If x2-x-2 > 0, which of the following is the solution set for x?
Ox>-1
Ox>2
O -1 < x < 2
Ox< -1 or x> 2
O No solutions are possible.

The position function x(t) of a moving particle with the given acceleration a(t)=3t is 3 *t^2 / 2.

The position is the object can depend on where you are, and the description might also change if it is based on where other objects are.

The velocity is the time rate of change of position of a body in a specified direction. the rate of speed with which something happens.

Acceleration is the act or process of moving faster or happening more quickly: the act or process of accelerating rapid acceleration is the acceleration of economic growth.

a(t) = 3t

d^2/dx^2=(3t)

x(t) = [tex]\int\limits {3t} \, dt[/tex]

    = 3 *t^2 / 2

Hence the position function x(t) of a moving particle with the given acceleration a(t)=3t is 3 *t^2 / 2.

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The given infinite geometric series 2/3+4/9+8/27+ ...... is convergent and the sum is 2

The given geometric series is:

  2/3 + 4/9 + 8/27 + ......

The common ratio (r) of a geometric series is given by:

  r = a(n) / a(n - 1)

Notice that in the given series:

a(1) = 2/3

a(2) = 4/9

a(3) = 8/27

Hence, the common ratio is

   r = a(2) / a(1) = (4/9) / (2/3) = 2/3

An infinite geometric series is convergent if 0 < | r | < 1.

Since r = 2/3, then the series is convergent and the sum exists.

Use the sum formula:

S = a(1) / (1 - r)

Substitute a(1) = 2/3  and r = 2/3 into the formula:

S = (2/3) / (1 - 2/3)

   = (2/3) / (1/3)

   =  2

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g(x) = |14x + 3| is a function whose graph represents a horizontal stretch by a factor of 4 of the graph of f(x)=|x+3|.

So, we must write a function g whose graph represents a horizontal stretch of f(x)=|x+3| by a factor of 4.

Now perform horizontal stretch 4:

Therefore, g(x) = |14x + 3| is a function whose graph represents a horizontal stretch by a factor of 4 of the graph of f(x)=|x+3|.

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The correct question is given below:
Write a function g whose graph represents a horizontal stretch by a factor of 4 of the graph of f(x)=|x+3|.

g(x)=

Pattern of the given terms -4,-3,-2,-1, . . is arithmetic progression and common difference 'd' = 1 , next three terms are 0, 1,2

As given,

Given pattern is -4,-3,-2,-1, . . .

a₁ =-4

a₂ =-3

a₃ =-2 ….

d =a₂ - a₁

  =-3 - (-4)

  =1

Pattern is arithmetic progression with d=1.

aₙ =a₁ + (n-1)d

a₅ =a₁ + (5-1)d

  =-4 +4(1)

  =0

a₆ =-4 + 5(1)

    =1

a₇ =-4 +6(1)

   =2

Therefore, pattern of the given terms -4,-3,-2,-1, . . is arithmetic progression and common difference 'd' = 1 , next three terms are 0, 1,2

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.

By determining the conjecture is not valid by the law of detachment.

A statement in mathematics that has not been formally proven is referred to as a conjecture. Observing a pattern that holds true in numerous instances leads to conjectures. But just because a pattern appears frequently, it does not imply that it will appear frequently in all instances. The mathematical observation cannot be fully accepted unless conjectures are proven. A conjecture becomes a theorem if it has been thoroughly proven.

Hypothesis: Tommy makes cookies tonight.

Conclusion: Tommy must have an oven.

Even though the stated statement, "Tommy has an oven," matches the conclusion, the hypothesis is not always true. Tommy might own an oven, but he could bake something other than cookies in it.

Hence, the hypothesis is unfounded.

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Answer:

1.2

Step-by-step explanation:

Answer:[tex]2/3+5/9= \frac{2x3}{3x3} + 5/9 =6/9 +5/9+\frac{6+5}{9} = 11/9[/tex]

Step-by-step explanation: answer : 11/9

Hope this helps u ; )

Answer:

-60 x 2= -120

Step-by-step explanation:

Answer:

-40 * 3

Step-by-step explanation:

Just one example of many

The Spaceship Earth geosphere at Epcot in Disney World in Orlando, Florida, a sphere building measuring 165 feet in diameter, has a volume of 2,352,071 cubic feet.

Volume refers to the amount of space occupied by a three-dimensional object.

Based on the problem, the Spaceship Earth geosphere at Epcot in Disney World in Orlando, Florida is a sphere building measuring 165 feet in diameter. If radius is half of the diameter, then it has a radius of 82.5 feet.

The volume of the Spaceship Earth geosphere can be calculated using the formula for the volume of a sphere given by:

V = 4/3 π r^3

V = 4/3 π (82.5 feet)^3

V = 4/3 π (561,5151.625 cubic feet)

V = 2,352,071.15 cubic feet

Rounding off to the nearest cubic foot,

V = 2,352,071 cubic feet

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Answer:

Step-by-step explanation:

if you multiply a negative number with another negative number, it will be positive: ( - ) x ( - ) = ( + )

and if you multiply a negative number with a positive number, it will be negative: ( - ) x ( + ) = ( - )

so          -(-4) = 4                  and             +(-9) = -9

-5+9-4+4-9-12+7=-10

I hope this helps

Answer:

D.

[tex]x > - 3[/tex]

Step-by-step explanation:

[tex] - 2x - 7 > 5x + 14 \\ - 2x - 5x < 14 + 7 \\ - 7x < 21 \\ x < \frac{21}{ - 7} \\ x > - 3[/tex]

Answer:

Step-by-step explanation:

3

2

​

−

2

3

​

y+

3

1

​

y+4=0

Combine −

2

3

​

y and  

3

1

​

y to get −

6

7

​

y.

3

2

​

−

6

7

​

y+4=0

Convert 4 to fraction  

3

12

​

.

3

2

​

−

6

7

​

y+

3

12

​

=0

Since  

3

2

​

 and  

3

12

​

 have the same denominator, add them by adding their numerators.

3

2+12

​

−

6

7

​

y=0

Add 2 and 12 to get 14.

3

14

​

−

6

7

​

y=0

Subtract  

3

14

​

 from both sides. Anything subtracted from zero gives its negation.

−

6

7

​

y=−

3

14

​

Multiply both sides by −

7

6

​

, the reciprocal of −

6

7

​

.

y=−

3

14

​

(−

7

6

​

)

Multiply −

3

14

​

 times −

7

6

​

 by multiplying numerator times numerator and denominator times denominator.

y=

3×7

−14(−6)

​

Do the multiplications in the fraction  

3×7

−14(−6)

​

.

y=

21

84

​

Divide 84 by 21 to get 4.

y=4

We can use the pythagorean theorem to answer this question.

We know that [tex]l[/tex] is the hypotenuse, and the 2 sides are 7 and 7.

So, we can build the equation:

[tex]7^2+7^2 = l^2[/tex]

[tex]98 = l^2[/tex]

[tex]\sqrt{98} = l[/tex]

The variable expression for the word phrase, "the product of a number z and 7", is C. 7z.

A variable expression is defined as a mathematical phrase that contains variables and numbers combined together with any mathematical operations. The most common variable used to denote something is the variable x.

Given the word phrase "the product of a number z and 7"

let z be the variable denoted for a number

and a product of a number z and 7 can be written as:

7z

Therefore, the variable expression for the word phrase "the product of a number z and 7" is 7z.

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Answer:

An army ant queen can lay 299,742 more eggs

The army ant queen will lay 120 times more eggs than the honeybee queen.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a honeybee queen can lay 2.5 × 103 eggs per day. An army ant queen can lay up to 300,000 eggs per day.

The ratio will be calculated as,

Army ant/honeybee queen = 300,000 / (2.5 x 10³)

Army ant/honeybee queen = 300,000 / 2500

Army ant = 120 x ( honeybee queen )

Therefore, the army ant queen will lay 120 times more eggs than the honeybee queen.

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Answer:

4/12

Step-by-step explanation:

If the ratio 4:8 is a part-to-part ratio, it means that there are 4 of something and 8 of something else with a total of 12. To convert a part-to-part ratio such as 4:8 as a fraction, you make the left side of the colon the numerator and the total the denominator: 4:8 → 4/12

Answer:

x=1

Step-by-step explanation:

Perimeter of the square is 4 times the side = 4*(4x-1)

Perimeter of Rectangle = 2 L + 2 W = 2*(2x+2) + 2*2x

4*(4x-1) = 2*(2x+2) +4x

16x-4= 4x+4+4x

16x-4 = 8x+4

16x-8x = 4+4

8x = 8

x = 8/8

x=1

Hope this helps!^^

Answer:

search up

Step-by-step explanation:

A

The value of x is 4.89 ≈ 5 units

Given,

The figure includes two right angled triangles.

Consider the first right angled triangle:

Hypotenuse = 7 units

Base = 3 units

Altitude = a

By using Pythagorean theorem, we can find a.

That is,

Hypotenuse² = Altitude² + Base²

7² = a² + 3²

49 = a² + 9

a² = 49 - 9

a² = 40

Altitude = [tex]\sqrt{40}[/tex]  units

Now consider second right angled triangle:

Hypotenuse = [tex]\sqrt{40}[/tex] units

Altitude = 4 units

Base = x units

Apply Pythagorean theorem:

Hypotenuse² = Altitude² + Base²

([tex]\sqrt{40}[/tex])² = 4² + x²

40 = 16 + x²

x² = 40 - 16

x² = 24

x = [tex]\sqrt{24}[/tex]

Base, x = 4.89 ≈ 5 units.

Therefore, the value of x is 4.89 which is approximately equals to 5 units.

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The 5th term of the given geometric sequence is 768.

A geometric sequence is a sequence of numbers, which the next term is obtained by multiplying the previous term with a constant, called a ratio.

a(n) = a(n-1) . r

Where:

a(n) = nth term

r = ratio

The given geometric sequence is:

   3,12,48,192, . . .

Find the ratio

r = a(n)/a(n-1)

  = a(2)/a(1) = 12/3 = 4

Use the formula for the nth term.

a(n) = a(1) . r^(n-1)

In the given sequence a(1) = 3.

Substitute a(1) = 3, r = 4, and n = 5:

a(5) = 3 . 4⁵⁻¹

      = 3 . 4⁴ = 768

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Step-by-step explanation:

Combine like terms on the right side,

42= 3x+6.

Subtract 6 from each side

36=3x

Divide each side by 3

x=12, which is our lowest integer.

The next two integers we find with 12+2=14 and 12+4=16. Or just simply take the next two even integers. Thus, 12+14+16=42.

Hope this helps.

Answer:

A. F/5 = 4

Step-by-step explanation:

F is the total of fish so F is divided by the total of dolphins, which is 5

so F/5 = 4

Answer:

F/5=4

Step-by-step explanation:

F is the total amount of fish. Since there are 5 dolphins to feed, you should divide F by 5.

answer in the form a√2 where a is an integer.​  √18 √50= 4 root 2

Solution:

Mean

Mean is one of the important and most commonly used measures of central tendency. There are several types of means in mathematics. In statistics, the mean for a given set of observations is equal to the sum of all the values of a collection of data divided by the total number of values in the data. In other words, we can simply add all the values in a data set and divide it by the total number of values to calculate the mean. However, the general method and formulas vary depending upon the type of data given, grouped data, or ungrouped data.

Grouped data is the data set formed by aggregating individual observations of a variable into different groups, while ungrouped data is a random set of observations

Observation :

An observation is a fact or figure we collect about a given variable. It can be expressed as a number or as a quality. An example of a number is the observation "25" for the age of a mother at the birth of her first child.

Using mean formula

Mean = {Sum of Observation} ÷ {Total numbers of Observations}

= [tex]\sqrt{18} +\sqrt{50}[/tex]

=[tex]3\sqrt{2} + 5\sqrt{2}\\ = 5\sqrt{2}[/tex]

sum of observation is 8[tex]\sqrt{2}[/tex]

total number of observation = 2

[tex]8\sqrt{2} /2\\=4\sqrt{2}[/tex]

Answer in the form a√2 where a is an integer.​ = 4 [tex]\sqrt{2}[/tex]

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ans = [tex]4\sqrt{2}[/tex]

2. For the given cylinders, we have that:

A. The volume is of 72π cm³ and the curved surface area is of 48π cm².

B. The volume is of 112π cm³ and the curved surface area is of 56π cm².

5. There are 330 liters of water in the container.

The volume of a cylinder of radius r and height h is given as follows:

V = πr²h.

The curved surface area of a cylinder of radius r and height h is given as follows:

S = 2πrh.

For problem 2 item a, we have that the parameters are given as follows:

r = 3, h = 8.

Hence:

The volume is of 72π cm³ and the curved surface area is of 48π cm².

For problem 2 item b, we have that the parameters are given as follows:

r = 8/2 = 4, h = 7.

Hence:

The volume is of 112π cm³ and the curved surface area is of 56π cm².

For item 5, the parameters are given as follows:

r = 0.65/2 = 0.325m, h = 1m.

Hence the volume is:

V = πr²h = π(0.325)² = 0.33 m³.

Each m³ has 1000 liters, hence:

0.33 x 1000 = 330 liters.

There are 330 liters of water in the container.

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The integer that makes the expression, (____ + -3 = -4), true is -1.

According to the question,

We have the following expression:

__ + (-3) = -4

Now, let's take the integer to be filled in the blank as x.

Now, putting x in the given expression:

x + (-3) = -4

x = -4+3 (3 was negative on the left hand side. So, it is positive on the right hand side.)

x = -1

(More to know: when two numbers are given with two different signs then the smaller number is subtracted from the larger number but the sign remains of the number which is larger.)

Hence, the integer that makes the given addition sentence true is -1.

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Step-by-step explanation:

16. [tex]PQ = \frac{IK}{2} ⟹ \frac{24}{2} [/tex]

[tex]PQ = 12[/tex]

I can't really solve no. 17

A)  x, i.e. price of each ticket should be charged 20 dollars to maximize revenue.

B) The maximum revenue is 6060 dollars.

C) Two prices between which a profit is made are $19 and $21.

Given:

profit function P(x)= -15x² + 600x + 60

The value of a is -15, which is negative, so the graph is opening downwards.

The graph of the function is a parabola and it opens downward therefore it has a maximum point. The formula used to find the vertex of the parabola  f(x) is given by

x-coordinate of the vertex = -b/2a

y-coordinate of the vertex =  f(-b/2a)

We have the x-coordinate of the parabola as:

⇒  -600 / 2(-15)

⇒ -600/-30 = 20

A)  x, i.e. price of each ticket should be charged 20 dollars to maximize revenue.

B) y-coordinate of the vertex is given by

    f(20) = -15(20)² + 600(20) + 60

             = 6060

The maximum revenue is 6060 dollars.

C)   f(21) = -15(21)² + 600(21) + 60

             = 6045

       f(19) = -15(19)² + 600(19) + 60

             = 6045

   at $21, the profit is $6045

   at $19, the profit is $6045

Two prices between which a profit is made are $19 and $21.

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Based on the time that Rex walked and the time that Samir walked, we can say that Samir walked TWO times as many hours as Rex walked.​

To find out how many times more Samir walked than Rex, divide the number of hours walked by Samir by the hours walked by Rex.

Solving gives:

= 3¹/₃ ÷ 1²/₃

= 10/ 3 ÷ 5/3

= 10/3 x 3/5

= 30/ 15

= 2 times more

In conclusion, Samir walked two times more.

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Answer:

Step-by-step explanation:

Based on the time that Rex walked and the time that Samir walked, we can say that Samir walked TWO times as many hours as Rex walked.​

How many times more did Samir walk?

To find out how many times more Samir walked than Rex, divide the number of hours walked by Samir by the hours walked by Rex.

Solving gives:

= 3¹/₃ ÷ 1²/₃

= 10/ 3 ÷ 5/3

= 10/3 x 3/5

= 30/ 15

= 2 times more

In conclusion, Samir walked two times more.

Answer:

< - 9, 11 >

Step-by-step explanation:

consider the end points of the vector

(5, - 2 ) and (- 4, 9 )

x- direction is then - 4 - 5 = - 9

y- direction is 9 - (- 2) = 9 + 2 = 11

then vector in component form is < - 9, 11 >