The endpoints of RS are R(−4,3) and S(16,18). Complete each statement using a fraction.
a. (8,12) is the point​ ___ of the way from R to S.
b. (0,6) is the point​ ___ of the way from R to S.

Answers

Answer 1

Answer:

a) (8,12) is the point [tex]\frac{3}{5}[/tex] of the way from R to S, b) (0, 6) is the point [tex]\frac{1}{5}[/tex] of the way from R to S.

Step-by-step explanation:

Let be [tex]X[/tex] a point in the line between endpoints [tex]R[/tex] and [tex]S[/tex]. The ratio of the line segment [tex]RX[/tex] to the line segment [tex]RS[/tex] is given by:

[tex]r = \frac{RX}{RS}[/tex]

Where:

[tex]RX = \sqrt{(x_{X}-x_{R})^{2}+(y_{X}-y_{R})^{2}}[/tex]

[tex]RS = \sqrt{(x_{S}-x_{R})^{2}+(y_{S}-y_{R})^{2}}[/tex]

Let be [tex]x_{R} = -4[/tex], [tex]y_{R} = 3[/tex], [tex]x_{S} = 16[/tex] and [tex]y_{S} = 18[/tex].

a) If we know that [tex]x_{X} = 8[/tex] and [tex]y_{X} = 12[/tex], the ratio of the line segment [tex]RX[/tex] to the line segment [tex]RS[/tex] is:

[tex]RX =\sqrt{[8-(-4)]^{2}+(12-3)^{2}}[/tex]

[tex]RX = 15[/tex]

[tex]RS =\sqrt{[16-(-4)]^{2}+(18-3)^{2}}[/tex]

[tex]RS = 25[/tex]

Then,

[tex]r = \frac{15}{25}[/tex]

[tex]r = \frac{3}{5}[/tex]

(8,12) is the point [tex]\frac{3}{5}[/tex] of the way from R to S.

b) If we know that [tex]x_{X} = 0[/tex] and [tex]y_{X} = 6[/tex], the ratio of the line segment [tex]RX[/tex] to the line segment [tex]RS[/tex] is:

[tex]RX =\sqrt{[0-(-4)]^{2}+(6-3)^{2}}[/tex]

[tex]RX = 5[/tex]

[tex]RS =\sqrt{[16-(-4)]^{2}+(18-3)^{2}}[/tex]

[tex]RS = 25[/tex]

Then,

[tex]r = \frac{5}{25}[/tex]

[tex]r = \frac{1}{5}[/tex]

(0, 6) is the point [tex]\frac{1}{5}[/tex] of the way from R to S.


Related Questions

6(4.5x-12)=9
A. X= 0.6
B. x = 28
C. x= 3
D. x= 3.3

Answers

Answer:

Step-by-step explanation:

27x - 72 = 9

27x = 81

x = 3

answer is C

Colton and his children went into a movie theater and he bought $48.50 worth of bags of popcorn and candies. Each bag of popcorn costs $5.50 and each candy costs $3.50. He bought a total of 11 bags of popcorn and candies altogether. Determine the number of bags of popcorn and the number of candies that Colton bought.

Answers

Answer:

5 bags of popcorn and 6 candies.

Step-by-step explanation:

(5 * $5.50) + ($3.5*6) = $48.5

Alvin's mom loves to cook. For her birthday, Alvin surprises her with a new container for
her cooking spoons. The round container is divided into 5 equal sections. Alvin fills 4 sections
with wooden spoons.
What fraction of the container does Alvin fill with wooden spoons?

Answers

Answer:

4/5

Step-by-step explanation:

There Are 5 Sections, 5 Is The Denominator For Our Answer

He Fills 4 Sections, And That Means He Filled Four-Fifths Of The Container.

Hope This Helps!

Answer:

It's all about parts.

Step-by-step explanation:

Since the container has 5 sections we can look at it as ?/5. With every section that Alvin fills, we add 1 more to the fraction. So, if he fills 1 section, we have 1/5. If he fills 2 sections, we have 2/5, and so on. I hope this helps you.

is the number 8.25 a rational number or an irrational number

Answers

Answer:

Rational

Step-by-step explanation:

An irrational number can't be written as a simple fraction. an irrational number will continue on forever without repeating. a rational number is any number that can be written by dividing two integers so basically any number that can be written as a fraction or decimal.

Answer:

Rational number.

Step-by-step explanation:

An irrational number is any real number that cannot be written as a simple fraction. Like square roots.

. Elijah's workout at the gym consists of just the elliptical and treadmill. After burning 450
calories on the elliptical machine, Elijah switched to the treadmill. If he is burning 12.5 calories
per minute on the treadmill, find the total number of calories he will have burned during his
workout if he spends 30 minutes on the treadmill.

Answers

Answer:

375

Step-by-step explanation:

30*12.5 is equal to 15*25

15*25= 375

The total number of calories he will have burned during his workout if he spends 30 minutes on the treadmill will be 375 calories.

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Elijah's workout at the gym consists of just the elliptical and treadmill. After burning 450 calories on the elliptical machine, Elijah switched to the treadmill.

The number of calories burnt will be calculated below,

30 x 12.5  

15 x 25

15 x 25= 375 calories

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The Sports Brand Company is making a new shoe that has a wholesale price of $40, and it wishes to advertise a retail price of $89.99. What is the markup percentage? Give answer to nearest whole percent. (hint: change decimal to percent, % will not be typed)

Answers

Answer:

Markup Percentage = 125%

Step-by-step explanation:

The wholesale price is $40, the "selling price" is $89.99.

90-40=50 (Profit)

Now that we know the profit , we need to find the percentage.

To find this percentage we can use the formula: (M=Markup percent)

[tex]M=profit/cost*100%[/tex]

In this situation, we can insert PROFIT= 50, Cost=40

M=50/40*100

= 1.25*100

=125%

I had $3.00. My mom gave me $10.00. My dad gave me $30.00. My aunt and uncle gave me $100.00. I had another $7.00. How much did I have?

Answers

$150 dollars in all hope this helps

Two numbers are in the ratio 9:7 if one number is 324, what is the other number?

Answers

Answer:

[tex]\boxed{\bold{\huge{\boxed{\sf x = 252}}}}[/tex]

Step-by-step explanation:

The ratio is 9 : 7

The first number is 324

Let's build the proportion for it.

9 : 7 = 324 :  x     [We've to find x]

Product of Extremes = Product of Means

=> 9 * x = 324 * 7

=> 9x = 2268

Dividing both sides by 9

=> x = 252

So, The other number is 252.

Subtract.
Enter your answer, in simplest form, in the box.
-3 3/8 - 7/8

Answers

Answer:

The answer is

[tex] - \frac{17}{4} \: \: or \: \: - 4 \frac{1}{4} [/tex]

Step-by-step explanation:

[tex] - 3 \frac{3}{8} - \frac{7}{8} [/tex]

First of all convert the mixed number to an improper fraction

We have

[tex] - 3 \frac{3}{8} = \frac{27}{8} [/tex]

So we have

[tex] - \frac{27}{8} - \frac{7}{8} [/tex]

Since they have the same denominator we can subtract them directly

We have

[tex] - \frac{27}{8} - \frac{7}{8} = - \frac{34}{8} [/tex]

Reduce the fraction with 2

We have the final answer as

[tex] - \frac{17}{4} \: \: or \: \: - 4 \frac{1}{4} [/tex]

Hope this helps you

What is the product of 3y
product of (3y^)(274)

Answers

3y^-4 × (2y^-4) = 6y^-8

= 6/1/y^8

= 6/y^8

.................................................

1) When x^1 multiply with x^2, 1 will add to 2 and become 3

= x^3

2) y^-1 = 1/y

3^-2 = 1/3^2 = 1/9

5^-2 = 1/5^2 = 1/25

If the number 3 were added to the set {1,1,3,3,4,4,5}, which central tendency would change? A)Mean B)Mode C)Range D)Median

Answers

Answer:

Mode

Step-by-step explanation:

I took the test and got it correct!

GEOMETERYY!!!! PLEASE HELP HJ=5p JK=p KH=3

Answers

Answer:

P=5.4

Step-by-step explanation

H=5 times

K=3/5=0.6

K=0.6

P=0.6x3x3=1.8x3=5.4

P=5.4

What is the volume of the figure? Enter the answer in the Box. In cubic centimeters

Answers

Answer:

264 cm³

Step-by-step explanation:

(5*5*8)+(*8*8*1)

200+64=

264 cm³

The volume of the figure 264 cubic centimeters.

What is rectangular prism?

"It is a three-dimensional solid shape which has six faces that are rectangles."

Formula to calculate the volume of rectangular prism:

V = l w h, where l is the length, w s the width and h is the height of the  rectangular prism.

Given figure consists of two rectangular prisms.

For the smaller rectangular prism,

length(a) = 8 [tex]V_2= 8\times 5\times 5[/tex]cm, width(b) = 8 cm and height(h) = 1 cm

For the larger rectangular prism,

length(p) = 8 cm, width(q) = 5 cm and height(r) = 5 cm

Let [tex]V_1,V_2[/tex] represents the volume of the smaller and larger rectangular prisms respectively.

The volume of the smaller rectangular prism would be,

⇒ [tex]V_1=a\times b\times c[/tex]

⇒ [tex]V_1=8\times 8\times 1[/tex]

⇒ [tex]V_1=64[/tex] cu.cm.

The volume of the larger rectangular prism would be,

⇒ [tex]V_2=p\times q\times r[/tex]

⇒ [tex]V_2=8\times 5\times 5[/tex]

⇒ [tex]V_2 = 200[/tex] cu.cm.

The volume of the figure is:

= [tex]V_1+V_2[/tex]

= 64 + 200

= 264 cubic centimeters

The volume of the figure 264 cubic centimeters.

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Jamie has 105 pieces of candy leftover from Halloween. She would like to distribute them evenly to the 7 kids on her block. Write an equation to show how many pieces of candy each kid will receive. x = seven divided by one hundred five x = one hundred five divided by seven 7 + x = 105 x = 105 − 7

Answers

105x + 7
so 105 divided by 7 = 15 só it should = 15 at the end of that equation

- m(2m + m2); m =
-4

Answers

Answer:

-(-4)(2×-4+(-4×2).

4(-8+(-8)).

4(-16).

= -64.

Answer:-64

Step-by-step explanation:

-4(2×4+4×2)

-4(8+8)

-32-32=-64

[(8-6 x 7]-3 can you guys tell me what's the answer?

Answers

Answer:

the answer is 11

A class of 33 students elected a class treasurer. There were 11 votes for Candidate A and 15 votes for Candidate B. The remaining students did not vote. Which expression gives the percent of voters who voted for Candidate A?

Answers

Answer:

[tex]\frac{11}{11+15}[/tex] * 100

Step-by-step explanation:

The voters would be 11+15 and since there were 11 votes for A, that is the equation you should use.

A bus first travels west for
38 kilometers. Then it turns south and
travels for 25 kilometers. Next it goes
east for 38 kilometers. Finally, it travels
north for an unknown number of
kilometers. At the end of the journey,
the bus is back at the original location.
How far did it travel northward?

Answers

A train is going on a journey. First it travels east for 50 kilometers. Then it turns north and travels for 22 kilometers. Next it goes west for 50 kilometers. Finally, it travels south for a certain number of kilometers. At the end of its journey it is back at its original location. How many kilometers did it travel in the southward direction?

three angles are adjacent to each other and form 140.the largest angle is twice the smaller angle and the angle which is middle size is 24 more than the smallest. find the angles​

Answers

The angles are 29°, 53° and 58°

Answer:

Smallest: 29, Middle: 53, Largest: 58

Step-by-step explanation:

We can represent the angles in this problem using an equation.

We'll use x to represent the smallest angle, and work out other ways to represent the others.

As the largest angle is twice that of the smaller angle, we can represent the largest angle as 2x as 2x is two times x.

The middle angle is 24 more than the smallest, so we can represent that one as x + 24, since it is 24 more than the smallest.

Now we have our angles all represented with x:

Smallest angle = x

Middle = x+24

Largest = 2x

We know that they all add together to 140 so our equation is:

x+2x+(x+24) = 140

Now we can solve for x!

We can remove the brackets (addition does not change the terms) and combine the terms:

x+2x+x+24=140

4x+24=140

Next we move the 24 to the other side so we can solve for x:

4x + 24 - 24 = 140 - 24

4x = 116

Finally we divide both sides by 4:

x=29

The smallest angle is 29!

Now we can use our representations to find the other angles:

Middle angle = x+24, therefore it is 29+24 = 53

Largest angle = 2x therefore it is 2*29 = 58

58+53+29=140 so we have successfully worked out our angles!

Hope this helped!

The point (2,-4) is on the line given by which equation below?
2,-4)
A. y = -x + 3
B. y = x - 4
C. y=-2x
D. y = 2x

Answers

Answer:

C ) y = -2x

Step-by-step explanation:

(2, -4)

y = -2x

subsitute x for the value of x

y = -2(2)

-2 × 2 = -4

y = -4

so

the equation for the point (2, -4) is

y = -2x

After examining a child at his 2-year checkup, the boy's pediatrician said that the z-score for his height relative to other 2-year-olds in the country was 1.59. The pediatrician explains to the parents that the most extreme 5% of cases often require special treatment or attention. a) Does this child fall into that group? b) What do you need to assume about the heights of 2-year-olds to find your answer to part a? a) The child _______into this group because he is___________than_______ standard deviation from the mean.b) Choose al that apply. A. the distribution of heights is skewed B. the heights are independent C. the distribution of heights is symmetric D. the number of heights is very large E. the distribution of heights is unimodal

Answers

a)The child falls into the most extreme 5% group, we need to compare the z-score of 1.59 to the critical value for the 5th percentile.

b)The information to make assumptions about the skewness, symmetry, or the number of heights is not provided.

A z-score of 1.59 means that the child's height is 1.59 standard deviations above the mean height for 2-year-olds. To decide if the child falls into the most extreme 5% group, we need to find the critical value for the 5th percentile. The critical value corresponds to the z-score that separates the lowest 5% of the distribution from the rest.

b) To find the answer to part a we need to assume certain properties about the heights of 2-year-olds:

A. The distribution of heights is skewed -  Skewness is not mentioned in the problem, so we cannot assume the distribution is skewed or not skewed based on the given information.

B. The heights are independent - The heights of 2-year-olds are independent in the sense that one child's height does not influence or depend on another child's height. This is a reasonable assumption in most cases.

C. The distribution of heights is symmetric - The given z-score doesn't tell us directly about the symmetry of the distribution, so we cannot assume the distribution is symmetric based on this information alone.

D. The number of heights is very large - The  information about the size of the population is not provided, so we cannot assume that the number of heights is very large.

E. The distribution of heights is unimodal - We do not have information about the number of modes (peaks) in the height distribution. The z-score doesn't give us any insight into whether the distribution is unimodal or multimodal.

Thus, the result of the following questions will be:

a) The child falls into the most extreme 5% group, we need to compare the z-score of 1.59 to the critical value for the 5th percentile.

b)The information to make assumptions about the skewness, symmetry, or the number of heights is not provided.

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Use the following information to answer questions .
A purchasing unit for a state government has found that 60% of the winning bids for office- Cleaning contracts come from regular bidders, 30% from occasional bidders, and 10% from first- uime bidders. The services provided by successful bidders are rated satisfactory or unsatisfactory anter one year on the job. Experience indicates that 90% of the jobs done by regular bidders are satisfactory, as are 80% of the jobs done by occasional bidders and 60% of the jobs done by first- time bidders.
1. What is the probability a job will be done by a first-time bidder and be satisfactory?
a. 0.06
b. 0.09
c. 0.10
d. 0.60
2. What is the probability that a job will be satisfactory?
a. 0.54
b. 0.60
c. 0.84
d. 0.95
3. Given that a job is satisfactory, what is the probability that it was done by a regular bidder?
a. 0.5778
b. 0.6141
c. 0.6429
d. 0.9000

Answers

Answer:

1

 The  correct option is  A

2

 The  correct option is  C

3

 The  correct option is  C

Step-by-step explanation:

From the question we are told that

   The proportion of the winning bid from a regular bidder is  [tex]P(R) = 0.60[/tex]

   The proportion of the winning bid from a occasional bidders is  [tex]P(O) = 0.30[/tex]

     The proportion of the winning bid from a first- time bidders is  [tex]P(F) = 0.10[/tex]

    The proportion of  satisfactory jobs done by a regular bidders is [tex]P(R|S) = 0.90[/tex]

The proportion of  satisfactory jobs done by a occasional bidders is    [tex]P(O|S) = 0.80[/tex]

The proportion of  satisfactory jobs done by a first- time bidders is   [tex]P(F|S) = 0.60[/tex]

Generally the probability that a job will be done by a first-time bidder and be satisfactory is mathematically represented as

          [tex]P(F n S) = P(F) * P(S|F)[/tex]

=>        [tex]P(F n S) = 0.10 * 0.60[/tex]

=>       [tex]P(F n S) = 0.060[/tex]

Generally the probability that a job will be satisfactory is mathematically represented as

       [tex]P(S) = 0.60 * 0.90 + 0.30 *0.80+ 0.10*0.60[/tex]

=>     [tex]P(S) = 0.84 [/tex]

Generally given that a job is satisfactory, what is the probability that it was done by a regular bidder is mathematically evaluated as

              [tex]P( S | R) = \frac{0.90* 0.60}{0.60}[/tex]

               [tex]P( S | R) = 0.6429[/tex]

       

One side of a triangle is 8 feet longer than the second side. The third side is 4 feet longer than the second side. The perimeter of a triangle is 36 feet. Find the length of each side.

Answers

Answer:

The second side is 8.

The third side is 12.

The last side is 16.  

Step-by-step explanation:

The third side is 12 because it is 8+4. Given these facts, it is 20 feet so far. And the last side of the triangle is 16, for it is 8+8. So, 16+20 is 36. Hope thsi helped.

Terry is filling spherical water balloons with a faucet that puts out 100cm^3 of water per second. At that rate, it takes Terry 6 seconds to fill a balloon.

What is the radius of a filled balloon?
Round to the nearest centimeter.

Answers

Answer:

To the nearest centimeter

Radius= 5 cm

Step-by-step explanation:

Rate of filling balloon= 100cm³/s

Time to feel the balloon= 6 s

Volume of the filed balloon

= Rate*time

= 100*6

= 600 cm³

Volume of balloon= 4/3πr³

Volume of balloon=600cm³

600= 4/3πr³

(600*3)/4π= r³

1800/4π= r³

450/π= r³

143.239 = r³

5.232= r

To the nearest centimeter

Radius= 5 cm

Answer:

5

Step-by-step explanation:

Volume:

(100)(6) = 600

Radius:

[tex]\frac{4}{3}[/tex] [tex]\pi[/tex][tex](r)^{3}[/tex] x [tex]\frac{/}{/\pi}[/tex]

[tex]\sqrt[3]{143.2}[/tex] = [tex]\sqrt[3]{r^{3} }[/tex]

= 5.2 = r

round it up = 5

SO: your answer is 5

Also I did it on khan

brainliest plz?

I need to get slope intercept form

Answers

The slope intercept form might be: -2/3x+490

Which properties of equality are used in the example shown on the left? Check all of the boxes that apply.

Answers

Answer:

Addition Property and substitution property

Evaluate the numerical expression 3+21-180÷9. The value of the expression is?

Answers

Answer:

the answer is 4.

the steps are...

180÷9=20 then 3+21=24 the subtract 20 and 24 then you will get 4

Answer:

The answer is number 4

Step-by-step explanation:

4x9/108+21-3

Order of operations A set of three scores consists of the values 6, 3, and 2. 1. Σ2X – 2 =______.a. 35.b. 33.c. 22.d. 6.2. Σ(2X)² =______.a. 248.b. 124.c. 61.d. 39.

Answers

Answer:

Step-by-step explanation:

Given the order of operations A set of three scores to consists of the values 6, 3, and 2, we are to evaluate the following

1) Σ2X – 2

= 2(6)+2(3)+2(2) – 2

= 12+6+4–2

= 22–2

= 20

2) Σ(2X)² = (2×6)²+(2×3)²+(2×2)²

Σ(2X)² = 12²+6²+4²

Σ(2X)² = 144+36+16

Σ(2X)² = 144+52

Σ(2X)² = 196

The results of the order of operations are: [tex]\sum 2x -2 = 16[/tex] and [tex]\sum (2x)^2 =196[/tex]

The scores are given as:

x = 6, 3 and 2

(a) The first set of operation

This is represented as:

[tex]\sum 2x -2[/tex]

So, we have:

[tex]\sum 2x -2 = 2 \times 6 - 2 + 2 \times 3 - 2 + 2 \times 2 - 2[/tex]

Evaluate the products

[tex]\sum 2x -2 = 12 - 2 + 6 - 2 + 4- 2[/tex]

[tex]\sum 2x -2 = 16[/tex]

(a) The second set of operation

This is represented as:

[tex]\sum (2x)^2[/tex]

So, we have:

[tex]\sum (2x)^2 =(2 \times 6)^2 + (2 \times 3)^2 + (2 \times 2)^2[/tex]

Evaluate the products

[tex]\sum (2x)^2 =12^2 + 6^2 + 4^2[/tex]

Evaluate the squares

[tex]\sum (2x)^2 =144 + 36 + 16[/tex]

[tex]\sum (2x)^2 =196[/tex]

Hence, the results of the order of operations are:

[tex]\sum 2x -2 = 16[/tex] and [tex]\sum (2x)^2 =196[/tex]

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the number of PI is 3.14 why do we use a special symbol for it​

Answers

Because 3.14 is only an estimation, pi is actually a never ending number, and so far we have only discovered so many digits (which you can google). We use 3.14 for equations that don’t need to be exact, and the symbol to represent the actual number, meaning it will be more accurate.
we use a special symbol for PI to simplify the answer because it is a never ending number

Mr.wilkins deposited $2,500 in a new account at his bank . •the bank pays 6.5% interest compounded annually on this account •mr.wilkins makes no additional deposits or withdrawals Which amount is closest to the balance of the account at the end of 2 years

Answers

Answer:

Step-by-step explanation:

$2,662.50

Other Questions
Does technology and the ability to contact and organize people quickly through social networking help to make our "extended republic" a little less extended? Which of the following expresses the sum of 54 and 30 as a product? * O 6 (54 + 30) O 6(9+5) O 9 (6+5) O 9 (54 + 30) 5. Theresa decides to donate money to cancerresearch each year. Her brother, Tony, also decidesto contribute. Together, they donate $1,000 peryear to cancer research. If Tony is able to donate1 1/2 times the amount that Theresa is able todonate, what is the amount in dollars that Tonywill donate after 5 years, assuming the amountand proportions remain the same cach year?A. $2.000B. $2.100C. $2.450D. $3.000E. $3.600 When the skills model was developed, what were Mumford and the other researchers trying to explain? This model delineated components of effective leader performance. List the three competencies, define and describe each. Who is Louis the xiv What is Nakht story about A store sells the basic model of a phone for $60 and the upgraded model for $200. It costs the store $10 to buy eachbasic model and $50 to buy each upgraded model from the phone company, On Tuesday, the store has $1,800 insales for these two models, and it paid the phone company $400 to buy these phones. How many upgraded modelsdid the store sell on Tuesday?O 6 upgraded phones10 upgraded phones15 upgraded phones42 upgraded phones What was the primary reason that William Penn granted religious freedom in his colony?O To antagonize the Puritan New England colonies in response to their disdain of the Quaker religionTo encourage settlers to come to his colonyTo provide a haven for all religions being persecuted EuropeTo foster peaceful coexistence with the Native American population in Pennsylvania 9. Which CLAIM is the strongest for the following thesis statements?(2 points)1. Violent video games are harmful for young people to play.2. Violent video games are harmful for young people to play because children can become desensitized todeath.3. Violent video games are harmful to young people, and it should be stopped.4. Violent video games are harmful for young people because they should be reading a book. Isabel wrote 10 letters to friends each month for x months in a row. Write an expression to show how many totalletters Isabel wrote. Which of the following words best describes the voice in this memoir (Typhoid Fever)? A. Angry B. Poetic C. Unemotional D. Instructive Explain, in your own words, how you would use the light microscope to view a wet mount of a protist, assuming the microscope is plugged in and that the light source is on. Please use at least the following 9 structures in your description and underline them as you use them: stage, stage clip(s), stage knob(s), eyepiece, scanning objective lens, low power objective lens, high power objective lens, coarse focus knob, and fine focus knob. {6} E { {6}, {14} } true or false Which of the following are examples of prose? A. The Hunger Games book series B. The lyrics of a popular song C. A painting by Michelangelo D. An article in Time magazine E. A complaint letter to a restaurant F. A poem by Emily Dickinson Select the invalid declaration from the lines of Java code belowint zebraCnt = 40000;long birdCnt = 222_222_222_222_222L;a. float avg = 23.5;b. double avg = 98.32121;c. None of the above. d. All are legal declaration. PLEASE HELP! this is due today! find the slope of the line containing the points (3,-2) and (-1,6) Express the given quantity in terms of the indicated variable.The area (in ft) of a rectangle that is eight times as long as it is wide;w = width of the rectangle (in ft)ft2XNeed Help?Read itWatch ItMaster it A race car driver completes 30 laps and 15 minutes at a constant speed. What is the drivers speed? Which of the following is true about the relation of the Energy Grade Line (EGL) to the Hydraulic Grade Line (HGL) at a reservoir?A. EGL is above the HGL.B. EGL is below the HGL.C. EGL is the same height as the HGL.