Leslie analyzed the graph to determine if the function it represents is linear or non-linear. First she found three points on the graph to be (–1, –4), (0, -3), and (2, 5). Next, she determined the rate of change between the points (–1, –4) and (0, -3) to be StartFraction negative 3 minus (negative 4) Over 0 minus (negative 1) EndFraction = StartFraction 1 Over 1 EndFraction = 1. and the rate of change between the points (0, -3) and (2, 5) to be StartFraction 5 minus (negative 3) Over 2 minus 0 EndFraction = StartFraction 8 Over 2 EndFraction = 4. Finally, she concluded that since the rate of change is not constant, the function must be linear. Why is Leslie wrong?

A. The points (–1, –4), (0, –3), and (2, 5) are not all on the graph.
B. The expressions StartFraction negative 3 minus (negative 4) Over 0 minus (negative 1) EndFraction and StartFraction negative 3 minus (negative 5) Over 2 minus 0 EndFraction both equal 1.
C.She miscalculated the rates of change.
D.Her conclusion is wrong. If the rate of change is not constant, then the function cannot be linear.

The correct answer is B. The graph of h is the graph of g vertically shifted up 1 unit.

The correct answer is:

B. The graph of h is the graph of g vertically shifted up 1 unit.

Explanation:

The original function g(x) = x² represents a basic quadratic function, which is a parabola that opens upward and has its vertex at the origin (0, 0).

When we consider the function h(x) = g(x) + 1, we are adding a constant value of 1 to the output (y) values of the function g(x). This results in a vertical shift of the graph of g(x) by 1 unit upward.

In other words, for every x-value, the corresponding y-value of the function h(x) will be 1 unit higher than the corresponding y-value of the function g(x).

Visually, this means that the graph of h(x) will be the same shape as the graph of g(x), but it will be shifted upward by 1 unit. The vertex of the parabola, which was originally at the origin, will now be at (0, 1).

The statement "The graph of h is the graph of g horizontally shifted left 1 unit" (Option A) is incorrect because there is no horizontal shift in this transformation.

The statement "The graph of h is the graph of g vertically shifted down 1 unit" (Option B) is incorrect because the transformation results in a vertical shift upward, not downward.

The statement "The graph of h is the graph of g horizontally shifted right 1 unit" (Option D) is incorrect because there is no horizontal shift in this transformation.

Therefore, the correct answer is B. The graph of h is the graph of g vertically shifted up 1 unit.

for more such question on graph visit

https://brainly.com/question/19040584

#SPJ8

The first four terms of the Maclaurin series of f(x) are f(x) is \(9 - 4x + 6x^2 + (11x^3)/6\)

To find the Maclaurin series of a function f(x) given its derivatives at x = 0, we can use the following formula:

f(x) = f(0) + f'(0)x + (f''(0)x^2)/2! + (f'''(0)x^3)/3! + ...

Given the values f(0) = 9, f'(0) = -4, f''(0) = 12, and f'''(0) = 11, we can substitute these values into the formula to find the first four terms of the Maclaurin series:

f(x) = 9 + (-4)x + (12x^2)/2! + (11x^3)/3!

Simplifying each term, we have:

f(x) \(= 9 - 4x + 6x^2 + (11x^3)/6\)

Therefore, the first four terms of the Maclaurin series of f(x) are:

f(x) \(= 9 - 4x + 6x^2 + (11x^3)/6\)

It's important to note that this series is an approximation of the function f(x) near x = 0. As we include more terms in the series, the approximation becomes more accurate.

Learn more about Maclaurin series here

https://brainly.com/question/28170689

#SPJ11

The most appropriate statement that expresses a possible relationship between the variables, rate of pedaling and speed of a bicycle, is option A: "As the rate of pedaling increases, the speed of a bicycle increases."

This statement suggests that there is a positive correlation between the rate of pedaling and the resulting speed of the bicycle. When a cyclist pedals faster, it generates more force and power, translating into increased speed. This relationship aligns with basic principles of physics, as a greater input of energy and effort through pedaling leads to a higher velocity or speed output.

Option B implies that decreasing bicycle speed necessitates an increase in the rate of pedaling, and option C indicates that increasing bicycle speed is associated with a decrease in the rate of pedaling.

Learn more about variables here : brainly.com/question/28997695

#SPJ11

Answer:

y= (3/4)x +1

Step-by-step explanation:

The width of the border is 1/2 feet

From the information given, we have that;

Cherry wood of area to border and surrounded glass of area 9 square feet.

The combined area will be area of glass + area of the border made from cherry wood

The total area of coffee table would be ;

= 9 + 7 = 16 square feet.

Since the center glass piece is a square thus the surrounding border of cherry wood also would be of square shape.

So each side of the square is √16 = 4 feet

Outside of cherry border has 4 feet length and width while the inside of cherry border, which is same as the length and width of glass is 3 feet.

The difference is 4 -3 = 1 feet

Since border is on both sides therefore the width of the border= 1/2 feet

Learn more about area at: https://brainly.com/question/25292087

#SPJ1

In a hyperbolic plane, a Lambert quadrilateral ABCD with right angles at A, B, and C. This result tells us about the properties of hyperbolic geometry.

In hyperbolic geometry, the sum of angles in a triangle is less than 180 degrees, which means that a right angle is acute. Therefore, in a Lambert quadrilateral ABCD, angle D is acute. Additionally, in hyperbolic geometry, parallel lines diverge from each other, which means that the sides adjacent to D in a Lambert quadrilateral are greater than their respective opposite sides. This property holds true for all sides adjacent to an acute angle in a Lambert quadrilateral.

Thus a  Lambert quadrilateral ABCD in a hyperbolic plane with right angles at A, B, and C implies that angle D is acute and the sides adjacent to D are greater than their respective opposite sides, highlighting the properties of hyperbolic geometry and the absence of rectangles in the hyperbolic plane.

To learn more about hyperbolic plane click here: brainly.com/question/28272514

#SPJ11

6 blocks :) I won’t explain it tho lol

In linear equation, 72 campers can you fit if you have 12 tents.

What is a linear equation in math?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

there are six campers per tent.

no of tents = 12

 campers can you fit = 12 * 6

                               = 72

Learn more about linear equation,

brainly.com/question/11897796

#SPJ1

answer

43 minutes

explanation

:)

Answer:

Option B is the correct option.

Step-by-step explanation:

\( \sf{ \frac{3}{5} = \frac{x - 1}{8} }\)

Apply cross product property

⇒\( \sf{ 5(x - 1) = 3 \times 8}\)

Distribute 5 through the parentheses

⇒\( \sf{5x - 5 = 3 \times 8}\)

Multiply the numbers

⇒\( \sf{5x - 5 = 24}\)

Move 5 to right hand side and change it's sign

⇒\( \sf{5x = 24 + 5}\)

Add the numbers

⇒\( \sf{5x = 29}\)

Divide both sides of the equation by 5

⇒\( \sf{ \frac{5x}{5} = \frac{29}{5} }\)

⇒\( \sf{x = \frac{29}{5} }\)

Hope I helped!

Best regards!!

Answer:

-51 months

Step-by-step explanation:

To solve, we can use the second model since we're told the money is compounded monthly

\(A=P(1+r/n)^n^t\\\\1000=4000(1+0.027/12)^1^2^t\\\\1/4=(4009/4000)^1^2^t\\\\log(1/4)=log(4009/4000)^1^2^t\\\\log(1/4)=12t*log(4009/4000)\\\\log(1/4)/log(4009/4000)=12t\\\\1/12*(log(1/4)/log(4009/4000))=t\\\\-51.40197623=t\\-51=t\)

To solve this problem, we'll use the formula A=P(1+r/n)^nt, where A is the future value, P is the initial investment, r is the interest rate, n is the number of times compounded per year, and t is the number of years.

In this case, we know that P=$4000, r=2.7%, and n=12 (since interest is compounded monthly). We're trying to find the time required for the account to earn $1000, so A=P+$1000=$5000.

Plugging these values into the formula, we get:

$5000=$4000(1+0.027/12)^(12t)

Simplifying, we can divide both sides by $4000 and take the natural logarithm of both sides:

ln(1.25)=ln(1+0.027/12)^(12t)

Using the properties of logarithms, we can bring the exponent down:

ln(1.25)=12t*ln(1+0.027/12)

Dividing both sides by 12ln(1+0.027/12), we get:

t=ln(1.25)/(12ln(1+0.027/12))

Using a calculator, we find that t is approximately 3.5 years. Rounded to the nearest month, this is 42 months.

Therefore, it would take approximately 42 months (or 3 years and 6 months) for the account to earn $1000 with an initial investment of $4000 at an interest rate of 2.7% compounded monthly.

Learn more about compound interest here:

https://brainly.com/question/29335425

#SPJ11

There are several methods for factoring expressions, including factoring out the greatest common factor (GCF), by grouping, using the difference of squares or sum/difference of cubes, using the FOIL method or the reverse FOIL method or using special cases such as perfect square trinomials or difference of squares.

Factoring out the GCF: This method involves finding the greatest common factor of all the terms in an expression and then dividing it out of each term. For example, if we have the expression 12x^2 + 8x^2, the GCF is 4x^2, so we can factor it out and write the expression as 4x^2(3 + 2).

Factoring by grouping: This method involves grouping the terms of an expression into pairs and factoring out a common factor. For example, if we have the expression x^2 + 3x + 2x + 6, we can group the first two terms and the last two terms and factor out a common factor of x from the first group and 2 from the second group. This gives us x(x + 3) + 2(x + 3)

Factoring quadratics: There are a few methods to factor quadratics, such as factoring a difference of squares, or factoring a sum or difference of cubes. For example, if we have the expression x^2 - y^2, we can factor it as (x-y)(x+y) using difference of squares.

Factoring trinomials: There are a few methods to factor trinomials, such as FOIL method or reverse FOIL method. The FOIL method is a mnemonic acronym for first, outer, inner, and last, which is used to multiply two binomials. Reverse FOIL is used to factor a trinomial that is the product of two binomials. For example, if we have the expression x^2 + 5x + 6, we can factor it as (x+2)(x+3) using reverse FOIL method.

Factoring special cases: There are some special cases of factoring that have specific methods. For example, factoring perfect square trinomials such as x^2 + 2x + 1 is factored as (x+1)^2 and factoring difference of squares such as x^2 - y^2 is factored as (x-y)(x+y)

To know more on factoring

https://brainly.com/question/11994048

#SPJ4

Step-by-step explanation:

PLS MARK ME AS BRAIN LIST ANSWER

Answer:

75

Step-by-step explanation:

5 miles-8km

x miles-120 km

x=120×5÷8

x=75 (miles)

Answer:

s

Step-by-step explanation:

since 5 miles is the same as 8 kilometers,how many miles is 120 kilometers..use ratio and proportion

5miles:8kilometers

x. :120kilometers

8x/8=600/8

x=75miles

I hope this helps

Answer:

7.4

Step-by-step explanation:

(a) No conditions. (b) The playlist must consist of exactly 3 songs from each artist. (c) The playlist must consist of at least 2 songs from each artist.

Working:

To build a playlist of 6 songs from 25 unique songs, we can use the formula for combinations:

nCr = n! / r!(n-r)!

where n is the total number of songs and r is the number of songs we want to include in the playlist.

So the number of ways to build the playlist is:

25C6 = 25! / 6!(25-6)! = 177,100

Therefore, there are 177,100 ways to build the playlist without any conditions.

(b) The playlist must consist of exactly 3 songs from each artist.

To build a playlist of 6 songs with exactly 3 songs from each artist, we can use the formula for combinations again:

nCr = n! / r!(n-r)!

We need to choose 3 songs from artist A and 3 songs from artist B, so we can calculate the number of ways to do this separately:

Number of ways to choose 3 songs from artist A:

10C3 = 10! / 3!(10-3)! = 120

Number of ways to choose 3 songs from artist B:

15C3 = 15! / 3!(15-3)! = 455

To get the total number of ways to build the playlist, we can multiply these two numbers together:

120 * 455 = 54,600

Therefore, there are 54,600 ways to build the playlist with exactly 3 songs from each artist.

(c) The playlist must consist of at least 2 songs from each artist.

To build a playlist of 6 songs with at least 2 songs from each artist, we can break this down into cases:

Case 1: 2 songs from artist A and 4 songs from artist B

Number of ways to choose 2 songs from artist A:

10C2 = 10! / 2!(10-2)! = 45

Number of ways to choose 4 songs from artist B:

15C4 = 15! / 4!(15-4)! = 1,386

Total number of ways for case 1:

45 * 1,386 = 62,370

Case 2: 3 songs from artist A and 3 songs from artist B

We already calculated the number of ways for this case in part (b):

54,600

Case 3: 4 songs from artist A and 2 songs from artist B

Number of ways to choose 4 songs from artist A:

10C4 = 10! / 4!(10-4)! = 210

Number of ways to choose 2 songs from artist B:

15C2 = 15! / 2!(15-2)! = 105

Total number of ways for case 3:

210 * 105 = 22,050

Total number of ways to build the playlist with at least 2 songs from each artist:

62,370 + 54,600 + 22,050 = 139,020

Therefore, there are 139,020 ways to build the playlist with at least 2 songs from each artist.

Visit here to learn more about Total brainly.com/question/30883537

#SPJ11

Answer:

1.1x

Step-by-step explanation:

Here's the answer, goodluck

Answer:

The greatest common factor of 44 and 22 is 22.

Step-by-step explanation:

First, you should list all the factors of 44 and 22. For 44, the factors are: 1, 2, 4, 11, 22 and 44

For 22, the factors are: 1, 2, 11 and 22

The greatest common factor is 22.

Answer: 22

Step-by-step explanation:

In order to find GCF of 44 and 22, take the prime factorization of the two numbers

22: 11*2

44: 11*4=11*2*2

Notice they both have 11*2 in their prime factorization.

11*2=22

GCF of 44 and 22 is 22

Answer:

5

Step-by-step explanation:

because it is asking what minus 9 is equal to -4

Answer:

5

Step-by-step explanation:

5 - 9= - 4

I don't know if this is confusing but you could also just subtract 5 from 9 (9-5) which is 4 and then put a - in front of it

Answer:

{15, 3, 0}

Step-by-step explanation:

Plugin the domain values into the equation then solve:

(fx) = x²- 4x + 3

First value

y = -2²- 4(-2) + 3                      replace f(x) with y

y = 4 - (-8) + 3                         -2² = -2 times -2 = 4 and 4 times -2 = -8

y = 12 + 3                                 add

y = 15                                       final result; first range value

Second value

y = 0²- 4(0) + 3                      replace f(x) with y

y = 0 - 0 + 3                          0² = 0 times 0, which is 0 and 4 times 0 is 0

y = 0 + 3                                add

y =  3                                     final result; second range value

Third value

y = 1²- 4(1) + 3                       replace f(x) with y

y = 1 - 4 + 3                           1 times 1 is 1, 4 times 1 is 4

y = -3 + 3                               add

y = 0                                      final result; third (last) range value

Therefore, Range: {15, 3, 0}

Learn more: https://brainly.com/question/10734654

Answer:

Slope is -8

Step-by-step explanation:

The slope is the number in front of x.

the graph increases when the values ​​in y are increasing

we must mention the part of x where the function increases

so

Increassing:

because the graph is increasing from a very small number to the number 1

the graph decreases when the values ​​in and are less and less

we must mention the part of x where the function decreasing

so

Decreasing:

because the graph starts to decrease from the number 1 to a very large number

the range is the part of y that the graph uses, from the lowest point to the highest

Range:

because the smallest number is a very small number and the largest number that takes in y is 2

a) Amount of sugar in the tank initially is 0.

b) The amount of sugar in the tank after t minutes is 13.6(1 - \(e^{\frac{4t}{1360} }\)).

c) The concentration of sugar in the solution in the tank after 60 minutes is 3.672.

a) Assign the sugar content of the tank for time t to the symbol A(t). Starting with only clean water, the tank

A(0) = 0

b) Sugar flows in at a rate of

(0.02 kg/L) × (2 L/min) = 0.04 kg/min

and flows out at a rate of

(A(t) ÷ 1360 kg/L) × (2 L/min) = (2A(t) ÷ 1360) kg/min

so that the net rate of change of A(t) is governed by the ODE,

dA(t) ÷ dt = (4 ÷ 100) - (2A(t) ÷ 1360)

A'(t) + (2A(t) ÷ 1360) = 2 ÷ 100

Multiply both sides by the integrating factor \(e^{\frac{4t}{1360} }\) to condense the left side into the derivative of a product:

\(e^{\frac{4t}{1360} }\) A'(t) + (2 \(e^{\frac{4t}{1360} }\) A(t) ÷ 1360) = 4 \(e^{\frac{4t}{1360} }\) ÷ 100

( \(e^{\frac{4t}{1360} }\) A(t))' = 4 \(e^{\frac{4t}{1360} }\) ÷ 100

Integrate both sides:

\(e^{\frac{4t}{1360} }\) A(t) = ∫ 4 \(e^{\frac{4t}{1360} }\) ÷ 100

\(e^{\frac{4t}{1360} }\) A(t) = 13.6 \(e^{\frac{4t}{1360} }\) + C

Solve A(t);

A(t) = 13.6 + C \(e^{\frac{4t}{1360} }\)

A(0) = 0, substitute the value

0 = 13.6 + C \(e^{\frac{4t}{1360} }\)

C = -13.6

so that the amount of sugar at any time t is,

A(t) =  13.6 - 13.6\(e^{\frac{4t}{1360} }\)

A(t) = 13.6(1 - \(e^{\frac{4t}{1360} }\))

c) As t → 60, the exponential term converges to 0 and is left with

\(\lim_{t \to \(60}\) A(t) = 13.6 × (1 - 0.73)

\(\lim_{t \to \(60}\) A(t) = 3.672 kgs of sugar.

Learn more about the rate of flow at

https://brainly.com/question/29050709?referrer=searchResults

#SPJ4

Answer:

h(x)= x^2+11x+30

Step-by-step explanation:

A quadratic function is in the form h(x) = ax^2 + bx + c.

Since the zeros are -6 and -5, take the opposite signs and add them to the variable x separately.

It should look like this: h(x)= (x+6)(x+5)

Since this is the factored form, we have to solve this equation further.

h(x)= (x+6)(x+5)

h(x)= x^2+6x+5x+30

h(x)= x^2+11x+30

Answer:

  m∠EJH = 212°

Step-by-step explanation:

The external angle (F) is half the difference of the arcs intercepted.

  F = (EJH -EG)/2

Solving for EJH, we get ...

  2F +EG = EJH

  2(65°) +82° = m∠EJH = 212°

The horizontal asymptote of the function is y=36 and vertical asymptote is x = 6 and its end behavior is f(x)→6.

As the independent variable approaches a certain value, the function approaches asymptotes, but does not cross them. They could be angled, vertical, or horizontal.

ascending asymptotes

There will be a vertical asymptote at x=a if the denominator factor of a rational function, (x - a), is not matched by the same factor in the numerator.

horizontal asymptotes:

When x is large, the value of a rational function approaches the ratio of the highest-degree terms in the numerator and denominator.

Given the function is f(x) = 6x/x-36

limx→±∞ 6x/x-36

= limx→±∞ 6/1-36/x

= 6 ⇒ horizontal asymptote: y = 6

Consider denominator = 0 ↔ x-36 = 0 ↔ x=36

limx→₊₂₅ 6x/x-36

= 6×36/0⁺ = ∞ ⇒ vertical asymptote: x = 36

End behavior of f(x):

As x → -∞ or x → ∞, f(x) → 6.

Hence we get the asymptote and the end behavior of the function.

Learn more about asymptote here:

brainly.com/question/4138300

#SPJ1

well, if that function f(x) were to be continuos on all subfunctions, that means that whatever value 7x + k has when x = 2, meets or matches the value that kx² - 6 has when x = 2 as well, so then 7x + k = kx² - 6 when f(2)

\(f(x)= \begin{cases} 7x+k,&x\leqslant 2\\ kx^2-6&x > 2 \end{cases}\qquad \qquad f(2)= \begin{cases} 7(2)+k,&x\leqslant 2\\ k(2)^2-6&x > 2 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ 7(2)+k~~ = ~~k(2)^2-6\implies 14+k~~ = ~~4k-6 \\\\\\ 14~~ = ~~3k-6\implies 20~~ = ~~3k\implies \cfrac{20}{3}=k\)

Answer:

y = -2x + 9

Step-by-step explanation:

The equation of the new line is the same as that of this given line, EXCEPT that the constant will be different.

Start with y = mx + b; substitute 1 for y, 4 for x and -2 for m:

1 = -2(4) + b

Then b = 9, and y = -2x + 9

Answer:

I think it's B not sure though.