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Answer:

Step-by-step explanation:

20. A rational function [tex]\frac{p(x)}{q(x)}[/tex] (where [tex]p,q[/tex] are polynomials in [tex]x[/tex]) has a removable discontinuity at [tex]x=a[/tex] if for some positive integer [tex]n[/tex] we can factorize

[tex]p(x) = (x-a)^n p^*(x)[/tex]

[tex]q(x) = (x-a)^n q^*(x)[/tex]

[tex]\implies \dfrac{p(x)}{q(x)} = \dfrac{(x-a)^n p^*(x)}{(x-a)^n q^*(x)} = \dfrac{p^*(x)}{q^*(x)}[/tex]

That is, we "remove" the discontinuity at [tex]x=a[/tex] because while [tex]x\neq a[/tex], we have [tex]\frac{x-a}{x-a}=1[/tex]. The discontinuity is still there, since [tex]\frac{p(a)}{q(a)}[/tex] is undefined, but in the limit sense we can essentially ignore the factors of [tex]x-a[/tex]. The graph of [tex]\frac{p(x)}{q(x)}[/tex] will have all the features of [tex]\frac{p^*(x)}{q^*(x)}[/tex] aside from a hole at [tex]x=a[/tex].

In this case, we have

[tex]f(x) = \dfrac{x+4}{x^2-x-20} = \dfrac{x+4}{(x+4)(x-5)}[/tex]

and when [tex]x\neq-4[/tex], we can cancel the factor of [tex]x+4[/tex] so that

[tex]f(x) = \begin{cases}\dfrac1{x-5} & \text{if }x \neq -4 \\\\ \text{DNE} & \text{if }x = -4\end{cases}[/tex]

("DNE" = "does not exist", i.e. is undefined. For some reason "undefined" wouldn't render...)

This means [tex]x=-4[/tex] is a removable discontinuity.

We cannot do the same with the factor of [tex]x-5[/tex], so in contrast [tex]x=5[/tex] is a non-removable discontinuity.

21. The pieces of [tex]f(x)[/tex] defined on [tex]x<2[/tex] and [tex]x>2[/tex] are themselves continuous since they are polynomials. Then the continuity of [tex]f(x)[/tex] over the entire real line depends on the point where the pieces meet.

Here we have

[tex]f(x) = \begin{cases}x+3 & \text{if }x\le2 \\ cx+6 & \text{if }x>2\end{cases}[/tex]

so the pieces meet at [tex]x=2[/tex]. Continuity at this point requires that the both limits from either side of [tex]x=2[/tex] be the same. This means

[tex]\displaystyle \lim_{x\to2^-} f(x) = \lim_{x\to2} (x+3) = 2+3 = 5[/tex]

[tex]\displaystyle \lim_{x\to2^+} f(x) = \lim_{x\to2} (cx+6) = 2c + 6[/tex]

Solve for [tex]c[/tex].

[tex]2c + 6 = 5 \implies 2c = -1 \implies \boxed{c = -\dfrac12}[/tex]

Answer:

linear

Step-by-step explanation:

From the table, we can deduct that y = 1.3x, which means it is a linear function. A linear function, when graphed, is a straight line.

Answer:

(x-{-2})^2+(y-{4})^2={36}

Equation:

x^2+y^2=r^2

r=radius

Blank following x/y is flipped center(of circle) coordinate for x/y

The yield to maturity best defined by the option c. The overall return the investor makes if they purchase a bond today and hold to maturity.

It is the total return of rate that will have been incomed by a bond when it makes all liability payments and repays the principal amount.

Since, as per the definition of yield to maturity, investor would get the original price of bond plus and the rate of interest that  finalized (at the time of bond purchase) when the maturity period will over.

Thus, the overall return the investor makes if they purchase a bond today and hold to maturity. Best describes yield to maturity.

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The minimum cost for this spanning tree has been calculated as $1100.

This is solves as

AC + CD + DF + FE + EB

This would be

15 + 25+ 23 + 22 + 25

= 110

The minimum cost would be gotten by multiplying this valus with the amount per foot

= 10 * 110

= $1100

Hence the minimum cost of the spanning tree is $1100

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x = 39 degrees

(alternate angles)

Angles in triangle = 180

49 + 39 = 88

So, the missing angle inside the triangle is 92

Angles on straight line = 180

180 - 92 = 88

y = 88 degrees

Hope this helps!

The type of table that has the largest area is circular table

area of a square = l²

where

Therefore,

area of the square table = 39² = 1521 inches²

area of a rectangle = lw

where

Therefore,

area of the rectangular table = 23 × 71 = 1633 inches²

area of a circle = πr²

where

Therefore,

area of a circular table = π × (48 / 2)² = 576π = 1808.64 inches²

Therefore, the table that has the largest area is the circular table.

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Anja’s phrase should have ended with “less than –15”, not “at least –15”.

Given statement:

Anja represents the inequality (4-g)/8 <-15

With the phrase “the quotient of the difference of 4 and a number and 8 is at least –15.”

Let the number be g.

“the quotient of the difference of 4 and a number and 8" translated to (4-g/8)

"at least" means : <

“the quotient of the difference of 4 and a number and 8 is at least –15.” translated to (4-g)/8 <-15

Therefore, Anja’s phrase should have ended with “less than –15”, not “at least –15”.

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Answer:

North West

Step-by-step explanation:

The middle of North and West is North West and if theoretically the smoke is going in both directions it has to be genuinely staying in the North West if that makes sense.

The length of XY on the line segment WY is 6 units.

The full line segment is WY.

Point X is on the line segment WY.

Therefore,

WY = 16 units

WX = 10 units

XY = WY - WX

Hence,

XY = 16 - 10 = 6 units.

Therefore, the length of XY on the line segment WY is 6 units.

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Answer:

  A.  Subitizing

Step-by-step explanation:

The skill to recognize small numbers of objects without counting is known as subitizing.

__

Additional comment

Some people are able to quickly recognize numbers as large as 8. More commonly in humans, the limit is about 6.

Most animals (and some insects) have an inborn ability to recognize and count up to 3. After that, the group size gets generalized to "many." Predators that hunt in groups take advantage of this limitation in their prey.

Answer:

16 I can't find the lengths but Angle A = Angle B = Angle C = 60 degrees.

17 X = 55 degrees, Y = 60 degrees, Z = 65 degrees.

18 Angle B and Angle C

19 BC and AC

20 They are all 60 degrees and are all equal to each other.

Hope I helped!

The missing values of x² column of the table are; 9 and 16 respectively and the value of ΣX² is; 47.

If follows from the table that the three columns of the table record values x, y and x².

On this note, if fill that the first missing value in which case, x = 3 and y = 2 is; 3² = 9. And in the second case where, x = 4 and y = 3 is; 4² = 16.

Hence, the value of ΣX² = 9 + 9 +9 + 4 +16 = 47.

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There are 362,880 ways that members of this group can gather.

A permutation is an act of arranging items or elements in the correct order.

Amie, Bruce, Corey, Dwayne, Eric, Frank, Georgia, Helen and Isis, members of an architectural firm, plan to meet in the company conference room to discuss the project coordinator's plans for their next project.

Denote these nine people by A, B, C, D, E, F, G, H, and I.

Then the total number of ways that members of this group can gather will be

⇒ 9!

⇒ 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

⇒ 362,880

There are 362,880 ways that members of this group can gather.

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Answer:

a gap analysis is a method of assessing the performance of a business unit to determine whether business requirements order objectives are being met and if not what steps should be taken me them a gap analyse may also be referred to as need analysis need assessment or need gap analysis

Renting a car on a monthly basis after 19 days makes it cheaper than renting on a daily basis.

How to solve such questions?

The key concept for solving such questions is by calculating the number of days on which both renting a car on a monthly basis equals renting a car on daily basis. So on the very next day as renting a car on daily basis still adds up the expense it will become costlier and renting a car on monthly basis makes it cheaper.

Given:-

Cost of renting car on a daily basis = $40

Cost of renting car on a monthly basis = $750

Let number of days on which both renting a car on a monthly basis equals renting a car on daily basis be x.

Therefore

40 × x = 750

x =  [tex]\frac{750}{40}[/tex]

x = 18.75 days

From 19th day onwards cost of renting on a daily basis will exceed cost of renting car on a monthly basis.

Thus , Renting a car on a monthly basis after 19 days makes it cheaper than renting on a daily basis.

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The most accurate statement about progress monitoring is progress monitoring is a useful way to ensure children are participating in targeted, purposeful, and meaningful math instruction and allows for the teacher to identify the skills children may need additional support in. Option A

Progress monitoring can be defined as a standard process of evaluating or checking progress toward a performance target on the basis of level of improvement from frequent assessment of a skill.

Thus, the most accurate statement about progress monitoring is progress monitoring is a useful way to ensure children are participating in targeted, purposeful, and meaningful math instruction and allows for the teacher to identify the skills children may need additional support in. Option A

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The volume of the cone is 4775.94 cu.cm

A cone is a three dimensional shape which has a circular base and then tapers down to a point called as Vertex.

It is given that the cone has

Height = 27 cm

Radius = 13 cm

The volume of the cone is given by

V = (1/3)πr²h

Volume = (1/3) * 3.14 * (13)² * 27

Volume = 4775.94 cu.cm

Therefore the volume of the cone is 4775.94 cu.cm

The complete question is

Find the volume of the cone of height = 27 cm and radius is 27 cm.

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Answer:

ABCDE is a regular pentagon with congruent diagonals BE and BD. a) Justify AABE = ACBD with a test for congruent triangles. b) Name a pair of congruent quadrilaterals.

The present age of Madison is 1027 years and that of his mother is 3080 years (rounded off to nearest whole numbers), solved using the linear equation in one variable: (x + 614) + (3x + 614) = 5334, where x represents the present age of Madison.

Linear equations in one variable are the linear relationship between two algebraic expressions not involving more than one variable throughout the equation.

In the question, we are informed that the present age of Maison's mother is 3 times that of Madison. After 614 years, the sum of their age will be 5334 years.

We are asked to determine their present ages.

We assume the present age of Madison to be x years.

Therefore, the present age of Madison's mother = 3x years {3 times that of Madison}.

Now, after 614 years, both of their ages will increase by 614 years.

Therefore, age of Madison after 614 years = x + 614 {Present + 614}.

Age of Madison's mother = 3x + 614 {Present + 614}.

We are given that after 614 years, the sum of their ages will be 5334.

This can be represented by the linear equation in one variable:

(x + 614) + (3x + 614) = 5334

This linear equation in one variable can be simplified and solved in the following way:

or, 4x + 1228 = 5334 {Simplifying},

or, 4x + 1228 - 1228 = 5334 - 1228 {Subtracting 1228 from both sides}

or, 4x = 4106 {Simplifying}

or, 4x/4 = 4106/4 {Dividing both sides by 4},

or, x = 1026.5 {Simplifying}.

Therefore, the present age of Madison = x = 1026.5 = 1027 years (nearest whole number).

The present age of Madison's mother = 3x = 3*1026.5 = 3079.5 = 3080 years (nearest whole number).

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Step-by-step explanation:

arithmetic operations with functions just means to do these operations with the function expressions. and the result is the resulting function.

so,

(f - g)(x) = f(x) - g(x) = (2x² + 3) - (x² - 7) =

= 2x² + 3 - x² + 7 = x² + 10

Answer:

The numbers between 8 and 8

9 is 8.5

8, 8.5, 9

Answer:

-2

Step-by-step explanation:

To find slope, we need to use the formula

[tex]\frac{y2-y1}{x2-x1}[/tex]

Substituting your coordinates (-1,8) and (5,-4) , we get -2 as a result.

Hope this helped!!

Answer:

slope = - 2

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 8 ) and (x₂, y₂ ) = (5, - 4 )

m = [tex]\frac{-4-8}{5-(-1)}[/tex] = [tex]\frac{-12}{5+1}[/tex] = [tex]\frac{-12}{6}[/tex] = - 2

Answer:

it's a sin

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Answer:

x = 39°

y = 90°

Step-by-step explanation:

Answer:

x = 39°

y = 92°

Step-by-step explanation:

x = 39° because alternate (or z) angles are equal.

x = 92° because all angles in a triangle add up to 180°.

so

49+39=88

angles on a straight line are equal to 180°

180°-88° = 92

Hope this helps!

Answer:

  C, E, D

Step-by-step explanation:

A "unit rate" is a rate that has 1 unit in the denominator. Here, the rates are all given in terms of the number of apples in 1 basket. (The 1 basket is the 1 unit.)

When rates are given with some number of units other than 1 in the denominator, divide the numerator by the denominator to find the unit rate.

Here, the unit rates are all more than one apple in each basket, so the number of apples must be a multiple of the number of baskets. Phrases "A" and "B" both have more baskets than apples, so will not be used.

  C: (304 apples)/(8 baskets) = (304/8) apples/basket = 38 apples/basket

  D: (294 apples)/(7 baskets) = (294/7) apples/basket = 42 apples/basket

  E: (405 apples)/(9 baskets) = (405/9) apples/basket = 45 apples/basket

  (38 apples)/(1 basket) = C: 38 apples/basket

  (45 apples)/(1 basket) = E: 45 apples/basket

  (42 apples)/(1 basket) = D: 42 apples/basket

The correct difference between the expressions is 4z⁵. The correct option is the first option 4z⁵

From the question, we are to simplify the given expression by subtracting the expressions

The given expression is

-3z⁵ - (-7z⁵)

Clear the parenthesis by multiplying

-3z⁵ +7z⁵

Simplifying

4z⁵

The simplified form of the expression is 4z⁵

Hence, the correct difference between the expressions is 4z⁵. The correct option is the first option 4z⁵

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Answer:

Step-by-step explanation:

Answer:

solution

Given,

70 kg rice =Rs.5600

1 kg= Rs5600÷70

=Rs.80

Rs.80 is for per kg.

For 1 quintal

1 quintal=100 kg

Then,

100×80

=Rs.8000.