Which model represents the equation 6x = 18

Answer:

Volume= 62.8 cubic inch

Step-by-step explanation:

V=B×h

B=

[tex]\pi {r}^{2} [/tex]

= 3.14×2^2=12.56

V=12.56×5= 62.8 cubic inch

The maximum height which the rocket attains is 80 m and the time taken by the rocket is 8 sec.

Given,

the following formula yields the height h,

h= -5t² + 40t +45

45m is the height of the launch pad.

We take the first derivative of the function h and then set it to zero to determine the height the rocket reaches.

h' = 0

-10t + 40 =0

-10t = -40

 t = 4

Therefore, height reached by the rocket in time t = 4 is,

h= -5t² + 40t +45

  = -5(4)²  + 40(4) + 45

  =125 m

As a result, the rocket can reach:

125- 45

= 80 m

(To determine the real height the rocket travels, we have subtracted the height of the launch pad.)

The rocket takes twice as long to launch as it does to reach the peak.

t = 2*4 = 8 sec

Therefore,

the rocket goes 80 meters in height

the rocket's flight time is 8 seconds.

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Answer:

Step-by-step explanation:

Answer: (C) or (44in^2 )

Step-by-step explanation:

Answer:

A = 40 in²

Step-by-step explanation:

the figure is composed of a rectangle and a triangle.

then area (A) is calculated as

A = area of rectangle + area of triangle

  = (16 × 2) + ( [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

here b = 6 - 2 = 4 and h = 20 - 16 = 4 , then

A = 32 + ( [tex]\frac{1}{2}[/tex] × 4 × 4)

  = 32 + 8

  = 40 in²

For the given Trapezoid ABCD the value of BC:BN is BC:BN=8:3.

What is Trapezoid?

A trapezoid is a quadrilateral in American and Canadian English that has at least one pair of parallel sides. A trapezium is the term used in British and other varieties of English. In Euclidean geometry, a trapezoid is invariably a convex quadrilateral. The trapezoid's parallel sides are referred to as its bases.

Given:

In the trapezoid ABCD ( AB ∥ CD ) point M∈ AD , so that AM:MD=3:5.

Line l ∥ AB and going trough point M intersects diagonal AC and leg BC at points P and N respectively.

We have to find BC:BN

ABCD is a trapezoid and there is a point m which belongs to AD such that AM:MD=3:5.Line "l" parallel to AB intersects the diagonal AC at p and BD at N.

Now, we know that the parallel lines divide the transversal into the segments with equal ratio, therefore, BN:NC=AM:MD

But, BC= BN+NC

Therefore, BC:BN = (BN + NC): BN

⇒ BC:BN = (3 + 5): 3

⇒ BC:BN = 8:3

Hence, for the given Trapezoid ABCD the value of BC:BN is BC:BN=8:3.

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Answer: D

Step-by-step explanation:

The simplified monomial for the first scenario will be 1/8². The simplified monomial for the second situation will be (-3)¹.

Exponent, then, is the number of times a number has been multiplied by itself. For instance, the number 6 is multiplied by itself four times, yielding 6*6*6*6. You can write this as 6^4. In this case, the exponent is 4 and the base is 6. This can be understood as 4 increased to the power of 6. A number or letter written above and to the right of a mathematical expression known as the base is termed an exponent. It denotes that the base is to be increased in strength. The base is x, while the exponent or power is n.

Here,

The law of exponents say that,

aⁿ/aˣ=aⁿ⁻ˣ

1. 8/8³

=8¹-³

=8⁻²

=1/8²

2. (-3)⁴/(-3)³

=(-3)⁴⁻³

=-3¹

For first case, the monomial resulted after simplifying will be 1/8². For second  case, the monomial resulted after simplifying will be (-3)¹.

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The value of ordered pair of   (x,y) is (-2, -3)

x - 5y = 13

4x - 3y = 1

Solve the equation for x

x - 5y = 13

Move '5y' to R.H.S and change it's sign

x=13+5y

Substitute the given value of X into the equation

4x - 3y = 1

4(13+5y)-3y = 1

Solve the equation for y

distribute 4 through the parentheses

52+20y -3y =1

Collect like terms

52+17y = 1

Move constant to R.H.S and change it's sign

17y = 1 - 52

Calculate

17y =  - 51

Divide both sides of the equation by 17

17y/17 = -51/17

Calculate

y = -3

Now, substitute the given value of y into the equation

x = 13 + 5y

x= =13+5x(-3)

Solve the equation for x

Multiply the numbers

= 13 - 15

Calculate the difference

= -2

The possible solution of the system is the ordered pair

( x , y )

( x , y ) = ( - 2 , - 3 )

-----------------------------------------------------------------------

Check if the given ordered pair is the solution of the system of equation

-2-5×(-3)=15

4×(-2)-3×(-3)=1

Simplify the equalities

13 = 13

1=1

Since all of the equalities are true, the ordered pair is the solution of the system

( x , y ) = ( - 2 , - 3 )

Therefore the value of ordered pair of   (x,y) is (-2, -3)

The complete question is : Solve the system by substitution. x−5y=13 4x−3y=1 Enter your answer as an ordered pair (x,y).

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The distance between the two points is 2√10

Distance between two points:

The formula for the distance between two points (x₁, y₁) and (x₂, y₂) is given by Distance = √ [(x₂-x₁)² + (y₁ - y₁)²]

This formula can be used to find the length of a line whose endpoints are (x₁, y₁) and (x₂, y₂)

Here we have

The endpoints of the line are (1, 2) and (7, 4)

As we know d =√ [(x₂-x₁)² + (y₁ - y₁)²]

Take (x₁, y₁) = (1, 2) and (x₂, y₂) = (7, 4)

By the given formula,

Distance of line = √ [(7 - 1)² + (4 - 2)²]

=  √[(6)² + (2)²]  

=  √(36 + 4)

=  √40  

= 2√10

Therefore,

The distance between the two points is 2√10

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Answer: A y<3 and y>2/3x+1

Step-by-step explanation: y<3 shades everything under the line because 3 is greater than all the possible values.

y>2/3x+1 shades everything over the line because 2/3x+1 is less than all the possible values.

7.702 is the proper decision.

What exactly is a p-value?

The values of y when x is 0 1 2  is 0,3,6

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.

To get the values of y, we substitute for the values of x  in the equation 3x=y

When x = 0

3(0)=y; y = 0

When x = 1

3(1)=y; y = 3

When x = 2

3(2)=y; y = 6

x   |     3x     |    y    |    (x, y)

----------------------------------------

0   |     3(0)  |   0    |   (0, 0)

----------------------------------------

 1   |     3(1)    |    3   |   (1, 3)

----------------------------------------

 2   |     3(2)  |    6   |    (2, 6)

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No, the estimate should be higher

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

As, Maximum miles driven=highest consumption per gallon × Maximum  

                                                                                                         gallons

where;

Maximum miles driven per person=64 mile

Maximum miles driven = 64×4

                                     =256 miles

So, highest consumption =24.56 miles per gallon

let the Maximum gallons needed be x

256=24.56 x

24.56 x=256

x ≥ 256/24.56

x ≥10.42 gallons

Hence, No, the estimate should be higher

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The value of b is -11/2.

What is the slope of the equation?

The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).

To find the value of b, we need to find the slope of the given line and the line that is perpendicular to it.

The slope of the line 8x + 12y = 40 is -8/12 = -2/3.

The slope of a line that is perpendicular to this line is the negative reciprocal of -2/3, which is 3/-2 = -3/2.

The slope of the line y = (5 + b)x - c is 5 + b. Therefore, to find the value of b, we need to set 5 + b equal to -3/2:

5 + b = -3/2

b = -3/2 - 5

b = -11/2

Therefore, the value of b is -11/2.

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The probability that both choose Black Panther as their favourite character is 189/3875.

KHS students' list of their favourite Marvel comic character:

Spiderman - 45

Hulk - 30

Black panther - 28

Black widow - 17

Rocket raccoon - 5

Total = 125

             [tex]125C_{2}=\frac{125*124}{1*2} \\\\125C_{2}=\frac{15500}{2}\\\\125C_{2}= 7750[/tex]

              [tex]28C_{2}=\frac{28* 27}{1*2} \\\\28C_{2}=\frac{756}{2}\\\\28C_{2}= 378[/tex]

               [tex]P(BP) = \frac{28 C _{2}}{125C_{2}} \\\\P(BP) = \frac{378}{7750} \\\\P(BP) = \frac{189}{3875}[/tex] or  0.04877

          So, option c is correct.

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Answer:

Step-by-step explanation:

i want to know too:((

The equation for the second plan is y = 95x, therefore, option (d) is correct.

Two or more expressions with an equal sign are defined as an equation.

Given that, the second plan costs $95 for each ticket and free shipping.

The total cost, y, for x tickets are:

y = 95x.

Hence. the equation for the second plan is y = 95x, therefore, option (d) is correct.

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Answer:

Z< 3

Step-by-step explanation:

Hope this helps :)

Answer:

81

Step-by-step explanation:

it is asking only for the difference nothing else so do

14+67 because the value is in the - we use addition for this scenario if it's for example

difference between 10f and 50f you minus it

10-50 = 40

the 96th term of the arithmetic sequence 3, -14, -25 is -1048.

An arithmetic sequence is an ordered set of numbers that have a common difference between each consecutive term.

The general form of an arithmetic sequence is

aₙ = a₁ + d(n-1)

where aₙ is the nth term, a₁ is the initial term, and d is the common difference.

Given that n =96, a₁=-3, and d = -11

Substituting these value in the above equation

a₉₆ = -3 - 11(96-1) = -3 - (11*95) = -3-1045 = -1048

Hence, -1048 is the 96th term of the given arithmetic sequence.

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Answer:

41

Step-by-step explanation:

Answer:

The three consecutive even integers are 40, 42 and 44.

Step-by-step explanation:

Let the consecutive even integers be

The sum of the first and second of three consecutive even integers is 126.

So,

x + (x + 2) + (x + 4) = 126

Open the brackets

x + x + 2 + x + 4 = 126

Combine like terms we get,

3x + 6 = 126

Subtract 6 from both sides we get,

3x + 6 - 6 = 126 - 6

3x = 120

Divide 3 from both sides we get,

3x/3 = 120/3

x = 40

The value of x is 40 and the the consecutive even integers are

x = 40

x + 2 = 40 + 2 = 42

x + 4 = 40 + 4 = 44

Thus, The three consecutive even integers are 40, 42 and 44.

Equation : 200 = 15x + 5y + 120

Answer:

No Solution

Step-by-step explanation:

[tex]\tt -2\left(4x-1\right)=-8x-1[/tex]

Expand:-

[tex]\tt -8x+2=-8x-1[/tex]

Add 8x to both sides:-

[tex]\tt -8x+2+8x=-8x-1+8x[/tex]

Simplify:-

[tex]\tt 2=-1[/tex]

The sides are not equal, therefore there is No Solution.

_____________________

Hope this helps!
Have a nice day!

f(x)=x^3-12x^2+36x-32 completely given that (x-2) is a factor is [tex](x-2)^2(x-8)[/tex].

What is factor?

In mathematics, an integer m that can be multiplied by another integer to produce n is known as a divisor of an integer n, also known as a factor of n. One can also state that n is a multiple of m in this situation.

Knowing that (x−2) is a factor you can divide the polynomial:

2.....|.......1.........-12.........+36.........-32

........|...................2..........-20.........+32

........|.......1.........-10..........+16...........0

and find:

[tex]x^3-12 x^2+36 x-32=(x-2)\left(x^2-10 x+16\right)[/tex]

We could use the quadratic formula to find the factors of [tex]$q(x)=\left(x^2-10 x+16\right)$[/tex]

or go simply by inspection:

1) q(x) has two changes in sign, so it has two positive real roots.

2) The product of the roots is 16

3) the sum of the roots is 10

It's easy to see that x=2 and x=8 are such roots, and thus:

[tex]x^3-12 x^2+36 x-32=(x-2)^2(x-8)[/tex]

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The probability of having the first head at the k-th trial is 1/2.

The formula for the binomial distribution of probability is shown below. It can be used to determine the likelihood of getting K heads out of N coin tosses.

[nC k]* [pk]* [qn-k]

p= probability of receiving a head and

q= probability of having a tail.

Both p and q are 1/2.

As a result, the equation is [f12n! * f! r! * (n-r)!]

If you obtain exactly r successes, you also get (n - r) failures at the same time.

qn - rpr = P(getting r successes and n - r failures) (since the n trials are independent) Using the product theorem

There is no mention of the challenges from which the results were attained. There are nCr methods for selecting successful trials among r trials. The remaining (n - r) trials should be failures once the r trials that were picked for successes have been chosen. These nCr methods are incompatible. P(obtaining exactly r successes) in each of these nCr methods equals qn - rpr.

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Answer:

3.6

Step-by-step explanation: