Prove that a cubic equation x 3 + ax 2 + bx+ c = 0 has 3 roots by finding the roots.

Answers

Answer 1

That's a pretty tall order for Brainly homework.  Let's start with the depressed cubic, which is simpler.

Solve

[tex]y^3 + 3py = 2q[/tex]

We'll put coefficients on the coefficients to avoid fractions down the road.

The key idea is called a split, which let's us turn the cubic equation in to a quadratic.  We split unknown y into two pieces:

[tex]y = s + t[/tex]

Substituting,

[tex](s+t)^3 + 3p(s+t) = 2q[/tex]

Expanding it out,

[tex]s^3+3 s^2 t + 3 s t^2 + t^3 + 3p(s+t) = 2q[/tex]

[tex]s^3+t^3 + 3 s t(s+t) + 3p(s+t) = 2q[/tex]

[tex]s^3+t^3 + 3( s t + p)(s+t) = 2q[/tex]

There a few moves we could make from here. The easiest is probably to try to solve the simultaneous equations:

[tex]s^3+t^3=2q, \qquad st+p=0[/tex]

which would give us a solution to the cubic.

[tex]p=-st[/tex]

[tex]t = -\dfrac p s[/tex]

Substituting,

[tex]s^3 - \dfrac{p^3}{s^3} = 2q[/tex]

[tex](s^3)^2 - 2 q s^3 - p^3 = 0[/tex]

By the quadratic formula (note the shortcut from the even linear term):

[tex]s^3 = q \pm \sqrt{p^3 + q^2}[/tex]

By the symmetry of the problem (we can interchange s and t without changing anything) when s is one solution t is the other:

[tex]s^3 = q + \sqrt{p^3+q^2}[/tex]

[tex]t^3 = q - \sqrt{p^3+q^2}[/tex]

We've arrived at the solution for the depressed cubic:

[tex]y = s+t = \sqrt[3]{q + \sqrt{p^3+q^2}} + \sqrt[3]{ q - \sqrt{p^3+q^2} }[/tex]

This is all three roots of the equation, given by the three cube roots (at least two complex), say for the left radical.  The two cubes aren't really independent, we need their product to be [tex]-p=st[/tex].

That's the three roots of the depressed cubic; let's solve the general cubic by reducing it to the depressed cubic.

[tex]x^3 + ax^2 + bx + c=0[/tex]

We want to eliminate the squared term.  If substitute x = y + k we'll get a 3ky² from the cubic term and ay² from the squared term; we want these to cancel so 3k=-a.

Substitute x = y - a/3

[tex](y - a/3)^3 + a(y - a/3)^2 + b(y - a/3) + c = 0[/tex]

[tex]y^3 - ay^2 + a^2/3 y - a^3/27 + ay^2-2a^2y/3 + a^3/9 + by - ab/3 + c =0[/tex]

[tex]y^3 + (b - a^2/3) y = -(2a^3+9ab) /27 [/tex]

Comparing that to

[tex]y^3 + 3py = 2q[/tex]

we have [tex] p = (3b - a^2) /9, q =-(a^3+9ab)/54 [/tex]

which we can substitute in to the depressed cubic solution and subtract a/3  to get the three roots.  I won't write that out; it's a little ugly.


Related Questions

i
dont
get
this
help
rn

Answers

Answer:

6 first box. 12 second box. 21 third box. 10 fourth box. 4 fifth box.

Step-by-step explanation:

Look for common denominaters, that will show you what to multiply the equation by to get rid of fractions.

Find the number of possible outcomes Five books need to be placed on a shelf. You randomly arrange the books on the shelf from left to right.

Answers

Answer:

120

Step-by-step explanation:

Let's say you put them on the shelf one by one, from left to right.

You can pick 1 of the 5 for the first position.

5

Now you have 4 books left. You pick one out of those 4 for the second position.

5 * 4

There are 3 choices left for the 3rd position.

5 * 4 * 3

2 left for the 4th position.

5 * 4 * 3 * 2

Finally, there is one book left for the 5th position.

5 * 4 * 3 * 2 * 1

Now we multiply:

5 * 4 * 3 * 2 * 1 = 120

The SAT scores have an average of 1200 with a standard deviation of 60. A sample of 36 scores is selected. a) What is the probability that the sample mean will be larger than 1224

Answers

Answer:

the probability that the sample mean will be larger than 1224 is  0.0082

Step-by-step explanation:

Given that:

The SAT scores have an average of 1200

with a  standard deviation of 60

also; a sample of 36 scores is selected

The objective is to determine  the probability that the sample mean will be larger than 1224

Assuming X to be the random variable that represents the SAT score of each student.

This implies that  ;

[tex]S \sim N ( 1200,60)[/tex]

the probability that the sample mean will be larger than 1224 will now be:

[tex]P(\overline X > 1224) = P(\dfrac{\overline X - \mu }{\dfrac{\sigma}{\sqrt{n}} }> \dfrac{}{}\dfrac{1224- \mu }{\dfrac{\sigma}{\sqrt{n}} })[/tex]

[tex]P(\overline X > 1224) = P(Z > \dfrac{1224- 1200 }{\dfrac{60}{\sqrt{36}} })[/tex]

[tex]P(\overline X > 1224) = P(Z > \dfrac{24 }{\dfrac{60}{6} })[/tex]

[tex]P(\overline X > 1224) = P(Z > \dfrac{24 }{10} })[/tex]

[tex]P(\overline X > 1224) = P(Z > 2.4 })[/tex]

[tex]P(\overline X > 1224) =1 - P(Z \leq 2.4 })[/tex]

From Excel Table ; Using the formula (=NORMDIST(2.4))

P(\overline X > 1224) = 1 -  0.9918

P(\overline X > 1224) = 0.0082

Hence;  the probability that the sample mean will be larger than 1224 is  0.0082

What is the value of y iin this equation? 4(y-3) =48

Answers

Answer:

y = 15

Step-by-step explanation:

Question:

4(y - 3) = 48

1. Distribute

4y - 12 = 48

2. Simplify Like terms

4y - 12 = 48

    + 12 + 12

4y = 60

3. Solve

4y = 60

/4       /4

y = 15

4. Check:

4(y - 3) = 48

4((15) - 3) = 48

4(12) = 48

48 = 48     Correct!

Hope this helped,

Kavitha

Answer:

[tex]y=15\\[/tex]

Step 1:

To find y, we first have to multiply [tex]4(y-3)[/tex]. When we do that (4 * y, 4 * - 3), we get [tex]4y-12[/tex].

Step 2:

Our equation looks like this now:

[tex]4y-12=48[/tex]

To solve this equation, we have to add 12 on both sides so we can cancel out the -12 on the left side of the equation.

[tex]4y-12(+12)=48(+12)[/tex]

[tex]4y=60[/tex]

Now, we can divide 4 on both sides to get y  by itself.

[tex]4y/4\\60/4[/tex]

[tex]y=15[/tex]

√9m^2n^2 + 2√m^2n^2 - 3mn

Answers

Answer:

I think it is

Step-by-step explanation:

Answer:

5n√2m^ - 3mn

Step-by-step explanation:

The number that is 75% of one less than a number n. As an expression THX!!!! i Promise to mark you brainliset

Answers

Answer:

x = [tex]\frac{3}{4}(n-1)[/tex]

Step-by-step explanation:

It's given in the question that '' The number is 75% of one less than a number n"

Let the number is 'x'.

One less than a number 'n' will be = (n - 1)

75% of one less than a number will be = 75% of (n -1)

                                                                = [tex]\frac{75}{100}(n-1)[/tex]

                                                                = [tex]\frac{3}{4}(n-1)[/tex]

Therefore, the desired expression to get the number 'x' will be,

x = [tex]\frac{3}{4}(n-1)[/tex]

Answer:

3/4(n-1)

Step-by-step explanation:

did it in rsm

I have attached the file

Answers

Answer:

sorry i am not able to understood

Step-by-step explanation:

An HR manager would like to test the hypothesis that the proportion of agenda-less meetings is more than 45%. Based on the information below, choose the correct conclusion for this hypothesis test. To test this, he randomly selected minutes from 100 past meeting, and found that 65 of them had no agenda. The following is the setup for this hypothesis test: H0:p=0.45 Ha:p>0.45 The p-value for this hypothesis test is 0.025. At the 5% significance level, should he reject or fail to reject the null hypothesis? Select the correct answer below: Reject the null hypothesis because 0.45>0.05. Fail to reject the null hypothesis because 0.45>0.05. Reject the null hypothesis because the p-value =0.025 is less than the significance level α=0.05. Fail to reject the null hypothesis because the p-value =0.025 is less than the significance level α=0.05.

Answers

Answer: Reject the null hypothesis because the p-value =0.025 is less than the significance level α=0.05.

Step-by-step explanation: Trust me

please show on graph (with x and y coordinates) state where the function x^4-36x^2 is non-negative, increasing, concave up​

Answers

Answer:

[tex] y'' =12x^2 -72=0[/tex]

And solving we got:

[tex] x=\pm \sqrt{\frac{72}{12}} =\pm \sqrt{6}[/tex]

We can find the sings of the second derivate on the following intervals:

[tex] (-\infty<x< -\sqrt{6}) , y'' = +[/tex] Concave up

[tex]x=-\sqrt{6}, y =-180[/tex] inflection point

[tex] (-\sqrt{6} <x< \sqrt{6}), y'' =-[/tex] Concave down

[tex]x=\sqrt{6}, y=-180[/tex] inflection point

[tex] (\sqrt{6}<x< \infty) , y'' = +[/tex] Concave up

Step-by-step explanation:

For this case we have the following function:

[tex] y= x^4 -36x^2[/tex]

We can find the first derivate and we got:

[tex] y' = 4x^3 -72x[/tex]

In order to find the concavity we can find the second derivate and we got:

[tex] y'' = 12x^2 -72[/tex]

We can set up this derivate equal to 0 and we got:

[tex] y'' =12x^2 -72=0[/tex]

And solving we got:

[tex] x=\pm \sqrt{\frac{72}{12}} =\pm \sqrt{6}[/tex]

We can find the sings of the second derivate on the following intervals:

[tex] (-\infty<x< -\sqrt{6}) , y'' = +[/tex] Concave up

[tex]x=-\sqrt{6}, y =-180[/tex] inflection point

[tex] (-\sqrt{6} <x< \sqrt{6}), y'' =-[/tex] Concave down

[tex]x=\sqrt{6}, y=-180[/tex] inflection point

[tex] (\sqrt{6}<x< \infty) , y'' = +[/tex] Concave up

6. Find x. (2 pt)
48°
X

Answers

Answer:

x = 96

Step-by-step explanation:

Inscribed Angle = 1/2 Intercepted Arc

48 = 1/2 ( x)

Multiply by 2

96 = x

Answer:

[tex]\boxed{x=96}[/tex]

Step-by-step explanation:

Apply the inscribed angle theorem, where the measure of an inscribed angle is half the measure of the intercepted arc.

[tex]48=\frac{1}{2}x[/tex]

Multiply both sides by 2.

[tex]48(2)=\frac{1}{2}x(2)[/tex]

[tex]96=x[/tex]

There are 3 times as many novels as comic books in a bookstore.If there are 2480 books altogether, how many comic books are there in the bookstore.​

Answers

Answer:

there are 620 comic books

Step-by-step explanation:

let number of comic books be x

total books=3x+x

2480=4x

2480/4=x

620=x

Answer:

620

Step-by-step explanation:

Let comic books be ' X '

Let Novels be ' 3x '

Now, finding the value of X

According to Question,

[tex]3x + x = 2480[/tex]

Collect like terms

[tex]4x = 2480[/tex]

Divide both sides of the equation by 4

[tex] \frac{4x}{4} = \frac{2480}{4} [/tex]

Calculate

[tex]x = 620[/tex]

Thus, There are 620 comic books in the book store.

Hope this helps...

Best regards!!

Determine the measure of the unknown variables.

Answers

Answer:

75

Step-by-step explanation:

x = 75°

yes x = 75°(OPPOSITE ANGLES ARE EQUAL)

..

If y>0, which of these values of x is NOT in the domain of this equation? y=x2+7x

Answers

Answer:

[tex]\boxed{\sf \ \ \ [-7,0] \ \ \ }[/tex]

Step-by-step explanation:

Hello

[tex]y=x^2+7x=x(x+7) >0\\<=> x>0 \ and \ x+7 >0 \ \ or \ \ x<0 \ and \ x+7<0\\<=> x>0 \ \ or \ \ x<-7\\[/tex]

So values of x which is not in this domain is

[tex]-7\leq x\leq 0[/tex]

which is [-7,0]

hope this helps

Consider the recursive function,
f(1) = 2
f(n) = 5•f(n − 1), for n > 2

Answers

Answer:

yes?

Step-by-step explanation:

??? can u say exactly what the question is please? thank you

Answer:

the question is:

Which statement is true?

A. The value of F(6) is 2 times the value of f(3).

B. The value of f(6) is 15 times the value of f(3).

C. The value of f(6) is 1/125 times the value of f(3).

D. The value of f(6) is 125 times the value of f(3).

Step-by-step explanation:

comment the answer below for everyone please.

What is the formula for the area A of a trapezoid with parallel sides of length B and D, nonparallel sides of length A and C and height H?

A. A = 1/2h (a+c)
B. A = 1/2h (b + d)
C. A = a+b + c + d
D. A= abcd
E. A = 1/2h (a+b+c+d)

Answers

Answer:

[tex](B) \dfrac12H (B+D)[/tex]

Step-by-step explanation:

[tex]\text{Area of a trapezoid }= \dfrac12 ($Sum of the parallel sides) \times $Height\\Parallel Sides = B and D\\Height =H\\Therefore:\\\text{Area of the trapezoid }= \dfrac12 (B+D) H[/tex]

The correct option is B.

Use an appropriate series to find Taylor series of the given function centered at the indicated value of a. Write your answer in summation notation.

sinx, a= 2π

Answers

Answer:

The Taylor series is   [tex]$$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x)^{2n+1}][/tex]

Step-by-step explanation:

From the question we are told that

      The function is  [tex]f(x) = sin (x)[/tex]

This is centered at  

       [tex]a = 2 \pi[/tex]

Now the next step is to represent the function sin (x) in it Maclaurin series form which is  

          [tex]sin (x) = \frac{x^3}{3! } + \frac{x^5}{5!} - \frac{x^7}{7 !} +***[/tex]

=>       [tex]sin (x) = $$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x)^{2n+1}][/tex]

   Now since the function is centered at  [tex]a = 2 \pi[/tex]

We have that

           [tex]sin (x - 2 \pi ) = (x-2 \pi ) - \frac{(x - 2 \pi)^3 }{3 \ !} + \frac{(x - 2 \pi)^5 }{5 \ !} - \frac{(x - 2 \pi)^7 }{7 \ !} + ***[/tex]

This above equation is generated because the function is not centered at the origin but at [tex]a = 2 \pi[/tex]

           [tex]sin (x-2 \pi ) = $$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x - 2 \pi)^{2n+1}][/tex]

Now due to the fact that [tex]sin (x- 2 \pi) = sin (x)[/tex]

This because  [tex]2 \pi[/tex] is a constant

   Then it implies that the Taylor series of the function centered at [tex]a = 2 \pi[/tex] is

             [tex]$$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x)^{2n+1}][/tex]

WHY CAN'T ANYONE HELP ME? PLEASE What one is the standard form of the equation y = – 1/4 x – 2? A. x + 4y = 8 B. x + 4y = – 2 C. x + 4y = – 8 or D. –x + 4y = – 8

Answers

Answer:

C. x+4y=-8

Step-by-step explanation:

The standard form of an equation is Ax+Bx=C

y= -[tex]\frac{1}{4}[/tex]x-2

Multiply 4 by both sides

4y= -x-8

1+4y= -8

A certain brand of automobile tire has a mean life span of 35,000 miles, with a standard deviation of 2250 miles. Assume the life spans of the tires have a bell-shaped distribution.
(a) The life spans of three randomly selected tires are 34,000 miles, 37,000 miles, and 30,000 miles. Find the z-score that corresponds to each life span. Determine whether any of these life spans are unusual.
(b) The life spans of three randomly selected tires are 30,500 miles, 37,250 miles, and 35,000 miles. Using the Empirical Rule, find the percentile that corresponds to each life span.

Answers

Answer:

Step-by-step explanation:

From the information given:

mean life span of a brand of automobile = 35,000

standard deviation of a brand of automobile = 2250 miles.

the z-score that corresponds to each life span are as follows.

the standard z- score formula is:

[tex]z = \dfrac{x - \mu}{\sigma}[/tex]

For x = 34000

[tex]z = \dfrac{34000 - 35000}{2250}[/tex]

[tex]z = \dfrac{-1000}{2250}[/tex]

z = −0.4444

For x = 37000

[tex]z = \dfrac{37000 - 35000}{2250}[/tex]

[tex]z = \dfrac{2000}{2250}[/tex]

z = 0.8889

For x = 3000

[tex]z = \dfrac{30000 - 35000}{2250}[/tex]

[tex]z = \dfrac{-5000}{2250}[/tex]

z = -2.222

From the above z- score that corresponds to their life span; it is glaring  that the tire with the life span 30,000 miles has an unusually short life span.

For x = 30,500

[tex]z = \dfrac{30500 - 35000}{2250}[/tex]

[tex]z = \dfrac{-4500}{2250}[/tex]

z = -2

P(z) = P(-2)

Using excel function (=NORMDIST -2)

P(z) = 0.022750132

P(z) = 2.28th percentile

For x =  37250

[tex]z = \dfrac{37250 - 35000}{2250}[/tex]

[tex]z = \dfrac{2250}{2250}[/tex]

z = 1

Using excel function (=NORMDIST 1)

P(z) = 0.841344746

P(z) = 84.14th percentile

For x = 35000

[tex]z = \dfrac{35000- 35000}{2250}[/tex]

[tex]z = \dfrac{0}{2250}[/tex]

z = 0

Using excel function (=NORMDIST 0)

P(z) = 0.5

P(z) = 50th percentile

a.  The z score of each life span should be -0.4444, 0.889, and 2.2222.

b.  The percentile of each life span should be 0.0228, 0.8413 and  0.5000.

Given that,

mean life span of 35,000 miles, with a standard deviation of 2250 miles.

The calculation is as follows:

(a)

The z score should be

[tex]Z1 = \frac{34000-35000}{2250} = -0.4444\\\\Z2 = \frac{37000-35000}{2250} = 0.8889\\\\Z3 = \frac{30000-35000}{2250} = -2.2222\\\\[/tex]

The tire with life span of 30000 miles would be considered unusual

(b)

The percentile should be

[tex]Z1 = \frac{30500-35000}{2250} = -2[/tex]

p(Z1 < -2) = NORMSDIST(-2) = 0.0228

[tex]Z2 = \frac{37250-35000}{2250} = 1[/tex]

p(Z2 < 1) = NORMSDIST(1) = 0.8413

[tex]Z3 = \frac{35000-35000}{2250} = 0[/tex]

p(Z3 < 0) = NORMSDIST(0) = 0.5000

Find out more information about standard deviation here:

https://brainly.com/question/12402189?referrer=searchResults

PLLZZZZ help me find x you are AWSOME!! I need this ASAP

Answers

Answer:

27°

Step-by-step explanation:

D is 72° because it alternates with B, alternate angles are equal.

2x+72°+2x= 180° because it is a straight line.

4x+72°=180°

4x=108°

x=27°

PLEASE HELP Two prisms are composed to form a V shape. The thickness of each prism is 1 unit, and width of each prism is 2 units. If the length of one prism is greater than the length of the other prism by 1 unit and the total volume of the figure is 30 cubic units, what are the lengths of the prisms?

Answers

Answer:

  7 units, 8 units

Step-by-step explanation:

Apparently, the cross section of each prism is a rectangle 1 unit by 2 units. Hence the total length will be ...

  (30 units³)/((1 unit)(2 units)) = 15 units

Two numbers that differ by 1 and have a sum of 15 are 7 and 8.

The lengths of the prisms are 7 units and 8 units.

3 is what percentage of 12?

Answers

Answer:

25%

Step-by-step explanation:

First you have the fraction of 3/12 and need to turn it into a decimal. So to do that you divide 3 by 12 = 0.25. So your percent is 25%

Find a formula for an for the arithmetic sequence.

Answers

Answer:

[tex]a_{n} = a + 2(n-1)[/tex]

Step-by-step explanation:

[tex]a_{5}= a_{1} + 4d \\4 = -4 +4d\\8= 4d\\d= 2\\\\Therefore \\a_{n} = a_{1} + 2(n-1)[/tex]

At noon a passenger train leaves the Dupont Railway station and travels due east for 2 hours. At 12:45 pm the same day a second passenger train leaves the same railway station and travels due west for 1 hour and 15 minutes at a speed 10 kilometers per hour slower than the first passenger train. At 2pm the two trains were 215 kilometers apart. How fast had each train been traveling

Answers

Answer:

The speed of the first train is 70 km/hr

The speed of the second train is 60 km/hr

Step-by-step explanation:

For the first train:

Travel time = 2 hours

The speed = ?

we designate the speed as V

For the second train:

The travel time = 1 hr 15 min = 1.25 hrs (15 minutes = 15/60 hrs)

speed = 10 km/hr slower than that of the first train, we can then say

the speed = V - 10

The total distance traveled by both trains in the opposite direction of one another is 215 km

we can put this problem into an equation involving the distance covered by the trains.

we know that distance = speed x time

the distance traveled by the first train will be

==> 2 hrs x V = 2V

the distance traveled by the second train will be

==> 1.25 hrs x (V - 10) = 1.25(V - 10)

Equating the above distances to the total distance between the trains, we'll have

2V + 1.25(V - 10) = 215

2V + 1.25V - 12.5 = 215

3.25V = 215 + 12.5

3.25V = 227.5

V = 227.5/3.25 = 70 km/hr     this is the speed of the first train

Recall that the speed of the second train is 10 km/hr slower, therefore

speed of the second train = 70 - 10 = 60 km/hr

The speed of the trains are 70km/hr and 60km/hr respectively.

The distance of the first train will be represented by: = 2 × D = 2D

The distance of the second train will be represented by: = 1.25 × (D - 10) = 1.25(D - 10).

Based on the information given in the question, the equation to solve the question will be:

2D + 1.25(D - 10) = 215

Collect like terms

2D + 1.25D - 12.5 = 215

3.25D = 215 + 12.5

3.25D = 227.5

D = 227.5/3.25

D = 70km/hour

The speed of the second train will be:

= 70 - 10 = 60km per hour.

Read related link on:

https://brainly.com/question/24720712

You change oil every 6000 miles and drive 2000 miles a month; how many times a year do you change oil?

Answers

Answer:

you would change it 4 times a year

Step-by-step explanation:

if there is 12 months in a year and 3 mounths equal 6000 then divide 12/3=4

Determine the domain of the function. f as a function of x is equal to the square root of x plus three divided by x plus eight times x minus two.

All real numbers except -8, -3, and 2
x ≥ 0
All real numbers
x ≥ -3, x ≠ 2

Answers

Answer:

[tex]\huge \boxed{{x\geq -3, \ x \neq 2}}[/tex]

Step-by-step explanation:

The function is given,

[tex]\displaystyle f(x)=\frac{\sqrt{x+3 }}{(x+8)(x-2)}[/tex]

The domain of a function are all possible values of x.

There are restrictions for the value of x.

The denominator of the function cannot equal 0, if 0 is the divisor then the fraction would be undefined.

[tex]x+8\neq 0[/tex]

Subtract 8 from both parts.

[tex]x\neq -8[/tex]

[tex]x-2\neq 0[/tex]

Add 2 on both parts.

[tex]x\neq 2[/tex]

The square root of x + 3 cannot be a negative number, because the square root of a negative number is undefined. x + 3 has to equal to 0 or be greater than 0.

[tex]x+3\geq 0[/tex]

Subtract 3 from both parts.

[tex]x\geq -3[/tex]

The domain of the function is [tex]x\geq -3[/tex], [tex]x\neq 2[/tex].

The domain of the given function will be x ≥ -3 and x ≠ 2.

What is the domain of a function?

The entire range of independent input variables that can exist is referred to as a function's domain or,

The set of all x-values that can be used to make the function "work" and produce actual y-values is referred to as the domain.

As per the data given in the question,

The given expression of function is,

f(x) = [tex]\sqrt{\frac{x+3}{(x-8)(x-2)} }[/tex]

The fraction would indeed be undefined if the base of the function were equal to zero, which is not allowed.

x + 8 ≠ 0

x ≠ -8

And, x - 2 ≠ 0

x ≠ 2

Since the square root of a negative number is undefined, x+3 cannot have a negative square root. x+3 must be bigger than zero or identical to zero.

So,

x + 3 ≥ 0

x ≥ -3

So, the domain of the function will be x ≥ -3 and x ≠ 2.

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A distribution has a mean of 90 and a standard deviation of 15. Samples of size 25 are drawn randomly from the population. Find the probability that the sample mean is more than 85 g

Answers

Answer:

The probability is 0.04746

Step-by-step explanation:

Firstly, we calculate the z-score here

Mathematically;

z-score = x-mean/SD/√n

Where from the question;

x = 85, mean = 90 , SD = 15 and n = 25

Plugging these values into the equation, we have;

Z = (85-90)/15/√25 = -5/15/5 = -1.67

So the probability we want to calculate is ;

P(z > -1.67)

We use the standard normal distribution table for this;

P(z > -1.67) = 0.04746

which graph represents a function? Please help!

Answers

Answer:

The last graph (to the far right).

Step-by-step explanation:

As long as each x-value has one y-value, it is a function. However, the last graph has an x-value at -1 where there are two y-values. So, it does not pass the Vertical Line Test, and it is a relation rather than a function.

Hope this helps!

Graph the line y=4/3x +1

Answers

The slope would be 4/3 and the y-intercept is 1

Create a table x and y and in x there is -3/4 and 0 and for the y side is 0 and 1. The line would be in the 2 quadrant with 2 points on on the y axis 1 and the other on the x axis 0.9 and that would be the graphed description of the line. Sorry if this is hard to understand i don’t have a access to draw or insert an image.

The graph of the linear equation is on the image at the end.

How to graph the line?

To do it, we need to find two points on the line, so let's evaluate it.

When x = 0

y = (4/3)*0 + 1 = 1 ----> (0, 1)

When x = 3

y = (4/3)*3 + 1 = 5 ---> (3 , 5)

Now just graph these two points and connect them with a line, that will be the graph of the linear equation.

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Another math problem. Can you solve it? I can't... For a good answer I'll make it 'The Best' I hope you can help me... Thanks

Answers

Answer:

[tex]\boxed{\sf \ \ \ 10^2+11^2+12^2=13^2+14^2 \ \ \ }[/tex]

Step-by-step explanation:

Hello,

let's note a a positive integer

5 consecutive integers are

a

a+1

a+2

a+3

a+4

so we need to find a so that

[tex]a^2+(a+1)^2+(a+2)^2=(a+3)^2+(a+4)^2\\<=>\\a^2+a^2+2a+1+a^2+4a+4=a^2+6a+9+a^2+8a+16\\<=>\\3a^2+6a+5=2a^2+14a+25\\<=>\\a^2-8a-20=0\\<=>\\(a+2)(a-10)=0\\<=>\\a = -2 \ or \ a = 10\\[/tex]

as we are looking for positive integer the solution is a = 10

do not hesitate if you have any question

Write the following Arithmetic Sequence using a Recursive Formula: a = -7 + 3(n - 1)
A : A1 = -7, an = an-1 + 3
B : A1= -7, a, = an+1 + 3
C : A1 = 3, an = an+1 - 7
D : A1 = 3, an = an-1 - 7

NEED ANSWER ASAP

Answers

Answer:

A : A1 = -7, an = an-1 + 3

Step-by-step explanation:

a1=-7, a2=-7+(1)3=-4

a3=-7+(2)3=-1

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