Match the graph of the function with the function rule.

y = 3 • 2x
y = 2 • 3x
y = 1 • 3x
y = 4 • 3x

Match The Graph Of The Function With The Function Rule.y = 3 2xy = 2 3xy = 1 3xy = 4 3x

Answers

Answer 1

By applying the definition of exponential function, we find that the function f(x) = 3 · 2ˣ match with the graph of the picture. (Correct choice: A)

What is the equation behind the exponential curve seen in the graph?

In this question we have the graph of a exponential function, whose expression have to be found based on the definition of exponential function:

y = a · bˣ      (1)

Where:

a - Initial value of the exponetial function.b - Base of the exponential function.x - Independent variabley - Dependent variable

Now we find the values for a and b:

Initial value (x = 0, y = 3)

3 = a · b⁰

a = 3

Base of the exponential function (x = 1, a = 3, y = 6)

6 = 3 · a

a = 6 / 3

a = 2

By applying the definition of exponential function, we find that the function f(x) = 3 · 2ˣ match with the graph of the picture. (Correct choice: A)

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Related Questions

A graph titled Population of Old Town has Time (years after 2000) on the x-axis, and number of people on the y-axis. A line goes through points (4, 7,000) and (6, 6,500). What is the slope for this scenario? -500 -250

Answers

The slope of the scenario is calculated as: -250.

How to Find the Slope Value?

Slope (m) = change in y / change in x = (y2 - y1)/((x2 - x1).

Given the points:

(4, 7,000) = (x1, y1)

(6, 6,500) = (x2, y2)

Plug in the values

Slope (m) = (6,500 - 7,000) / (6 - 4)

Slope (m) = (-500) / (2)

Slope (m) = -250

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Consider a situation where your sales have been quite stable in the month, but you have done exceptionally better in the past two days. what trendline is more sensitive to this change?

Answers

The trendline has a positive slope and 3-day moving average is the trendline that is more sensitive to this change.

In this question,

Trendlines are used to give traders a good idea of the direction an investment's value might move. In a healthy trend, it's ideal to enter your trades on a pullback (towards the moving average).

Understanding the direction of an underlying trend is one of the most basic ways to increase the probability of making a successful trade because it ensures that the general market forces are working in your favor.

A moving average is a technical indicator that investors and traders use to determine the trend direction of securities. It is one of the commonly used technical tools best known as trend following or lagging indicator, because it is based on past prices.

The sales have been quite stable in the month, but the sales was exceptionally better in the past two days. If the analyst draws a line between these price points, they have an upward trend and 3-day moving average is the trendline that is more sensitive to this change.

The options for this question are a) 3 days moving average, b) 7 days moving average, c) They are both equally sensitive, d) None of them is sensitive to this change.

Hence we can conclude that the trendline has a positive slope and option (A) 3-days moving average is the trendline that is more sensitive to this change is the correct answer.

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What is the greatest possible error if irina measured the length of her window as 3.35 feet? 0.5 0.05 0.005 0.0005

Answers

3.35 feet have a maximum inaccuracy of 0.005 feet.

The correct option is C.

What is error analysis?

When students consistently commit mistakes, an approach known as error analysis is frequently employed to determine the root of the problem. Reviewing student work is the first step in the process, after which misunderstood patterns are sought out. Mathematics mistakes can be conceptual, procedural, or factual, and they can happen for a variety of reasons.

Given:

The window is 3.35 feet long.

Find the biggest error you can

According to the given data:

Half of the measuring unit is considered to be the maximum amount of measurement error.

3.35 feet are calculated to the nearest centimeter, or 0.01 feet

Consequently, the largest conceivable error is equal to half of the measurement unit.

= .01/2

= .005

Therefore, the maximum inaccuracy for 3.35 feet is 0.005 feet.

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15 POINTS
Data Analysis and Probability
Constructing a box-and-whisker plot

Answers

The box and whisker plot for the data-set is given at the end of the question.

What is a box plot?

It is a plot that focuses the interquartile range of the population, which is the difference between the third and the first quartile, but gives a five number summary of the population, composed by these following measures.

The smallest value.The first quartile.The median.The third quartile.The highest value.

For this problem, we have that:

The smallest value is of 50, hence the left dot has to be at 50 in your graph.The highest value is of 77, hence the right dot has to be at 50 in your graph.The data-set has an even cardinality, of 17, hence the median is the 9th element, which is of 65, which means that the middle vertical line should be at 65.The first quartile is the median of the first eight elements, hence the mean of the 4th and 5th elements, which are 55 and 57, hence the first quartile is of 56, which means that the left vertical line should be at 56.The third quartile is the median of the first eight elements, hence the mean of the 4th and 5th elements of the second half, which are both 71, hence the third quartile is of 71, which means that the right vertical line should be at 71.

The graph at the end gives a vertical version of the box plot.

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If point O represents the origin, PQ = 12 units, and P'Q' = 3 units, find the scale factor. (Note: point O represents the origin, what is the scale factor to dilate a shape on the other side of the origin?)

Answers

Answer:

1/4

Step-by-step explanation:

To transform PQR into P'Q'R, dilate the preimage by 1/4, or shrink it by a scale factor of 4 because 3/12 = 1/4

1/4
Guguguguguguguggugugugugugugugug
Btw it’s tra

which expression is equivalent to (125^2/ 124^4/3)

Answers

The answer is 25.

What is numerator and denominator?The value above the horizontal line is the numerator in a fraction. It represents the number of pieces removed from the whole. The denominator of a fraction is the numerical value that comes before the vinculum. It indicates the overall total of all of the equal portions.For instance, the fraction bar is the line that separates the numbers 4 and 5, and 45 is a fraction. Here, the numerator is the number above the fraction bar, and the denominator is the number below the fraction bar. The denominator, or the number of pieces out of the whole, is represented by a numerator.Multiplying the numerator times the numerator and denominator. Denominator. The answer should be lowered to a mixed number in the simplest form.

The expression is equivalent to [tex]\frac{125^{2} }{125^{\frac{4}{3}} }[/tex] :

[tex]\frac{125^{2} }{125^{\frac{4}{3}} } =125^{2-(\frac{4}{3}) }[/tex]

       [tex]=125^{\frac{2}{3} }[/tex]

 [tex]125=5x^{3}[/tex]

[tex](5^{3} )^{\frac{2}{3}} =5\frac{6}{3} =5^{2} =25[/tex]

Therefore, The answer is 25.

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HELP ILL BRAINLIST WHO EVER HELPS
PICTURE BELOW

Answers

Applying the SAS congruence theorem and the definition of angle bisector, the complete proof is shown in the image attached below.

What is the SAS Theorem?

The SAS theorem (side-angle-side theorem) state that two triangles are congruent to each other if they have two pairs of congruent sides that are corresponding to each other and a pair of congruent angles that are corresponding to each other.

What is an Angle Bisector?

A line segment that divides an angle into two equal parts is referred to as an angle bisector.

From the proof given, we know that;

m∠DEK = 2(m∠DEF)

m∠DEK = 2(44) = 88°

With the given information and using the reflexive property, we know that triangles DEF and KEF have two pairs of congruent sides that are corresponding to each other and a pair of congruent angles that are corresponding to each other.

Therefore, ΔDEF ≅ ΔKEF based on the SAS congruence theorem. Because they are congruent triangles, DF = KF based on the CPCTC theorem.

Then, KF = 1/2(DK) = 1/2(16) = 8.

The complete proof is show in the image attached below.

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Are 14, 6 + 8, and (6 + 8) equivalent expressions? Explain your reasoning.

Answers

The expressions 14, 6 + 8, and (6 + 8) are equivalent because they are all equal to 1

Equivalent expression

14

6 + 8

= 14

(6 + 8)

= 14

The coefficient of (6 + 8) is 1, so, the expression remains the same.

What is equivalent expression?

Equivalent expressions refers to those expressions that work the same even though they look different.

The importance or significance of equivalent expression is that its makes expressions easier to work with and solve.

Therefore, the expressions 14, 6 + 8, and (6 + 8) are all equivalent to 14.

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Select the correct answer.
What is the approximate measure of exterior angle B in the polygon?

Answers

Answer:

C

Step-by-step explanation:

the sum of the exterior angles of a polygon = 360°

sum the 4 exterior angles and equate to 360

8x + 9x + 5 + 5x + 4 + 9x + 3 = 360 , that is

31x + 12 = 360 ( subtract 12 from both sides )

31x = 148 ( divide both sides by 31 )

x ≈ 11.23 ( to 2 dec. places )

then exterior angle at B is

9x + 3 = 9(11.23) + 3 ≈ 104° → C

The approximate measure of exterior angle B in the polygon is 104° option (C) is correct.

What is a regular polygon?

A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight-line segments are joined end to end to form a closed shape. The vertices, also known as corners, are the points where two line segments meet and form an angle.

[tex]\rm Area = |\dfrac{(x_1y_2-y_1x_2)+(x_2y_3-y_2x_3)....+(x_ny_1-y_nx_1)}{2}|[/tex]

It is given that:

A polygon is given in the picture with angle measures.

As we know,

The sum of the exterior angles of a polygon = 360°

8x + 9x + 5 + 5x + 4 + 9x + 3 = 360

31x + 12 = 360

31x = 148

x ≈ 11.23

= 9x + 3 = 9(11.23) + 3

≈ 104°

Thus, the approximate measure of exterior angle B in the polygon is 104° option (C) is correct.

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divide the polynomials:
x^2-3x+9/x-2

Answers

The value of dividing x^2-3x+9 by x-2 is x + 3

Ways of dividing polynomials

There are several ways to divide polynomial functions; some of these ways include

By factorizationBy long divisionBy synthetic divisionBy using technology such as graph

How to divide the polynomials?

The expression for the polynomial division is given as:

x^2-3x+9/x-2

To divide polynomial functions, we make use of the division by factorization method

Start by expanding the numerator of the polynomial division

x^2-3x+9/x-2 = x^2 + 3x - 6x + 9/x-2

Factorize the equation

x^2-3x+9/x-2 = x(x + 3) - 2(x + 3)/x - 2

Factor out x + 3 from the numerator

x^2-3x+9/x-2 = (x- 2)(x + 3)/x - 2

Cancel out the common factors

x^2-3x+9/x-2 = x + 3

Hence, the value of dividing x^2-3x+9 by x-2 is x + 3

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Please help me solve this problem with work

Answers

Answer:

  m∠B ≈ 51.5°

Step-by-step explanation:

A triangle solver can find this answer simply by entering the data. If you do this "by hand," you need to first find length BC using the Law of Cosines. Then angle B can be found using the Law of Sines.

Length BC

The Law of Cosines tells us ...

  a² = b² +c² -2bc·cos(A)

  a² = 21² +13² -2(21)(13)cos(91°) ≈ 619.529

  a ≈ 24.8903

Angle B

The Law of Sines tells us ...

  sin(B)/b = sin(A)/a

  B = arcsin(sin(A)×b/a) = arcsin(sin(91°)×21/24.8903)

  B ≈ 57.519°

The measure of angle B is about 57.5°.

A circle with center O. Two tangents to the circle from the point C meet the circle at points A, and B. Two lines O B, and O C forms an exterior angle of 250 degrees. Two lines B D, and A D are drawn from a point D on the circle.
In this figure, m∠BDA =
° and m∠BCA =
°.

Answers

Based on the calculations, the measure of m∠BDA and m∠BCA are 55° and 70° respectively.

What is a tangent?

In geometry, a tangent is also referred to as a tangent line and it can be defined as a straight line that touches a plane curve at a specific point.

What is a circle?

A circle can be defined as a closed, two-dimensional curved geometric shape with no edges or corners. Also, a circle simply refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).

First of all, we would determine angle BOA:

∠BOA + ∠BOA = 360° (Angles at a point)

∠BOA + 250° = 360°

∠BOA = 360° - 250°

∠BOA = 110°

Next, we would determine angle BDA:

2 × m∠BDA = ∠BOA (Angle inscribed at the center is twice the angle at the circumference)

2 × m∠BDA = 110°

m∠BDA = 110°/2

m∠BDA = 55°.

What is the theorem of intersecting secants?

The theorem of intersecting secants states that when two (2) lines intersect outside a circle, the measure of the angle formed by these lines is equal to one-half (½) of the difference of the two (2) arcs it intercepts.

By applying the theorem of intersecting secants, angle BCA will be given by this formula:

m∠BCA = ½ × (m<AO - m<BO)

Substituting the given parameters into the formula, we have;

m∠BCA = ½ × (250 - 110)

m∠BCA = ½ × 140

m∠BCA = 70°.

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Answer:

70

Step-by-step explanation:

HELP
answer the questions 61 and 62 SHOW UR WORK please i’ll mark brainliest
help me

Answers

Answer:

Step-by-step explanation:

i do not know how to get what they are asking me too

Answers

The percent increase is inside parenthesis

1.115 multiplied by 100

111.5% - 100% = 11.5% rate of increase

What is [tex]\frac{a+3}{8}[/tex] x [tex]\frac{2}{a}[/tex]

Answers

Answer: [tex]\frac{2a+6}{8a}[/tex]

Step-by-step explanation:

[tex]\frac{2(a+3)}{8a}=\frac{2a+6}{8a}[/tex]

Quick algebra 1 question for 10 points!

Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!

Answers

Using a calculator, the line of best fit for the function is given by:

y = 51.7x - 5.7.

How to find the equation of linear regression using a calculator?

To find the equation, we need to insert the points (x,y) in the calculator. For this problem, a linear regression is used because the data only increases.

From the given table, the points are:

(1, 68), (2,97), (3, 134), (4, 176), (5, 241), (6,335).

Inserting these points on the calculator, the line of best fit for the function is given by:

y = 51.7x - 5.7.

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i don't know how to solve this. help please?

Answers

Answer:

51   74

Step-by-step explanation:

x = smaller

x +23 = larger

added together   (x   + x+23)    equal to 28 less than 3x      = 3x-28

x    + x+23  = 3x-28      subtract 2x from both sides of the equation

   23 = x -28      add 28 to both sides

 51 = x      then the larger   =  51 + 23 = 74

Answer:

51 and 74

Step-by-step explanation:

Let the smaller of the two numbers be represented by x. The larger of the two numbers is 23 greater than the smaller, and therefore can be written as x + 23.

Set up an Equation

First, we can write the sum of the two numbers in terms of the smaller number. "three times the smaller" is 3x, and "28 less" is 3x-28.

Therefore our equation is:

[tex]x+x+23=3x-28[/tex]

Solve the Equation

Start by adding like terms

[tex]2x+23=3x-28[/tex]

Subtract 23 from both sides

[tex]2x=3x-51[/tex]

Subtract 3x from both sides

[tex]-x=-51[/tex]

Divide both sides by -1

[tex]x=51[/tex]

The larger term is: [tex]x+23\Rightarrow51+23\Rightarrow74[/tex]

Check

[tex]51+74=125[/tex]

[tex]3(51)-28=153-28=125[/tex]

[tex]125=125[/tex]

The smaller number is 51 and the larger number is 74

Rick runs 5 miles which burns approximately 500 calories. how many miles would rick have to run to burn one pound of adipose tissue?

Answers

35miles Rick have to run to burn one pound of adipose tissue.

According to the given question.

Rick runs 5miles to burn 500 calories.

⇒ 1 mile burns the amount of calories = 500/5 = 100 calories.

As we know that

1 pound = 3,500 calories.

So the number of miles Rick needed to run to burn 1 pound of adipose tissue = 3500/100 = 35miles

Hence, 35miles Rick have to run to burn one pound of adipose tissue.

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Factor the cubic polynomial 6x3 – 11x2 – 12x 5. use the rational root theorem and synthetic division

Answers

The factorization of given cubic polynomial 6x³ - 11x² - 12x + 5 is:  

6x³ - 11x² - 12x + 5 = (x + 1)(x - [tex]\frac{5}{2}[/tex])(x - [tex]\frac{1}{3}[/tex])

For given question,

We have been given the cubic polynomial 6x³ - 11x² - 12x + 5

We need to factorize given cubic polynomial.

By the rational roots theorem, any rational zero of f(x) is expressible in the form ± [tex]\frac{p}{q}[/tex] for integers p, q with p a divisor of the constant term 5 and q a divisor of the coefficient 6 of the leading term.

Factors of p = 5: 1, 5

Factors of q = 6: 1, 2, 3, 6

That means that the only possible rational zeros are:

±{ [tex]\frac{1}{1} ,\frac{1}{2} ,\frac{1}{3} ,\frac{1}{6} ,\frac{5}{1} ,\frac{5}{2} ,\frac{5}{3} ,\frac{5}{6}[/tex] }

= ±{ [tex]1 ,\frac{1}{2} ,\frac{1}{3} ,\frac{1}{6} ,5 ,\frac{5}{2} ,\frac{5}{3} ,\frac{5}{6}[/tex] }

We need to find the exact zeros of given cubic polynomial.

For x = 1,

6(1)³ - 11(1)² - 12(1) + 5 = -12

This means, x = 1 is not a zero of given cubic polynomial.

For x = -1,

6(-1)³ - 11(-1)² - 12(-1) + 5 = 0

This means, x = -1 is a zero of given cubic polynomial and (x + 1) is a factor.

To factorize given cubic polynomial we use synthetic division.

The synthetic division (6x³ - 11x² - 12x + 5) ÷ (x + 1) is as shown in following image.

⇒ 6x³ - 11x² - 12x + 5 = (x + 1)(6x² - 17x + 5)

The factors of above quadratic polynomial 6x² - 17x + 5 are:

⇒ 6x² - 17x + 5 = (x - [tex]\frac{5}{2}[/tex])(x - [tex]\frac{1}{3}[/tex])

So, the factors of given cubic polynomial are:

⇒ 6x³ - 11x² - 12x + 5 = (x + 1)(x - [tex]\frac{5}{2}[/tex])(x - [tex]\frac{1}{3}[/tex])

Therefore, the factorization of given cubic polynomial 6x³ - 11x² - 12x + 5 is:  6x³ - 11x² - 12x + 5 = (x + 1)(x - [tex]\frac{5}{2}[/tex])(x - [tex]\frac{1}{3}[/tex])

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pls help!
using the numbers 1-9 fill in the boxes so that it meets the criteria. use each number only once per red box and once per blue box

Answers

The way to solve this is to try to get the vales that would best fill the empty spaces in the diagram. This has been done below

a. log6⁰, log 2 . 1, log 8/3

b. log 1 .4 , 1 , log 4. 6

c. log 9/2, log 3. 5 , log 5⁷

How to find the logarithm of a number

To do this, you have to decide on that specific  number whose logarithm you are trying to determine. Next you have to find the base of that number.

The logarithm of the number is the power that it would have to be raised for us to obtain a different number.

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what is the value of x= and y=

Answers

Answer:

x = 18

y = 18

Step-by-step explanation:

We are given a right triangle (notice the 90 degree angle), with one of the angles being 45°.

We also know that the hypotenuse (the side opposite of the 90° angle) is 18√2.

We want to find the value of x and y.

First, let's figure out what the value of the other angle is.

The angles in a triangle all add up to 180 degrees.

Let's call the value of the angle we don't know s.
s + 45 + 90 = 180

Add 45 and 90 together.

s + 135 = 180

Subtract 135 from both sides.

s = 45

So the value of the other angle is 45 degrees.

When a right triangle is a 45-45-90 triangle (the numbers referring to the measures of the degrees), there is actually something special about it; if the legs (the sides that make up the 90 degree angle) have the value a (they would both be congruent because a 45-45-90 triangle is isosceles), then the hypotenuse will be a√2.

Keeping this in mind, let's solve for a.

Set 18√2 equal to a√2.

18√2=a√2

Divide both sides by √2.

18 = a

The value of a, aka the legs is a.

Both x and y would be equal to a in this case.

Therefore, x = 18, and y = 18.

Question mode multiple choice question despite the large number of media options today, the average millennial still blank______ for an average of 10 hours every week.

Answers

the answer is it still needs

Ekaete collected 12 raffle tickets. Roseline collected twice as many. How many raffle tickets did they collect in all?

Answers

Answer:

36

Step-by-step explanation:

12 times 2 which is 24 then u add 12 cause it's the amount they have together so you get 36

Verify that the intermediate value theorem applies to the indicated interval and find the value of c guaranteed by the theorem. f(x) = x2 7x 1, [0, 9], f(c) = 19 c =

Answers

we verified the intermidiate value theorem applies to the function f(x) = x^2 + 7x  + 1 . And the value of c is 2.

According to the given question.

We have a function.

f(x) = x^2 + 7x  + 1

As, we know that "the Intermediate Value Theorem (IVT) states that if f is a continuous function on [a,b] and f(a)<M<f(b), there exists some c∈[a,b] such that f(c)=M".

Now, we will apply the theorem for the given function f(x).

So,

f(0) = 0^2 +7(0) + 1 = 1

And,

f(9)=9² + 7(9) + 1 = 81 + 63 + 1 = 145

Here,  f(0) = 1< 19< 145 = f(9).

So, f is continous since it is a polynomial. Then the IVT applies, and such c exists.

To find, c,

We have to solve the quadratic equation f(c) =19.

This equation is

c² + 7c + 1 = 19.

Rearranging, c²+ 7c - 18=0.

Factor the expression to get

c² + 9c - 2c -18 = 0

⇒ c(c + 9) - 2( c + 9) = 0

⇒ (c - 2)(c + 9) = 0

⇒ c = 2 or -9

c = -9 is not possible beacuse it is not in the interval [0, 9].

So, the value of c is 2.

⇒ f(2) = 2^2 + 7(2) + 1 = 4 + 14 + 1 = 19

Hence, we verified the intermidiate value theorem applies to the function f(x) = x^2 + 7x  + 1 . And the value of c is 2.

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Which of the following shows the simplified function of csc x sin(pi/2 -x)?

Answers

Answer:

cot x

Step-by-step explanation:

using the identities

csc x = [tex]\frac{1}{sinx}[/tex]

sin([tex]\frac{\pi }{2}[/tex] - x) = cos x

then

csc x × sin ([tex]\frac{\pi }{2}[/tex] - x)

= [tex]\frac{1}{sinx}[/tex] × cosx

= [tex]\frac{cosx}{sinx}[/tex]

= cot x

Kelley writes the expression n 2 to model the phrase "xander studied two more hours than nandini." which best explains the accuracy of kelley’s expression? it is accurate. in the phrase "two more hours than nandini," "two" is "2," "more" is " ," and nandini’s study time is unknown or "n," so 2 n or n 2 are correct translations. it is inaccurate. in the phrase "two more hours than nandini," "two" is "2," "more" is " ," and nandini’s study time is unknown or "n," so 2 n is the correct translation. it is inaccurate. in the phrase "two more hours than nandini," "two" is "2," "more than" is ">," and nandini’s study time is unknown or "n," so 2 greater-than n is the correct translation. it is inaccurate. in the phrase "two more hours than nandini," "two" is "2," "more than" is "<," and nandini’s study time is unknown or "n," so 2 less-than n is the correct translation.

Answers

It is accurate. In the phrase “two more hours than Nandini,” n + 2 are correct translations. Then the correct option is A.

What is Algebra?

Algebra is used to analyze mathematical symbols, and logic is used to manipulate those symbols.

As an example, Kelley models the sentence "Xander studied two more hours than Nandini" using the equation n + 2.

Consequently, the following will describe Kelley's expression's accuracy the best:

It is precise. Since "two" is translated as "2," "more" as "+," and "Nandini's study time is unknown or "n," 2 + n or n + 2 are the appropriate translations for the sentence "two more hours than Nandini."

So, option A is the best choice.

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I understand that the question you are looking for is :

Kelley writes the expression n + 2 to model the phrase “Xander studied two more hours than Nandini.” Which best explains the accuracy of Kelley’s expression?

It is accurate. In the phrase “two more hours than Nandini,” “two” is “2,” “more” is “+,” and Nandini’s study time is unknown or “n,” so 2 + n or n + 2 are correct translations.

It is inaccurate. In the phrase “two more hours than Nandini,” “two” is “2,” “more” is “+,” and Nandini’s study time is unknown or “n,” so 2 + n is the correct translation.

It is inaccurate. In the phrase “two more hours than Nandini,” “two” is “2,” “more than” is “>,” and Nandini’s study time is unknown or “n,” so 2 greater-than n is the correct translation.

It is inaccurate. In the phrase “two more hours than Nandini,” “two” is “2,” “more than” is “<,” and Nandini’s study time is unknown or “n,” so 2 less-than n is the correct translation.

In the figure below, AD is the perpendicular bisector of CB. Based on this information, which other statement can be proven to be
true?
OA AB AC
OB. AB CB
OCAC CB
OD AD CB
A
C
D
B

Answers

Answer:

463833

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Medium

Solution

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In △ABD and △ACD, we have

DB=DC ∣ Given

∠ADB=∠ADC ∣ since AD⊥BC

AD=AD ∣ Common

∴ by SAS criterion of congruence, we have.

△ABD≅△ACD

⇒AB=AC ∣ Since corresponding parts of congruent triangles are equal

Hence, △ ABC is isosceles.

Answer:

A.

Step-by-step explanation:

With the given information, triangles ABD and ACD can be proved congruent, and by CPCTC, segments AB and AC are congruent.

Select the reason that best supports statement 2 in the given proof.

Answers

Answer:

Transitive property

The reason that best supports statement 2 in the given proof is division property of equality. Therefore, the correct answer is option D.

Given that, 3(m∠A)=90° and m∠B=m∠A.

We need to prove m∠B=30°.

According to the division property of equality, the quotients of an equation remain equal when both sides are divided by a common real integer that is not equal to 0.

Here,

    Statement:               Reason:

1. 3(m∠A)=90°              1. Given

2. m∠A=30°                 2. Division property of equality

3. m∠B=m∠A              3. Reflexive property

4. m∠B=30°                 4. Transitive Property

Therefore, the correct answer is option D.

Learn more about the division property of equality here:

https://brainly.com/question/30209190.

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(50 POINTS PLEASE HELP!!!)

!!!THE QUESTION THAT I NEED TO BE ANSWERED IS THE PICTURE ATTACHED!!! BELOW IS JUST THE REQUIREMENTS AND EXAMPLE!!!

He has hired you as their new production manager. Your job is to look at four different figures and determine which would best suit the needs of the company for packaging the candy. You will choose one of the four options shown below. The candy is animal gummies. The package must hold between 80 and 100 cubic inches (roughly 5-7 cups of space). The cost of the plastic for the packaging is $0.004 per square inch. When finding cost you would multiply the Total Surface Area by $0.004.
For example:
Total Surface Area = 86 sq. in
Cost per sq in = $0.004
86 * .004 = .344 when rounded to nearest penny = $0.34

Your project should include the volume, total surface area, and materials cost for each figure given below, including the formulas you used and each step of your work. Be sure to find all measures for each figure, even if the figure does not meet the restraints that the company has given. Make sure to use the formulas given in your lessons, round your volume and area to the nearest hundredth, and round your cost to the nearest penny.

Answers

The figure in the question is a box with dimensions of 6 in. by 2 in. by 9 in., which gives;

Surface area of the packaging = 168 in.²

Package volume = 108 in.³

Cost of packaging = $0.672

Which method can be used to provide the packaging estimates for the company?

The dimensions of the box in the given figure are;

Length, L = 9 in.

Width, W = 2 in.

Height, H = 6 in.

The surface area, A, of a box is found using the following formula;

A = 2•L•W + 2•L•H + 2•H•W

Therefore;

A = 2×9×2 + 2×9×6 + 2×2×6 = 168

The surface area of the figure, A = 168 in.²

The volume of a box, V, is calculated as follows;

V = L•W•H

For the given figure, therefore;

V = 9 × 2 × 6 = 108

The volume of the given figure, V = 108 in.³

Cost of packaging per square inch, c = $0.004

Cost to package the figure, C, is therefore;

C = c × A

Which gives;

C = $0.004/in.² × 168 in.² = $0.672

Packaging cost, C = $0.672

Learn more about working with formulas in mathematics here:

https://brainly.com/question/16735912

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Describe what a line with zero rate of change looks like.

Answers

Answer:

Step-by-step explanation:

rate of change = change in y/ change in x

The rate of change is 0 if the change in y = 0

                        0 = 0 / change in x

The graph is a horizontal line since the y values do not change.

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