PLEASE HELP ME WITH THIS

PLEASE HELP ME WITH THIS

Answers

Answer 1

The simplified form of the given expression is x + a - 4

Simplifying an Expression

From the question, we are to simplify the given expression

From the given information, we have that

g(x) = x² - 4x,

Now,

We are to simplify

[tex]\frac{g(x)-g(a)}{x -a}[/tex]

First, we will determine g(a)

From the given function,

g(x) = x² - 4x

∴ g(a) = a² - 4a

Thus,

[tex]\frac{g(x)-g(a)}{x -a}[/tex] becomes

[tex]\frac{x^{2} -4x-(a^{2}-4a)}{x -a}[/tex]

[tex]\frac{x^{2} -4x-a^{2}+4a}{x -a}[/tex]

[tex]\frac{x^{2} -a^{2} -4x+4a }{x -a}[/tex]

Factoring

[tex]\frac{(x+a)(x-a)-4(x-a) }{x -a}[/tex]

Further factorization

[tex]\frac{(x-a)((x+a)-4) }{x -a}[/tex]

Dividing

((x +a) -4)

x + a - 4

Hence,

The simplification gives x + a - 4

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Related Questions

Combine the like terms in this expression: -x3 + 2xy + 4y - xy + 2x - 11y

A. -7xy
B. 2xy + 15
C. 23X + y
D. - X + XY -7y

Answers

Answer is equals to (a) -7xy

Answer:

[tex]{ \rm{ {x}^{3} + 2xy + 4y - xy + 2x - 11y}} \\ \\ = { \rm{ {x}^{3} + (2xy - xy) + 2x + (4y - 11y)}} \\ \\ = { \rm{ {x}^{3} + 2x + xy - 7y}}[/tex]

Kelsey earned some Money doing odd jobs last summer and put it in a savings account that earns 5% interest compounded quarterly after 7 years there is 400.00 in the account how much did Kelsey earn doing odd jobs

Answers

The final amount is

[tex]\begin{gathered} A=P(1+\frac{R}{n\times100})^{nT} \\ Here,\text{ A is the final amount, P is the principal or the money earned by Kelsey, T is time in years, n is the number of tnes the comound interest is taken.} \end{gathered}[/tex]

Here,A=400, R=5%, N=4,T=7. We have to find the principal.Substituting the values,

[tex]\begin{gathered} 400=P(1+\frac{5}{4\times100})^{4\times7} \\ \text{ 400=P(1+}\frac{5}{400})^{28} \\ \text{ P=}\frac{400}{\text{(1+}\frac{5}{400})^{28}} \\ \text{ =282.48} \end{gathered}[/tex]

Therefore, the money earned by Kelsey doing odd jobs​ is 282.48.

There are 4 triangles and 2 circles. What is the simplest ratio of circles to total shapes?

Answers

Answer:

1:3

Step-by-step explanation:

circles:total

2:4+2

=2:6

=1:3

Answer is the ratio 1:3

Reason

There are 2 circles and 4+2 = 6 shapes total.

The ratio of circles to total shapes is 2:6 which reduces to 1:3

The order is important since 3:1 is different from 1:3.

Addison has x pennies and y nickels. She has a minimum of 16 coins worth no more
than $0.40 combined. Solve this system of inequalities graphically and determine
one possible solution.

Answers

The solution would be anything in the shaded region as long as it is a whole number for both x and y and is not negative

In a class of 50 students, on average, 10 will be left-handed. If a class includes 25 "lefties", estimate how many students are in the class.

Answers

The total number of lefties present in the class are 125.

What is meant by the term percentage?Percentage is an assessment of a portion in relation to a whole, frequently expressed as how many of some there are per 100.A group with half girls as well as half boys is an instance of a situation in which the percentage of boys with in group is equal to 50%.

For the given question;

The total students in the class are 50.

There are 10 out of 50 on an average students be left-handed.

Let the percentage of left handed be 'x'.

Then, x% of 50 = 10

x = 10×100 / 50

x = 20%.

Now the average number of left-handed students are 25.

The total students will be.

Let 'y' be the total number of students.

Then, 25 is the 20% of y.

20% of y = 25.

y = 25 ×100 / 20

y = 125

Thus, the total number of lefties present in the class are 125.

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Valentina knits 16 centimeter of scarf each night.How manynightswillValentinahavetospendknittinginordertoknitatotalof48centimetersofscarf?

Answers

You have the following information:

- Valentina knits 16 cm of scarf each night.

To determine how many night does Valentina need to knit 48 cm of scarf, you simply calculate the quotient between 48 cm and 16 cm, just as follow:

48/16 = 3

Hence, Valentina needs 3 days to knit 48 cm of scarf

Dina goes to a carnival. Some rides at the carnival have a height requirement, but others do not. Dina is tall enough to go on all rides.
What is a mathematical question you can ask about this situation? What information would you need to know to answer your question?

Answers

The mathematical question that can be asked in a situation when Dina goes to a carnival and some rides have a height requirement is how many extra centimeters of height Diana has? The information required to solve this question is the required height for the ride and the height of Diana.

According to the question,

We need to ask a mathematical question. Let's solve a mathematical question in the given situation by taking one example.

If the required height to ride is 150 cm and the height of Diana is 165 cm, how many extra centimeters of height Diana has than the required height?

Solution:

Required height = 150 cm

Dian's height = 165 cm

Extra height = Diana's height - required height of the ride

Extra height = 165 cm - 150 cm

Extra height = 15 cm

Hence, in this supposed situation, Diana's height is 15 cm extra than the required height of the ride.

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Write an equation of the parabola that has the same shape as the graph of f(x) = 4x², but with the point (10,4) as the vertex.

Answers

An equation of the parabola that has the same shape as the graph of f(x) = 4x², but with the point (10,4) as the vertex is y = 4x² - 80x + 404.

What is the vertex form of the parabola?The standard vertex form of the parabola is given by,

             y = a(x - h)² + k  where (h, k) is the vertex.

Real numbers, a, h, and k are included here, where a ≠ 0. A point on the parabola is represented by the variables x and y, respectively.

Given:

f(x) = 4x²

Vertex =  (10,4)

a = 4

The value of a in the vertex form of the equation is taken to be 4 since the coefficients of x² must match for the parabola to have the same shape as the given parabola.

The equation can be written as,

y = a(x - h)² + k  where (h, k) is the vertex.

Replacing the value of the vertex, we get

y = 4(x - 10)² + 4

y = 4(x² - 20x + 100) + 4

y = 4x² - 80x + 400 + 4

y = 4x² - 80x + 404

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Anita's, a fast-food chain specializing in hot dogs and garlic fries, keeps track of the proportion of its customers who decide to eat in the restaurant (as opposed to ordering the food "to go"), so it can make decisions regarding the possible construction of in-store play areas, the attendance of its mascot Sammy at the franchise locations, and so on. Anita reports that 48% of its customers order their food to go. If this proportion is correct, what is the probability that, in a random sample of 50 customers at Anita's, exactly 3 order their food to go?

Answers

The probability that, in a random sample of 50 customers at Anita's, exactly 3 order their food to go is 0.3240

Probability:

The probability of an event can be calculated by probability formula by simply dividing the favorable number of outcomes by the total number of possible outcomes.

The value of the probability of an event to happen can lie between 0 and 1 because the favorable number of outcomes can never cross the total number of outcomes.

Given,

Anita's, a fast-food chain specializing in hot dogs and garlic fries, keeps track of the proportion of its customers who decide to eat in the restaurant (as opposed to ordering the food "to go"), so it can make decisions regarding the possible construction of in-store play areas, the attendance of its mascot Sammy at the franchise locations, and so on. Anita reports that 48% of its customers order their food to go.

Here we need to find the probability that, in a random sample of 50 customers at Anita's, exactly 3 order their food to go.

Let us consider this as,

Binomial Problem with

n = 5 and

By converting the percentage into decimal value,

=> 48/100 = 0.48

p(to go) = 0.48

Then the value is,

P(x=3) = 5C3(0.52)^3*(0.48)2

P(x=3) = 0.3240

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fcbdxfhbdxfnxfgmndfgxhbnxf

Answers

ANSWER:

A. The midline of the function is y = 2

STEP-BY-STEP EXPLANATION:

we can determine the answer from the graph, just like this:

Therefore, the only correct option is A. The midline of the function is y = 2

Rick's car gets 29.7 miles per gallon on the highway. If his fuel tank holds 10.45 gallons, then how far can he travel on one full tank of gas?

Answers

We will investigate how to use the mileage meter of a car to determine the amount of distance a car can travel per given fuel.

Mileage is a economic performance parameter of a car that gives the fuel economy. It is usually expressed as a ratio of:

[tex]\text{Mileage = }\frac{Total\text{ Distance Travelled}}{Total\text{ Fuel consumed}}[/tex]

The mileage of a car is given as follows:

[tex]\text{Mileage = 29.7 }\frac{miles}{gallon}[/tex]

We can say that this car can travel 29.7 miles per gallon on highway.

We now stop at the petrol station for re-fueling. We fuel up the car to:

[tex]\text{Fuel = 10.45 gallons}[/tex]

We need to determine the distance that this car can travel for the amount of re-fueling. This is where we can use the mileage to determine the distance the car can travel as follows:

[tex]\begin{gathered} \text{Distance = Mileage}\cdot Fuel \\ \end{gathered}[/tex]

Plug in the respective quantitites and solve for the distance that the car can travel as follows:

[tex]\begin{gathered} \text{Distance = 29.7}\frac{miles}{gallon}\cdot10.45\text{ gallons} \\ \\ \textcolor{#FF7968}{Dis\tan ce}\text{\textcolor{#FF7968}{ = 310.365 miles}} \end{gathered}[/tex]

For the amount of re-fueling the distance travelled is 310.365 miles

Please help me find the horizontal asymptote.

Answers

Answer:

[tex]y=3/2[/tex]

Step-by-step explanation:

[tex]f(t)=\frac{3t^{1/3}}{(64t^2 +4)^{1/6}} \\ \\ =\frac{3}{(64+4t^{-2})^{1/6}} \\ \\ \\ \lim_{t \to \infty} f(t)=\frac{3}{64^{1/6}}=3/2 \\ \\ \\ \lim_{t \to -\infty} f(t)=\frac{3}{64^{1/6}}=3/2 \\ \\ \therefore y=3/2[/tex]

Write an equation in slope-intercept form of the lime that passes through the point(6,2) and is perpendicular to y=-2x+5

Answers

Consider that the slope-intercept of a line is given by,

[tex]y=mx+c[/tex]

Here, 'm' is the slope and 'c' is the y-intercept of the line.

The equation of the given line is,

[tex]y=-2x+5[/tex]

Comparing the coefficients, it can be observed that the slope of the given line is -2,

[tex]m=-2[/tex]

It is asked to determine the equation of line perpendicular line to this given line.

Let the slope of this perpendicular line be 'k'. Then, the equation of this perpendicular line will take the form,

[tex]y=kx+c^{\prime}[/tex]

Theorem: The product of slopes of perpendicular lines is -1.

[tex]\begin{gathered} k\cdot m=-1 \\ k\cdot(-2)=-1 \\ k=\frac{-1}{-2} \\ k=\frac{1}{2} \end{gathered}[/tex]

Now, the equation becomes,

[tex]y=\frac{1}{2}x+c^{\prime}[/tex]

Consider that any point lying on the line must satisfy the equation of that line.

So the point (6,2) must also satisfy the equation of the perpendicular line,

[tex]\begin{gathered} 2=\frac{1}{2}(6)+c^{\prime} \\ 2=3+c^{\prime} \\ c^{\prime}=2-3 \\ c^{\prime}=-1 \end{gathered}[/tex]

Substitute the values of 'k' and c' in the equation,

[tex]\begin{gathered} y=\frac{1}{2}x+(-1) \\ y=\frac{1}{2}x-1 \end{gathered}[/tex]

Thus, the required equation of the line is obtained as,

[tex]y=\frac{1}{2}x-1[/tex]

You are multiplying as many 5s and 2s as you want but you must have at least one of each. What could the last digit of the product be?

Answers

The last digits of multiplying 5s and 2s with at least one of each will be zero (0)

Multiplication of numbers

From the question, we are to determine what the last digit of the product could be

From the given information,

We are multiplying as many 5s and 2s as we want but we must have at least one of each

Since we must have at least one of each of 5 and 2, we will always have a 5 × 2

But, 5 × 2 = 10

NOTE: 10 multiplied by any number will always result in a number with a last digit of zero (0)

Example

2 × 5 × 2 × 2 × 2 × 2 = 160

5 × 2 × 5 × 5 × 5 × 5 = 6250

Thus, the last the digit of the product will be 0

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Solve for x and simplify the answer

2x^2+2x=-3

Answers

Answer:
x∈/R

AKA: No Real Solution

9. Please help. Thank you

Answers

Explanation

By definition, a one-to-one function is a function that maps distinct elements of its domain to distinct elements of its codomain.

Graph 1

From this graph, we see that for distinct elements of x, we have the same value of y. For example:So this function is NO a one-to-one function.

• f(2) = f(-2) = 4.

T

Graph 2

From this graph, we see that for distinct elements of x, we have the same value of y. For example:is function is NO a one-to-one function

• f(2) = f(4) = 4.

Th.

Graph 3

From this graph, we see that for distinct elements of x, we have different values of y.This function is a one-to-one function.

Graph 4

From this graph, we see that for distinct elements of x, we have different values of y.This function is a one-to-one function.

Graph 5

From this graph, we see that for distinct elements of x, we have different values of y.This function is a one-to-one function.

Graph 6

From this graph, we see that for distinct elements of x, we have the same value of y.This function is NO a one-to-one function.

Answer

• Graph 1: No

,

• Graph 2: No

,

• Graph 3: Yes

,

• Graph 4: Yes

,

• Graph 5: Yes

,

• Graph 6: No

What is the equation of the parabola with focus at (1, 1) and directrix y = -1?

Answers

The equation of the parabola having focus (1,1) and directix y = -1 is

y = x²/4 - x/2 + 1/4

The focus of the parabola (h , k + p) = (1,1)

The directrix of the parabola is y = -1

From, the focus

           k + p = 1

           k = 1 - p

The formula of directrix is

              y = k - p                                                    (1)

Substituting the value of directrix and k

              -1 = 1 -p -p

              -1-1 = -2p

               -2 = -2p

               p = 1

Substituting the value p in equation (1)

                k = 0

Now, we have got the vertex of the parabola (h ,k) is (1,0)

The equation of the parabola is

    (x-h)² = 4p (y - k)

     (x - 1)² = 4 (1) (y - 0)

     ( x -1 )² = 4(y )

     x² - 2x + 1 = 4y

     x²/4 - 2x/4 + 1/4 = y

    y = x²/4 - x/2 + 1/4

which is the equation of the parabola.

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In his music class, Mr. Thompson played short samples of 80 classical pieces of music. The students were able to identify 16 of the pieces.
What percent of the classical pieces did the students identify?

Answers

The students were able to identify 16 of the pieces out of 80 which is 20 % in the percentage form.

What is the percentage?

The percentage is defined as a ratio expressed as a fraction of 100.

For example, If Saima obtained a score of 57% on her exam, that corresponds to 67 out of 100. It is expressed as 57/100 in fractional form and as 57:100 in ratio form.

The students were able to identify 16 of the pieces out of 80.

We have to determine the percentage of the classical pieces the students identify.

As per the given information, the required solution would be as:

⇒ (16/80) × 100

⇒ (0.20) × 100

⇒ 20 %

Therefore, the percentage of the classical pieces the students identify would be 20 %.

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number 7 please help mequestions: find the sum of each infinite geometric serie

Answers

The sum to infnity of the series is;

[tex]S\infty\text{ = 1,066}\frac{2}{3}[/tex]

Here, we want to find the sum to infinity of the given geometric series

We have this as follows;

[tex]S_{\infty}\text{ =}\frac{a}{1-r}[/tex]

a is the first term which is 800

The common ratio is r and it is the second term divided over the first or the third over the second

We have this as;

[tex]\frac{200}{800}\text{ = }\frac{50}{200}\text{ = }\frac{1}{4}\text{ =0.25}[/tex]

Substituting these values, we have it that;

[tex]S_{\infty}\text{ = }\frac{800}{1-0.25}\text{ = }\frac{800}{0.75}\text{ = 1,066 }\frac{2}{3}[/tex]

ZA and ZB are supplementary angles. If m/A= (7x - 20)° and
m/B = (2x - 7)°, then find the measure of ZB.

Answers

Answer:

Measure of angle B = 39

Step-by-step explanation:

(7x-20) + (2x-7) = 180 (combime like terms)

9x - 27 = 180 (move 27 to the other side)

9x = 207 (divide both sides by 9)

x = 23

2x - 7 (subsititute x with 23)

2 (23) - 7

46 - 7

39

measure of angle b = 39

will post a full pictures it did not fit

Answers

They will be parallel because the same transformations have been applied to it

Mary multiplied a number by-3.When she added the result to 6,she got 12. What is her number?

Answers

Explanation

Step 1

set the equation

a) let x represents the number

[tex]number=x[/tex]

b) now , translate

[tex]i)Mary\text{ multiplied a number by 3}\Rightarrow x*3=3x[/tex]

then

[tex]\begin{gathered} ii)shed\text{ added the result to 6} \\ 3x+6 \end{gathered}[/tex]

finally

[tex]\begin{gathered} iii)\text{ she got 12, hence} \\ 3x+6=12 \end{gathered}[/tex]

therefore, the equation is

3x+6=12

Step 2

now, solve the equation

[tex]3x+6=12[/tex]

The subtraction property of equality states that if the same number is subtracted from both sides of an equation, then the equality still holds, so we can subtract 6 in both sides in order to isolate the term where x is, hence

[tex]\begin{gathered} 3x+6=12 \\ 3x+6-6=12-6 \\ 3x=6 \end{gathered}[/tex]

finally, apply the division property of equality and divide both sides by 3

[tex]\begin{gathered} 3x=6 \\ \frac{3x}{3}=\frac{6}{3} \\ x=2 \end{gathered}[/tex]

so, the number is 2

I hope this helps you

Which function is shown in the graph? A. f(x) = x2 – 3x – 10 B. f(x) = x2 + 3x – 10 C. f(x) = x2 + x - 12 D. f(x) = x2 – 5x – 8

Answers

Explanation:

The graph shown have roots of x = -2 and x = 5

We could solve for x in each of the quadratic equations or we could plot the graphs of each of the quadratic equation.Then we pick the one with the roots of -2 and 5.

Plotting the graphs:

The roots of quadratic functionis the value of x when y is equal to zero.

From the graph attached above, f(x) = x² + 3x – 10 representing the blue parabola has roots of (-5, 0) and (2, 0).

This means the roots are -5 and 2.

Hence, the function in the graph is f(x) = x² + 3x – 10

Your local library holds a penny drive in which people in the community are asked to donate their spare pennies to the library. When you stop by to donate some pennies, you hear someone announce that she plans to donate pennies for one month in the following manner: she will donate 1 penny today, 2 pennies tomorrow, 4 pennies the next day, and will continue to double the number of pennies that she donates each day thereafter.

Answers

The amount donated by the person follows a geometric progression, which is given by an exponential function.

First part:

The relationship between the amount donated and the day of the month is not a constant rate relationship

Second part;

Please find attached the graph of the Amount Donated to the Days which is shaped as the graph of an exponential equation

What is an exponential function?

An exponential function is one in which the input variable is an index of a constant

A constant rate relationship is one in which at all points of the function, the ratio of the output to input stays the same or is a constant.

The given parameters are;

The Pennies a person plans to donate to the library on each day of the month, is given by the following table;

Day. Amount Donated

1. 1

2 2

3 4

4 8

First part

Required;

If the relationship between the day and the amount donated is a constant rate relationship

Solution;

Given that we have;

1/1 = 2/2 ≠ 4/3 ≠ 8/4, the relationship between the day of the month and the amount donated is not a constant rate relationship

Second part;

The shape of the graph of Day to the Amount Donated

Solution;

The sequence of the day has a constant difference of one day, which is given by the equation;

U = 1 × n

Where;

U = The day of the month

n = The number of days

The sequence for the amount donated is given by the exponential function;

S = a•r^n

Where;

a = The first term = 1

r = The common ratio = 2

U = The number of days

The graph of Amount Donated to the Days is therefore the graph of an exponential function, please see the attached graph of Amount Donated to the Day of the month

The possible questions obtained from a similar question are;

First part; If the amount donated and the days have a constant rate relationship

Second part; The shape of the graph of the Amount Donated to the Day of the month

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Tyler was making a meal for his family. For every 3/4 pound of beef, the recipe calls for 9/8 cups of broccoli. How many cups of broccoli would be needed for a pound of beef?

a1/2 cup of broccoli per beef

b2/3 pound of broccoli per beef

c1 and ½ cup of broccoli per beef

d5/4 cup of broccoli per beef

Answers

The number of cups of broccoli that would be needed for a pound of beef is C. 1 1/2 cup of broccoli per beef.

How to calculate the value?

From the information, it was stated that Tyler was making a meal for his family and that for every 3/4 pound of beef, the recipe calls for 9/8 cups of broccoli.

Therefore, the cups of broccoli that would be needed for a pound of beef will be:

3/4/1 = 9/8/x.

where x = cups of broccoli

Cross multiply

3/4x = 9/8

x = 9/8 ÷ 3/4

x = 9/8 × 4/3

x = 3/2

x = 1 1/2cups

Therefore, the correct option is C.

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Answer:

[tex]\textsf{c) \quad $1 \frac{1}{2}$ cups of broccoli per 1 lb of beef}.[/tex]

Step-by-step explanation:

Given information:

For every ³/₄ lb of beef, the recipe calls for ⁹/₈ cups of broccoli.

Create a ratio of pounds of beef to cups of broccoli, where x is the number of cups of broccoli to one pound of beef:

[tex]\implies \dfrac{3}{4}: \dfrac{9}{8}=1:x[/tex]

[tex]\implies \dfrac{\frac{3}{4}}{\frac{9}{8}}=\dfrac{1}{x}[/tex]

Cross multiply:

[tex]\implies \dfrac{3}{4}x=\dfrac{9}{8}[/tex]

[tex]\implies x=\dfrac{9}{8} \div \dfrac{3}{4}[/tex]

To divide fractions, flip the second fraction (make the numerator the denominator, and the denominator the numerator) then multiply it by the first fraction:

[tex]\implies x=\dfrac{9}{8} \times \dfrac{4}{3}[/tex]

[tex]\implies x=\dfrac{9 \times 4}{8 \times 3}[/tex]

[tex]\implies x=\dfrac{36}{24}[/tex]

[tex]\implies x=\dfrac{3 \cdot \diagup\!\!\!\!\!\!12}{2 \cdot \diagup\!\!\!\!\!\!12}[/tex]

[tex]\implies x=\dfrac{3}{2}[/tex]

[tex]\implies x=1 \frac{1}{2}[/tex]

Therefore, 1¹/₂ cups of broccoli would be needed to one pound of beef.

What is the missing angle

Answers

Answer:

45 degrees

Step-by-step explanation:

The triangle is a 45, 45, 90 meaning that both angles other than the 90 are the same.

Another way to solve is you know that a triangle's angles = 180

Take the 180 and subtract 90 for the right angle

and then subtract 45 for the labeled angle and your answer is 45

Throughout the 2016 Presidential election primaries, Millennials (those aged 20 t 36 years)
consistently supported Senator Bernie Sanders over Secretary Hillary Clinton. According to the
2016 Gallup poll of 1,754 Millenials, 55% had a favorable opinion of Sanders than Hillary Clinton
(38%). Calculate the 90% confidence interval for for Hillary Clinton.
*round to two decimals
The 90% confidence interval for Hillary Clinton is
to

Answers

Answer:

favorable opinion of Sanders than Hillary Clinton

(38%). Calculate the 90% confidence interval for for Hillary

4m

Giana has started collecting sea shells. Every month she adds 66​ new shells to her collection. After 66​ months of collecting, she has 3838​ shells in her collection. Using this information, create an equation written in point-slope form that models the amount of shells y​ in Giana’s collection after x​ months

Answers

She has 3838 shells in her collection after 66 months of gathering. The equation using this data is 33x+33y=1919.

Given that,

Giana has begun to gather seashells. She grows her collection by 66 new shells each month. She has 3838 shells in her collection after 66 months of gathering.

We have to create an equation using this data that models the number of shells y Giana's collection will include after x months in point-slope form.

We can write as

The total number of shells she collected =(The amount of shells she collect each month)×y+(The month of collecting the shells)×x

3838=66y+66x

66x+66y=3838

33x+33y=1919

Therefore, the equation using this data that models the number of shells Giana's collection will include after x months in point-slope form is 33x+33y=1919.

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Answer: give correct answers only or people on here will do the same thing u did to them bozo

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What is the slope of the line that passes through the points (9,1) and (10,−1)? Write your answer in simplest form.

Answers

The slope of the linear equation that passes through the points (9,1) and (10,−1) is -2.

How to get the slope of the line?

For a linear equation that goes through two points (x₁, y₁) and (x₂, y₂), the slope is given by the formula:

slope = (y₂ - y₁)/(x₂ - x₁)

In this case, we know that our line goes through the points (9,1) and (10, −1), so we can use these two values in the equation for the line, we will get:

slope = (-1 - 1)/(10 - 9) = -2/1 = -2

So the slope of the linear equation is -2.

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For the following situation make an input- output table

The nearby amusement park charges $15 for admission, which includes 5 rides.
After 5 rides, each extra ride costs $1.50. The input, r, is the number of rides you
take. The output, c, is the total cost for the day at the amusement park. Let r = 0, r
3, 5, 6, 10, and 15 rides.

Answers

The input- output table for the total cost of the amusement park charges is made.

What is defined as the linear equation?A linear equation is just an algebraic expression of a form y=mx+b, according to Wolfram MathWorld involving just a constant and a first-order (linear) term, for which m represents the slope and b represents the y-intercept. The above is sometimes referred to as a "linear equation of two variables," in which y and x are the variables.

For the given question;

The admission charge of the amusement park = $15 (including 5 rides).

For extra rides $1.50 per ride.

Let r be the total rides.

Let n be the extra rides above 5 rides.

Let C be the total cost of the ride.

Then, the liner equation forming the condition is;

C = 1.5n + 15.

For n = 1, 2 , 3...

The value of C will be determined.

Thus, the input- output table for the total cost of the amusement park charges is made.

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