.02}{0.15}=x\implies 106.8=x[/tex]

How do u find the height of the base??

Answers

[tex]\bf \textit{height of an equilateral triangle}\\\\ h=\cfrac{s\sqrt{3}}{2}\qquad \begin{cases} s=length~of\\ \qquad a~side\\ ------\\ s=12 \end{cases}\implies h=\cfrac{12\sqrt{3}}{2}\implies h=6\sqrt{3}\\\\ -------------------------------\\\\ \textit{area of an equilateral triangle}\\\\ A=\cfrac{s^2\sqrt{3}}{4}\qquad \begin{cases} s=length~of\\ \qquad a~side\\ ------\\ s=12 \end{cases}\implies A=\cfrac{12^2\sqrt{3}}{4}\implies A=36\sqrt{3}[/tex]

and of course as you already know the volume of the prism is just the area of the base times the length, namely A * 20.

How long does it take for a letter to get from orlando to los angeles?

Answers

On average 2 to 3 days :)

In p.
e. A parachute is laid out on the gym floor. The parachute has a radius of 16 feet. Which measurement is closest to the circumference of the parachute in feet.

Answers

The circumference by definition is given by:
C = 2 * pi * r
Where,
r: radius of the circle.
Substituting values we have:
C = 2 * 3.14 * 16
C = 100.48 feet
Answer:
A measurement that is closest to the circumference of the parachute in feet is:
C = 100.48 feet

The circumference of the parachute is Option A (100.48 feet).

To find the circumference of the parachute, we use the circumference formula for a circle:

C = 2πr

Given the radius (r) is 16 feet, we substitute it into the formula:

C = 2π(16) = 32π

Using the approximate value of π (3.1416), we get:

C ≈ 32 × 3.1416 = 100.48 feet

Thus, the measurement closest to the circumference of the parachute in feet is 100.48 feet (Option A).

Complete question:

In PE a parachute is laid out on the gym floor. The parachute has a radius of 16 feet. Which measurement is closest to the circumference of the parachute in feet?

A. 100.48ft

B. 198.4ft

C. 49.6ft

D. 803.84ft

A safe has a 4-digit lock code that does not include zero as a digit and no digit is repeated. What is the probability of a lock without all even digits? There to get a lock code with all even digits. There are 3,024 different 4-digit lock codes. There are to get a lock code without all even digits. The probability of a 4-digit lock code without all even digits is

Answers

Answer:

it's 24, 3000, and 3000/3024

Step-by-step explanation:

Final answer:

The probability for a 4-digit lock code using numbers 1-9 with no repeats and not all even is 2,904/3,024.

Explanation:

To solve this, we need to find the total number of possible 4-digit lock codes using digits 1-9 with no repeats and not all even, then divide it by the total number of 4-digit lock codes using digits 1-9 with no repeats. Specifically, the lock code includes 5 different even numbers (2,4,6,8), and 4 different odd numbers (1,3,5,7,9). If the lock code is all even, we will have 5*4*3*2 = 120 possibilities. However, the total possibilities for 4-digit lock codes are 9*8*7*6 = 3,024. Thus the number of codes that are not all even digits is 3,024 - 120 = 2,904. Therefore, the probability for a 4-digit lock code not having all even digits is 2,904/3,024.

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Rewrite the expression log(3x) as an equivalent logarithmic expression using only addition.

Answers

[tex]\log 3 + \log x[/tex]

5/8 ≠ (3/4 + 1/16) because 5/8 < 3/4 EXPLAIN THIS PROBLEM AND WHAT IT MEANS

Answers

5/8 = 3/4+1/16 is false because, the final values compared on each side of equation is not the same

- 5/8 = 0.625
- 3/4+1/16 = 0.8125

0.625 = 0.8125, it is not equal but less than

Find the fifth roots of 32(cos 280° + i sin 280°).

Answers

I) Let z = 32 (cos 280 degrees + i sin 280 degrees)
= 32 (cos (k* 360 + 280) + isin (k*360 + 280)), where k = integer
II) z^ (1/5) = (32 (cos (k*360 + 280) + i sin (k*360 + 280))) ^ (1/5)
then,
z^ (1/5) = 2(cos ((k*360 + 280)/5) + i sin((k*360 + 280)/5))
We apply De Moivre's theorem:
z^ (1/5) = 2(cos(72k + 56) + i sin (72k +56))
We can get the five roots by assigning k = 0, 1, 2, 3, and 4
When K = 0, 1st root = 2 + i sin (cos 56 + i sin 56)k = 1, 2nd root = 2 (cos 128 + i sin 128)k = 2, 3rd root = 2 (cos 200 + i sin 200)k = 3, 4th root = 2 (cos 272 + i sin 272)k = 4, 5th root = 2 (cos 344 + i sin 344)

The fifth root is 5th root = 2 (cos 344 + i sin 344)

Correct Answer:

z1= 2(cos 56 deg + i sin 56 deg)

z2= 2(cos 128 deg + i sin 128 deg)

z3 = 2(cos 200 deg + i sin 200 deg)

z4 = 2(cos 272 deg+ i sin 272 deg)

z5 = 2(cos 344 deg+ i sin 344 deg)

Step-by-step explanation:

De Moivre's Theorem--> e^i theta = cos theta + i sin theta

The fifth root of 32 is 2 and 280/5 is 56

z1= 2(cos 56 deg + i sin 56 deg)

360deg/ 5 = 72 deg

(If it was asking for cubed root u would do 360/3. whatever the root is you divide that by 360)

z2= 2(cos 56 + 72) + (i sin 56 + 72)

z2= 2(cos 128 deg + i sin 128 deg)

z3 = 2(cos 128 + 72) + ( i sin 128 + 72)

z3 = 2(cos 200 deg + i sin 200 deg)

z4 = 2(cos 200 + 72) + (i sin 200 + 72)

z4 = 2(cos 272 deg + i sin 272 deg)

z5 = 2(cos 272 + 72) + (i sin 272 + 72)

z5 = 2(cos 344 deg + i sin 344 deg)

deg means degrees

An average infant is 20 inches long and weighs 7.6 pounds. if the child grows to 80 inches and keeps the same proportions,how much will the child weigh

Answers

he will weight 30.4 pounds cause 7.6 times 4 is 30.4

What is the length of an arc cut off by an angle of 3 radians on a circle of radius 8 inches?

Answers

A formula for arc length, s, given the radius, r and central angle, Ф (in radians) is s = r × Ф.

s = 8 × 3 = 24 inches

What is the value of x?

Answers

straight line = 180, so 180-100=80, a triangle = 180, x equals to 180-(70+80) =30, the answer is a

This is actually a relatively simple problem, but because the other angle is missing, it seems complex.

The angle adjacent to the 100 degree outside the triangle is 80 degrees. We know this because it is a supplementary angle, or an angle that, when added along with another angle’s measurement, makes 180 degrees. The line is straight, so the other angle must be 80 degrees to add up with the 100 to make 180 degrees.

Now that we know the other unknown angle, we can use the fact that the sum of angles within a triangle make 180 degrees. The two angles inside the triangle that we know make 150 degrees (80 plus 50), so the final angle ‘x’ must be 30 degrees (180-150=30).

Given that f(x) = x2 − 4x − 3 and g(x) = the quantity of x plus three, over four, solve for f(g(x)) when x = 9.

−6

3

6

9

Answers

Hello! To find the composition of functions we want to take all the x values in f(x) and replace them with g(x). Then to solve for a specific value, we plug in that value for x. Let's look at the steps below
[tex] f(x)=x^{2} -4x-3[/tex]
[tex]g(x)=\frac{x+3}{4}[/tex]

So we find
[tex]f(g(x))=f(g(9))=(\frac{9+3}{4})^2 - 4(\frac{9+3}{4})-3[/tex]
[tex] =3^2 - 4(3)-3 [/tex]
[tex]= 9-12-3=-6[/tex]
Now we want to find the solution when x is 9 so we plug in a 9 whenever we see an x

Final answer:

The solution to f(g(x)) when x = 9 is -6.

Explanation:

In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the codomain), where each input is related to exactly one output.

Given:

f(x) = x2 - 4x - 3, g(x) = (x + 3) / 4

To find f(g(x)) when x = 9:

Calculate g(9): Substitute x = 9 into g(x) to get (9 + 3) / 4 = 12 / 4 = 3Substitute g(9) into f(x): Substitute g(9) = 3 into f(x) to get f(3) = 32 - 4(3) - 3 = 9 - 12 - 3 = -6

Therefore, f(g(x)) when x = 9 is -6.

The mean of a set of five numbers is 4.8. Given that the sixth number is x and the mean of these six numbers is 5.5, find the value of x.

Answers

Given that the mean of the five numbers is 4.8, the total of the numbers will be:
5×4.8
=24
after adding x, the total will be:
(24+x)
the mean will be:
(24+x)/6=5.5
solving for x we get:
24+x=33
hence
x=33-24
x=9

The sixth number is 9

They traveled 200 kilometers in total, and they biked 40 kilometers more than they were bussed. how many kilometers did they travele by bike

Answers

Let the distance travelled by bus be x and the distance travelled by bike be (x+40)

So...

x + (x+40) = 200

2 x = 160

1 x = 80

200 - 80 = 120km by bike.

A line has a slope of -5 and passes through (1,-1). Which is the equation of the line in point-slope form?

Answers

The general form for point slope is y-y1=m(x-x1). Just substitute the information. y+1=-5(x-1).

y = 2f(g(x))
dy/dx = 2f'(g(x)) * g'(x)
Differentiate again:
d^2y/dx^2 = 2f''(g(x)) * g'(x) * g'(x) + 2f'(g(x)) * g''(x)
d^2y/dx^2 = 2f''(g(x)) * (g'(x))^2 + 2f'(g(x)) * g''(x)
Am I correct in saying answer D?

Answers

Yes you used the chain rule properly to follow the correct steps to get the right answer. Great job.

If you wanted, you can come up with examples for f(x) and g(x) to help confirm the answer. A quick way to do this is to use something like GeoGebra to help graph the two expressions and you'll notice that the curves match up perfectly (indicating equivalent expressions). Note: GeoGebra can handle derivatives through the Derivative[] comand or you can type the function in the input bar with a tickmark after it to tell GeoGebra to derive the function.

statement must be true??

Answers

Given that AB is the bisector of DC. The third options of all the options are True.

B is the midpoint of DC.

In geometry, to bisect an entity means to disassociate it into two equal parts. A bisector is a line, ray, or segment that divides an entity into two equal parts. For illustration, a line that bisects an angle divides the angle into two angles with equal measures. A segment that bisects a line segment divides the line segment into two segments with equal lengths. A ray that bisects an angle extends from the vertex of the angle and divides the angle into two angles with equal measures.

As it is given that AB is the bisector of DC,

therefore, B, being the foot of AB on CD is the midpoint of DC.

Since DC is bisected by AB,

therefore, [tex]\angle[/tex] ABD = [tex]\angle[/tex] ABC.

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The sum of the digits of a two-digit number is 16. if the digits are reversed, the new number is 18 less than the original number. find the original number.

Answers

Equation
Let one digit be x
Let the other digit = y

x + y = 16
Let the original number = 10x + y
Let the reverse number = 10y + x

10x + y - 18 = 10y + x

Comment
Bring the letters to the left and the number 18 to the right.
10x - x + y - 10y = 18 Combine like terms.
9x - 9y = 18 Divide both sides by 9
x - y = 2

Set up a set of equations and add.
x + y = 16
x - y = 2 Now add
2x = 18 Divide by 2
x = 18/2
x = 9

x + y = 16
9 + y = 16 Subtract 9 from both sides.
y = 16 - 9
y = 7

Check
Original number = 97
Reversed number 79
Difference 18 and it checks.

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