A number, h, rounded to 1 d.p. is 47.2
Another number, k, rounded to 1 d.p. is 4.8
What are the lower and upper bounds of
h - k?

Answer:

Step-by-step explanation:

The expression is:

Find its value when n = 3, substitute n with 3 in the expression:

The matching answer choice is B.

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.

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.

Learn more about the regular polygon here:

brainly.com/question/11810316

#SPJ2

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

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

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

Read more about polynomial division at:

https://brainly.com/question/25289437

#SPJ1

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

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.

#SPJ3

Answer:

Step-by-step explanation:

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.

Learn more about trendlines and moving averages here

https://brainly.com/question/14254610

#SPJ4

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

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

Learn more about the slope on:

https://brainly.com/question/3493733

#SPJ1

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])

Learn more about the polynomial here:

https://brainly.com/question/16594008

#SPJ4

The given function s/(s^2 +3s -4) is proved with the help of inverse Laplace theorem.

According to the statement

we have to find the inverse of the Laplace theorem with the help pf the given theorem in the statement.

So, For this purpose, we know that the

Laplace transformation is a transformation of a function f(x) into the function g(t) that is useful especially in reducing the solution of an ordinary linear differential equation with constant coefficients to the solution of a polynomial equation.

Now, We assume you want to find the inverse transform of [tex]s/(s^2 +3s -4).[/tex]

This can be written in partial fraction form as

[tex]\frac{(4/5)}{(s+4)} + \frac{(1/5)}{(s-1)}[/tex]

which can be found in a table of transforms to be the transform of

[tex]\frac{4}{5} e^{-4t} + \frac{1}{5} e^t[/tex]

There are a number of ways to determine the partial fractions. They all start with factoring the denominator.

[tex]s^2 +3x -4 = (s+4)(s-1)[/tex]

After that, you can postulate the final form and determine the values of the coefficients that make it so.

For example:

[tex]\frac{A}{(s+4)} + \frac{B}{s-1} = (A+B)s + \frac{(4B-A)}{(s^2 +3x -4)}[/tex]

This gives rise to two equations:

(A+B) = 1

(4B-A) = 0.

So, The given function s/(s^2 +3s -4) is proved with the help of inverse Laplace theorem.

Disclaimer: This question was incomplete. Please find the full content below.

Question:

Use appropriate algebra and theorem 7.2.1 to find the given inverse laplace transform. (write your answer as a function of t.) ℒ−1 s s2 + 3s − 4.

Learn more about Laplace here

https://brainly.com/question/11630973

#SPJ4

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.

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

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°.

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

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.

For this problem, we have that:

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

More can be learned about box plots at https://brainly.com/question/27721471

#SPJ1

Answer:

Step-by-step explanation:

The standard form equation for a circle is

[tex](x-h)^2+(y-k)^2=r^2[/tex]

where h and k are the coordinates of the center. Our center is given as (-6,7)  and the radius is given as 9, so that information fits into our standard form like this:

[tex](x-(-6))^2+(y-7)^2=9^2[/tex] and simplified, it looks like this:

[tex](x+6)^2+(y-7)^2=81[/tex]

That's choice C

Answer:

I think it's A (parallel)

Answer:

A. its parallel

Step-by-step explanation:

all angles are equal... two sides are perpendicular and two are parallel

First of all, your question should be: Factor completely 2xy – 6mn – 3my + 4nx, and not Factorize completely 2xy – 6mn – 3m + 4nx. This noted, we proceed to the solution, which is:

2xy – 6mn – 3my + 4nx

→ y(2x – 3m) + 2n(–3m + 2x)

→ (2x – 3m) (y + 2n)

.: Final answer: (2x – 3m) (y + 2n)

(2x – 3m) (y + 2n) is the factorized form of  2xy -6mn - 3m + 4nx

Two or more expressions with an Equal sign is called as Equation.

Factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.

The given expression is 2xy – 6mn – 3my + 4nx

Two times of xy minus six times of mn minus three times of m y plus four times of nx

2xy – 6mn – 3my + 4nx

By using commutative property arrange the terms

2xy –3my– 6mn+ 4nx

Take y as common from first two terms and 2n as common in last two terms

y(2x – 3m) + 2n(–3m + 2x)

(2x – 3m) (y + 2n)

Hence, (2x – 3m) (y + 2n) is the factorized form of  2xy -6mn - 3m + 4nx

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ2

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.

Find dout more information about intermidiate value theorem here:

https://brainly.com/question/14456529

#SPJ4

1) The Inequalities for Tammy and Keith are respectively; For Tammy: 10x + 5y > 200 and for Keith: 12x + 3y > 180

2) The possible combination of the number of lawns they could have each mowed and the number of yards they could have raked are;

(11, 17), (14, 5), (16, 0), (18, 2)

Tammy earns $10 for each lawn mowed.

Tammy earns $5 for each yard raked.

We are told that She wants to earn more than $200 from her part-time jobs. Thus, the inequality for Tammys would be;

10x + 5y > 200

Keith earns $12 for each lawn mowed

Keith earns $3 for each yard raked.

We are told that Keith wants to earn more than $180 for each part time job. Thus, the inequality is;

12x + 3y > 180

B) To know the possible combination of the number of lawns they could have each mowed and the number of yards they could have raked, i have drawn a graph of both inequalities and the possible points from there are;

(11, 17), (14, 5), (16, 0), (18, 2)

The complete question is;

Tammy and Keith each work two part-time jobs in the summer mowing lawns andraking yards . Tammy earns $10 for each lawn she mows and $5 for each yard sherakes . She wants to earn more than $200 from her part-time jobs . Keith earns $12 for each lawn he mows and $3 for each yard he rakes. He wants to earn more than $180 for each part time job.

A) Write a system of Inequalities to model the number of lawns they each mow (x) and the number of yards they each rake.

B.) What is a possible combination of the number of lawns they could have each mowed and the number of yards they could have raked? Explain how you chose the combination and why you know that combination is correct.

Read more about Inequalities at; https://brainly.com/question/25275758

#SPJ1

Answer:

c

Step-by-step explanation:

In geometry, an equilateral triangle is a triangle in which all three sides have the same length.

Answer:

{-2, -1, 1}

Step-by-step explanation:

Since we are given all the possible inputs {-8, -3, 7} we can use them one by one in the equation to find the outputs.

5y = x - 2 , if x is -8

5y = -8 - 2

5y = -10

y = -2

Next,

5y = x - 2, if x = -33

5y = -3 - 2

5y = -5

y = -1

Last,

5y = x - 2 when x =7

5y = 7 - 2

5y = 5

y = 1

So the set is {-2, -1, 1}

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

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.

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°.

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°.

Read more on intersecting secants here: https://brainly.com/question/1626547

#SPJ1

Answer:

70

Step-by-step explanation:

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

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.

To know more about Algebra visit:

https://brainly.com/question/3624808

#SPJ4

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.

Answer:

3 consecutive no.s are

5×6×7=210

sum of them is= 5+6+7

=18

So, I hope. it helps !!

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

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

For the given figure, therefore;

V = 9 × 2 × 6 = 108

Cost of packaging per square inch, c = $0.004

Cost to package the figure, C, is therefore;

Which gives;

C = $0.004/in.² × 168 in.² = $0.672

Learn more about working with formulas in mathematics here:

https://brainly.com/question/16735912

#SPJ1

Answer:

Step-by-step explanation:

A chord is a straight line that connects two points on a curve. An arrangement of three or more notes that blend harmoniously when played together.

A section of a circle has both endpoints on the circle. Chords are the sections of a circle.

Therefore, the final answer is "chords".

I hope this helps, let me know if you have any questions.

To learn more about chords:

https://brainly.com/question/13046585

#SPJ2

Complexes with a coordination number 4 mostly adopt tetrahedral and squar planar geometries.

Complexes with a coordination number 4 mostly adopt tetrahedral and squar planar geometries.

To learn more about geometries, refer to:

https://brainly.com/question/19241268

#SPJ4

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.

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]

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]

[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

Answer:

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x)=-4^x+5\\g(x)=x^3+x^2-4x+5 \end{cases}[/tex]

This is an exponential function.

An exponential function includes a real number with an exponent containing a variable.

x-intercept (when y = 0):

[tex]\begin{aligned}f(x) & = 0\\\implies -4^x+5 & =0\\ 4^x &=5\\\ln 4^x &= \ln 5\\x \ln 4 &= \ln 5\\x&=\dfrac{ \ln 5}{\ln 4}\\x&=1.16\:\: \sf(2\:d.p.)\end{aligned}[/tex]

Therefore, the x-intercept of f(x) is (1.16, 0).

y-intercept (when x = 0):

[tex]\begin{aligned}f(0) & = -4^{0}+5\\& = 1+5\\& = 6\end{aligned}[/tex]

Therefore, the y-intercept of f(x) is (0, 6).

End behavior

[tex]\textsf{As }x \rightarrow \infty, \: f(x) \rightarrow \infty[/tex]

[tex]\textsf{As }x \rightarrow -\infty, \: f(x) \rightarrow 5[/tex]

Therefore, there is a horizontal asymptote at y = 5 which means the curve gets close to y = 5 but never touches it.  Therefore:

This is a polynomial function of degree 3 (since the greatest exponent of the function is 3).

A polynomial function is made up of variables, constants and exponents that are combined using mathematical operations.

x-intercept (when y = 0):

There is only one x-intercept of function g(x).  It can be found algebraically using the Newton Raphson numerical method, or by using a calculator.

From a calculator, the x-intercept of g(x) is (-2.94, 0) to 2 decimal places.

y-intercept (when x = 0):

[tex]\begin{aligned}g(0) & = (0)^3+(0)^2-4(0)+5\\& = 0+0+0+5\\& = 5 \end{aligned}[/tex]

Therefore, the y-intercept of g(x) is (0, 5).

End behavior

[tex]\textsf{As }x \rightarrow \infty, \: f(x) \rightarrow \infty[/tex]

[tex]\textsf{As }x \rightarrow -\infty, \: f(x) \rightarrow - \infty[/tex]

Therefore:

Conclusion

Key features both functions have in common: