Tell whether the data in the table can be modeled by a linear equation. Explain. A table listing pairs of x and y values. First pair. Negative 3 and 16. Second pair. Negative 1 and 10. Third pair. 1 and 4. Fourth pair. 3 and negative 2. Fifth pair. 5 and negative 8. The data be modeled by a linear equation because the rate of change constant. Question 2 If possible, write a linear equation that represents y as a function of x. If not possible, leave blank.

Area = (π*r^2*α)/360°

α =72°

r = 9 mi

Then

A = (π * 81 * 72°)/360° = 81/5π square meters

The most appropriate choice for domain of a  functions will be given by -

What is a domain of a function

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

The set of values for which the function is defined is called domain of the function.

Here, from the graph, the set of values of x axis for which the graph is drawn is [tex]-6\leq x \leq 6[/tex].

And values of x - axis represents the domain.

So domain of function is {x ∈ [tex]\mathbb{R}[/tex], [tex]-6 \leq x \leq 6[/tex]}

Third option is correct.

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The 'x' and 'y' variables are highlighted in the box

Answer:

x = 7

y = 15

Step-by-step explanation:

Disclosure:  After I had completed my answer, I found that Answerwell had already posted a solution.  It is more straightforward than my approach.  While the answers are the same, I'm still adding mine because 1) I worked hard on it, and 2) it illustrates there can be different ways of reaching a solution.

See attached worksheet.

Answer:

area of triangle is length *breathe

4.5 * 5.5 = 24.75

Aiden's tennis ball will reach the ground 0.65 seconds than Mason's tennis ball

The function of time with respect to distance is given as

(sqrt(d)/(4))

Rewrite the function properly

This is represented as follows

√d/4

It can also be written as

t = 1/4√d

From the question, we have

Aiden = 50 meters

Mason = 20 meters

The time difference is then calculated as

T = t₁ - t₂

So, we have

T = 1/4√d₁ - 1/4√d₂

The equation becomes

T = 1/4√50 - 1/4√20

This gives

T = 1/4(√50 - √20)

Evaluate

T = 0.65

Hence, the time difference is 0.65 seconds

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Answer:

Step-by-step explanation:

radius, r = 2√2

let the center be A(a, b):

The distance from the center to any of the 2 points is r.

So for (7, 2):

it satisfies the equation:

(x-a)²+(y-b)² = r²

Substituting x and y:

(7-a)²+(2-b)² = (2√2)²

squaring both sides:

(7-a)² + (2-b)² = 8

a² +b² - 14a -4b + 49+ 4= 8

a² +b² - 14a -4b + 45= 0        (Eqn 1)

For (3, 2):

it also satisfies the equation:

(x-a)²+(y-b)² = r²

Substituting x and y:

(3-a)²+(2-b)² = (2√2)²

squaring both sides:

(3-a)² + (2-b)² = 8

a² +b² - 6a -4b + 9+ 4= 8

a² +b² - 6a -4b + 5= 0        (Eqn 2)

We can now proceed by elimination:

(Eqn 2) - (Eqn 1):

(a² +b² - 6a -4b + 5) - (a² +b² - 14a -4b + 45) = 0

- 6a - -14a+ 5  - 45 = 0

8a - 40 = 0

8a = 40

a = 40/8

Putting a back into (Eqn 2):

a² +b² - 6a -4b + 5= 0

5² +b² - 6(5) -4b + 5= 0

25 +b² - 30 -4b + 5= 0

b² -4b = 0

b(b -4) = 0

Values of b:

POSSIBLE EQUATIONS OF CIRCLE:

Since we have 2 values of b, we have 2 possible centers:

(5, 0) and (5, 4)

Putting the centers into the standard equation of the circle above, we obtain:

PLEASE VOTE AS BRAINLIEST.

BLAISE M.

We want to graph the line:

For doing so, we will choose two different x-values, and we will find its correspondent y-values. This gives us two different points, and when we trace the line that passes through those points, we will have the line we wanted.

In this exercise, we will choose x=0, and x=5.

For x = 0

This gives us the point (0,3).

For x = 5

This gives us the second point: (5,6).

Now, graphing the points on a cartesian plane, and drawing the line between them, we obtain:

Answer:

4[tex]\sqrt{3}[/tex]

Step-by-step explanation:

[tex]\sqrt{48}[/tex] is not in simplest form, however, 48 contains a perfect square as a factor, that is 16 × 3

using the rule of radicals

[tex]\sqrt{ab}[/tex] ⇔ [tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] , then

[tex]\sqrt{48}[/tex]

= [tex]\sqrt{16(3)}[/tex]

= [tex]\sqrt{16}[/tex] × [tex]\sqrt{3}[/tex]

= 4[tex]\sqrt{3}[/tex] ← in simplest form

Given data:

The first value of x is a=-16.

The first value of y is b=20.

The second value of x is c=-12.

The second value of y is d=15.

The expression for the rate change is,

x=(d-b)/(c-a)

Substitute the given values in thhe above expression.

x=(15-20)/(-12+16)

=-5/4

Thus, he constant rate of change is -5/4.

A Communication system consists of n components.

a) Binomial distribution,

P(X=x) = ⁿC ₓ p ˣ (1-p) ⁽ⁿ⁻ˣ⁾

b) For 5-component system,

P(X= 5) = ⁵Cₓ pˣ (1-p)⁵⁻ˣ , x= 3,4,5

c) 5-component system is effectively than a 3-component system if 0.5<p<1 where p is probability of functioning components.

Communication system consists of n components and functions with probability p . Then the probability of components which are not function from n components is q = 1-p .

(a) Let x denotes number of functioning components i.e., their probability value is p . And system is effectively operate when atleast one half of components are function. So, the distribution of x is binomial distribution P (X=x) = ⁿCₓ pˣ (1-p)⁽ⁿ⁻ˣ⁾ where n is total number of components, x numbers of functioning components, p is probability of functioning components.

(b) Now , 5-component system is function . That is n=5

Probability that 5-components system will function is P(X= 5)

= ⁵C ₓ p ˣ(1-p)⁽⁵⁻ˣ⁾ , x= 3,4 ,5 ( because one half of components are function)

(c) Because the number of functioning components is a binomial random variable with parameters (n, p), it follows that the probability that a 5-component system will be effective is

⁵ C₃ p³(1-p)² + ⁵C₄ p⁴ (1-p)¹+ ⁵C ₅ p⁵ (1-p)⁰ = 10 p³ (1-p)² + 5 p⁴(1-p) + p⁵

Whereas the corresponding probability for a 3-components system

³ C ₓ p ˣ ( 1-p)⁽ⁿ⁻ˣ⁾ , x= 2,3

³ C₂ p²(1-p)¹ + ³C₃p³(1-p)⁰ = 3 p² 1-p) + p³

5-Component system is better than 3-Components system if

10 p³ (1-p)² + 5p⁴ (1-p) + p⁵= 3p²(1-p) + p³

=> 10 p⁵ + 10 p³– 20 p⁴+ 5 p⁴ – 5p⁵ + p⁵ = 3p² + p³ – 3p²

Which reduce to

3( 2p -1) (1-p) 2 > 0 , either (2p-1) > 0 or 3(1-p) 2>0

either p> ½ or p <1

=> p belongs to ( 0.5, 1)

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The t-shirts she sell is 24.

What is profit and selling price?

Profit is considered as the gain amount from any business activity. Whenever a shopkeeper sells a product, his motive is to gain some benefit from the buyer in the name of profit.

The selling price is the price that the buyer pays to buy a product or goods. This is a price above cost and includes a profit ratio.

According to Question, Christine sold the t- shirts at $4 each and she earned a profit of $71 and his total expenses were $25

Let the total number of t- shirts sold by Christine be "x"

Profit = Selling price – Expenses

Selling price is given as:

selling price = total number to t-shirt sold ×price of each t shirt

selling price = n ×4

71 = (n×4) -24

71 + 25  = n×4

96/4 = n

n = 24

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The simplified form of the given expression is option c 1 1/2x - 1 3/4

Given,

The expression; 1/4 (3x - 7) + 3/4x

We have to simplify this expression;

Simplification of expressions;

To simplify a phrase, create an equivalent expression without any terms that are identical. The expression will then be rewritten using the fewest terms feasible.

Then,

1/4 (3x - 7) + 3/4x

= 1/4 × 3x - 1/4 × 7 + 3/4x

= 3/4x - 7/4x + 3/4x

= 6x/4 - 7/4

= 3x/2 - 7/4

= 1 1/2x - 1 3/4

Therefore,

The simplified form of the given expression is option c 1 1/2x - 1 3/4

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The equation that represents the sentence will be (1/14)xy ·[x² + 3y].

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

The act of converting a specified statement into an expression or equation is known as a sentence-to-equation transformation.

The sentence is given below.

One-fourteenth times x cubed times y plus three-fourteenths times x times y squared.

Convert the sentence into an expression. Then we have

⇒ (1/14)x³y + (3/14)xy²

Simplify the expression, then we have

⇒ (1/14)x³y + (3/14)xy²

⇒ (1/14)xy ·[x² + 3y]

The equation that represents the sentence will be (1/14)xy ·[x² + 3y].

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A Stem and Leaf Plot is a special table where each data value is split into a "stem" (the first digit or digits) and a "leaf" (usually the last digit).

With this in mind we conclude that:

There are 8 values in the data set which are greater than or equal to 20 and less than or equal to 29. This comes from the fact that we have to count how many leafs are in the stem 2.

There are 6 values in the data set which are greater than or equal to 10 and less than or equal to 19. This comes from the fact that we have to count how many leafs are in the stem 1.

There are 14 values in the data set which are greater than or equal to 40 and less than or equal to 49. This comes from the fact that we have to count how many leafs are in the stem 4.

The slope of the line = rise of the line / run of the line = 2/2 = 1.

The slope (m) of a line can be determined by finding the ratio of the rise of the line to the run of the line, which is, the change in y over the change in x.

Referring to the image attached below, the blue line in the given graph shows the rise of the line while the red line shows the run of the line.

Therefore:

Rise of the line = 2 units

Run of the line = 2 units

Slope of the line (m) = rise/run = 2 units/2 units

Slope of the line (m) = 1

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Total surface area = 620

Moreover, The total area covered by an isosceles triangle is called its area. For an isosceles triangle, the area is easily calculated if the height and base are known. Multiplying the height by the base and dividing it by 2 gives us the area of ​​an isosceles triangle.

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From the given table that represents the population in a small coastal communityfor the period 1997 to 2006, let's answer the following questions.

(a) Average rate of change of the population between 1999 and 2002.

To find the average rate of change, apply the formula below:

Where:

x1 = 1999

x2 = 2002

y1 = the population in 1999 = 1,336

y2 = the population in 2002 = 1,483

Thus, we have:

Therefore, the average rate of change of the population between 1999 and 2002 is

49

(b) What was the average rate of change of the population between 2001 and 2005.

To find the average rate of change, apply the formula:

Where:

x1 = 2001

x2 = 2005

y1 = population in 2001 = 1591

y2 = population in 2005 = 801

Thus, we have:

Therefore, the average rate of change in the population between 2001 and 2005 was -197.5

(c) For what period of time was the population increasing.

From the given table, we can see the table was increasing from 1997 to 2001

The population was increasing from 1997 to 2001

(d) For what period was the population decreasing.

From the table, the population was decreasing from 2002 to 2006

The population was decreasing from 2001 to 2006

ANSWER:

• (a) 49

• (b) -197.5

• (c) 1997 to 2001

• (d) 2001 to 2006

ok

I erased the answer but it is 22 whole strips

a. The amount remaining in the account after x week  is 700 - 40x

b. Olivia can withdraw can withdraw money from her account money for  approx. 13 weeks.

Let x represent the number of weeks. Then the amount of withdrawal in this time is 40x

So, the amount remaining in the account after x weeks is 700 - 40x

Since he needs 150$ in the account for safety net, we must have

700 – 40x ≥ 150

So,

700 - 150 ≥ 40x

550 ≥ 40x

550/40 ≥ x

x ≤ 13.75

Hence, he can withdraw money for  approx. 13 weeks.

Withdrawal involves removing money from a bank account, savings plan, pension or trust. In some cases, conditions must be met for funds to be withdrawn without penalty, and an early withdrawal penalty usually occurs when a condition of the investment agreement is violated. Withdraw money from account: With this account you can withdraw a maximum of $500 per day. withdraw money/money/savings With the financial crisis, people had to withdraw their savings.

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Answer:

Step-by-step explanation:

Area of rectangle formula:

Find the width by substituting the given values:

Based on the center of the regular decagon, we can find that the perimeter of the decagon would be 98.9 units.

When given the midpoint of a decagon and the measurement of the radius, the perimeter can be found by the formula:

= 10 x ( ( 2 x Radius of the decagon) / (1 + √5)))

Given a radius of 16 units, the perimeter of this decagon is:

= 10 x ( (2 x  16) / (1 + √5)))

= 10 x ( (32 / (1 + √5)))

= 98.9 units

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Perimeter of Decagon with radius and midpoint given is 100 units.

Polygon can be defined as a flat or plane, two-dimensional closed shape bounded with straight sides.

Given polygon is a decagon. A decagon is a polygon which have ten sides with same length with centre o.

The radius of the decagon is 16.

When radius and midpoint is given the perimeter can be given by formula

Perimeter= 10 x ( ( 2 x Radius of the decagon) / (1 + √5)))

=10×((2×16) / (1 + √5)))

=10×((32) / (1 + √5)

=320/1+√5

=320/1+2.2

=320/3.2

=100 units.

Hence perimeter of Decagon with radius and midpoint given is 100 units.

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The amount of money Kadeesha have in her account after 11 years is $1059.3.

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex]

Given that, principal=$900, rate of interest=1.5% and time period =11 years.

Now, amount =900(1+1.5/100)¹¹

= 900(1+0.015)¹¹

= 900(1.015)¹¹

= 900×1.177

= $1059.3

Therefore, the amount of money Kadeesha have in her account after 11 years is $1059.3.

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In every triangle the addition of all internal angles is always 180 degrees.

So this means we can build this equation

5x + 35 + 60 = 180

now separate x values and numerical values

5x = 180 - 60 - 35

x= (180 - 60 - 35)/ 5 = 85/5 = 17

The range is the difference between the largest and the smallest and the range is 5.2

This is a graph that is divided into two vertical axes such that one axes represent the stem and the other axis represents the leaf

From the question, we have the following parameters:

Stems = 12, 13, 14, 15, 16, and 17

Each of these stem elements have their own leaves

So, the complete stem and leaf plot is as follows

12     |  3, 3, 6, 7, 9, 9.

13     |  1, 1, 4, 5, 5.

14     |  0, 0, 2, 3, 3, 8, 8, 9.

15     |  2, 2, 2, 2, 2, 3, 5, 5, 7.

16     | 4, 5, 5, 9, 9.

17      | 3 5.

Key

12 | 3 means 12.3.

To determine the range, we simply take the smallest number and the largest number represented by the plot and calculate the difference

In (a), we have

The range is calculated from the smallest number and the largest number represented by the plot

So, we have

Smallest = 12.3

Largest = 17.5

So, the range is

Range = 17.5 - 12.3

Evaluate

Range = 5.2

Hence, the range is 5.2

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Answer:

y = 1/2x - 5

Step-by-step explanation:

The y intercept is negative 5. The line slowly goes one point up and two points to the right, staying positive. This makes it 1/2.

The value of f(x) - g(x) = 2x³ - 4x² + 6x + 4

What is Function?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

Given,

f(x) = 7x³ - 3x² + 5x+1

g(x) = 5x³+x²-x-3

We have to find the value of:

f(x) - g(x)

Substituting the value of f(x) and g(x)

f(x) - g(x) = (7x³ - 3x² + 5x+1 ) - (5x³+x²-x-3)

Now, open the brackets

f(x) - g(x) = 7x³ - 3x² + 5x+1 - 5x³ - x²+ x + 3

Now, arranging them by like terms

f(x) - g(x) = 7x³ - 5x³ - 3x² - x² + 5x + x +1 + 3

               = 2x³ - 4x² + 6x + 4

Hence, f(x) - g(x) = 2x³ - 4x² + 6x + 4

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The most appropriate choice for simple interest will be given by -

Amount obtained = $28.5

What is simple interest?

Simple interest is the interest earned on a certain principal at a certain rate over a certain period of time.

If principal is p, rate is r%, time is t years

Simple interest = [tex]\frac{p \times r \times t}{100}[/tex]

On adding principal and simple interest, we get amount.

Amount = Principal + Simple interest.

Principal = $15

Rate = 6%

Time = 15 years

Simple interest = [tex]\frac{15 \times 6 \times 15}{100}[/tex]

                         = $13.5

Amount obtained = $(15 + 13.5)

                             = $28.5

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[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textsf{GUIDE TO FOLLOW: }[/tex]

• [tex]\large\textsf{2 negatives equal positive}[/tex]
• [tex]\large\textsf{2 positives equal positive}[/tex]
• [tex]\large\textsf{1 negative \& 1 positive equal negative}[/tex]
• [tex]\large\textsf{1 positive \& 1 positive equal negative}[/tex]

[tex]\large\textsf{SOME OPERATIONS MAY BE DIFFERENT THAN OTHERS!}[/tex]

[tex]\large\textsf{ANYWHO, LET US ANSWER THIS QUESTION, SHALL WE? }[/tex]

[tex]\mathsf{(-12)(-8)}[/tex]

[tex]\mathsf{= 12(8)}[/tex]

[tex]\mathsf{= 96}[/tex]

[tex]\huge\textsf{Therefore, your answer should be: \boxed{\mathsf{96}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

665

Step-by-step explanation:

the reasoning is because you divide 525/15 and you get 35 with that you multiply by 19 because you are seeing how far you can get with 19 gallons of gas .

665 miles Santiago can travel on 19 gallons of fuel.

A ratio in mathematics demonstrates how many times one number is present in another.

Given, Santiago's car used 15 gallons to travel 525 miles. Since,

Santiago travels in 15 gallons  = 525 miles

Santiago travels in 1 gallons = 525/ 15 = 35

Santiago travels in 19 gallons = 35* 19 = 665

Therefore,  Santiago can travel 665 miles on 19 gallons of fuel.

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