What is the nth term rule of the quadratic sequence below?
6
,
20
,
40
,
66
,
98
,
136
,
.
.
.

Answers

Answer 1

Answer:

3n² + 5n - 2

Step-by-step explanation:

Given sequence:

6, 20, 40, 66, 98, 136, ...

Calculate the first differences between the terms:

[tex]6 \underset{+14}{\longrightarrow} 20 \underset{+20}{\longrightarrow} 40 \underset{+26}{\longrightarrow} 66 \underset{+32}{\longrightarrow} 98 \underset{+38}{\longrightarrow} 136[/tex]

As the first differences are not the same, calculate the second differences:

[tex]14 \underset{+6}{\longrightarrow} 20 \underset{+6}{\longrightarrow} 26 \underset{+6}{\longrightarrow} 32 \underset{+6}{\longrightarrow} 38[/tex]

As the second differences are the same, the sequence is quadratic and will contain an n² term.

The coefficient of the n² term is half of the second difference.

Therefore, the n² term is:  3n²

Compare 3n² with the given sequence:

[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5} 3n^2 & 3 & 12 & 27 & 48 \\\cline{1-5} \sf operation & +3&+8 & +13 & +18 \\\cline{1-5} \sf sequence & 6 & 20 & 40 & 66\\\cline{1-5}\end{array}[/tex]

The second operations are different, therefore calculate the differences between the second operations:

[tex]3 \underset{+5}{\longrightarrow} 8 \underset{+5}{\longrightarrow} 13\underset{+5}{\longrightarrow} 18[/tex]

As the differences are the same, we need to add 5n as the second operation:

[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5} 3n^2 +5n & 8&22 & 42 & 68\\\cline{1-5}\sf operation & -2 &-2 &-2 & -2 \\\cline{1-5} \sf sequence & 6 & 20 & 40 & 66\\\cline{1-5}\end{array}[/tex]

Finally, we can clearly see that the operation to get from 3n² + 5n to the given sequence is to subtract 2.

Therefore, the nth term of the quadratic sequence is:

3n² + 5n - 2


Related Questions

What effect does it have when there are exceptions to the overall trend in a relationship between two variables?

Answers

Option 3. The effect that it has when there are exceptions to the overall trend between two variable is that It is irrelevant to the relationship.

What is a trend between two variables?

This is used in statistics to show that there is the existence of two variables that are positively correlated.

These two variables would then have a positive slope trend line. Hence the answer to the question is option 3.

Complete question

What effect does it have when there are exceptions to the overall trend in a relationship between two variables?

O It increases the relationship

O It decreases the relationship

O It is irrelevant to the relationship.

Read more on trend variables here:

https://brainly.com/question/24679525

#SPJ1

Watch help video
Mason is a songwriter who collects royalties on his songs whenever they are played in
a commercial or a movie. Mason will earn $30 every time one of his songs is played in
a commercial and he will earn $80 every time one of his songs is played in a movie.
Mason earned a total of $470 in royalties on 9 commercials and movies. Write a
system of equations that could be used to determine the number of commercials and
the number of movies on which Mason's songs were played. Define the variables that
you use to write the system.

Answers

Answer:479

Step-by-step explanation:470+9=479

We can write the system of equation that determines the number of commercials and the number of movies on which Mason's songs were played as →  30x + 80y = 470   and    x + y = 9. The variables used in the system of equations are -

x - Number of times his song played in a commercial

y - Number of times his song played in a movie.

What is equation modelling?

Equation modelling is a method of writing a mathematical relation from a mathematical statement for mathematical analyses of the problem given.

Given is Mason who collects royalties on his songs whenever they are played in commercials or movies.

Assume that his song played in 'x' commercials and 'y' movies.

Cost per song when played in commercial = $30

Then for 'x' commercials, total cost will be = $30x

Cost per song when played in movie = $80

Then for 'y' movies, total cost will be = $80y

Total money earned through both = $470

We can write the system of equation that determines the number of commercials and the number of movies on which Mason's songs were played as -

30x + 80y = 470

The total number of commercials and movies combined -

x + y = 9

The variables used in the system of equations are -

x -   Number of times his song played in a commercial

y - Number of times his song played in a movie.

Therefore, We can write the system of equation that determines the number of commercials and the number of movies on which Mason's songs were played as →  30x + 80y = 470   and    x + y = 9. The variables used in the system of equations are -

x - Number of times his song played in a commercial

y - Number of times his song played in a movie.

To solve more questions on Equation modelling, visit the link below-

https://brainly.com/question/19537789

#SPJ5

Which exponential function has a faster rate f(x)=5^x or g(x)=(1/3)^x. How do you know?

Answers

Answer:

f(x)

Step-by-step explanation:

This question isn't to difficult, since all you need to know is: [tex](\frac{a}{b})^x=\frac{a^x}{b^x}[/tex]. If the you're not quite sure why this is true, I'll try to express this in another way. [tex](\frac{a}{b})^x=\frac{a}{b}*\frac{a}{b}*\frac{a}{b}...\text{ x amount of times}[/tex], and as you may know when multiplying fractions, you simply multiply the numerators by the numerators and the denominators by the denominators, this means that you can simplify it to: [tex]\frac{a*a*a...\text{ x amount of times}}{b*b*b...\text{ x amount of times}}[/tex] this is literally what an exponent is which is why you can distribute the exponent as such: [tex](\frac{a}{b})^x=\frac{a^x}{b^x}[/tex]. The next thing you need to know is that: [tex]1^x=1[/tex] for any real number. This is you can express this as: [tex]1*1*1...\text{ x amount of times} = 1[/tex], since 1 times 1 times 1, will always remain 1. You may think this will not apply for rational exponents, but it still does since: [tex]1^{\frac{a}{b}}=\sqrt[b]{1}^a[/tex], and no matter what b is, it's going to be 1. The square root of 1, is 1..., the cube root of 1 is 1.... This is because the very definition of a radical is what number times times it self index amount of times is equal to the number under the radical, and no matter how many times you multiply 1, you're going to get 1. If that's a bit confusing what I'm saying is: [tex]\sqrt[n]{b}\implies\text{?}^n=b[/tex].

Anyways hopefully you understand that, if not I'm sorry if I went a bit overboard trying to explain it. Anyways all you need to really know is that: [tex](\frac{1}{3})^x=\frac{1^x}{3^x}=\frac{1}{3^x}[/tex]. So this means as x increases, all you're really doing is increasing the denominator which is decreasing the number. The f function has an integer as a base, so the function will overall be increasing. This is not true for g(x) since as x increases the y-value decreases. So this means that f(x) has a faster rate. This is because the g(x) has a horizontal asymptote, since as x approaches infinity, g(x) approaches 0, since the denominator is increasing towards infinity. So the rate of change will be slowing down as x increases, since there is only so much the g(x) can change, since it has a horizontal asymptote. This is not true for f(x) as it has no horizontal asymptote and just goes towards infinity. So the f(x) has a faster rate.

19. What is the coordinate for the vertex of the function f(x)=-16x² + 64x?

Answers

Answer:

vertex = (2, 64 )

Step-by-step explanation:

given a parabola in standard form

f(x) = ax² + bx + c ( a ≠ 0 ) , then the x- coordinate of the vertex is

x = - [tex]\frac{b}{2a}[/tex]

f(x) = - 16x² + 64x ← is in standard form

with a = - 16, b = 64, c = 0 , then

x = - [tex]\frac{64}{-32}[/tex] = 2

substitute x = 2 into f(x) for corresponding y- coordinate

f(2) = - 16(2)² + 64(2) = - 16(4) + 128 = - 64 + 128 = 64

vertex = (2, 64 )

ext → Post Test: Systems of Linear Equations and Inequalities
1
Use the drawing tool(s) to form the correct answers on the provided graph.
1
Graph the system of equations given below on the provided graph.
2x - 3y = -18
3x + y = -5
Then, use the Mark Feature tool to plot the solution to the system.

Answers

The way to construct the equation in a graph is illustrated.

How to illustrate the information?

Converting the equation in slope-intercept form

2x-3y= -18

-3y= -2x-18

-3y= -(2x+18)

3y=2x+18

y=(2x+18)/3

And for equation 2

y= -5-3x

The points can be calculated by putting negative and positive values of x in both equations.

The graph is attached as a picture.

As we can see from the graph that two lines intersect at (-3,4) so it is the solution of the given system of linear equations.

Learn more about graph on:

https://brainly.com/question/19040584

#SPJ1

A circus is composed of acrobats, ballerinas, clowns, and dogs. The number of acrobats and ballerinas, minus the number of clowns, is one fewer than the number of dogs. Twice the combined number of acrobats and ballerinas is five more than three times the number of clowns. If the number of dogs is one more than the number of clowns, how many people and animals belong to the circus

Answers

If we make appropriate equation then we can find that there are 21 people and animals belong to the circus.

Given The number of acrobats and ballerinas, minus the number of clowns, is one fewer than the number of dogs. Double the combined number of acrobats and ballerinas is five more than three times the number of clowns.

We have to find total people and animals belong to the circus.

An equation is relationship between variables that are expressed in equal to form. It is solved to find the variables in equal to form Equations of two variables look like ax+ by=c.

let the number of acrobats be x, ballerinas be y, clowns be z, clowns be u.

According to given information in question the equations are:

x+ y-z=u-1-----------------------1

2(x+ y)=3z+5-------------------2

u=z+1----------------------------3

Put the value of u from 3 in 1

x+y- z=z+1-1

x+y-2z=0

from 2

z=2x+2y-5/3

put the value of z in x+y-2z=0

x+y-2(2x+2y-5/3)=0

-x-y+10=0

x+ y=10-------------------------4

put put the value of x+y=10 in 1

10-z=u-1

u+z=11-----------------------------5

solving 3

u-z=1------------------------6

Now add 5&6

u+z+u-z=11+12

2u=12

u=6

Put the value of u in 6

6-z=1

z=5

From above we get x+y=10, u=6, z=5

Add all three we get the total number of people and animals belong to circus.

x+y+u+z=10+6+5

=21

Hence there are total 21 people and animals belong to the circus.

Learn more about equations at https://brainly.com/question/2972832

#SPJ4

What is the range of the function shown in this table?


OA. (3, 4), (4, 4), (5, 2), (6, 5)
OB. (3,4)
O C. (2, 4, 5)
O D. (3, 4, 5, 6}

Answers

Answer: A

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The range is just the y-values. You don't have to write any of the repeated values. You do need to write them in numerical order.

4, 4, 2, 5

becomes

2,4,5

Alexandra needs to reshingle her roof. She leans a ladder against the the wall of the house so that the top of the ladder is 8 feet above the ground. The bottom of the ladder is 5 feet from the base of the wall. Find the angle formed between the ladder and the house. Round the answer to the nearest whole degree. A. B. C. D. Please select the best answer from the choices provided A B C D

Answers

If the top is 8 feet above the ground and ladder is 5 feet away from bottom of wall then the angle between ladder and house is 58°.

Given top is 8 feet above the ground, ladder is 5 feet away from bottom of the wall.

Trigonometric ratios are the ratios of the sides of a right angled triangle. sin is the ratio of perpendicular and hypotenuse , cos is the ratio of base and hypotenuse, tan is the ratio of perpendicular and base, cosec is the ratio of hypotenuse and perpendicular, sec is the ratio of hypotenuse and base, cot is the ratio of base and perpendicular.

Here we use tan d where d is the angle between ladder and wall of the house.

tan d= P/B

tan d=8/5

tan d=1.6

[tex]d=tan^{-1} 1.6[/tex]

d=57.99

After rounding off it will be 58°.

Hence the angle between ladder and house is 58°.

Learn more about trigonometric ratios at https://brainly.com/question/24349828

#SPJ4

For 7,440 blank shares could have been bought ?

Answers

Answer:

$2,000

Step-by-step explanation:

7,440/3.72

Which explains why the graph is not a function? It is not a function because the points are not connected to each other. It is not a function because the points are not related by a single equation. It is not a function because there are two different x-values for a single y-value. It is not a function because there are two different y-values for a single x-value.On a coordinate plane, solid circles appear at the following points: (negative 2, negative 5), (negative 1, 3), (1, negative 2), (3, 0), (4, negative 2), (4, 4).

Answers

The given points of the expression is not a function because there are two different y-values for a single x-value.

Given The points are : (-2,-5), (-1,3), (1,-2) , (3,0) ,(4,-2) (4,4)

Function refers to a relation or expression involving one or more variables. In a function each value of x corresponds to each value of y. A relation which is having two or more values of y for x values is not a function.

We have been given points  (-2,-5), (-1,3), (1,-2) , (3,0) ,(4,-2) (4,4).

These are not points of a function because of a simple reason that it has two values of y for each one value of x.

Value of relation at x=-2 is -5.

Value of relation at x=-1 is 3.

Value of relation at x=1 is -2.

Value of relation at x=3 is 0.

Value of relation at x=4 is -2.

Value of relation at x=4  also equal to  4.

It has two values at x=4 one is -2 and other one is 4.

Hence the relation is not a function because there are two different y-values for a single x-value.

Learn more about function at  https://brainly.com/question/10439235

#SPJ10

The given points of the expression is not a function because there are two different y-values for a single x-value.

Given The points are : (-2,-5), (-1,3), (1,-2) , (3,0) ,(4,-2) (4,4)

Function refers to a relation or expression involving one or more variables. In a function each value of x corresponds to each value of y. A relation which is having two or more values of y for x values is not a function.

We have been given points  (-2,-5), (-1,3), (1,-2) , (3,0) ,(4,-2) (4,4).

These are not points of a function because of a simple reason that it has two values of y for each one value of x.

Value of relation at x=-2 is -5.

Value of relation at x=-1 is 3.

Value of relation at x=1 is -2.

Value of relation at x=3 is 0.

Value of relation at x=4 is -2.

Value of relation at x=4  also equal to  4.

It has two values at x=4 one is -2 and other one is 4.

Hence the relation is not a function because there are two different y-values for a single x-value.

The radius of a sphere is 3 inches. Which represents the volume of the sphere?
• 12t cubic inches
• 367 cubic inches
• 647T cubic inches
• 817 cubic inches

Answers

Answer:

Step-by-step explanation:

The formula for the volume of a sphere of radius r is V = (4/3)(pi)r^3.

Here, with r = 3 in, the volume is

V = (4/3)(3.14)(3 in)^2, or  V  =  36(pi)(27 in)^3 = 36pi in^3

There were three parts to Rita's race. She ran the first part, which was 4/9
of the total distance, in 20 minutes. She ran the second part, which was 2/5
of the remaining distance, in 12 minutes. She finally ran the third part in 15 minutes at a speed of 300 meter per minute.
A) How long was the first part of the race? What was Rita's speed in that section of the race?
B)How long was the second part of the race? What was Rita's speed in that section of the race?

Answers

Answer:

300 meters per minute

Step-by-step explanation:

Step 1

Determine the fraction of the total distance for each part of the race.

Given:

1st part of race = 4/9 of total distance

2nd part of race = 2/5 of remaining distance

Step 2

Determine the distance of the third part of the race.

Given:

time = 15 minutes

speed = 300 meters per minute

Step 3

If the third part of the race (which is 1/3 of the total distance) is 4500m, then the distance of the whole race is:

Step 4

Determine the distance of the 1st part of the race:

Step 5

Determine the speed of the 1st part of the race:

Given:

time = 20 minutes

distance = 6000 m

Select the equivalent expression. 2^-4=
Choose 1 answer
a)1/2^4
b)-2^4
c)(-2)^4

Answers

Answer: A 1/2 ^4

Step-by-step explanation:

Answer:

a)1/2^4

Step-by-step explanation:

First solve 2^-4.

Use negative power rule: x^-a = 1/xa

⇒ 1/2^4

Simplify 2^4 to 16

⇒ 1/16

Just evaluate the other options.

The first one is correct.

Here's why:

⇒ Simplify 2^4 to 16.

⇒ 1/16

They have the same steps, therefore making Option A correct.

Note: This is the longer way, there is a easier way of dealing with these types of problems. Example: Without using a calculator problem.

The lengths of the sides of triangle XYZ are written in terms of the variable m, where m ≥ 6.

Triangle X Y Z is shown. The length of side X Y is m + 8, the length of side Y Z is 2 m + 3, the length of side Z X is m minus 3.

Which is correct regarding the angles of the triangle?
mAngleX < mAngleZ < mAngleY
mAngleY < mAngleZ < mAngleX
mAngleY < mAngleX < mAngleZ
mAngleZ < mAngleY < mAngleX

Answers

Answer:

Option (2)

Step-by-step explanation:

The angle opposite the shortest side is the smallest and the angle opposite the longest side is the largest.

Since m is greater than or equal to 6, we know that:

2m+3 > m+8 > m-3

Which of the following could represent the interval −4 ≤ x ≤ 6?

Answers

Answer:

Step-by-step explanation:

-4 [tex]\leq[/tex] x [tex]\leq[/tex] 6

x = {-4,-3,-2,-1,0,1,2,3,4,5,6}

Hope I helped...

ABC is a triangle. ACD is an isosceles triangle. Find ACB and ABC.

Answers

Answer:

∠ ACB = 128° and ∠ABC = 32°

Step-by-step explanation:

∠ ADC = ∠ CAD (base angles theorem)

∠ ACD = 82° (angles in a triangle add to 180°)

∠ ACB = 128° (angles around a point add to 360°)

∠ ABC = 32° (angles in a triangle add to 180°)

Find the volume of the prism.

Answers

Answer:

216km

Step-by-step explanation:

The formula for finding the volume of a triangular prims is:

0.5 * b * h * length, where b is the length of the base of the triangle, h is the height of the triangle and length is prism length.

So, let's substitute those variables with the base length, height length, and prism length

The base length is 6km, the height length is 8km, and the prism length is 9km

So, we get:

0.5 * 6 * 8 * 9

= 1/2 * 6 * 8 * 9

= 1/2 * 48 * 9

= 1/2 * 432

= 216

The volume of this prism is 216km.

Which expression is equivalent to 14 times 14?
2 squared
2 Superscript 14
14 squared
14 Superscript 14

Answers

Answer:

[tex]14^{2}[/tex]

Step-by-step explanation:

14*14

14 is the base.  We are multiplying 14 two times.  Two would be the exponent

14 ^2

14² = 14x14 (correct)
2² = 2x2 (wrong)

here is the histogram of a data distribution. all class widths are 1. which of the following is the closest to the mean of this ditribution

Answers

The answer your looking for is 2

Please need help ASAP

Answers

Answer:

Can u please upload more clearer pictures ?

3. Find the point of intersection of the graphs for each system. a.2x + 2y = 3 and 6x-6y = -1​

Answers

Given :

2x + 2y = 3 (Equation #1)6x - 6y = -1 (Equation #2)

Multiply Equation #1 by 3 :

3(2x + 2y) = 3(3)6x + 6y = 9 (Equation #3)

Add Equations 2 and 3 :

6x - 6y + 6x + 6y = -1 + 912x = 8x = 2/3

Now, input x in Equation #3 to find y :

6(2/3) + 6y = 94 + 6y = 96y = 5y = 5/6

∴ Hence, the point of intersection is (2/3, 5/6).

In your opinion, which is the best and simplest way to factor polynomials (including quadratics)? Explain why you chose this method compared to other methods. Are there some exceptions to this, maybe a polynomial that might factor better with another method?

Answers

The simplest way to factor polynomials is to use the greatest common factor.

How to illustrate the polynomial?

It should be noted that the polynomial simply means the expression of more than two algebraic terms.

In this case, the simplest way to factor polynomials is to use the greatest common factor. This simply had to do with the largest factor that the numbers share.

Other methods that can be utilized include the grouping method, the sum of the difference in cubes and in two squares.

Learn more about polynomial on:

brainly.com/question/2833285

#SPJ1

What is the solution to the equation 2^x+4 -12=20

Answers

Answer:

2^x = 28

Step-by-step explanation:

What is the solution to the equation?

[tex]2^{x}[/tex] + 4 - 12 = 20

[tex]2^{x}[/tex] = 20 - 4 + 12

[tex]2^{x}[/tex] = 16 + 12

[tex]2^{x}[/tex] = 28

Answer:

x-1

Step-by-step explanation:

because i said so

Multiply:
-9w(w + 10)
asap answer plsss

Answers

Answer:

-9w^2-90w

Step-by-step explanation:

You just use the distributive property and watch the negatives and positives.

[tex]\huge\boxed{-9w^2-90w}[/tex]

Distribute [tex]-9w[/tex] to both [tex]w[/tex] and [tex]10[/tex] as shown in the attached image. Then, just simplify the terms with multiplication.

[tex](-9w)\cdot w+(-9w)\cdot10\\\boxed{-9w^2-90w}[/tex]

To get from his house to the lecture hall at school, Lin walked west 651 feet. After class, he walked northeast 910 feet to the gym. Finally, he walked 615 feet back to his house from the gym.

A triangle has points gym, Lin apostrophe s house, and lecture hall. The distance between the lecture hall and gym is 910 feet. The distance between the gym and Lin apostrophe s house is 615 feet. The distance between the lecture hall and Lin apostrophe s house is 651 feet.

What general direction did Lin walk from the gym to his house, and what type of triangle did his walking path form?
Lin walked south, creating a right triangle.
Lin walked southwest, creating an obtuse triangle.
Lin walked southeast, creating an acute triangle.
Lin walked directly east, creating a right triangle.

Answers

The general direction that Lin walked from the gym to his house is; B: Lin walked southwest, creating an obtuse triangle.

How to interpret distance bearing?

We are given;

Distance between the lecture hall and gym = 910 feet.

Distance between the gym and Lin apostrophe's house = 615 feet.

Distance between the lecture hall and Lin apostrophe's house = 651 feet.

Now, since this 3 distances form a triangle and the 3 distances are unequal, then we can call it an obtuse triangle since he walked west and then walked northwest.

Now, since he walked back to his house from the gym, we can say that he walked southwest if we picture the bearing of his first two directions.

Read more about Distance Bearing at; https://brainly.com/question/22719608

#SPJ1

You buy 12 packages of discounted socks for a total cost of $85.50, which includes a 5% discount.

Before the discount, how much did a single package of socks cost?

a.)
$7.50

b.)
$4.75

c.)
$6.78

d.)
$10.68

Answers

Answer:

a) $7.50

Step-by-step explanation:

The total cost of $85.50 includes a 5% discount, so 95% of what price is $85.50?

[tex].95x = 85.50[/tex]

[tex]x = 90[/tex]

So the original price is $90. Divide this by 12, obtaining $7.50.

Answer:

a)$7.5

Step-by-step explanation:

Solution:

Let X represents socks

Given,

Selling price (SP) of 12x=$85.50

Discount precent (d%)=5%

So,

SP=(100-d)% of MP. [this formula really exist believe it or not]

85.50= (100-5)/100 ×MP

or, 85.50×100 =95×MP

or, 8550/95=MP

So,MP=$90

Now At last ,

cost of 1 shocks before discount is 90/12

which is $7.50 ans√

PLEASE HELP
This table contains an Arithmetic Sequence. Find the missing terms in the table.

Answers

2=^? Zlon square right

D
A fabric mill produces 4953 metres of fabric in a day. How much fabric will it
365 days]
produce in a year? [1 year =365 days

Answers

The fabric mill produce 1,807,845 meters of fabric in 365 days.

A fabric mill produces 4953 meters of fabric in a day.

What is simplification?

operations and interpretations to function to make function simple or more understandable called simplify and the process is called simplification.

We have 4953 meter of fabric in a day.
So for 365 days
fabric = 4953 x 365
= 1,807,845

Thus, the fabric mill produce 1,807,845 meters of fabric in 365 days.

Learn more about simplification here: https://brainly.com/question/12501526

#SPJ1

What is the inverse of function ??
f(x) = 64x³ - 1

Answers

Answer:

The inverse of the function f(x) = 64x³ - 1 is [tex]\frac{\sqrt[3]{x+1}}{4}[/tex]

Step-by-step explanation:

First replace x with y.

[tex]x=64y^3-1[/tex]

Then solve for y.

[tex]y^3=\frac{x+1}{64}[/tex]

Cube root both sides.

[tex]y=\frac{\sqrt[3]{x+1}}{4}[/tex]

Hence, the inverse is [tex]\frac{\sqrt[3]{x+1}}{4}[/tex]

One can convert temperature from fahrenheit into newton using the formula . what is the temperature in fahrenheit corresponding to n degrees newton?

Answers

newton si the most populat
Other Questions
Suppose that $x$ is a multiple of 6 (not necessarily positive). If the square of $x$ is less than 200, how many possible values of $x$ are there c)Phage therapy may be considered the 21st century answer to combattingbacterial infections. Discuss the potential merits and problems associated withusing this as a clinical treatment.What are the pros and cons? Find the number, d, if the sum of five times d and five times five is ahundred. Type the correct answer in each box. Use numerals instead of words.Functions f and g are represented in the table and the graph. Which of the following is an example of a positive feedback mechanism? A. Body temperature is increased if skeletal muscles move quickly and cause a person to shiver. B. During childbirth, the baby's head pushing on the cervix encourages uterine contractions. C. The kidneys retain more water if the organism's water level is low. D. Insulin causes cells to absorb glucose. A uniform rod with a mass of m = 1.94 kg and a length of l = 2.10 m is attached to a horizontal surface with a hi=nge. The rod can rotate around the hi=nge without friction. (See figure.)Initially the rod is held at rest at an angle of = 70.4 with respect to the horizontal surface. Then the rod is released.What is the angular speed of the rod, when it lands on the horizontal surface?1.61 rad/s is incorrect.What is the angular acceleration of the rod, just before it touches the horizontal surface?1.06 rad/s^2 is incorrect. Write an equation in slope intercept form for the line with slope -1/2 and y-intercept -5 The country with the least number of casualties was A. Austria-HungaryB. GermanyC. the Ottoman EmpireThe country with the highest casualty rate was A. GermanyB. Austria-HungaryC. the Ottoman Empire What does Antony say in this excerpt from Shakespeares Julius Caesar to portray himself as a patriot?ANTONYThe noble Brutus Hath told you Caesar was ambitious:If it were so, it was a grievous fault,And grievously hath Caesar answer'd it.Here, under leave of Brutus and the rest--For Brutus is an honourable man;So are they all, all honourable men--Come I to speak in Caesar's funeral.He was my friend, faithful and just to me:But Brutus says he was ambitious;And Brutus is an honourable man.He hath brought many captives home to RomeWhose ransoms did the general coffers fill:Did this in Caesar seem ambitious?When that the poor have cried, Caesar hath wept:Ambition should be made of sterner stuff:Yet Brutus says he was ambitious;And Brutus is an honourable man.You all did see that on the LupercalI thrice presented him a kingly crown,Which he did thrice refuse: was this ambition? (3.2.87-100)Group of answer choicesAntony insults Brutus and explains how Brutus is actually the evil one.Antony points out that Caesar cant be ambitious if he wept with the poor and turned down the crown three times.Antony insists that Brutus was much more immoral than Caesar ever was.Antony shows all of Caesars stab wounds in this speech, which spurs the Plebians to mutiny. PLEASE HELP!!!!!!!!!!!!!! Two different cubes of the same size are to be painted, with the color of each face being chosen independently and at random to be either black or white. What is the probability that after they are painted, the cubes can be rotated to be identical in appearance Summary of which way? Since data-flow diagrams concentrate on the movement of data between processes, these diagrams are often referred to as: A. flow charts. B. process models. C. flow models. D. data models. E. algorithm models. You go to see family in another city. So far you have gone 120 miles. The total trip is 360 miles. What fraction of the total trip, in lowest terms, has been traveled?a.12/36b.2/3c.3/4d.1/3for 20 points please help Using what you learned in this lab, how could you determine the polarity of other common household substances? What is ironic and tragic about Valencias death?Select one:a. She dies because she deserves it for being such a despicable, evil character.b. She dies because she neglects to take care of her health after years of neglect.c. She dies because she rushes to see Billy after his accident and doesnt take care of herself.d. She dies because she is aware that Billy has cheated on her with other women. This passage is from the testimony of Henry. Adams, a former enslaved man who testifiedbefore the Senate in 1880 about the treatmenthe encountered after emancipation. This passage is describing the proposition for asharecropping contract.COMPLETEIn two to three sentences, describe what makes this proposed contract one-sided. all of the amendments When a numberis decreased by 20% of itself the result is 64 3: Morgan Cruise earns net self-employment income of $221,600. She works a second job from which she receives FICA taxable earnings of $111,300.00.Self-Employment tax =137,700 cap