Use the zero product property to find the solutions to the equation x2 – 9 = 16.
x= -3 or x = 3
x= -6 or x = -3
Ox= -5 or x = 5
O x= 7 or x = 1

Answer:

√x+3-13

Step-by-step explanation:

This answer is a radical equation because a square root is used in the equation. This makes the equation radical. The other choices have no square roots so they can't be the answers.

Answer:

[tex]81\pi[/tex]

Step-by-step explanation:

[tex]Area = \pi * r^{2} \\\pi *9^{2} =81\pi[/tex]

Answer:

81 π

Step-by-step explanation:

formula is radius squared times pi or π so the answer would be 9x9=81 and you said to leave in terms of π so the answer is 81 π.

In polar coordinates, the inequality changes to

[tex]x^2+y^2\le4x\implies r^2\le4r\cos\theta\implies r\le4\cos\theta[/tex]

which is a circle of radius 2 and centered at (2, 0). The set D is then

[tex]D=\left\{(r,\theta)\mid0\le r\le4\cos\theta\land0\le\theta\le\pi\right\}[/tex]

The integral is then

[tex]\displaystyle\iint_D\frac{y^2}{x^2+y^2}\,\mathrm dx\,\mathrm dy=\int_0^\pi\int_0^{4\cos\theta}\frac{r^2\sin^2\theta}{r^2}r\,\mathrm dr\,\mathrm d\theta[/tex]

[tex]=\displaystyle\int_0^\pi\int_0^{4\cos\theta}r\sin^2\theta\,\mathrm dr\,\mathrm d\theta[/tex]

[tex]=\displaystyle\frac12\int_0^\pi((4\cos\theta)^2-0^2)\sin^2\theta\,\mathrm d\theta[/tex]

[tex]=\displaystyle8\int_0^\pi\cos^2\theta\sin^2\theta\,\mathrm d\theta[/tex]

There are several ways to compute the remaining integral; one would be to invoke the double-angle formula,

[tex]\sin(2\theta)=2\sin\theta\cos\theta[/tex]

so that the integral is

[tex]=\displaystyle8\int_0^\pi\frac{\sin^2(2\theta)}4\,\mathrm d\theta[/tex]

[tex]=\displaystyle2\int_0^\pi\sin^2(2\theta)\,\mathrm d\theta[/tex]

Then invoke another double-angle formula,

[tex]\sin^2\theta=\dfrac{1-\cos(2\theta)}2[/tex]

to change the integral to

[tex]=\displaystyle\int_0^\pi1-\cos(4\theta)\,\mathrm d\theta[/tex]

[tex]=(\pi-\cos(4\pi))-(0-\cos0)=\boxed{\pi}[/tex]

Answer:

100

Step-by-step explanation:

When t=0 (no time has passed), the coin is at height 100. This means the bridge must be 100 units high for this to be possible.

Answer:

100

Step-by-step explanation:

:3

Answer:

11453

Step-by-step explanation:

Answer:

Here are the formulas

Cube/Rectangular Prism:

Volume = Length*width*height

Surface area = 2(wl+hl+hw)

Lateral area= Area of vertical faces

Base area = length*width

Regular hexagonal prism:

Volume : (3sqrt3/2)*a^2*h

Surface Area  = 6ah+3sqrt(3)a^2

lateral area: 6ah

base area = 3sqrt(3)s^2/2

Triangular prism

Volume: The volume of a triangular prism can be found by multiplying the base times the height.

Surface area: A triangular prism has three rectangular sides and two triangular faces. To find the area of the rectangular sides, use the formula A = lw, where A = area, l = length, and h = height. To find the area of the triangular faces, use the formula A = 1/2bh, where A = area, b = base, and h = height.

Etc.

Answer:

(0,34)

Step-by-step explanation:

For each rise of 14 in the x direction, this graph rises by -8 in the y direction. This means that, when x is 0, and the graph intersects the y axis, the y value will be 50-8-8=34. Therefore, the y intercept of this line is (0,34). Hope this helps!

Answer:

The answer is (0,34)

Answer:

X+7

Step-by-step explanation:

Remove the parentheses:

4x+2-3x+5

Collect like terms:

4x-3x=x

2+5=7

Solution:

X+7

Hey there!

(4x + 2) - 3x + 5

= 4x + 2 - 3x + 5

COMBINE the LIKE TERMS

= (4x - 3x) + (2 + 5)

= 4x - 3x + 2 + 5

= 1x + 7

= x + 7

Therefore, your answer is: x + 7

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

  $1741.44

Step-by-step explanation:

The discounted amount is 100% -10% = 90% of the original. The amount of the discount is 10% of the original, or 1/9 of the discounted amount:

  10% = 90% × 1/9

The discount was ...

  $15,673/9 = 1,741.44

_____

Check

The original is the sum of the discounted amount and the discount:

  original price = $15,673.00 +1,741.44 = $17, 414.44

10% of that value is 1,741.44, as shown above.

Answer:

I guess that we want to find the function g(x) for the 4 cases.

first, f(x) = -9*x + 1.

a) The graph of g is a reflection in the y-axis of the graph of f.

First remember: if we have the point (x,y) and we reflect it over the y-axis, we get (-x,y)

then g(x) = f(-x) = -9*-x + 1 = 9*x + 1.

b) The graph of g is a reflection in the x-axis of the graph of f.

if we have a point (x, y) and we reflect it over the x-axis, the point transforms into (x, -y)

then we have: g(x) = -f(x) = 9*x - 1

c) The graph of g is a horizontal translation 16 units right of the graph of f.

When we want to have a translation in the x-axis, we must change x by x - A.

If A is positive, this transformation moves the graph by A units to the right, in this case, A = 16.

g(x) = f(x - 16) = -9*(x - 16) + 1

d) The graph of g is a vertical translation 16 units down of the graph of f.

For vertical translations, if we want to move the graph by A units down (A positive) we should do y = f(x) - A

In this case, A = 16.

then: g(x) = f(x) - 16 = -9*x + 1 - 16 = -9*x - 15.

Answer:

The scale factor is 3.

Step-by-step explanation

Figure B has side measures 16, 20, and 9. Figure A has side measures 48, 27, and 60. The ratio of each of the corresponding sides is 1:3 (16:48, etc). Therefore, the scale factor of Figure B to Figure A is 3.

Answer:

3

Step-by-step explanation:

0 pairs mean when two "boxes" add together to make 0. For the x's we only have one because x + (-x) = x - x = 0. For the other ones we have two (the + means 1 and the - means -1) because 1 + (-1) = 1 - 1 = 0. Therefore the answer is 1 + 2 = 3.

Answer:

x = sqrt(5)/2 - 1/2 or x = -1/2 - sqrt(5)/2

Step-by-step explanation:

Solve for x over the real numbers:

x - 2 + x/x + 1 - 1/x = -1

x - 2 + x/x + 1 - 1/x = x - 1/x:

x - 1/x = -1

Bring x - 1/x together using the common denominator x:

(x^2 - 1)/x = -1

Multiply both sides by x:

x^2 - 1 = -x

Add x to both sides:

x^2 + x - 1 = 0

Add 1 to both sides:

x^2 + x = 1

Add 1/4 to both sides:

x^2 + x + 1/4 = 5/4

Write the left hand side as a square:

(x + 1/2)^2 = 5/4

Take the square root of both sides:

x + 1/2 = sqrt(5)/2 or x + 1/2 = -sqrt(5)/2

Subtract 1/2 from both sides:

x = sqrt(5)/2 - 1/2 or x + 1/2 = -sqrt(5)/2

Subtract 1/2 from both sides:

Answer: x = sqrt(5)/2 - 1/2 or x = -1/2 - sqrt(5)/2

Answer:

x = 6                        x = -1

Step-by-step explanation:

When we have absolute value equations, we get two solutions, one positive and one negative

2x - 5 =7             2x -5= -7

Add 5 to each side

2x-5+5 = 7+5         2x -5+5 = -7+5

2x =12                     2x = -2

Divide each side by 2

2x/2 =12/2               2x/2 = -2/2

x = 6                        x = -1

Answer:

A. 1.8 ×[tex]10^{30}[/tex] Kg

B i. 3.0 × [tex]10^{17}[/tex] seconds

  ii. 9.6 × [tex]10^{9}[/tex] years

C. After 9.2 × [tex]10^{9}[/tex] (9.2 billion) years

Step-by-step explanation:

Given that the mass of the Sun = 2× [tex]10^{30}[/tex] Kg.

Mass of hydrogen when Sun was formed = 76% of 2× [tex]10^{30}[/tex] Kg

                            = [tex]\frac{76}{100}[/tex]  ×2× [tex]10^{30}[/tex] Kg

                           = 1.52 × [tex]10^{30}[/tex] Kg

Mass of hydrogen available for fusion = 12% of 1.52 × [tex]10^{30}[/tex] Kg

                           = [tex]\frac{12}{100}[/tex] × 1.52 × [tex]10^{30}[/tex] Kg

                           = 1.824 ×[tex]10^{30}[/tex] Kg

A. Total mass of hydrogen available for fusion over the lifetime of the sun is 1.8 ×[tex]10^{30}[/tex] Kg.

B. Given that the Sun fuses 6 × [tex]10^{11}[/tex] Kg of hydrogen each second.

i. The Sun's initial hydrogen would last;

                                     [tex]\frac{1.8*10^{30} }{6*10^{11} }[/tex]

                                 = 3.04 × [tex]10^{17}[/tex] seconds

The Sun's hydrogen would last 3.0 × [tex]10^{17}[/tex] seconds

ii. Since there are 31536000 seconds in a year, then;

The Sun's initial hydrogen would last;

                                     [tex]\frac{3.04*10^{17} }{31536000}[/tex]

                                 = 9.640 × [tex]10^{9}[/tex] years

The Sun's hydrogen would last 9.6 × [tex]10^{9}[/tex] years.

C. Given that our solar system is now about 4.6 × [tex]10^{9}[/tex] years, then;

                               [tex]\frac{9.6*10^{9} }{4.6*10^{9} }[/tex]

                             = 2.09

So that;   2 × 4.6 × [tex]10^{9}[/tex] = 9.2 × [tex]10^{9}[/tex] years

Therefore, we need to worry about the Sun running out of hydrogen for fusion after 9.2 × [tex]10^{9}[/tex] years.

Part(A): The total mass of hydrogen available 9.6 billion years.

Part(B): The total time is 5.10 billion years.

Part(D): The hydrogen will last [tex]5.04\times 10^9 \ years[/tex]

Our sun is the largest object in our solar system. The mass of the sun is approximately [tex]1.988\times 1030[/tex] kilograms

Part(A):

Given that,

The total mass of the Sun =[tex]2\times10^{30} kg[/tex]

Mass of hydrogen in Sun =  [tex]2\times10^{30} \times0.76\ kg[/tex]

The mass of hydrogen ever available for fusion is,

[tex]2\times10^{30} \times 0.76 \times 0.12 kg = 1.824\times 10^{29}[/tex]

Mass of hydrogen fuses each second = 600 billion kg/second.

Time hydrogen will last in seconds=[tex]1.824\times 10^{29}seconds.[/tex]

[tex]= 0.00304\times 10^{29 }= 3.04\times 10^{17}.[/tex]

Time hydrogen will last in seconds =[tex]1 year = 31,536,000 seconds.[/tex]

[tex]31,536,000 x = 3.04\times 10^{17} = 9.6 \ billion \ years.[/tex]

(B) Present age of sun = [tex]9.6-4.5 \ billion \ years[/tex]

The time when we need to worry about Sun running out of hydrogen for fusion = 5.10 billion years.

(D) The solar system is 4.6 billion years old that is [tex]4.6\times 10^9\ years[/tex]

And in part (B) we have calculated that hydrogen will last [tex]9.64\times 10^9[/tex] then,

[tex]9.64\times 10^9-4.6\times 10^9=5.04\times 10^9[/tex]

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Answer:   -9  ≤ f(6) - f(3)  ≤ 15

Step-by-step explanation:

In order to use the Mean Value Theorem, it must be continuous and differentiable. Both of these conditions are satisfied so we can continue.  

Find f(6) - f(3) using the following formula:

[tex]f'(c)=\dfrac{f(b)-f(a)}{b-a}[/tex]

Consider:    a = 3, b = 6

[tex]\text{Then}\ f'(c)=\dfrac{f(6)-f(3)}{6-3}\\\\\\\rightarrow \quad 3f'(c)=f(6) - f(3)[/tex]          

Given: -3 ≤  f'(x)  ≤ 5

          -9  ≤ 3f'(c) ≤ 15    Multiplied each side by 3

→   -9  ≤ f(6) - f(3)  ≤ 15  Substituted 3f'(c) with f(6) - f(3)

Answer:

Step-by-step explanation:

a. Null hypothesis: P = p

Alternatives hypothesis: P =/ p

Where P is the hypothesized population proportion and p is the sample proportion

b. Performing a test of proportions

Randomization: the sample was randomly selected in the study

The population size is at least 20 times as big as the sample size.

The sample includes both successes and failures with 29 success and 171 failures.

c. To perform the hypothesis test: we have to find the standard deviation first

Sd = sqrt[ P * ( 1 - P ) / n ]

where P is the hypothesized value of population proportion, n is the sample size.

Sd = √[0.12*(1-0.12)/200]

Sd = √[0.12*(0.88/200]

Sd = √[0.12*(0.0044)]

Sd = √0.000528

Sd = 0.023

Then we can find the z score

z = (p - P) / σ where p = 29/200 = 0.145

z = (0.145-0.12)/ 0.023

z = 0.025/0.023

z = 1.09

Calculation the p value using 0.05 level of significance and a two waited test (p value calculator),

A p-value of 0.2757 which is greater than 0.05, thus we will fail to reject the null stating that there is not enough strong evidence that the left-handed rate in the state of Maine is higher than the national average.

Answer:

= ( $18.2, $18.8)

Therefore, the 98% confidence interval (a,b) = ( $18.2, $18.8)

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = $18.50

Standard deviation r = $6.10

Number of samples n = 2253

Confidence interval = 98%

z(at 98% confidence) = 2.33

Substituting the values we have;

$18.5+/-2.33($6.1/√2253 )

$18.5+/-2.33($0.128513644290)

$18.5+/-$0.299436791196

$18.5+/-$0.3

= ( $18.2, $18.8)

Therefore at 98% confidence interval (a,b) = ( $18.2, $18.8)

Answer:

4 ft

Step-by-step explanation:

288=16 * 18

12+4=16

14+4=18

The dimensions increased by 4 feet.

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

Given;

Dimensions of rectangle = 12 + x and 14 + x

The area of the rectangle= (12 + x) (14 + x) = 288

x² + 26x + 168 = 288

x² + 26x - 120 = 0

(x + 30) (x - 4) = 0

x=-30, x =4

Hence, The dimensions increased by 4 feet.

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Answer:

A. it would be shifted up

Step-by-step explanation:

Y=MX+B

B is the Y-intercept.

Answer:

a. it would be shifted up

Step-by-step explanation:

the difference between the original and the new function is that the b value is changed from -6 to +8, meaning the y-intercept value has increased. this would shift the graph up by 14.

Answer:

Amount received per brother based on number of children plus debt is given as

Roberto, S/ 55,333.33

Luis, S/ 46,000

Armando, S/ 74,666.67

Step-by-step explanation:

English Translation

A prestigious businessman decides to distribute his inheritance of S / 176,000 among his three brothers Roberto, Luis and Armando, DP to the number of his children and IP to the amount of his debts. How much corresponds to each brother?

Roberto: No of children 4, Amount of debts (S /): 2 000

Luis: No. of children 3, Amount of debts (S /): 6,000

Armando: No of children 5, Amount of debts (S /): 8,000

Solution

The man shares the inheritance according to the number of children per person and according to each brother's debts.

Assuming the debts are first settled,

The total debts = 2000 + 6000 + 8000 = S/ 16,000

We assume that each brother receives the respective debt amounts first, then the remaining cash is divided amongst the 3 brothers according to the number of their children.

Total amount available = S/ 176,000

total debt = S/ 16,000

Amount available less debts = 176,000 - 16,000 = S/ 160,000

There are 4, 3 and 5 children respectively for the 3 brothers.

Total number of children = 4+3+5 = 12.

Amount corresponding based on a per child basis =( S/ 160,000/12) = S/ 13,333.33

Meaning that each brother receives the following amount based on their children's sake

Roberto, 4 × S/ 13,333 = S/ 53,333.33

Luis, 3 × S/ 13,333.33 = S/ 40,000

Armando, 5 × S/ 13,333 = S/ 66,666.67

Total amount each brother then receives when the amount received due to debts are added

Roberto, 53,333.33 + 2,000 = S/ 55,333.33

Luis, 40,000 + 6,000 = S/ 46,000

Armando, 66,666.67 + 8,000 = S/ 74,666.67

To check, 55,333.33 + 46,000 + 74,666.67 = 176,000 (total inheritance!)

Hope this Helps!!!

Queremos ver como se reparte una dada suma entre 3 hermanos, siendo que tenemos unas dadas restricciones, donde debemos trabajar con relaciones directamente proporcionales e inversamente proporcionales.

Veremos que:

Roberto recibe: $112,640

Luis recibe: $28,160

Armando recibe: $35,200

Sabemos que lo que se reparte es directamente proporcional al número de hijos de cada hermano, e inversamente proporcional a las deudas de cada hijo.

Entonces, definamos las variables:

R = lo que recibe Roberto.

L = Lo que recibe Luis

A = lo que recibe Armando.

Tendremos que:

R + L + A = $176,000

Entonces como lo que recibe cada hermano es directamente proporcional al número de hijos (x) e inversamente proporcional a la deuda (z) lo que cada hermano recibe será:

Entonces podemos escribir:

R + L + A = $176,000

k*4/2,000 +  k*3/6,000 + k*5/8,000 = $176,000

k*(4/2,000 + 3/6,000 + 5/8,000) = $176,000

k*(0.003125) =  $176,000

k = $176,000/(0.003125) = $56,320,000

Ahora que conocemos el valor de k, podemos calcular lo que cada hermano recibe:

R = $56,320,000*(4/2,000) = $112,640

L = $56,320,000*(3/6,000) = $28,160

A = $56,320,000*(5/8,000) = $35,200

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Answer:

The line on the graph is y = 4, where no matter what the value of x is, the value of y will always be 4. Therefore, any line parallel to this one will be y = ?. If it passes through (-4, -6), that means that the equation is y = -6.

Answer:

С)))) Y= -6

Step-by-step explanation:

just did on edg. :D

Answer: (-6, 0)

Step-by-step explanation:

X-intercepts of equations are any points on the equation that lie on the x-axis, or the horizontal line "y = 0".

In order to find the x-intercept of an equation, find the points that will satisfy the equation "y = 0":

y = (x + 6)(x - 3)

y = 0

(x + 6)(x - 3) = 0

With this equation, you can find which points lie on the x-axis.

When x = -6, the equation is: 0 * -9 = 0, which is correct.

When x = 3, the equation is 9 * 0 = 0, which is correct.

Make sure you're picking the correct coordinate out of the answer choices.

The x-coordinates are -6 and 3, and the y-coordinates are 0, because the points lie on the x-axis.

The correct answer is (-6, 0).

(3, 0) is also correct, but the question does not require it.

Answer:

D

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

I think because at if you divide 45 by 6 because its 45 minutes from 4:15 to 5:00 and it grows 6 inches longer every five min

Answer:

b. 0.25

c. 0.05

d. 0.05

e. 0.25

Step-by-step explanation:

if the waiting time x follows a uniformly distribution from zero to 20, the probability that a passenger waits exactly x minutes P(x) can be calculated as:

[tex]P(x)=\frac{1}{b-a}=\frac{1}{20-0} =0.05[/tex]

Where a and b are the limits of the distribution and x is a value between a and b. Additionally the probability that a passenger waits x minutes or less P(X<x) is equal to:

[tex]P(X<x)=\frac{x-a}{b-a}=\frac{x-0}{20-0}=\frac{x}{20}[/tex]

Then, the probability that a randomly selected passenger will wait:

b. Between 5 and 10 minutes.

[tex]P(5<x<10) = P(x<10) - P(x<5)\\P(5<x<10) = \frac{10}{20} -\frac{5}{20}=0.25[/tex]

c. Exactly 7.5922 minutes

[tex]P(7.5922)=0.05[/tex]

d. Exactly 5 minutes

[tex]P(5)=0.05[/tex]

e. Between 15 and 25 minutes, taking into account that 25 is bigger than 20, the probability that a passenger will wait between 15 and 25 minutes is equal to the probability that a passenger will wait between 15 and 20 minutes. So:

[tex]P(15<x<25)=P(15<x<20) \\P(15<x<20)=P(x<20) - P(x<15)\\P(15<x<20) = \frac{20}{20} -\frac{15}{20}=0.25[/tex]

Answer:

[tex]x=\frac{1}{6}[/tex]

Step-by-step explanation:

[tex]\sqrt{3-5x}=\sqrt{x+2}\\Square\:both\:sides\\\left(\sqrt{3-5x}\right)^2=\left(\sqrt{x+2}\right)^2\\\mathrm{Expand\:}\left(\sqrt{3-5x}\right)^2:\quad 3-5x\\\mathrm{Expand\:}\left(\sqrt{x+2}\right)^2:\quad x+2\\3-5x=x+2\\\mathrm{Solve\:}\:3-5x=x+2:\quad x=\frac{1}{6}\\x=\frac{1}{6}\\\mathrm{Verify\:Solutions}:\quad x=\frac{1}{6}\space\mathrm{True}\\\mathrm{The\:solution\:is}\\x=\frac{1}{6}[/tex]

Answer:

A- 1/6

Step-by-step explanation:

GOT IT RIGHT ON EDGE

Answer:  The correct answer is:  " 2x² " .

________________________________

Step-by-step explanation:

________________________________

We are asked:  "What is the sum of:  "x + x² + 2" and "x² − 2 − x" ?

Since we are to find the "sum" ;

  →  We are to "add" these 2 (two) expressions together:

     →     (x + x² + 2) +  (x² − 2 − x) ;

Note:  Let us rewrite the above, by adding the number "1" as a coefficient to:  the values "x" ; and "x² " ;  since there is an "implied coefficient of "1" ;

            → {since:  "any value" ; multiplied by "1"; results in that exact same value.}.

            →     (1x + 1x² + 2) +  (1x² − 2 − 1x) ;

Rewrite as:

             →     1x + 1x² + 2) +  (1x² − 2 − 1x) ;

Now, let us add the "coefficient" , "1" ; just before the expression:

             "(1x² − 2 − 1x)" ;  

         {since "any value", multiplied by "1" , equals that same value.}.

And rewrite the expression; as follows:

            →     (1x + 1x² + 2) +  1(1x² − 2 − 1x) ;

Now, let us consider the following part of the expression:

                     →  " +1(1x² − 2 − 1x) " ;

________________________________

Note the distributive property of multiplication:

   →  " a(b+c) = ab + ac " ;

and likewise:

   →  " a(b+c+d) = ab + ac + ad " .

________________________________

So; we have:

→  " +1(1x² − 2 − 1x) " ;

  = (+1 * 1x²)  +  (+1 *-2) + (+1*-1x) ;

  =       + 1x²    +    (-2)     +  (-1x) ;

  =       +1x²    −    2   −  1x  ;

  ↔    ( + 1x²  −  1x  −  2)

Now, bring down the "left-hand side of the expression:

1x + 1x² + 2 ;

and add the rest of the expression:

     →  1x  +  1x²  +  2  +   1x²  −  1x  −  2 ;

________________________________

Now, simplify by combining the "like terms" ; as follows:

   +1x² + 1x² = 2x²  ;

   +1x −  1x = 0 ;  

   + 2 −  2  = 0 ;

________________________________

The answer is: " 2x² " .

________________________________

Hope this is helpful to you!

   Best wishes!

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Answer:

The correct answer is:  " 2x² " .

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Step-by-step explanation:

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We are asked:  "What is the sum of:  "x + x² + 2" and "x² − 2 − x" ?

Since we are to find the "sum" ;

 →  We are to "add" these 2 (two) expressions together:

    →     (x + x² + 2) +  (x² − 2 − x) ;

Note:  Let us rewrite the above, by adding the number "1" as a coefficient to:  the values "x" ; and "x² " ;  since there is an "implied coefficient of "1" ;

           → {since:  "any value" ; multiplied by "1"; results in that exact same value.}.

           →     (1x + 1x² + 2) +  (1x² − 2 − 1x) ;

Rewrite as:

            →     1x + 1x² + 2) +  (1x² − 2 − 1x) ;

Now, let us add the "coefficient" , "1" ; just before the expression:

            "(1x² − 2 − 1x)" ;  

        {since "any value", multiplied by "1" , equals that same value.}.

And rewrite the expression; as follows:

           →     (1x + 1x² + 2) +  1(1x² − 2 − 1x) ;

Now, let us consider the following part of the expression:

                    →  " +1(1x² − 2 − 1x) " ;

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Note the distributive property of multiplication:

  →  " a(b+c) = ab + ac " ;

and likewise:

  →  " a(b+c+d) = ab + ac + ad " .

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So; we have:

→  " +1(1x² − 2 − 1x) " ;

 = (+1 * 1x²)  +  (+1 *-2) + (+1*-1x) ;

 =       + 1x²    +    (-2)     +  (-1x) ;

 =       +1x²    −    2   −  1x  ;

 ↔    ( + 1x²  −  1x  −  2)

Now, bring down the "left-hand side of the expression:

1x + 1x² + 2 ;

and add the rest of the expression:

    →  1x  +  1x²  +  2  +   1x²  −  1x  −  2 ;

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Now, simplify by combining the "like terms" ; as follows:

  +1x² + 1x² = 2x²  ;

  +1x −  1x = 0 ;  

  + 2 −  2  = 0 ;

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The answer is: " 2x² " .

Step-by-step explanation:

Answer: 0.0036

Step-by-step explanation:

0.00359 — 0.0036

The nine rounds up

Answer:

b. non-directional

Step-by-step explanation:

A directional hypothesis can be described as a hypothesis which predicts the direction of impact, either positive or negative, of one variable, especially independent variable, on the other variable which is known as an independent variable. For example, the hypothesis "age reduces memory performance" is a directional hypothesis. The reason is that "reduces" show the direction that age has a negative effect on memory performance.

On the other hand, non-directional hypothesis can be described as a hypothesis that does not predict the direction of impact but only states the relationship between two variables. For example, the research hypothesis is in the question that "age is related to memory performance" is non-directional hypothesis. This because the word "related" in the hypothesis only indicate that there is a relationship between the two variables, not the direction of effect of one variable on the other.

Answer:

Step-by-step explanation:

The original equation is [tex]121y''+110y'-24y=0[/tex]. We propose that the solution of this equations is of the form [tex] y = Ae^{rt}[/tex]. Then, by replacing the derivatives we get the following

[tex]121r^2Ae^{rt}+110rAe^{rt}-24Ae^{rt}=0= Ae^{rt}(121r^2+110r-24)[/tex]

Since we want a non trival solution, it must happen that A is different from zero. Also, the exponential function is always positive, then it must happen that

[tex]121r^2+110r-24=0[/tex]

Recall that the roots of a polynomial of the form [tex]ax^2+bx+c[/tex] are given by the formula

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

In our case a = 121, b = 110 and c = -24. Using the formula we get the solutions

[tex]r_1 = -\frac{12}{11}[/tex]

[tex]r_2 = \frac{2}{11}[/tex]

So, in this case, the general solution is [tex]y = c_1 e^{\frac{-12t}{11}} + c_2 e^{\frac{2t}{11}}[/tex]

a) In the first case, we are given that y(0) = 1 and y'(0) = 0. By differentiating the general solution and replacing t by 0 we get the equations

[tex]c_1 + c_2 = 1[/tex]

[tex]c_1\frac{-12}{11} + c_2\frac{2}{11} = 0[/tex](or equivalently [tex]c_2 = 6c_1[/tex]

By replacing the second equation in the first one, we get [tex]7c_1 = 1 [/tex] which implies that [tex] c_1 = \frac{1}{7}, c_2 = \frac{6}{7}[/tex].

So [tex]y_1 = \frac{1}{7}e^{\frac{-12t}{11}} + \frac{6}{7}e^{\frac{2t}{11}}[/tex]

b) By using y(0) =0 and y'(0)=1 we get the equations

[tex] c_1+c_2 =0[/tex]

[tex]c_1\frac{-12}{11} + c_2\frac{2}{11} = 1[/tex](or equivalently [tex]-12c_1+2c_2 = 11[/tex]

By solving this system, the solution is [tex]c_1 = \frac{-11}{14}, c_2 = \frac{11}{14}[/tex]

Then [tex]y_2 = \frac{-11}{14}e^{\frac{-12t}{11}} + \frac{11}{14} e^{\frac{2t}{11}}[/tex]

c)

The Wronskian of the solutions is calculated as the determinant of the following matrix

[tex]\left| \begin{matrix}y_1 & y_2 \\ y_1' & y_2'\end{matrix}\right|= W(t) = y_1\cdot y_2'-y_1'y_2[/tex]

By plugging the values of [tex]y_1[/tex] and

We can check this by using Abel's theorem. Given a second degree differential equation of the form y''+p(x)y'+q(x)y the wronskian is given by

[tex]e^{\int -p(x) dx}[/tex]

In this case, by dividing the equation by 121 we get that p(x) = 10/11. So the wronskian is

[tex]e^{\int -\frac{10}{11} dx} = e^{\frac{-10x}{11}}[/tex]

Note that this function is always positive, and thus, never zero. So [tex]y_1, y_2[/tex] is a fundamental set of solutions.