The rate of change in sales S is inversely proportional to time t (t > 1), measured in weeks. Find S as a function of t when the sales after 2 and 4 weeks are 162 units and 287 units, respectively.

Answer:

x = -5 or x = i sqrt(3) or x = -i sqrt(3)

Step-by-step explanation:

Solve for x:

x^3 + 5 x^2 + 3 x + 15 = 0

The left hand side factors into a product with two terms:

(x + 5) (x^2 + 3) = 0

Split into two equations:

x + 5 = 0 or x^2 + 3 = 0

Subtract 5 from both sides:

x = -5 or x^2 + 3 = 0

x = (0 ± sqrt(0^2 - 4×3))/2 = ( ± sqrt(-12))/2:

x = -5 or x = sqrt(-12)/2 or x = (-sqrt(-12))/2

sqrt(-12) = sqrt(-1) sqrt(12) = i sqrt(12):

x = -5 or x = (i sqrt(12))/2 or x = (-i sqrt(12))/2

sqrt(12) = sqrt(4×3) = sqrt(2^2×3) = 2sqrt(3):

x = -5 or x = (i×2 sqrt(3))/2 or x = (-i×2 sqrt(3))/2

(2 i sqrt(3))/2 = i sqrt(3):

x = -5 or x = i sqrt(3) or x = (-2 i sqrt(3))/2

(2 (-i sqrt(3)))/2 = -i sqrt(3):

Answer: x = -5 or x = i sqrt(3) or x = -i sqrt(3)

Answer:

C. x = −5, 1.7i, −1.7i

Step-by-step explanation:

Quick answer:

C. x = −5, 1.7i, −1.7i

explanation:

C. is the only answer option that does NOT have 0 as a root, which is impossible, because there is a constant term, which means that all roots are non-zero. In other words, we cannot extract x as a factor.

Complete answer:

All odd degree polynomials have at least one real root.

By the real roots theorem, we know that

if there is a real root, it must be of the form [tex]\pm[/tex]p/q where q is any of the factors of the leading coefficient (1 in this case) and p is any factor of the constant term d (15 in this case).

Values of [tex]\pm[/tex]p/q are

On trial and error, using the factor theorem, we see that

f(-5) = 0, therefore -5 is a real root.  By long division, we have a quotient of x^2+3 = 0, which gives readily the remaining (complex) roots of +/- sqrt(5) i

The answer is {-5, +/- sqrt(5) i}, or again,

C. x = −5, 1.7i, −1.7i

Answer:

4

Step-by-step explanation:

Length of one side=8

Area=32

Length of another side=x

8 into x = 32

X=32/8

=4

Answer:

(-5, 0) and (0,4)

Step-by-step explanation:

Given equation: -4x + 5y = 20

Sub. in the values

When x = -5 and y = 0 (-5,0),

[tex] - 4( - 5) + 5(0) = 20 [/tex]

When x = 0 and y = 4 (0,4),

[tex] - 4(0) + 5(4) = 20[/tex]

That's how I would do it, not sure if your school has another method. Hope this helps :)

Answer: x = -5 and y = 4

Step-by-step explanation: its the first option do you need me to exlain how cuz its multiple choice  

Answer:

Step-by-step explanation:

Let us first generate the frequency table from the information given:

Hurricane number(X)       Frequency(f)                f(X)

6                                            9                                   54

8                                            13                                  104

12                                           16                                  192

14                                            12                                168

Total                                     ∑(f) = 50                          ∑f(x) =518

In order to determine the last frequency (the remaining years), we will add the other frequencies and subtract the answer from 50, which is the total frequency (50 years). This is done as follows:

Let the last frequency be f

9 + 3 + 16 + f = 50

38 + f = 50

f = 50 - 38 = 12

Now, calculating mean:

[tex]\bar {X} = \frac{\sum f(x)}{\sum(f)} \\\\\bar {X} = \frac{518}{50} \\\\\bar {X} = 10.36[/tex]

Therefore mean number of hurricanes = 10.4 (to one decimal place)

Answer: The multiplicative inverse of – 1 in the set {-1,1} is -1.

Step-by-step explanation:

In algebra, the multiplicative inverse of a number(x) is a number (say y) such that

[tex]x\times y=1[/tex]  [product of a number and its inverse =1]

if x= -1, then

[tex]-1\times y=1\Rightarrow\ y=-1[/tex]

That means , the multiplicative inverse of -1 is -1 itself.

Hence, the multiplicative inverse of – 1 in the set {-1,1} is -1.

Answer: The answer in a is No while the answer in b is Yes

Step-by-step explanation:

Find the explanation in the attached file.

Answer:

2

Step-by-step explanation:

2,8 to 4,12 has a rise of 4 and a run of 2.

4/2 = 2

The slope is 2.

Remember rise/run!

Answer:

2

Step-by-step explanation:

We take take two points and use the slope formula

m = (y2-y1)/(x2-x1)

m = (12-8)/(4-2)

   = 4/2

   = 2

Answer:

a). Function (4)

b). Function (2)

c). Function (3)

Step-by-step explanation:

Characteristics of the functions given,

Function (1),

Form the given graph,

Slope = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]

          = [tex]-\frac{4}{1}[/tex]

          = -4

Y- intercept of the given function = 2

Function (2),

From he given table,

Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

         = [tex]\frac{5-3}{0+1}[/tex]

         = 2

y-intercept = 5 [Value of y for x = 0]

Function (3),

y = -x - 1

By comparing this equation with y = mx + b

Where 'm' = slope

and b = y-intercept

Slope = (-1)

y-intercept = (-1)

Function (4),

Slope = 5

y-intercept = (-4)

(a). Greatest slope of the function → Function (4)

(b). y-intercept greater than 3 → Function (2)

(c). Function with y-intercept closest to 0 → Function (3)

Answer:

No solution

Step-by-step explanation:

Given equation is,

[tex]\frac{x^{\frac{1}{2}}+x^{-\frac{1}{2}}}{1-x}+\frac{1-x^{-\frac{1}{2}}}{1+x^\frac{1}{2}}-\frac{(4+x)^\frac{1}{2}}{(1-x)^\frac{1}{2}}=0[/tex]

[tex]\frac{x^{\frac{1}{2}}+x^{-\frac{1}{2}}}{1-x}+\frac{1-x^{-\frac{1}{2}}}{1+x^\frac{1}{2}}=\frac{(4+x)^\frac{1}{2}}{(1-x)^\frac{1}{2}}[/tex]

[tex]\frac{(x+1)}{\sqrt{x}(1-x)}+\frac{(\sqrt{x}-1)}{\sqrt{x}(1+\sqrt{x})}=(\frac{4+x}{1-x})^{\frac{1}{2}}[/tex]

[tex]\frac{(\sqrt{x}+1)(x+1)+(\sqrt{x}-1)(1-x)}{\sqrt{x}(1-x)(1+\sqrt{x})}=(\frac{4+x}{1-x})^{\frac{1}{2}}[/tex]

[tex]\frac{x\sqrt{x}+x+\sqrt{x}+1+\sqrt{x}-1-x\sqrt{x}+x}{\sqrt{x}(1-x)(1+\sqrt{x})}=(\frac{4+x}{1-x})^\frac{1}{2}[/tex]

[tex]\frac{2x+2\sqrt{x}}{\sqrt{x}(1-x)(1+\sqrt{x})}=(\frac{4+x}{1-x})^\frac{1}{2}[/tex]

[tex]\frac{2(\sqrt{x}+1)}{(1-x)(1+\sqrt{x})}=(\frac{4+x}{1-x})^\frac{1}{2}[/tex]

[tex]\frac{2}{1-x}=(\frac{4+x}{1-x})^\frac{1}{2}[/tex]  if x ≠ ±1

[tex](\frac{2}{1-x})^2=\frac{4+x}{1-x}[/tex]  [Squaring on both the sides of the equation]

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

4 = (1 - x)(4 + x)

4 = 4 - 4x + x - x²

0 = -3x - x²

x² + 3x = 0

x(x + 3) = 0

x = 0, -3

But both the solutions x = 0 and x = -3 are extraneous solutions, given equation has no solution.

Answer:

Could you please help me Genius??????

Answer:

b

Step-by-step explanation:

b: sin^2 0 + tan^2 0 this is just a gut feelings its been awhile since i done this kind of think i hope i could help

The expression equal to the length of the hypotenuse of a right triangle formed inside the unit circle with a radius of 1 is Option (D) [tex]sin^{2}[/tex]θ+[tex]cos^{2}[/tex]θ

A right-angled triangle is a type of triangle that has one of its angles equal to 90 degrees.

A hypotenuse is the longest side of a right-angled triangle, the side opposite the right angle.

Here,

The length of the hypotenuse of a right triangle, formed inside the unit circle, with a radius of 1 is 1 unit.

We know that,

[tex]sin^{2}[/tex]θ+[tex]cos^{2}[/tex]θ=1

Hence, The expression equal to the length of the hypotenuse of a right triangle formed inside the unit circle with a radius of 1 is Option (D) [tex]sin^{2}[/tex]θ+[tex]cos^{2}[/tex]θ

Learn more about Right triangle and Hypotenuse here

https://brainly.com/question/2869318

#SPJ2

Answer:

a = 55°, b = 65°, c = 65°, d = 60°, e = 120°, f = 60°

Step-by-step explanation:

Vertical angles are congruent. Since a and 55° are vertical angles, we know that a = 55°. Since b and 65° are vertical angles, we know that b = 65°. Alternate interior angles are congruent. Since b and c are alternate interior angles and b = 65°, we know that c = 65° as well. Since 60° and d are alternate interior angles, we know that d = 60°. Supplementary angles add up to 180°. Since d and e are supplementary and d = 60°, we know that e = 180 - 60 = 120°. Since vertical angles are congruent, we see that d and f are vertical angles and we know d = 60°, we also know that f = 60°.

Answer:

-16

Step-by-step explanation:

8q

Let q = -2

8*-2

-16

Answer:

A  has the points plotted correctly

Step-by-step explanation:

We need to plot the data

A  has the points plotted correctly

B  has the point ( 10,5) plotted on (9,5)

C is missing (-6,-5)

D is missing (-6,-5) and has (-2,1) instead of (-2,-1)

Answer:

A.

Step-by-step explanation:

It would be very helpful to write the points individually from the data. Take the x value and place it with its corresponding y value:

(1,4) ; (2,2) ; (-2,-1) ; (-2,-6) ; (5,-4) ; (-6,-5) ; (10,5)

Now find the graph that has each of these points. You can write these down and cross them out if you find them on the graph, and once you find the graph where all of these points are crossed out, that's the correct graph.

The correct graph is A.

:Done

Answer:

Total games played = 25

Step-by-step explanation:

Percentage games won by the basketball team = 36%

Exact number of games won by the team = 9

Let the total games played by the team = x

Therefore, total number of games won = 36% of x

                                                                 = [tex]\frac{36}{100}\times x[/tex]

Equation which represents the games won by the team will be,

[tex]\frac{36}{100}\times x=9[/tex]

x = [tex]\frac{9}{0.36}[/tex]

x = 25

Therefore, total games played by the basketball team are 25.

Answer:  19.2222

Step-by-step explanation:

given data;

no of tornadoes = 2,1,0 because it’s fewer than 3.

period = 14 years

probability of a tornado in a calendar year = 0.12

solution:

probability of exactly 2 tornadoes

= ( 0.12 )^2 * ( 0.88 )^11 * ( 14! / 2! * 11! )

= 0.0144 * 0.2451 * 1092

= 3.8541

probability of exac one tornado

= ( 0.12 )^1 * ( 0.88 )^12 * ( 14! / 1! * 12! )

= 0.12 * 0.2157 * 182

= 12.7109

probability of exactly 0 tornado

= ( 0.12 )^0 * ( 0.88 )^13 * ( 14! / 0! * 13! )

= 1 * 0.1898 * 14

= 2.6572

probability if fewer than 3 tornadoes

= 3.8541 + 12.7109 +2.6572

= 19.2222

Answer:

6

Step-by-step explanation:

Given, 3sin2x−7sinx+2=03sin2⁡x-7sin⁡x+2=0

⇒(3sinx−1)(sinx−2)=0⇒3sin⁡x-1sin⁡x-2=0

⇒sinx=13 or 2⇒sin⁡x=13 or 2

⇒sinx=13    [∵sinx≠2]⇒sin⁡x=13    [∵sin⁡x≠2]

Let  sinα=13,0<α<π2,sinα=13,0<α<π2, then sinx=sinαsinx=sinα

now x=nπ+(−1)nα(n∈I)x=nπ+(−1)nα(n∈I)

⇒x=α,π−α,2π+α,3π−α,4π+α,5π−α⇒x=α,π−α,2π+α,3π−α,4π+α,5π−α Are the solution in [0,5π][0,5π]

Hence, required number of solutions are 6

Answer:

It's 8.3

Step-by-step explanation:

Answer:

8.3

Step-by-step explanation:

Complete Question

Assume that adults have IQ scores that are normally distributed with a mean μ=100 and a standard deviation σ=15. Find the probability that a randomly selected adult has an IQ between 81 and 119.

Answer:

The probability is  [tex]P( x_1 < X < x_2) = 0.79474[/tex]

Step-by-step explanation:

From the question we are told that

   The standard deviation is  σ = 15.

    The mean μ= 100

     The range we are considering is [tex]x_1 = 81 , \ x_2 = 119[/tex]

Now given that IQ scores are normally distributed

    Then the probability that a randomly selected adult has an IQ between 81 and 119 is mathematically represented as

               [tex]P( x_1 < X < x_2) = P(\frac{x_1 - \mu }{\sigma } <\frac{X - \mu }{\sigma } < \frac{x_2- \mu }{\sigma } )[/tex]

 Generally

                [tex]\frac{X - \mu }{\sigma } = Z(The \ standardized \ value \ of \ X )[/tex]

So

              [tex]P( x_1 < X < x_2) = P(\frac{x_1 - \mu }{\sigma } <Z < \frac{x_2- \mu }{\sigma } )[/tex]

substituting values

               [tex]P( x_1 < X < x_2) = P(\frac{81 - 100 }{15 } <Z < \frac{119- 100 }{15 } )[/tex]

               [tex]P( x_1 < X < x_2) = P( -1.2667 <Z <1.2667 )[/tex]

               [tex]P( x_1 < X < x_2) = P(Z <1.2667 )-P( Z < -1.2667 )[/tex]

From the standardized Z table

               [tex]P(Z <-1.2667 ) = 0.10263[/tex]

And        [tex]P(Z <1.2667 ) = 0.89737[/tex]

So

            [tex]P( x_1 < X < x_2) = 0.89737 - 0.10263[/tex]

            [tex]P( x_1 < X < x_2) = 0.79474[/tex]

Answer:

y = 8x + 70

Step-by-step explanation:

Start with the third line.

x = 3, y = 94

Subtract 1 from x and 8 from y:

x = 2, y = 86; this is the second line

Subtract 1 from x and 8 from y:

x = 1, y = 78; this is the first line

Subtract 1 from x and 8 from y:

x = 0; y = 70

For selling 0 games, she earns $70.

y = mx + b

y = mx + 70

For each game she sells, her commission is $8.

y = 8x + 70

Answer:

x1 = -4

x2 = 6

Step-by-step explanation:

The 2 vertical lines are "absolute values" meaning whatever they contain has to be positive

For Example

|-3| = 3

So we can ignore if the answer we get is positive or negative because it will forced to be a positive

|3 x 4| = 12

|x - 2| = 4

x1 = 6

x2 = -2

Step-by-step explanation:

your required answer is 60°.

Hello,

Here, in the figure;

angle 1= 120°

To find : m. of angle 2.

now,

angle 1 + angle 2= 180° { being linear pair}

or, 120° +angle 2 = 180°

or, angle 2= 180°-120°

Therefore, the measure of angle 2 is 60°.

Hope it helps you.....

Answer:

a) 5[tex]cm^{3}[/tex]

Step-by-step explanation:

Bodies have three dimensions (width, height and depth). Measuring volume is calculating the number of cubic units that can fit inside.

When raising to 3, these dimensions are included and therefore  5[tex]cm^{3}[/tex] is a measure of volume.

Answer:

5cm^3

Step-by-step explanation:

Volume for a form will always be in cubic units.

Area of a shape will always be in squared units.

Length will not be in cubic or squared units.

Hence, the first option is a measure for volume.

The second option is equal to 5cm^2 which represents a measure for area, as does the fourth option.

The third option represents a measurement of length, for example the length of a line segment or the height of a figure.

Answer:

46

Step-by-step explanation:

(14+x)/4 = 15

14 + x = 60

x = 46

Answer:

46

Step-by-step explanation:

Let a to d be number 1 to 4 respectively.

15 = (a + b + c + d) / 4

(a + b + c + d) = 60 ------> total sum of the 4 numbers

Since the sum of 3 numbers (assuming a to c) is 14,

Fourth number (d) = 60 - 14

= 46

That's how I would do it, hope this helps :)

Answer:

[tex] f(x) = 4x^2 - 3x + 6 [/tex]

Step-by-step explanation:

Quadratic function is given as [tex] f(x) = ax^2 + bx + c [/tex]

Let's find a, b and c:

Substituting (0, 6):

[tex] 6 = a(0)^2 + b(0) + c [/tex]

[tex] 6 = 0 + 0 + c [/tex]

[tex] c = 6 [/tex]

Now that we know the value of c, let's derive 2 system of equations we would use to solve for a and b simultaneously as follows.

Substituting (2, 16), and c = 6

[tex] f(x) = ax^2 + bx + c [/tex]

[tex] 16 = a(2)^2 + b(2) + 6 [/tex]

[tex] 16 = 4a + 2b + 6 [/tex]

[tex] 16 - 6 = 4a + 2b + 6 - 6 [/tex]

[tex] 10 = 4a + 2b [/tex]

[tex] 10 = 2(2a + b) [/tex]

[tex] \frac{10}{2} = \frac{2(2a + b)}{2} [/tex]

[tex] 5 = 2a + b [/tex]

[tex] 2a + b = 5 [/tex] => (Equation 1)

Substituting (3, 33), and c = 6

[tex] f(x) = ax^2 + bx + x [/tex]

[tex] 33 = a(3)^2 + b(3) + 6 [/tex]

[tex] 33 = 9a + 3b + 6 [/tex]

[tex] 33 - 6 = 9a + 3b + 6 - 6 [/tex]

[tex] 27 = 9a + 3b [/tex]

[tex] 27 = 3(3a + b) [/tex]

[tex] \frac{27}{3} = \frac{3(3a + b)}{3} [/tex]

[tex] 9 = 3a + b [/tex]

[tex] 3a + b = 9 [/tex] => (Equation 2)

Subtract equation 1 from equation 2 to solve simultaneously for a and b.

[tex] 3a + b = 9 [/tex]

[tex] 2a + b = 5 [/tex]

[tex] a = 4 [/tex]

Replace a with 4 in equation 2.

[tex] 2a + b = 5 [/tex]

[tex] 2(4) + b = 5 [/tex]

[tex] 8 + b = 5 [/tex]

[tex] 8 + b - 8 = 5 - 8 [/tex]

[tex] b = -3 [/tex]

The quadratic function that represents the given 3 points would be as follows:

[tex] f(x) = ax^2 + bx + c [/tex]

[tex] f(x) = (4)x^2 + (-3)x + 6 [/tex]

[tex] f(x) = 4x^2 - 3x + 6 [/tex]

Answer:

1/2 inch per month

Step-by-step explanation:

The average rate hair grows is about half an inch per month which is 6 inches per year.

Answer:

6

Step-by-step explanation:

36 - 20 - 32 x 1/4

=> 36 - 20 - 32/4

=> 36 - 20 - 8

=> 36 - 28

=> 6

Answer:

A) 144 yd²

Step-by-step explanation:

Base= 8x8=64

Side = 1/2*8*5=20

64+20+20+20+20=144 yd²

Answer:

168 sq yds

Step-by-step explanation:

5x8/2x2=40

8x8/2x2=64

8x8=64

40+64+64=168

Answer:

  145 degrees

Step-by-step explanation:

Adjacent angles in a parallelogram are supplementary.

  d2 = 180° -d1 = 180° -35°

  d2 = 145°

Answer:

(2,2) (-1,-1)

Step-by-step explanation

i think this is there answer im sorry if im wrong

Answer:

[tex]t \: = 3.92 \: sec[/tex]

Step-by-step explanation:

When (t =0)

Height of cliff = 248 feet = 75.5m

Using Newton's equations of motion:

[tex]s = ut + \frac{1}{2} a {t}^{2} [/tex]

75.5 = 0 * t + 4.9 * t^2

Solving further :

[tex]t \: = 3.92 \: sec[/tex]