Willis analyzed the following table to determine if the function it represents is linear or non-linear. First he found the differences in the y-values as 7 – 1 = 6, 17 – 7 = 10, and 31 – 17 = 14. Then he concluded that since the differences of 6, 10, and 14 are increasing by 4 each time, the function has a constant rate of change and is linear. What was Willis’s mistake?

9514 1404 393

Answer:

Step-by-step explanation:

The general shape of "up to the right" tells you this is an odd-degree polynomial with a positive leading coefficient. As such, the value of f(x) will have the same sign as the value of x when x gets large. The end behavior could be described by ...

  lim[x → -∞] f(x) → -∞

  lim[x → ∞] f(x) → ∞

__

The curve crosses the x-axis 3 times and touches it once without crossing. Each crossing is a real zero. Each touch is a a real zero with an even multiplicity. The shape (flatness) of the touch gives a clue as to the multiplicity. (Flatter means higher multiplicity.) Here the shape indicates the zero has a multiplicity of 2.

So, there are 4 distinct real zeros, one with a multiplicity of 2, for a total of 5 real zeros.

_____

Additional comment

An even-degree polynomial function has a generally U shape. If the leading coefficient is negative, the U is upside down: ∩. An even-degree polynomial will have the limits of f(x) having the same sign, regardless of the sign of x.

Answer:

just multiply 1.50 by the number of bottles and thats your answer

Answer:

-2

Step-by-step explanation:

The initial value on a graph is the value of y when x = 0.

x is how far to the right or left a point on the graph is, so when x is not to the right or left at all, it is at the point 0.

y is how far a point is up or down, so, as shown on the graph, when x is 0, y is -2.

Answer:

f(-3)=-8

Step-by-step explanation:

plug -3 in as x

-4(-3+5)

12-20

-8

The question is incomplete:

Netlfix charges $30 a month plus $5 per movie. Hulu charges $26 a month plus $7 per movie. How many movies will you need to watch for the Netflix membership to pay off and cost you less?

Answer:

3 movies

Step-by-step explanation:

From the information given, you can write an inequality that indicates that Netflix membership costs less than Hulu membership:

30+5x<26+7x

Now, you can solve for x:

30-26<7x-5x

4<2x

4/2<x

x>2

According to this, the answer is that you will need to watch 3 movies for the Netflix membership to pay off and cost you less.

Answer:

76 if you add it all together for the f6g

There are no possible real values for the first term 'a' that satisfy both equations.

Let's denote the first term of the geometric progression as 'a' and the common ratio as 'r'.

The sum of the first two terms can be expressed as:

a + ar = 16

To find the sum to infinity, we can use the formula:

Sum to infinity = a / (1 - r)

Given that the sum to infinity is 25, we have:

25 = a / (1 - r)

We now have two equations:

a + ar = 16

a / (1 - r) = 25

We can solve these equations simultaneously to find the possible values of 'a'.

From the first equation, we can factor out 'a' to get:

a(1 + r) = 16

Dividing both sides of the second equation by 25, we have:

a / (1 - r) = 1

We can rearrange this equation to get:

a = 1 - r

Substituting this expression for 'a' in the first equation, we get:

(1 - r)(1 + r) = 16

Expanding the equation, we have:

1 - r^2 = 16

Rearranging the terms, we get:

r^2 = -15

Since we are dealing with a geometric progression, the common ratio 'r' must be a real number. However, we observe that r^2 = -15 has no real solutions. Therefore, there are no possible real values for the first term 'a' that satisfy both equations.

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Answer: It's D.

Step-by-step explanation:

As you see when you +,-,x fractions, it's easier to -,+,x fractions by fractions.

Answer:

C

Step-by-step explanation:

I think it is C because you can multiply the negatives together

The initial equation is:

X + 5 = 11

Subtracting 5 on both sides of the equation:

X + 5 - 5 = 11 - 5

X = 6

Answer:

  1.147×10^-2 cm

Step-by-step explanation:

You want the difference between the two values 1.87×10^-2 and 7.23×10^-3 expressed in scientific notation.

Addition and subtraction of numbers in scientific notation requires that the multipliers have the same exponent. That exponent can be chosen so no adjustment of the exponent is required in the answer.

  \(1.87\times10^{-2}-7.23\times10^{-3}= 1.87\times10^{-2}-0.723\times10^{-2}\\\\=(1.87-0.723)\times10^{-2}=\boxed{1.147\times10^{-2}}\)

This measurement is in centimeters.

__

Additional comment

A calculator or spreadsheet can accept input and display results in scientific notation.

The difference in the diameter of of G and H is 1.147x 10⁻² cm

What are mathematics operations?

• An operation is a function in mathematics that converts zero or more input values (also known as "operands" or "arguments") to a well-defined output value.

• The operation's arity is determined by the number of operands.

• Binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, are the most commonly studied operations.

• A zero-arity operation, also known as a nullary operation, is a constant.

• The mixed product is an example of an arity 3 operation, also known as a ternary operation.

it is given that :

the diameter of cell G is = 1.87 x 10⁻² cm

the diameter of cell H is = 7.23 x 10⁻³ cm

Now, to find the difference between the diameter of two cells simply subtract the diameter of cell G and H :

difference in the diameter of of G and H = 1.87 x 10⁻² cm - 7.23 x 10⁻³ cm

difference in the diameter of of G and H=1.87 x 10⁻² cm - 0.723 x 10⁻² cm

                                                                  = 1.147x 10⁻² cm

Therefore, the difference in the diameter of of G and H is 1.147x 10⁻² cm

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Answer:

\(w^{22}\)

Step-by-step explanation:

\((w^3)^4\cdot(w^5)^2=w^{3*4}\cdot w^{5*2}=w^{12}\cdot w^{10}=w^{12+10}=w^{22}\)

When x is equal to 1, the Function f(x) = -4x - 5 yields a value of -9.

The find ƒ(1) for the function f(x) = -4x - 5, we need to substitute x = 1 into the function and evaluate the expression.

Replacing x with 1, we have:

ƒ(1) = -4(1) - 5

Simplifying further:

ƒ(1) = -4 - 5

ƒ(1) = -9

Therefore, when x is equal to 1, the value of the function f(x) = -4x - 5 is ƒ(1) = -9.

Let's break down the steps taken to arrive at the solution:

1. Start with the function f(x) = -4x - 5.

2. Replace x with 1 in the function.

3. Evaluate the expression by performing the necessary operations.

4. Simplify the expression to obtain the final result.

In this case, substituting x = 1 into the function f(x) = -4x - 5 gives us ƒ(1) = -9 as the output.

It is essential to note that the notation ƒ(1) represents the value of the function ƒ(x) when x is equal to 1. It signifies evaluating the function at a specific input value, which, in this case, is 1.

Thus, when x is equal to 1, the function f(x) = -4x - 5 yields a value of -9.

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To divide 30 into five parts such that the first and last parts are in the ratio of 2:3, we can follow these steps:

1. Determine the ratio between the first and last parts. In this case, it is 2:3.

2. Add the ratio values together to find the total number of parts: 2 + 3 = 5.

3. Divide the total value (30) by the total number of parts (5) to find the value of each part: 30 / 5 = 6.

4. Multiply the value of each part by the respective ratio values to obtain the individual parts:

- First part: 2 * 6 = 12

- Second part: 6

- Third part: 6

- Fourth part: 6

- Last part: 3 * 6 = 18

Therefore, the five parts of 30, with the first and last parts in the ratio of 2:3, are 12, 6, 6, 6, and 18.

Answer:

its b

Step-by-step explanation:

took the test on edge

The value of x is 14.

We know in an isosceles triangle an isosceles polygon is a polygon with at least two sides of equal length.

We have two sides measured 2x-9 and x+ 5.

From the figure the length of sides are equal then

2x-9 = x+ 5

2x- 9- x = 5

x-9 = 5

Add 9 to both sides of the equation:

x - 9 + 9 = 5 + 9

x= 14

Thus, the value of x is 14.

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Answer:

The expression is (80w+300)

Step-by-step explanation:

Let

y ----> the total amount of money in both accounts

s ----> the amount of money in saving account

c ----> the amount of money in checking account

w ----> the number of weeks

we know that

saving account

s=50w+200 -----> equation A

checking account

c=30w+100 ----> equation B

To find out the total amount of money in both accounts, sum equation A and equation B

y=s+c

substitute

y=(50w+200)+(30w+100)

y=(50w+30w)+(200+100)

y=80w+300

therefore

The expression is (80w+300)

The vertex of the graph is a maximum at (-2, 4)

From the question, we have the following parameters that can be used in our computation:

The graph

The graph is a quadratic function

From the graph, we can see that the graph has a maximum value

This maximum value represents the vertex of the graph

And it is located at (-2, 4)

So, we have

Maximum = (-2, 4)

Hence, the maximum value of the function is (-2, 4)

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The graph of the linear inequality y ≥ 2x - 5 is attached below with it's shaded part included.

The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality.

In the given problem, the inequality presented is;

y ≥ 2x - 5

To graph this, we would use a graphing calculator to find the boundary lines and plane.

In the graph below, the x and y intercept is at (2.5, -5) and the shaded part is on the left side of the graph.

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The width of the basketball court is 10 meters

The area of the basketball court = \(30\sqrt{20}\) meter square

The length of the basketball court = \(6\sqrt{5}\) meter

The basketball is in rectangular shape. So we have to find the width of the rectangle

The area of the rectangle = The length of the rectangle × The width of the rectangle

The width of the rectangle = The area of the rectangle / The length of the rectangle

Substitute the values in the equation

The width of the rectangular basketball court = \(30\sqrt{20}\) ÷ \(6\sqrt{5}\)

Divide the terms

= 10 meters

Hence, the width of the basketball court is 10 meters

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Answer:

Option 4

Step-by-step explanation:

The domain of this function is the possible values of n that are suitable for this function. Since n represents a number of vehicles, the domain of n should be a whole number (since you cannot have a negative number of vehicles or half of a vehicle).

hope this helps :)

Answer:

1

Step-by-step explanation:

i bet u its right

Answer:

D. x = 1

Step-by-step explanation:

i got it right

Answer:

h=3.83

Step-by-step explanation:

6.51 - 9.32 + h = 1.02         --> first, subtract: 6.51 - 9.32

-2.81+h=1.02                    --> add 2.81 to both sides

h=3.83                                     --> answer

Answer:

the answer is 41 degrees

Just subtract

180-139

=41

(Please katie im not doing anything wrong)

Step-by-step explanation:

Answer:

∠x=41°

Step-by-step explanation:

Supplementary Angles are angles that equal 180°

1. Use the equation

∠x+∠y=180°

2. Fill in the given values

∠x+139°=180°

3. Solve

Subtract 139 from both sides

∠x+139°=180°

      -139° -139°

4. Answer

∠x=41°

Answer:

the relationship between them is 7

Step-by-step explanation:

3x7=21   21÷7=3 etc

4x7=28    

5x7=35

6x7=42

Answer:

7

Step-by-step explanation:

3×7=21

4×7=28

5×7=35

6×7=42

Answer: Log9,(11/7)^4

Step-by-step explanation:

according to the rules of logarithm

1)Subtraction sign(-) becomes division(÷),while addition(+)becomes multiplication (x)

2) the number in front of the log figure becomes an indices

Answer:

log9 (11/7)4

Step-by-step explanation:

got it right on the test

By answering the presented question, we may conclude that As a result, the slope of \(y_3\) = -4(x - 5) is -4.

The slope of a line indicates how steep it is. The term "gradient overflow" refers to a mathematical equation for the gradient (the change in y divided by the change in x).

The slope is defined as the ratio of the vertical change (rise) between two places to the horizontal change (run). The slope-intercept form of an equation is used to express a straight line's equation, which is written as y = mx + b.

The y-intercept is found where the slope of the line is m, b is b, and (0, b). For example, the slope and y-intercept of the equation y = 3x - 7 (0, 7). The slope of the line is m. b is b at the y-intercept, and (0, b).

The above equation is in point-slope form: y - \(y_1\)= m(x - \(x_1\)), where (\(x_1\), \(y_1\)) is a point on the line and m is the slope.

We can see by comparing the provided equation to the point-slope form that \(x_{1} ,y_1\)) = (5, 3) and m = -4.

As a result, the slope of \(y_3\) = -4(x - 5) is -4.

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Answer:

A. a. 34.5 feet

b. 60 feet

Step-by-step explanation:

Parabola equation

\(y=-0.005x^2+0.3x\)

Differentiating with respect to x we get

\(\dfrac{dy}{dx}=-0.01x+0.3\)

Equating with zero

\(-0.01x+0.3=0\\\Rightarrow -0.01x=-0.3\\\Rightarrow x=\dfrac{0.3}{0.01}\\\Rightarrow x=30\)

Double derivative of the parabolic equation

\(\dfrac{d^2y}{dx^2}=-0.01<0\)

So, \(x=30\) is maximum.

\(y=-0.005\times 30^2+0.3\times 30\\\Rightarrow y=4.5\)

So, the maximum height of the arch will be 4.5 feet.

From the ground the highest point of the arch will be \(30+4.5=34.5\ \text{ft}\)

We are taking the x axis as the width of the bank.

\(0=-0.005x^2+0.3x\\\Rightarrow 0.005x^2=0.3x\\\Rightarrow x=\dfrac{0.3}{0.005}\\\Rightarrow x=60\)

So, the width of the bank will be 60 feet.

Answer:

He would spend $5,200 a year.

Step-by-step explanation:

32,500 x 0.16 = 5,200