Which quadratic equation equation is equivalent to (x^2-1)^2 -11(^2-1) +24=0

Answers

Answer 1

[tex](x^2-1)^2-11(x^2-1)+24=0[/tex]

Use substitution: [tex]x^2-1=t[/tex]

[tex]t^2-11t+24=0\\\\t^2-8t-3t+24=0\\\\t(t-8)-3(t-8)=0\\\\(t-8)(t-3)=0\iff t-8=0\ \vee\ t-3=0\\\\t=8\ \vee\ t=3[/tex]

we're going back to substitution:

[tex]x^2-1=8\ \vee\ x^2-1=3\ \ \ \ |add\ 1\ to\ both\ sides\ of\ the\ equations\\\\x^2=9\ \vee\ x^2=4[/tex]

therefore

[tex]x=\pm\sqrt9\ \vee\ x=\pm\sqrt4\\\\\boxed{x=-3\ \vee\ x=3\ \vee\ x=-2\ \vee\ x=2}[/tex]

Answer 2

Answer:

x = ± 3 and ± 2

Step-by-step explanation:

The given quadratic equation is

[tex](x^{2}-1)^{2}-11(x^{2}-1)+24=0[/tex]

To make this question easier we will consume ( x² -1 ) = a

a² - 11a + 24 = 0

Now we can factorize this equation easily

a²- 8a - 3a + 24 = 0

a (a-8) - 3 ( a-8) = 0

( a-3 ) ( a-8 ) = 0

Therefore, a - 3 = 0 ⇒ a = 3

or a - 8 = 0 ⇒ a = 8

Now we put the value a

when a = 3 (x² - 1) = 3

x² = 3 + 1 = 4

x = √4

= ± 2

when a = 8 (x² - 1) = 8

x² = 9

x = √9

= ± 3

Therefore, x = ± 3 and ± 2 will be the answer.

Related Questions

37% of a certain country's voters think that it is too easy to vote in their country. you randomly select 12 likely voters. find the probability that the number of likely voters who think that it is too easy to vote is (a) exactly three, (b) at least four, (c) less than eight.

Answers

The probability that the number of likely voters who think that it is too easy to vote is:

a) exactly three = 0.17422

(b) at least 4 = 0.70533

How to use binomial probability theorem?

The general formula for binomial probability theorem is:

P(X = x) = ⁿCₓ * pˣ * (1 - p)⁽ⁿ ⁻ ˣ⁾

Where:

n = 12

p = 0.37

(a) exactly three,

P(x = 3) = ¹²C₃ * 0.37³ * 0.93⁹

= 0.17422

(b) at least 4,

P(4 ≤ x ≤ 12) = P(4) + P(5) + P(6) + P(7) + P(8) + P(9) + P(10) + P(11) + P(12)

= 0.70533

P(x < 8) = P(0) + P(1) + P(2) + P(3) + P(4) + P(5) + P(6) + P(7)

= 0.96406

Can you guys please help me posted picture of question

Answers

Number of outcomes of rolling a die = 6
Number of outcomes from the spinner = 8

First we have to draw the 6 leaves to represent the 6 outcomes of rolling the die. Next on each of these leaves 8 possible outcomes of the spinner will be drawn using leaves.

So 6 leaves are being divided into further 8 leaves.

Thus total number of leaves will be = 6 x 8 = 48 leaves

Therefore, the correct answer is option D

Assume that the number of watches produced every hour is normally distributed with a mean of 500 and a standard deviation of 100. what is the probability that in a randomly selected hour the number of watches produced is greater than 500

Answers

To evaluate the probability that in a randomly selected hour the number of watches produced is greater than 500 we proceed as follows:
z=(x-μ)/σ
where:
x=500
μ=500
σ=100
thus
z=(500-500)/200=0

Thus:
P(x>500)=1-P(x<500)=1-P(z<0)=1-0.5=0.5

Answer: 0.5~50%

Answer: 0.5

Step-by-step explanation:

Given : The number of watches produced every hour is normally distributed with a mean of 500 and a standard deviation of 100.

i.e. [tex]\mu = 500\text{ and } \sigma= 100[/tex]

Let x be the number of watches produced every hour.

Then, the probability that in a randomly selected hour the number of watches produced is greater than 500 will be :

[tex]P(x>500)=1-P(x\leq500)\\\\=1-P(\dfrac{x-\mu}{\sigma}\leq\dfrac{500-500}{100})\\\\=1-P(z\leq0)\ \ [\because\ z=\dfrac{x-\mu}{\sigma}]\\\\=1-0.5\ \ [\text{ By z-table}]\\\\=1-0.5=0.5[/tex]

Hence, the probability that in a randomly selected hour the number of watches produced is greater than 500 =0.5.

Carlos has $50 in his savings account. He deposits $100 on his birthday, and then another $25 every month. Which equation can be used to find the number of months it would take him to reach a balance of $500? Let m = number of months.

Answers

Thank you for posting your question here on Brainly! We love to see that more students are interacting and helping each other with their education. Feel free to ask more questions!

Before one month, you will know that Carlos has a minimum of $150, because he deposited $100 to his already $50 account. The following equation is true: [FILL] $500 = 25m + $150

Have a wonderful day, and may God bless you! :D

Answer:

[tex]150+25m = 500[/tex]

Step-by-step explanation:

Given : Carlos has $50 in his savings account. He deposits $100 on his birthday, and then another $25 every month.

To Find: Which equation can be used to find the number of months it would take him to reach a balance of $500?

Solution:

Carlos has $50 in his savings account.

He deposits $100 on his birthday.

Let m be the number of months

He save $25 every month

So, he saves in x months = 25 m

Now wants to reach a balance of $500.

So, equation becomes:[tex]50+100+25m = 500[/tex]

:[tex]150+25m = 500[/tex]

Hence Equation can be used to find the number of months it would take him to reach a balance of $500 is [tex]150+25m = 500[/tex]

A brother and a sister are in the same math class. There are 8 boys and 10 girls in the class. One boy and one girl are randomly chosen. What is the probability that the brother and sister are chosen? Write your answer as a fraction in simplest form.

Answers

[tex] |\Omega|=8\cdot10=80\\ |A|=1\\\\ P(A)=\dfrac{1}{80} [/tex]

Factor completely.

3x squared + 2xy - y squared

Answers

The factors of given expression are (x-y) and (3x-y). The solution is shown below:

[tex]3 x^{2} +2xy- y^{2} \\ \\ 3 x^{2} +3xy-xy- y^{2} \\ \\ 3x(x-y)-y(x-y) \\ \\ (x-y)(3x-y) [/tex]

hey can you please help me posted picture of question

Answers

I believe the answer is C, but I am not 100% sure. Though, I hope this helps.

When you subtract (x -2)² from both sides of the equation, you get
y² = 64 -(x -2)²
y² = 64 -(x² -4x +4)
y² = -x² +4x +60

The answer is ...
D. y² = -x² +4x +60

Hey can you please help me posted picture of question

Answers

The answer is B
F(x)= (x-1)^2+3

The parent function is G(x) = x²

First the graph is shifted right by 1 unit which can be expressed as:

(x - 1)²

Next the function is shifted up by 3 units, so the final function can be expressed as:

F(x) = (x - 1)² + 3

So, the correct answer is option B

Please help me with coordinates. IT'S DO IN 3 HOURS

Answers

I cannot help you with the exact answer, but i can make the solution easier

Get graphs (standard X,Y graphs) and start placein the numbers in the following format (x,y) If they are negative, it will be placed to the left of the graph, if positive to the right of the graph

A farmer wishes to build a rectangular plot with 800 meters of wire fencing. use calculus to find the maximum area that can be enclosed by the fence

Answers

He has to build a square, so 800÷4=200
200²=40 000 m²

Answer:

40,000 meters squared

Step-by-step explanation:

Find the optimum and constraint equations. (They are just fancy terms for the two equations you need).

The Constraint is 2x + 2y= 800 (As the plot is a normal rectangle and there is 800 m to make a fence, you would use the perimeter formula for a rectangle)

The optimum is xy= A. The area equals length times width (or in this case) xy.

You will need to plug in the simplified constraint into the optimum.

2y= -2x + 800 (divide by two next)

y= -x + 400

Plug in this to the Optimum

x(-x + 400)

this equals -xsquared + 400x

Find the derivative of it

-2x plus 400

Set it equal to )

x=200, this is only one of the lengths of the side.

In order to find the other, plug in x=200 to the constraint

-x + 400

-200 + 400

y = 200 also

So, going back to the Optimum 200 times 200 equals 40,000.

This means that the maximum area is in fact 40,000 meters squared.

Name the pattern block used to cover 1 third of the hexagon

Answers

See the attached figure

By sketching a hexagon and dividing it to 3 equal shapes.
we will shading one of the 3 equal shapes.
So, the shaded area is a parallelogram with equal sides which is called rhombus

The correct answer is:
The pattern block used to cover 1 third of the hexagon is rhombus

27 33 34 35 37 39 40 41 54 84,75,90,87,99,91,85,88,76,92,94 median: first quartile: third quartile: interquartile range:

Answers

Final answer:

For the given data, the median is 85, the first quartile is 37, the third quartile is 90.5, the interquartile range (IQR) is 53.5, and the range is 72.

Explanation:

The median in a dataset is the middle value when the values are arranged in numerical order. For the given data 27, 33, 34, 35, 37, 39, 40, 41, 54, 75, 84, 75, 90, 87, 99, 91, 85, 88, 76, 92, 94, after arranging them in ascending order, the median (Q2) is the value positioned at the center of the dataset. Since there are 21 values, the median is the 11th value, which is 85. The first quartile (Q1) is the median of the first half (lower half) of the dataset, which is the value in the 5.5th position, so we average the 5th and 6th values to get 37. Similarly, the third quartile (Q3) is the median of the second half (upper half) of the dataset, which would be the average of the 16th and 17th values, yielding 90.5. The interquartile range (IQR) is the difference between the third quartile and the first quartile, so IQR = Q3 - Q1 = 90.5 - 37 = 53.5. The range of the dataset is the difference between the maximum and minimum value which is 99 - 27 = 72.

Which polynomial represents the difference below?

Answers

5x² +9x+3 - (6x² - 3x) = 5x² +9x+3 - 6x² + 3x = -x²+12x +3

Correct answer is B.

The difference between given two polynomials is [tex](- x^{2} + 12x + 3)[/tex].

What is a polynomial?

"A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables."

Given two polynomials are [tex](5x^{2} + 9x + 3)[/tex] and [tex](6x^{2} - 3x)[/tex].

Therefore, the difference between these two polynomials

[tex]= (5x^{2} + 9x + 3) - (6x^{2} - 3x)\\= (5x^{2} - 6x^{2}) + (9x + 3x) + 3\\= - x^{2} + 12x + 3[/tex]

Learn more about polynomial here:

https://brainly.com/question/21610884

#SPJ3

The population standard deviation of the numbers 3, 8, 12, 17, and 25 is 7.563 correct to 3 decimal places. what happens if each of the five numbers is multiplied by 3

Answers

Let's figure this out as though we have no idea what the answer would be.

Step One
Find the new five numbers.
3*3, 8*3, 12*3, 17*3, 25*3
9 , 24 , 36, 51, 75

Step 2
Find the average
(9 + 24 + 36 + 51 + 75)/5 = 195/5 = 39

Step 3
Subtract the individual numbers from the average
(39 - 9) = 30
(39 -24) = 15
(39 - 36) = 3
(39 - 51) = - 12
(39 - 75) = -36

Step 4
Square the results from Step 3
30^2 = 900
15^2 = 225
3^2 = 9
(-12)^2 = 144
(-36)^2 = 1296

Step 5
Take the average of the results from step 4
(900 + 225 + 9 + 144 + 1296)/5
2574 / 5 = 514.8

Step 6
Take the square root of the result from step 5
deviation = sqrt(514.8)
deviation = 22.689

Step seven
Compare the two standard deviations.
s2/s1 = 22.689 / 7.563 = 3

Conclusion
If you are given 1 set of numbers to find a population standard deviation and you multiply each member by a, then the result will be a * the standard population deviation of the first set of numbers.

Note
Your calculator will do this as well, but you have to know how to enter the data into your calculator. That requires that you follow the directions carefully.

WHAT IS 1/3 OF 97.50

Answers

The answer is 32.5. You can also do 97.5 * 0.333 = 32.46 (rounded up is 32.5).

ans: 32.5 because you multiply it both together.....i really dont know i used the calculator XD sorry

Evaluate the integral e^xy w region d xy=1, xy=4, x/y=1, x/y=2

Answers

Make a change of coordinates:

[tex]u(x,y)=xy[/tex]
[tex]v(x,y)=\dfrac xy[/tex]

The Jacobian for this transformation is

[tex]\mathbf J=\begin{bmatrix}\dfrac{\partial u}{\partial x}&\dfrac{\partial v}{\partial x}\\\\\dfrac{\partial u}{\partial y}&\dfrac{\partial v}{\partial y}\end{bmatrix}=\begin{bmatrix}y&x\\\\\dfrac1y&-\dfrac x{y^2}\end{bmatrix}[/tex]

and has a determinant of

[tex]\det\mathbf J=-\dfrac{2x}y[/tex]

Note that we need to use the Jacobian in the other direction; that is, we've computed

[tex]\mathbf J=\dfrac{\partial(u,v)}{\partial(x,y)}[/tex]

but we need the Jacobian determinant for the reverse transformation (from [tex](x,y)[/tex] to [tex](u,v)[/tex]. To do this, notice that

[tex]\dfrac{\partial(x,y)}{\partial(u,v)}=\dfrac1{\dfrac{\partial(u,v)}{\partial(x,y)}}=\dfrac1{\mathbf J}[/tex]

we need to take the reciprocal of the Jacobian above.

The integral then changes to

[tex]\displaystyle\iint_{\mathcal W_{(x,y)}}e^{xy}\,\mathrm dx\,\mathrm dy=\iint_{\mathcal W_{(u,v)}}\dfrac{e^u}{|\det\mathbf J|}\,\mathrm du\,\mathrm dv[/tex]
[tex]=\displaystyle\frac12\int_{v=}^{v=}\int_{u=}^{u=}\frac{e^u}v\,\mathrm du\,\mathrm dv=\frac{(e^4-e)\ln2}2[/tex]

find the solution of this system of equation 8x-4y=-32 -3x 4y=42

Answers

What are the answers?

1. A line passes through the ordered pairs (7,2) and (5,4). What is the slope? please show work

2. A sphere has a diameter od 20 cm. What would be the volume of sphere?

Answers

[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 7 &,& 2~) % (c,d) &&(~ 5 &,& 4~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{4-2}{5-7}\implies \cfrac{2}{-2}\implies -1[/tex]

since the sphere has a diameter of 20, its radius is half that, or 10.

[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\ -----\\ r=10 \end{cases}\implies V=\cfrac{4\pi (10)^3}{3}[/tex]

twenty milligrams of the drug lincomycin is to be given for each kilogram of a person's weight. The drug is to be mixed with 250 cc of a normal saline solution, and the mixture is to be administered intravenously over a 1 hour period. Clyde Dexter, who weighs 196 lb, is to be given the drug. Determine the dosage of the drug he will be given?

Answers

Final answer:

To determine the dosage of lincomycin for Clyde Dexter, his weight is first converted to kilograms (88.9 kg), then the prescribed dosage of 20 mg/kg is applied, resulting in a required dosage of 1778 mg.

Explanation:

To calculate the dosage of lincomycin for Clyde Dexter, we first need to convert his weight from pounds to kilograms. Knowing that there are approximately 2.20462 pounds in a kilogram, we can calculate his weight in kilograms. Following this, we will calculate the dosage of lincomycin required based on the prescribed 20 milligrams per kilogram of body weight.

Step 1: Convert Weight to Kilograms

Clyde’s weight in pounds: 196 lb

Conversion factor: 1 kg = 2.20462 lb

Clyde’s weight in kilograms: 196 lb / 2.20462 = 88.9 kg (approximately)

Step 2: Calculate Dosage

Prescribed dosage: 20 mg/kg

Clyde's weight: 88.9 kg

Required dosage of lincomycin: 88.9 kg * 20 mg/kg = 1778 mg

The calculated dosage of lincomycin for Clyde Dexter, based on his body weight, is therefore 1778 mg. This dose is to be mixed with 250 cc of normal saline solution and administered intravenously over a 1 hour period.

A multivitamin tablet contains 16.5mg of calcium. How much calcium does a bottle of 20 tablets contain

Answers

Final answer:

To find the total calcium in a bottle of 20 tablets, multiply the calcium content of one tablet (16.5 mg) by the number of tablets (20), resulting in 330 mg of calcium in the entire bottle.

Explanation:

To calculate the total amount of calcium in a bottle of 20 multivitamin tablets, you simply multiply the amount of calcium in one tablet by the number of tablets. If one tablet contains 16.5mg of calcium, the total amount of calcium in a bottle can be found with the following calculation:

Total amount of calcium = Amount of calcium per tablet × Number of tablets

Total amount of calcium = 16.5 mg/tablet × 20 tablets = 330 mg

So, a bottle of 20 tablets contains 330 mg of calcium.

Q # 2 please find the area

Answers

its answer # 1, 15 squared, this is because the width of the triangle (10) multiplied by the length of the triangle (3) is 30. 30 divided by 2 is 15. You have to dived it by 2, because if you left it as 30, that would be the area if a square made of two of those triangles.

Hope this makes sense :)

Answer:
area = 15 yd²

Explanation:
The area of the triangle can be calculated as follows:
area of triangle = 0.5 * base * height

In the given, we have:
base = 10 yd
height = 3 yd

Substitute with the givens in the above equation to get the area as follows:
area of triangle = 0.5 * 10 * 3 = 15 yd²

Hope this helps :)

simplify the expression (-5)2. -10 10 -25 25

Answers

(-5)² = (-5)*(-5) = 25

_____
There are an even number of negative factors, so the result is positive.

Anna plans a business model to compete with two video stores, where she hopes to draw in customers from one store but not lose money on the deal. Movie Mania charges a subscription fee of $30 and an additional $5 per movie, x. Movie Time charges a subscription fee of $25 and an additional $6 per movie, x. Based on this information, which system of inequalities could be used to determine how many movies need to be rented for a customer on Anna’s plan, y, to pay her more than they would at Movie Time, but less than they would at Movie Mania?

Answers

Movie Mania charges a subscription fee of $30 and an additional $5 per movie, x. So the total charges at Movie Mania for x movies will be:

30 + 5x

Movie Time charges a subscription fee of $25 and an additional $6 per movie, x. So the total charges at Movie Time for x movies will be:

25 + 6x

Anna wants her plan to her amount y which is more than Movie Time but Less than Movie Mania. So we can set up the equation as:

Cost at Movie Time < y < Cost at Movie Mania

Using the values, we can write:

25 + 6x < y < 30 + 5x

Using this system of inequalities Anna can determine how many movies need to be rented for a customer on her plan

Answer:D. y<5x+30/x

y>6x+25/x

Step-by-step explanation:

got right on edmentum

hey can you please help me posted picture of question

Answers

The inverse of F(x) will contain the points in inverse order.

So x-value of F(x) will be the y-value of its inverse.
And y-value of F(x) will be the x-value of its inverse.

So, (-3, 7) on F(x) will be translated to (7, -3) on its inverse.

Thus, the correct answer is option A

Value of m varies directly as value of n and n=5 when m=12. What is n when m=18?

Answers

Simplify the problem down, so:

m = 12 & n = 5
m = 6 & n = 2.5 (divided each number by 20)

Now m is a factor of 18. Multiply each number by 3.
Answer: m = 18 & n = 7.5

Hey can you please help me posted picture of question

Answers

Stretching or compression changes the shape of a function, i.e the function can be made narrower or wider by stretching/compression.

So, the correct statement will be:

To change the shape of a function you need to stretch or compress it.

Thus, option C is the correct answer.

What percent of 7 is 2?

Answers

It is 350% I think, because you are trying to find how many groups of 2 go into 7. So, you have to divide 7 by 2. You get 3.5. 3.5 in percentage form is 350%

hey can you please help me posted picture of question

Answers

Answer is TRUE.

The original relation would be: [tex] x^{2} -2[/tex] with domain equal to the range of the given inverse and range equal to the domain of the given inverse.

The relation passes the vertical line test, so it will be a function. So the statement is true

Can someone help me with this problem? please explain.

Answers

The units attached to the numbers can help you out. They work just like variables when you go to add, subtract, multiply, or divide.

You have weight (5.76 pounds) and density (0.08 pounds/in³). The units of volume (in³) are in the denominator of the density, but we want them in the numerator of a number that gives the volume of the brick. At the same time, we want to cancel units of pounds. We can do all that by dividing weight by density.

volume = weight/density
volume = (5.76 pounds)/(0.08 pounds/in³) = (5.76/0.08) in³ = 72 in³

We know the volume of a rectangular prism (brick) is given by the product of its length, width, and height. We now have enough information to find the height.
volume = length*width*height
72 in³ = (8 in)*(2.25 in)*height . . . . . substitute known numbers
72 in³/((8*2.25) in²) = height . . . . . .. solve for height
72/18 in = height = 4 in . . . . . . . . . . . do the arithmetic. (in³)/(in²) = in

The height of the brick is 4 inches.

A system with 6 independent components is such that the system will fail if at least one of the individual components fail. the probability that a component fails is 0.02. let a be the event that the system fails. what is the probability of a ?

Answers

The components operate independently, so the probability of "total" system failure is the same as the product of each probability of component failure. That is, if [tex]A_i[/tex] denotes the event that component [tex]i[/tex] fails, then

[tex]\mathbb P(A)=\mathbb P(A_1\cup\cdots\cup A_6)=\mathbb P(A_1)\times\cdots\times\mathbb P(A_6)[/tex]

The [tex]A_i[/tex] are independent and identically distributed, so [tex]\mathbb P(A_i)=\mathbb P(A_j)[/tex] for all [tex]i,j[/tex]. So

[tex]\mathbb P(A)=\mathbb P(A_1)^6=0.02^6=6.4\times10^{-11}=0.000000000064[/tex]

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