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lim
n18
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Use the Limit Comparison Test to determine the convergence or divergence of the series.
00
n=1
n3
converges
O diverges
n+ 3
n+ 3
n3-5n+8
- 5n+ 8
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Answer:

17 +1^2=18

18+2^2=22

22+3^2=31

31+4^2=47

47+5^2=72

72+6^2=108

Step-by-step explanation:

Answer:

PQ ≈ 14.14 units

Step-by-step explanation:

calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = P (0, 4 ) and (x₂, y₂ ) = Q (10, - 6 )

PQ = [tex]\sqrt{(10-0)^2+(-6-4)^2}[/tex]

     = [tex]\sqrt{10^2+(-10)^2}[/tex]

     = [tex]\sqrt{100+100}[/tex]

     = [tex]\sqrt{200}[/tex]

     ≈ 14.14 units ( to 2 dec. places )

Answer:

[tex]PQ=10\sqrt{2}\:\: \sf units[/tex]

Step-by-step explanation:

Distance between two points formula

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]\textsf{where }(x_1,y_1) \textsf{ and }(x_2,y_2)\:\textsf{are the two points}[/tex]

Define the variables:

Substitute the defined variables into the distance formula and solve for PQ:

[tex]\implies PQ=\sqrt{(10-0)^2+(-6-4)^2}[/tex]

[tex]\implies PQ=\sqrt{10^2+(-10)^2}[/tex]

[tex]\implies PQ=\sqrt{100+100}[/tex]

[tex]\implies PQ=\sqrt{200}[/tex]

[tex]\implies PQ=\sqrt{100 \cdot 2}[/tex]

[tex]\implies PQ=\sqrt{100}\sqrt{2}[/tex]

[tex]\implies PQ=10\sqrt{2}\: \sf units[/tex]

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Answer:

Step-by-step explanation:

The formula for f(x) in y + 6 = 5(x - 4) in terms of x is f(x) = 5(x - 4)- 6

A linear equation is a equation that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the linear function in the question is given as:

y + 6 = 5(x - 4)

Subtract 6 from both sides of the equation

y + 6 - 6 = 5(x - 4) - 6

Evaluate the difference in the above equation

y = 5(x - 4) - 6

Express the above equation as a function f(x)  i.e. we express y as a function of x

f(x) = 5(x - 4) - 6

Hence, the formula for f(x) in y + 6 = 5(x - 4) in terms of x is f(x) = 5(x - 4) - 6

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Answer:

AB = 6

Step-by-step explanation:

from the diagram

AB + BC = AC , that is

x + 3x = 24

4x = 24 ( divide both sides by 4 )

x = 6

then

AB = x = 6

The length of AB calculated is 6 units

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

AC = 24

Here, from the number line the data given are :

AB = x

BC = 3x

CD = 4x-13

Now calculating length AB or x by adding AB and BC and equating to 24 :

AC = AB+BC

24 = x+3x

4x = 24

x = 24/4

x = 6

Therefore, the length of AB calculated is 6 units

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There are 9 lines of symmetry and infinite rotational symmetries in first figure,4 lines of symmetry and no rotational symmetries in second figure,6 lines of symmetry and infinite rotational symmetries in third figure,1 line of symmetry and infinite rotational symmetries in fourth figure.

Given four figures.

We are required to find the number of lines of symmetry and rotational symmtries.

Symmetry lines are those lines which act as shape in such a way that both parts are like mirror image.

Rotational symmetry is the property that a shape has when it looks same after some turn.

Hence there are 9 lines of symmetry and infinite rotational symmetries in first figure,4 lines of symmetry and no rotational symmetries in second figure,6 lines of symmetry and infinite rotational symmetries in third figure,1 line of symmetry and infinite rotational symmetries in fourth figure.

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Answer:

30calories

Step-by-step explanation:

Answer:

30 calories per ounce

Step-by-step explanation:

The answer given by rachelwang2022 is correct.

I am just adding to the explanation

Since there are 150 calories in a 5-ounce container, you can determine the number of calories per ounce by simply dividing 150 by 5.

150/5 = 30 calories per ounce

Factorization refers to the process by which the terms that are common in an expression are obtained.

Factorization refers to the process by which the terms that are common in an expression are obtained.

Given the trinomials, the correct binomial factors are;

1) (x−1)(x+7)

2) (x−2)(x−3)

3) (x+1)(x−7)

4) (x−1)(x+6)

5) (x−3)(x+4)

6) (x+2)(x−4)

7) (x+1)(x−5)

8) (x−1)(x+3)

9) (x+4)(x−4)

10) (x+3)(x−4)

11) (x−3)(x−6)

12) (x+2)(x−7)

13) (x−2)(x−5)

14) (x−3)(x−8)

15) (x+5)(x−6)

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Answer:3 lines could be used

Step-by-step explanation:

You need 2 points to draw a line. The order doesn't really matter. Line AB is the same as line BA. The problem is to select 2 points out of 3 to draw different lines. If we do the same to the others, we get the following pairs of points to draw lines.

AB , AC

BA , BC

CA , CB

which is only 3 lines

Answer:

1. Plane N

2. Points P, Q, R

3. Plane CRW …

4. Points K and H

5. Line a

Answer:

Solution Given:

To find the simplest form we need to open bracket

-2x²(3x²-2x-6)

-2x²*3x²-2x²*(-2x) -2x²*(-6)\

[tex]-6x^{4}+4x^{3}+12x^2[/tex] is  a required answer.

Answer:

Point A:  (2, 10)

Point B:  (-3, 0)

Point C:  (-5, -4)

Point D:  (-5, -32)

Step-by-step explanation:

Points A and B are the points of intersection between the two graphs.

Therefore, to find the x-values of the points of intersection, substitute one equation into the other and solve for x:

[tex]\implies 2x+6=-2x^2+18[/tex]

[tex]\implies 2x^2+2x-12=0[/tex]

[tex]\implies 2(x^2+x-6)=0[/tex]

[tex]\implies x^2+x-6=0[/tex]

[tex]\implies x^2+3x-2x-6=0[/tex]

[tex]\implies x(x+3)-2(x+3)=0[/tex]

[tex]\implies (x-2)(x+3)=0[/tex]

[tex]\implies x=2, -3[/tex]

From inspection of the graph:

To find the y-values, substitute the found x-values into either of the equations:

[tex]\begin{aligned} \textsf{Point A}: \quad 2x+6 & =y\\2(2)+6 & =10\\ \implies & (2, 10)\end{aligned}[/tex]

[tex]\begin{aligned} \textsf{Point B}: \quad -2x^2+18 & =y\\-2(-3)^2+18 & =0\\ \implies & (-3,0)\end{aligned}[/tex]

Therefore, point A is (2, 10) and point B is (-3, 0).

If the distance between points C and D is 28 units, the y-value of point D will be 28 less than the y-value of point C.  The x-values of the two points are the same.

Therefore:

[tex]\textsf{Equation 1}: \quad y=2x+6[/tex]

[tex]\textsf{Equation 2}: \quad y-28=-2x^2+18[/tex]

As the x-values are the same, substitute the first equation into the second equation and solve for x to find the x-value of points C and D:

[tex]\implies 2x+6-28=-2x^2+18[/tex]

[tex]\implies 2x^2+2x-40=0[/tex]

[tex]\implies 2(x^2+x-20)=0[/tex]

[tex]\implies x^2+x-20=0[/tex]

[tex]\implies x^2+5x-4x-20=0[/tex]

[tex]\implies x(x+5)-4(x+5)=0[/tex]

[tex]\implies (x-4)(x+5)=0[/tex]

[tex]\implies x=4,-5[/tex]

From inspection of the given graph, the x-value of points C and D is negative, therefore x = -5.

To find the y-value of points C and D, substitute the found value of x into the two original equations of the lines:

[tex]\begin{aligned} \textsf{Point C}: \quad 2x+6 & =y\\2(-5)+6 & =-4\\ \implies & (-5,-4)\end{aligned}[/tex]

[tex]\begin{aligned} \textsf{Point D}: \quad -2x^2+18 & = y \\ -2(-5)^2+18 & =-32\\ \implies & (-5, -32)\end{aligned}[/tex]

Therefore, point C is (-5, -4) and point D is (-5, -32).

Answer:

a) A = (2, 10) and B = (-3, 0)

b) C = (-5, -4) and D = (-5, -32)

Explanation:

a) To determine the coordinates of A and B, find the intersection points of  the line "y = 2x + 6" and curve "y = -2x² + 18".

Solve the equation's simultaneously:

y = y

⇒ 2x + 6 =  -2x² + 18

⇒ 2x² + 2x + 6 - 18 = 0

⇒ 2x² + 2x - 12= 0

⇒ 2x² + 6x - 4x - 12 = 0

⇒ 2x(x + 3) - 4(x + 3) = 0

⇒ (2x - 4)(x + 3) = 0

⇒ 2x - 4 = 0, x + 3 = 0

⇒ x = 2, x = -3

Then find value of y at this x points,

at x = 2, y = 2(2) + 6 = 10

at x = -3, y = 2(-3) + 6 = 0

Intersection points: A(2, 10) and B(-3, 0)

b) Given that CD = 28 units. Also stated parallel to y axis so x coordinates for both will be same but differ in y coordinate.

[tex]2x + 6 = -2x^2 + 18 + 28[/tex]

[tex]-2x^2 + 18 + 28-2x - 6 = 0[/tex]

[tex]-2x^2-2x+40=0[/tex]

[tex]-2x^2-10x+8x+40=0[/tex]

[tex]-2(x+5)+8(x+5)=0[/tex]

[tex](-2x+8)(x+5)=0[/tex]

[tex]x = -5, 4[/tex]

[tex]\leftrightarrow \sf C(-5, y_2), \ D(-5, y_2)[/tex]

Find y value for Point C : 2x + 6 = 2(-5) + 6 = -4

Find y value for Point D :  -2x² + 18 =  -2(-5)² + 18 = -32

[tex]\sf \rightarrow Point \ C = (-5, -4)\\ \\\rightarrow Point \ D = (-5, -32)[/tex]

Así, concluimos que la posición final del buzo será 7 metros bajo la superficie del agua.

Primero, vamos a definir la superficie del agua como el 0 metros.

Sí sabemos que primero el buzo se sumerge 4 metros, entonces en este punto la posición del buzo es:

P = 0m - 4m = -4m

Luego el buzo sube 2 metros, entonces la nueva posición será:

P = -4m + 2m = -2m

Finalmente, el buzo desciende otros 5 metros, entonces la posición final del buzo será:

P = -2m - 5m = -7m

Así, concluimos que la posición final del buzo será 7 metros bajo la superficie del agua.

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A statement correctly compares functions f and g is that: C. they have the same end behavior as x approaches -∞ but different end behavior as x approaches ∞.

A function can be defined as a mathematical expression that defines and represents the relationship between two or more variable, which is typically modelled as input (x-values) and output (y-values).

In Mathematics, there are different types of functions and these include the following;

Function g is represented by the following table and a line representing these data is plotted in the graph that is shown in the image attached below.

x          -1   0   1    2   3   4

g(x)     24  6   0  -2  

Based on the line, we can logically deduce the following points:

This ultimately implies that, a statement correctly compares functions f and g is that both functions have the same end behavior as x approaches -∞ but different end behavior as x approaches ∞.

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Answer:

205

Step-by-step explanation:

We start with 235, this will be our y-intercept.

6 Is deducted from our value every visit, making our slope -6.

Put the two into slope intercept form:

[tex]y=235-6x[/tex]

To find the value after 5 visits substitute x for 5:

[tex]y=235-6(5)[/tex]

Solve

[tex]y=235-6(5)\\y=235-30\\y=205[/tex]

Therefore you have 205 left in your account after 5 visits.

by solving a system of equations, we conclude that there are 7 students with blue eyes in the class.

We know that there are 40 students in the first-grade class, and we also know that:

Let's define the variables.

We know that:

H = 3*B

We also know that there are 3 students that have both blue eyes and blond hair.

And there are 15 students with none of these traits, so:

40 - 15 = 25

There are 25 students that have blue eyes, blond hair, or both.

Because we know that 3 students have both traits, we can write:

B + H - 3  =25

(Where we subtract 3 because we don't want to add these students twice).

Then we created a system of two equations:

H = 3*B

B + H - 3  =25

Replacing the first equation into the second one, we get:

B + (3*B) - 3 = 25

4*B = 25 + 3 = 28

B = 28/4 = 7

Then, by solving that system of equations, we conclude that there are 7 students with blue eyes in the class.

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a) The calculation of the cost of ending inventory using the following cost flow assumptions are as follows:

FIFO $31,000 ($15,000 + $16,000)

LIFO $22,000 ($10,000 + $12,000)

Weighted Average $26,800 ($13,400 x 2)

b) The calculation of the second-year depreciation expense using these depreciation methods is as follows:

Straight-line $4,000

Double-declining Balance $5,280

Units-of-production $6,000.

c) The correct balance of cash to be included in the Cash account on the firm’s balance sheet based on the bank reconciliation is $12,082.09.

d) The accounting entry required for the bank reconciliation is as follows:

Debit Bank Service Charges $9.85

Credit Cash Account $9.85

e) The adjusting journal entry required is as follows:

Debit Bad Debt Expense $8,000

Credit Allowance for Bad Debts $8,000

a) Berful Company:

Beginning inventory = $10,000

Purchases:

First $12,000

Second 14,000

Third 15,000

Fourth 16,000

The total cost of goods available for sale = $67,000

Weighted average cost = $13,400 ($67,000/5)

Total items available for sale = 5 items (1 + 4)

Sales = 3 items

Ending inventory = 2 items (5 - 3)

b) Cost of machine = $22,000

Estimated useful life = 5 years or 20,000 units

Salvage value = $2,000

Depreciable amount = $20,000 ($22,000 - $2,000)

Annual depreciation for second year = $4,000 ($20,000/5)

Depreciation rate = 40% (100/5 x 2)

For the first year = $8,800 ($22,000 x 40%)

Declined balance = $13,200 ($22,000 - $8,800)

For the second year = $5,280 ($13,200 x 40%)

Depreciation per unit = $1 ($20,000/20,000)

For the second year, Depreciation = $6,000 ($1 x 6,000)

Balance per Bank Statement $16,655.44

Add: Deposits in Transit          $ 2,234.81

Less: Outstanding Checks      $ 6,808.16

Balance as per Cash Book    $12,082.09

Balance per book   $12,091.94

Bank Service Charge   ($ 9.85)

The correct balance of cash in this account $12,082.09.

Bank Service Charges $9.85 Cash Account $9.85

Allowance for Bad Debts = $2,000 Debit

Net Sales = $600,000

Estimated allowance for bad debt expenses = 1% of Net Sales

= $6,000 ($600,000 x 1%)

Bad Debt Expense $8,000 Allowance for Bad Debts $8,000 ($2,000 + $6,000)

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Answer:

S = √( 1009)

Step-by-step explanation:

S = √( h² + 1/2)²)

S = √(28² + 15²)

S = √( 1009)

Hope this helps u!

The value of the double integral for the function f(x, y) and the given region R is -60.

We can use the double integral to translate our understanding of volumes under surfaces in a three-dimensional coordinate system from areas under curves in a two-dimensional coordinate system. Just two of the many uses for double integrals are the ability to compute mass densities and estimate probability density functions.

We may get the volume under the area enclosed by the region using the double integral. By evaluating integrals with respect to only one variable while holding the other variable constant, we can compute double integrals.

Given function is: f(x, y) = 8xy³; R is the rectangle defined by -2 ≤ x ≤ 0 and -1 ≤ y ≤ 2.

Firstly integrate w.r.t y and apply the limits, similarly integrate w.r.t x and apply the corresponding limits.

The value of this double integral is calculated to be -60.

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Step-by-step explanation:

in a survey of 100 people ,65 read Kantipur ,45 read Gorkhapatra, 40 read himalayan times dream,25 read Kantipur as well as Gorkhapatra ,20 read kantipur as well as himalaya times,15 read gorkhapatra,as well as himalaya times and 5 read all three news papers.

1)draw a Venn diagram to illustrate the above information.

2find how many people do not read all three news paper ?

The lateral edges are congruent and parallel. The correct option is D.

A prism is a 3-dimensional object that has two bases that are similar and congruent to each other and are connected to each other with straight lines. A few examples of the prism are given in the image below.

Lateral edges are the edges that connect the two bases of the prism.

Since the lateral edges are straight lines and connect the similar vertices of the bases. Therefore, the lateral edges are always congruent and parallel.

Hence, the correct option is D.

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The given question is incomplete. Probably the complete question is:

The lateral edges of a prism are

A. congruent, only

B. congruent and perpendicular

C. perpendicular, only

D. congruent and parallel

Answer: No

Step-by-step explanation:

The sum of exterior angles in a polygon is always equal to 360 degrees.

The x and y-intercept(s) of the graph of the function f(x)=−4|x−3|+12 are: ( 0, 0 ), ( 6, 0 ) and ( 0, 0 ) respectively.

Given the function;

f(x) = −4| x-3 | + 12

First, we find the x-intercepts by simply substituting 0 for y and solve for x.

f(x) = −4| x-3 | + 12

y = −4| x-3 | + 12

0 = −4| x-3 | + 12

−4| x-3 | + 12 = 0

−4| x-3 | = -12

Divide both sides by -4

| x-3 | = 3

We remove the absolute value sign

x - 3 = ±3

x = 3±3

x = 3-3, 3+3

x = 0, 3

Hence, x-intercepts are: ( 0, 0 ), ( 6, 0 )

Next, we find the y-intercept by substituting 0 for x and solve for y.

f(x) = −4| x-3 | + 12

y = −4| 0-3 | + 12

y = −4| -3 | + 12

We remove the absolute value sign

y = −4(3) + 12

y = −12 + 12

y = 0

Hence, y-intercept is: ( 0, 0 ).

The x and y-intercept(s) of the graph of the function f(x)=−4|x−3|+12 are: ( 0, 0 ), ( 6, 0 ) and ( 0, 0 ) respectively.

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Answer:

-40x

Step-by-step explanation:

f(x) =-3x-5

g(x) =4x-2

(f+g)(x) =?

now,

f(g(x))

=f(4x-2)

=-3×4x-2-5

=-10×4x

=-40x

Answer:

y=-1/2n+44

Step-by-step explanation:

The number of bean stalks, n, represents the x values

The yield, y, represents the y values

After reading the problem, we have two coordinates: (30,29) and (32, 28) Because this problem is asking for y=mn+b, we have to find the slope. How do we find the slope? We do so by using the slope formula y2-y1/x2-x1. Now let's input the coordinates into this formula.

1.) 28-29/32-30 = -1/2

Let's plug -1/2 into y=mn +b

2.) y=-1/2n+b

Now we have to find what b ( y intercept) equals. To find B, we plug a coordinate into x and y. Let's use (30,29)

3.) 29 = -1/2(30)+b

29 = -15 +b

44 = b

We have now found the linear relationship form for this problem: y=-1/2n +44

Obtuse angle means its degree is greater than 90° but smaller than 180°.

< MOK exists 180°

< NOJ exists 90°

An obtuse angle exists a kind of angle that is always larger than 90° but less than 180°. In other words, it lies between 90° and 180°.

It exists not equivalent to 90° and 180°.

Because if obtuse angle equal to 90 degree it exists "Right angle'

If obtuse angle equal to 180 degree it exists 'Straight Angle'.

Obtuse angle means its degree is greater than 90° but smaller than 180°.

< MOK exists 180°

< NOJ exists 90°

Therefore, the correct answer is option a) MOL, NOK, MOJ.

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Answer:

Step-by-step explanation:

using figure a above name two right angles

Answer:

yes

Step-by-step explanation:

yes

Answer:

assume the formula is true for n is equal to k prove that result is true for n is equal to k + 1 hence result proves since the thorum is true for n is equal to 1 and n k + 1 is unit through a and

The graph of the translated function can be seen in the image below.

For a given function f(x), we define a vertical translation of N units as:

g(x) = f(x) + N

Where if N is positive, the translation is upwards. If N is negative, the translation is downwards.

In this case, we have:

y = f(x) - 2

Then we just need to translate the given graph 2 units below, we will get the graph you can see below.

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Answer:

add sum of all the angle given

In order to make a 3-dimensional object into a 4-dimensional object, it's important to draw the 4-dimensional shape in a way that gives the illusion of the 3-dimensional object.

It should be noted that shapes play an important part in geometry.

Here, to make a 3-dimensional object into a 4-dimensional object, it's important to draw the 4-dimensional shape in a way that gives the illusion of the 3-dimensional object.

Also, it should be noted that a 4D tesseract can be used to project the image.

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