estimate the line of best fit using two points on the line.​

Answer:

First box: 2

Second box: 30

Third box: 42

Step-by-step explanation:

5 sixes means 5 · 6, which equals 30. An unknown amount of sixes equals 12, which is 2 because 2 · 6 = 12.

30 + 12 = 42

7 · 6 = 42, so 42 is the answer.

I hope this helped! :)

Answer:

x = ± 12

Step-by-step explanation:

Given

f(x) = x² - 144

To find the roots set f(x) = 0, that is

x² - 144 = 0 ( add 144 to both sides )

x² = 144 ( take the square root of both sides )

x = ± [tex]\sqrt{144}[/tex] = ± 12

Final answer:

The roots of the given quadratic function f(x) = x² - 144 are x = 12 and x = -12.

Explanation:

The roots of a quadratic function can be found by setting the function equal to zero and solving for x. In the case of f(x) = x² - 144, this is equivalent to solving the equation x² - 144 = 0. This equation is a difference of squares and can be factored as (x - 12)(x + 12) = 0. The roots of the equation are the values of x that make the equation true, which in this case are x = 12 and x = -12.

Answer:

there is no mode

Step-by-step explanation:

The mode is the value that appears most frequently in a data set. In this set of numbers none appear more than once. There is no mode.

Answer:

-2x+3y=15

Step-by-step explanation:

y=2/3x+5

y-2/3x=5

-2/3x+y=5

3(-2/3x+y)=3(5)

-2x+3y=15

They next ring together will be at 6:50 a.m.

Step-by-step explanation:

The given is:

We need to know at what time will they next ring together

To solve the problem lets find the lowest common multiple of 10 and 25

∵ The multiples of 10 are 10 , 20 , 30 , 40 , 50 , 60 , 70 , 80 , 90 , 100 , .....

∵ The multiples of 25 are 25 , 50 , 75 , 100 , ........

∵ The common multiples of 10 and 25 are 50 , 100 , ......

∴ The lowest common multiple of 10 and 25 is 50

∵ The two bells start ringing together at 6 a.m.

∵ The first bell rings every 10 minutes

∴ The first bell rings at 6:10 a.m. , 6:20 a.m. , 6:30 a.m. , 6:40 a.m. ,

   6:50 a.m. , .........

∵ The second bell rings every 25 minutes

∴ The second bell rings at 6:25 a.m. , 6:50 a.m. , ........

∴ They start ringing together at 6:50 a.m.

They next ring together will be at 6:50 a.m.

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Final answer:

To determine when two bells will next ring together, find the Least Common Multiple (LCM) of their ringing intervals. The LCM of 10 and 25 is 50, therefore the bells will next ring together at 6:50 a.m.

Explanation:

The question is about finding the next time two bells, ringing at different intervals, will ring together. To solve this, we need to find the Least Common Multiple (LCM) of the two bell ringing intervals: 10 minutes and 25 minutes. The LCM of 10 and 25 is 50 since 10 × 5 = 50 and 25 × 2 = 50. Since the bells start ringing together at 6 a.m., they will next ring together 50 minutes later.

Adding 50 minutes to 6 a.m., we get 6:50 a.m. Therefore, the two bells will next ring together at 6:50 a.m.

Answer: 371697

Step-by-step explanation:

For continuously compounded values, we use the formula Pe^rt, or Pert. P is our principal/initial value, 230000. e is the constant e, r is our rate, 4% or .04, t is our time, 12. So, 230000*e^(.04*12)=371697.112504, rounding down, 371697.

The average rate of change of d(t) from t = 3 to t = 6 represent: A. The coin travels an average distance of 44.1 meters from 3 seconds to 6 seconds.

In Mathematics and Geometry, the average rate of change (ARoC) of a function f(x) on a closed interval [a, b] can be calculated by using this mathematical equation (formula):

Average rate of change (ARoC) = [tex]\frac{f(b) - f(a)}{(b - a)}[/tex]

Based on the given quadratic function, we can reasonably infer and logically deduce the following:

[tex]d(t)=4.9t^2\\\\d(3)=4.9(3)^2[/tex]

f(a) = d(3) = 44.1

[tex]d(t)=4.9t^2\\\\d(6)=4.9(6)^2[/tex]

f(a) = d(3) = 176.4

Next, we would determine the average rate of change (ARoC) of the function over the interval [3, 6]:

Average rate of change (ARoC) = [tex]\frac{176.4 - 44.1}{(6 - 3)}[/tex]

Average rate of change (ARoC) = 44.1 meters.

In this context, we can logically deduce that the coin travels an average distance of 44.1 meters from 3 seconds to 6 seconds.

The class average on test 2 is 76 points

Given that, the class average on test 1 was 84.  

And the class average on test 2 was 8 points lower.  

We have to find what was the class average on test 2?  

Now, according to the given information.

Class average on test 2 is 8 points lower than class average on test 1.

So, class average on test 2 = class average on test 1 – 8 points

Class average = 84 – 8  

Class average = 76 points.

Hence, the class average on test 2 is 76 points

Answer:

e. It will take 11 seconds to reach the maximum height of 1,936 feet.

f. It will take 22 seconds to return to the earth.

Step-by-step explanation:

Given:

Initial velocity [tex]v_0[/tex] = 352 ft/sec

Solving for question e.

To find the time required to reach the maximum height we will use the formula,

[tex]h(t) = -16t^2+v_0t+h_0[/tex],

where [tex]v_0[/tex] is the starting velocity

[tex]h_0[/tex] is the initial height.

Using the velocity and starting height from our problem we have,

[tex]h(t) = -16t^2+352t+0[/tex],

The path of this rocket will be a downward facing parabola, so there will be a maximum.

This maximum will be at the vertex of the graph.

To find the vertex we start out with [tex]x= \frac{-b}{2a}[/tex] which in our case is,

[tex]x=\frac{-352}{2(-16)}=\frac{-352}{-32}= 11[/tex]

So, It will take 11 seconds for the rocket to reach its maximum height.

We will find maximum height using the formula by substituting value of t we get,

[tex]h(11)=-16(11^2)+352(11)+0\\h(11) = -16 \times121+ 352 \times 11 = -1936+3872= 1936 \ ft[/tex]

Hence the maximum height will be [tex] 1936 \ ft[/tex]

Now Solving for question f.

To find the time required for rocket to reach earth.

We will set our formula to 0 to find the time.

[tex]0= -16t^2+352t+0\\-16t(t-22)=0[/tex]

Using the zero product property, we know that either -16t = 0 or t - 22 = 0.  When -16t = 0 is at t = 0, when the rocket is launched. t - 22 = 0 gives us an answer of t = 22.

So the rocket reaches the Earth again at 22 seconds.

Answer:

See explanation

Step-by-step explanation:

Let [tex]F(x)=\left(\dfrac{2}{3}\right)^x.[/tex] Plot the graph of this function. From the graph:

A. The domain of the function is [tex]x\in (-\infty,\infty).[/tex]

B. The range of the function is [tex]y\in (0,\infty).[/tex]

C. The y-intercept of the graph of F(x) is [tex](0,1).[/tex]

D. The horizontal asymptote is x-axis.

E. The graph of the function F(x) is decreasing from left to right.

F. The value [tex]\frac{2}{3}[/tex] determines that the graph of the function is decreasing from the left to the right.

Answer:

what he said above me

Step-by-step explanation:

f(18) = 39.50

This gives the monthly cost Kelsey will pay if she streams 18 movies in a month

Step-by-step explanation:

Given function is:

[tex]f(x) = 1.50x+12.50[/tex]

Here x is the number of movies

so for f(18), this means that the total number of movies will be 18

Solving

[tex]f(18) = 1.50(18)+12.50\\f(18) = 27+12.50\\f(18) = 39.50[/tex]

Hence,

f(18) = 39.50

This gives the monthly cost Kelsey will pay if she streams 18 movies in a month

Keywords: functions, Domain,range

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Price of one ream of paper is $6.5

Step-by-step explanation:

Let,

x be the total cost.

Cost of one ream of paper = y

Cost of binder = $4.50

Cost of ink cartridge = $17.50

According to given statement;

x = 4.50 + 6y    Eqn 1

x = 17.50 + 4y   Eqn 2

As both spent the same amount, therefore,

Eqn 1 = Eqn 2

[tex]4.50+6y=17.50+4y\\6y-4y=17.50-4.50\\2y=13\\[/tex]

Dividing both sides by 2

[tex]\frac{2y}{2}=\frac{13}{2}\\y=6.5[/tex]

Price of one ream of paper is $6.5

Keywords: linear equation, division

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Answer:

798

Step-by-step explanation:

hsushshxhuxvshsjsvs

The area of a rectangle is given as:

Area = Length x width

Length = 38

Width = 21

The value of 38 x 21 as an area model is 798.

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

38 x 21 as an area model.

This can be considered as,

Length = 38

Width = 21

Now,

The area of a rectangle.

= 38 x 21

= 798

Thus,

The value of 38 x 21 as an area model is 798.

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Answer:

5n+p>40

n+p<20

Step-by-step explanation:

Since pennies are worth 1 cent and nickels 5, using n as the number of nickels and p as the number of pennies, we can say that 5*n+1*p>40. Then, n+p is less than 20, so n+p<20. Our answer is then

5n+p>40

n+p<20

The currency called the dollar can be split into smaller forms called nickels, pennies, dimes, and quarters.

The system of inequalities that represents how many pennies and nickels that Jada could have is given as:

Let's represent the number of :

pennies = p

nickels = n

It is important to also note that:

1 penny = $0.01

1 nickel = $0.05

40 cents can also be written as: $0.40

Jada has p pennies and n nickels that add up to more than 40 cents.

The word more than means greater than and this can be represented by the inequality sign ">". Hence, our inequality equation is given as:

$0.01 x p + $0.05 x n > $0.40

0.01p + 0.05n > 0.40

She had fewer than 20 coins altogether.

The word fewer means less than and this can be represented by the inequality sign "<". Hence, our inequality equation is given as:

p + n < 20

Therefore, the system of inequalities that represents how many pennies and nickels that Jada could have is given as:

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Answer:

9/2

Step-by-step explanation:

(3/4)/6=(3/4)(6/1)=18/4=9/2

Answer:

x=5

Step-by-step explanation:

Since a Trapizode has 360 Degrees total and since the sides are equal we can say that

180=110+17x-15

70=17x-15

85=17x

x=5

The value of x in the trapezoid is 5

The sum of the sides on a trapezium is 180 ;

Using the expression :

17x + 95 = 180

17x = 180 - 95

17x = 85

x = 85/17

x = 5

Therefore, the value of x is 5.

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Answer:

6 + 8 + 10 = 24

Answer: 6, 8, and 10

Step-by-step explanation:

x-first number

x+2-second

x+4-third

x+x+2+x+4=24

3x=18

x=6

6, 8, and 10

Answer:

Here we do not have the image, but i will try to give a explanation about this type of problem.

When we have the function f(x), the graph of the function h(x) = f(x - x0) means that the graph is displaced by x0 units to the right.

This is because the value of f(x = 0) is equivalent to h( x = x0), but the first one corresponds to the pair (0, f(0)) and the other corresponds to (x0, f(0))

This means that:

g(x) = 3√(x - 4) is displaced 4 units to the right.

g(x) = 3√(x + 4) = g(x) = 3√(x - (-4)) is diplaced 4 units to the left.

g(x) = 3√(x - 1.5) is displaced 1.5 units to the right.

g(x) = 3√(x + 1.5) is displaced 1.5 units to the left.

Answer:

90°

Step-by-step explanation:

5, 12 and 13 are the sides of a right triangle ( Pythagorean triple )

13 is the measure of the hypotenuse whose opposite angle is 90°

Answer:

90°

Step-by-step explanation:

5^2+ 12^2 = 13^2

25 + 144 = 169

The Converse Pythagorean Theorem (Egyptian triangle) states that if the length of the sides of a triangle, say a, b, and c, satisfy a^2 + b^2 = c^2, then this is a right triangle with a right angle opposite to side c.

And since 5^2 + 12^2 = 13^2 satisfies the statement a^2 + b^2 = c^2, c (which is 13) is opposite to a 90° angle.

Answer:

10

Step-by-step explanation:

3 + 7 = 10

780 students prefer chocolate milk.

Step-by-step explanation:

Let,

the total percentage = 100%

Students who prefer plain white milk = 35%

Students who prefer chocolate milk = 100 - 35 = 65%

Number of students = 1200

No. of students who prefer chocolate milk = 65% of total students

No. of students who prefer chocolate milk = [tex]\frac{65}{100}*1200[/tex]

No. of students who prefer chocolate milk = [tex]\frac{78000}{100}\\[/tex]

No. of students who prefer chocolate milk = 780

780 students prefer chocolate milk.

Keywords: percentage, subtraction

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Answer:

b. [tex]\frac{(10+x)}{(y-3)}[/tex]

Step-by-step explanation:

Question:

Look at each expression. Is it equivalent to "the quotient of 10 plus x and y minus 3"?

a. (10+x)/(y)

b. (10+x)/(y-3)

c. 10+(x)/(y)-3

d. (10+x-3)/(y)

Solution:

Given statement:

The quotient of 10 plus [tex]x[/tex] and [tex]y[/tex] minus 3

From the statement we can have the following:

Dividend =[tex]10+x[/tex]

Divisor [tex]=y-3[/tex]

The quotient is given by dividend divided by divisor.

The quotient thus can be expressed as:

[tex]\frac{(10+x)}{(y-3)}[/tex]

Answer:

[tex]a_{n} = a_{1} + (n-1)[/tex]this is the required representation for showing the position of a term in the sequence.

Step-by-step explanation:

Given:

The sequence is as follow:

0, 1, 2, 3, .......

To Find:

The expression while using 'n' to represent the position of a term in the sequence where n = 1 for the first term 0, 1, 2, 3, ....

Solution:

n = to represent the position of the term in the sequence.

[tex]a_{1} = \textrm{represent the first term in the sequence.} = 0[/tex]

d = Common difference.,i.e difference between the consecutive term.

d = second term - first term.

or

d = third term - second term.

Here we have d = 1 - 0 = 1

or                     d = 2 - 1 = 1

So, the required expression is

[tex]a_{n} = a_{1} + (n-1)\times d[/tex]

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

If we require first term put n = 1

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

[tex]a_{1} = 0[/tex]

If we require second term put n = 2

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

[tex]a_{2} = 0 + 1[/tex]

[tex]a_{2} = 1[/tex]

If we require third term put n = 3

[tex]a_{3} = a_{1} + (3-1)[/tex]

[tex]a_{3} = 0 + 2[/tex]

[tex]a_{3} = 2[/tex]

and so on.......

Answer:

3x^2 + 12x + 4y^2 - 8y = 32

Step-by-step explanation:

3(x^2+4x)+4(y^2-2y)=32

At first we have to break the parenthesis to get the variables in normal position. To break those, we have to multiply each with the help of algebraic expression:

or, (3*x^2) + (3 × 4x) + (4 × y^2) - (4 × 2y) = 32

or, 3x^2 + 12x + 4y^2 - 8y = 32

Since the equation does not have anything to add or deduct, therefore, it is the answer.

Answer:

3.09

Step-by-step explanation:

Answer:

3.09

The drawing will help

Answer: The answer will be C.

Answer:

the process of retting softens the tissue and helps to separate the fibres

Step-by-step explanation:

the process of retting softens the tissue and helps to separate the fibres

Thanks

Answer:

4200 tickets of [tex]\$28[/tex] and 1800 tickets of [tex]\$40[/tex] were sold

Step-by-step explanation:

Given:

Tickets are sold at price [tex]\$28[/tex] and [tex]\$40[/tex].

Let Number of tickets sold at price [tex]\$28[/tex] be [tex]x[/tex].

Let Number of tickets sold at price [tex]\$40[/tex] be [tex]y[/tex].

Theater has maximum capacity of 6000 seat.

Hence,

[tex]x+y=6000 \ \ \ \ equation \ 1[/tex]

Total revenue to be generated is [tex]\$189600[/tex]

[tex]\therefore 28x + 40y= 189600 \ \ \ \ equation \  2[/tex]

Now Multiplying equation 1 by 40 we get,

[tex]x+y=6000\\40x+40y=240000\ \ \ \ equation \ 3[/tex]

Now Subtracting equation 2 by equation 3 we get,

[tex](40x+40y=240000)- (28x + 40y= 189600)\\12x=50400\\\\x=\frac{50400}{12}=4200[/tex]

Now substituting value of x in equation 1 we get,

[tex]x+y=6000\\4200+y=6000\\y=6000-4200= 1200[/tex]

Hence a total of 4200 tickets of [tex]\$28[/tex] and 1800 tickets of [tex]\$40[/tex] were sold

To generate a total revenue of $189,600, 4200 tickets should be sold at $28 and 1800 tickets should be sold at $40.

To find the number of tickets to be sold at each price, we can set up a system of equations. Let's assign variables:

       Let x be the number of tickets sold at $28.

The total revenue from selling x tickets at $28 is 28x, and the total revenue from selling y tickets at $40 is 40y. Since the total revenue is $189,600, we can write the equation:

28x + 40y = 189,600

We also know that the total number of tickets sold is x + y = 6000.

We can solve this system of equations to find the values of x and y. One way is to multiply the second equation by 28 and subtract it from the first equation:

28x + 40y - 28x - 28y = 189,600 - 28(6000)

12y = 189,600 - 168,000

12y = 21,600

y = 21,600 / 12 = 1800

Substituting the value of y in the equation x + y = 6000, we get:

x + 1800 = 6000
x = 6000 - 1800 = 4200

Therefore, 4200 tickets should be sold at $28 and 1800 tickets should be sold at $40 to generate a total revenue of $189,600.

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