A machinist creates a washer by drilling a hole through the center of a circular piece of metal. If the piece of metal has a radius of x + 7 and the hole has a radius of x + 6, what is the area of the washer?

Answers

Answer 1

The area of the washer (which is a circle, but the inner part cut out) is given by:
[tex]A_c = \pi r^2[/tex]

Now, we need to find the radius of the entire metal circle which the hole was drilled on:
[tex]R_w = (x+7) - (x+6) = 1[/tex]

Plug it in to find the area of the metal plate:
[tex]A_p = \pi (1)^2 = \pi [/tex]

Now, you subtract the area of the hole from the area of the plate. The area of the hole will be:
[tex]A_h = \pi (x+6)^2[/tex]
[tex]A_h = \pi (x^2+12x+36) = [/tex]

Subtract the area of the hole from the metal plate to get:
[tex]A_w = \pi - (\pi x^2+12 \pi x+36 \pi) = \pi x^2+12 \pi x -35 \pi[/tex]

That's your answer, although it looks wrong because not much information was provided.

Related Questions

A leaky pool loses 2 1/4 inches of water each day. Jermaine and Mildred are asked to determine the change in the amount of water in the pool over 5 days.

Jermaine’s Solution Mildred’s Solution

5(-2 1/4) 5(-2 1/4)
5(-2 -1/4) 5(-2 -1/4)
-10 -1/4 -10 -5/4
-10 1/4 -11 1/4

Which describes the reasoning used to determine whose solution is correct?

A. Jermaine is correct because -10 -1/4 equals -10 1/4.
B.Jermaine is correct because he distributed 5 correctly.
C.Mildred is correct because she multiplied 5 by –2 but not by -1/4.
D.Mildred is correct because she distributed 5 correctly.

Answers

Mildred's solution is correct.

5(-2 1/4) = 5(-2 + -1/4) = 5(-2) + 5(-1/4) = -10 + -5/4 = -10 + -1 1/4 = -11 1/4

Answer: D. Mildred is correct because she distributed 5 correctly.

Step-by-step explanation:

Since, the loss of water in one day = [tex]2\frac{1}{4}\text{ inches}[/tex]

⇒ The loss of water in 5 days = [tex]5(2\frac{1}{4})\text{ inches}[/tex]

⇒ The loss can be written with negative sign,

Thus, the expression that shows the changes in quantity of water in 5 days,

[tex]-5(2\frac{1}{4})[/tex]

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

[tex]=5(-2-\frac{1}{4})[/tex]

[tex]=-10-\frac{5}{4}[/tex]

[tex]=-10-1\frac{1}{4}[/tex]

[tex]=-10-1-\frac{1}{4}[/tex]

[tex]=-11-\frac{1}{4}[/tex]

[tex]=-11\frac{1}{4}[/tex]

Since, the above steps are similar to that of Mildred's solution,

⇒ Mildred is correct.

Also, By the above explanation it is clear that jermaine incorrectly distribute 5 in his third steps.

⇒ Option D is correct.

Arturo is customizing his next pair of basketball shoes. The following table shows the design components and how many options he has for each.
Design component Number of options
Primary color 8
Secondary color 8
Sole color 8
Lace color 5
How many different shoe combinations can Arturo create?

Answers

The total number of combinations is 2,560.

To find the total, we need to use the number of options for all 4 of the categories. Once we have those number, we just need to multiply them to find the total number of possibilities. This is called the Fundamental Counting Principle.

8 x 8 x 8 x 5 = 2560

Answer:

2,560

Step-by-step explanation:

okay so im working on it right now on khan

so you have to do 8x8x8x5

8x8 = 64 then 64x8=512 then 512x5=

2,560

now im not just going to leave you guys with this explaination because i dont really like people just putting answers up when it's wrong just for the points thats why i try to show proff on MOST of my work

the screenshot is below for proff

please mark me brainlist

Which relationship describes angles 1 and 2?

Select each correct answer.

supplementary angles
complementary angles
vertical angles
adjacent angles

Answers

They are both supplementary and adjacent angles.

The tallest man ever recorded was Robert Wadlow, who was 272 cm tall. The tallest woman on record was Zeng Jinlian. Her height was 91% of wadlow’s height. How tall was Zeng Jinlian.

(Round to the nearest cm.)

Answers

247.52 centimeters.

To find this answer, you have to find 91% of Robert Wadlow's height. To do that, you multiply 272 by 0.91, which gives you the height of Zeng Jinlian.

Hello!

Here we just need to find .91 of 272cm to find her height,

so we take .91percent * 272cm= 247.52 rounded to nearest cm is 248cm tall

hope this helps. any questions please ask! thank you!

A 6 mile walking trail has a distance marker every 1/3 mile.

Answers

I don’t see a question but i assume you’re asking how many distance markers there are and in that case the answer is 18.

Each 2 miles you find a marker because 6 divided by 1/3 is 2

How many different triangles can be drawn with one 60° angle and two sides measuring 2 inches each?

Answers

2 traingles use 30 degree angles

In a triangle, the sum of two of the angles is equal to the third. If the lengths of the two longer sides are 12 and 13, what is the length of the shortest side?

Answers

The sum of two angles is equal to the third

The longer sides (longer and longest) is 12 and 13

13 - 12 = 1

this means that the length of the shortest side is 1 (for 1 + 12 = 13)

hope this helps

5 is the answer thx hope this helps

Estimate the length of a sheet of notebook paper.
A. 24 mm
B. 2.4 cm
C. 24 cm
D. 2.4 mm

Answers

The required standard length of the paper of the notebook sheet is 24 cm. Option C is correct.

Given that,
To estimate the length of a sheet of notebook paper.

What is standard measurement?

All over the world, most things are in use as of common quantity, so people all over the world agree that they have to follow a common system of measurement and that the common system of measurement is called standard measurement.

What is the perimeter?

Perimeter is the measure of the figure on its circumference.

Here,
As per standard measurements, the length of the sheet of notebook paper for a standard notebook is 24 cm across the world.
This 24 cm is standardized as A4 size paper or A4 notebook.

Thus, The required standard length of the paper of the notebook sheet is 24 cm. Option C is correct.

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Evie has scores of 72, 78, 80 And 84 On four Science quizzes. What score must she get on the next quiz to have an average of at least 80?

Answers

x= the next quiz
(72+78+80+84+x)/5=80
*5 *5
72+78+80+84+x=400
314+x=400
-314 -314
x=86
Evie needs to get a score of 86 on her next science quiz.

how many rulers of 12-inches are needed to measure a door awnser

Answers

the dimensions of a door are variable, for effects of this problem we will assume a door height of 210 cm and a door width of 80 cm

Step 1
convert the dimensions of the door in cm to inches
we know that
1 in-------------> 2.54 cm
X----------------> 210 cm
X=210/2.54=82.67 in (height)

1 in-------------> 2.54 cm
X----------------> 80 cm
X=80/2.54=31.50 in (width)

the dimensions of a door are 31.50 in x 82.67 in

Step 2
calculate the amount of rules of 12-inches necessary to measure the height of the door
82.67 in (height)
if one rule-------------> measure 12 in
X----------------------> 82.67 in
X=82.67/12=6.8-----------> 7 rules

Step 3
calculate the amount of rules of 12-inches necessary to measure the width of the door
31.50 in (width)
if one rule-------------> measure 12 in
X----------------------> 31.50 in
X=31.50/12=6.8-----------> 2.62 ------------> 3 rules

the answer is
to measure a door are needed about 7 rules of 12-inches for the height and about 3 rules of 12-inches for the width

A farm is to be built in the shape of Quadrilateral ABCD as shown belo all fou sides are equal A = 13.2 feet B= 15.5 feet

Answers

The answer is (102.3) hope it helps and have a great day!

Help as fast as possible

Answers

please include the choices then msg me

49 is the answer because if hank did 9 fewer and he did 40 you would do 40 + 9

A circular racetrack
has a diameter of 1/2 mile. How far does a car travel in one lap aroiund the track? Round to the nearest tenth.

Answers

Circle Circumference= 2πr
Diameter is given, but the formula requires the radius.

Radius= diameter ÷ 2= 1/2 ÷ 2= 1/2 * 1/2= 1/4= 0.25

C= circumference
π= 3.14

C= 2πr
substitute in numbers
C= 2(3.14)(.25)
C= 1.57 rounded to 1.6 miles

ANSWER: 1.6 miles

Hope this helps! :)

what are three ordered pair of y=2x+0.5

Answers

3 Ordered Pairs could be: (0, 2.5); (5, 10.5); (2, 4.5). Hope this helps!

Solve for x.

4/5 = 7/x

Answers

the answer is 8.75 because 7 * 5 is 35 / 4 = 8.75

Which algebraic expressions are polynomials? Check all that apply. PLEASE HELP

Answers

I made a huge error. The correct answer is 2,3,5,6.
polynomials can't have root variables. Nor can they be of the form 1/x. They can be monomials and there does not seem to be a restriction on numerical coefficients or numbers without variables

Original Answer:
Polynomial is an expression of more than two algebraic terms.
So that makes 2, 3 and 6 polynomials

Edited Answer:
1) Binomials are included as polynomials
2) Variable must have power that is at least 1

Ans: 2, 3, 5, 6

(Apology for the mistake)

The local radio station played 9 hip-hop songs and 6 hard rock songs in one hour. What percent of the songs played during this hour was hip-hop?

Answers

60% was hip hop boom

60% i think but im not sure

Use the given conditional statement to determine the converse and inverse statements. If a line is vertical, then it has undefined slope.

Answers

1) Definitions:

1.1) Inverse statement: negating the hypothesis and the conclusion of the original statement, i.e.:

conditional statement: p → q

inverse: ~p → ~q (the symbol ~ means the negation)

1.2) Converse statement: switching the hypothesis and the conclusion of the conditional statement, i.e.:

conditional statement: p → q

converse: q → p

2) converse of the given statement

conditional: If a line is vertical, then it has undefined slope.

converse: switch the hypothesis and the conclusion

if a line has undefined slope, then it is vertical <------- answer

3) Inverse of the given statement

conditional: if a line is vertical, then it has undefined slope.

inverse: negate both hypothesis and conclusion.

if a line is not vertical, then it does not have an undefined slope <---answer

1.) if the line has an undefined slope, then it is a verticle line.

2.) if the line is not vertical then it does not have an undefined slope

Which of the following is the converse of the statement "if it is snowing, then it is my Birthday?

Answers

If it is my birthday, then it is snowing

That would be "If it is my birthday, then it is snowing."

Hope this helps!

- Juju

Graph the linear equation find three points that solve the equation then plot on the graph 2y=-x+2

Answers

I guess this is the line
[tex] \binom{0}{2} \binom{2}{3} \binom{4}{4} [/tex]

Answer:

Step-by-step explanation:

PLEASE HELP!!! NEED HELP ASAP!! EXTRA POINTS TO THE FIRST PERSON TO ANSWER!!

a school is constructing a new tennis courts. each rectangular court will, be enclosed by a 600 ft fence. the length of the rectangular region will be 60 ft longer than the width. what are the dimensions of the new courts? use an equation or a system of equations to explain how you determined your answer.

Answers

Tennis court perimeter: 600

L = 60 + w

L = 180
W = 120

180 - 120 = 60

180(2) + 120(2) = 600

In a division problem the ____ is the original number, which is being divided by the divisor, to get the quotient.

Answers

The original number in a division problem is called the dividend.

Dividend is divided by the divisor hopes this helps :)

X^2 + 5x + c find the value of c that makes each trinomial a perfect square

Answers

to do this you divide the coefficient of x by 2 . Here we have 5 / 2 = 2.5. Then c = this result squared Here it is 2.5^2 = 6.25

Answer c = 6.25

Final answer:

To make the trinomial a perfect square, we can complete the square. The value of c that makes the trinomial a perfect square is c = 25/4.

Explanation:

To make the trinomial a perfect square, we need to find the value of c. We can do this by completing the square. The trinomial can be written as x² + 5x + c = (x + a)², where a is a constant. Expanding the right side, we get x² + 2ax + a² which is equal to x² + 5x + c. Comparing the coefficients of x, we have 2a = 5. Solving for a, we get a = 5/2. Substituting this value back into the expression, we have x² + 5x + (5/2)² = (x + 5/2)². Therefore, the value of c that makes the trinomial a perfect square is c = (5/2)² or c = 25/4.

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Can you show me how to do this?

Answers

I think that Fran is correct

I think this because the problem states that 15 is the LEAST number of people in the shop, so there are MORE than 15 people

Billy left home at 9 am and rode his bike to the park at an average speed of 10 miles per hour. He arrived at the park at 9:30 am. How many miles from the park is Billy’s home?

Answers

Billy's house is 5 miles away.
Hope that helps.

5 miles
10 miles per hour. half and hour is 30 minutes. half of ten miles is five

In the neighborhood park there is a circular grassy picnic area but half of the grass has died the city wants to replace the grass but needs to know the square footage of the damaged area if the circular picnic area is 150 feet across what is the square footage of the damaged area

Answers

235.5 square feet need to be replaced

The tax rate on Jerome James 112000 vacation home is 25 Mills the property is assessed at full value how much will Jerome pay in taxes this year

Answers

Answer: $2,800

Step-by-step explanation:

Given: The assessment value of Jerome's home= [tex]$112,000[/tex]

We know that to calculate the property tax, we need to multiply the assessment value of the property by the mill rate and then divide by 1,000.

Then, the property tax is given by :-

[tex]\text{Property tax}=\dfrac{\$112,000\times25}{100}\\\\\Rightarrow=\text{Property tax}=\$2,800[/tex]

Therefore, Jerome pay $2,800 as property tax in this year.

Answer:

[tex]Property tax=$2800[/tex]

Step-by-step explanation:

Given: The assessment value of Jerome's home is given as =[tex]112000[/tex]

Solution: Since we know that in order to calculate the property tax, we need to multiply the assessment value of the property by the mill rate and also divide by [tex]1000[/tex].

Then, the property tax is given as :-

[tex]Property tax=\frac{112000{\times}25}{100}[/tex]

[tex]Property tax=$2800[/tex]

Thus, Jerome pay $2,800 as property tax in this year.

A recent survey reveals that of the 250 poodle owners interviewed, 93% of them regularly groom their dogs. If there are 50,000 registered poodle owners in the city, how many owners are expected to regularly groom their dogs?

A. 46,500
B. 93
C. 3,500
D. 7

Answers

It's A, I'm 100% sure.

Bertha and Vernon are competing in a diving competition. Bertha's dive ended -32 m from the starting platform. Vernon's dive ended -4 m from the starting platform. How many times farther was the end of Bertha's dive than the end of Vernon's dive?

Answers

What you must do for this case is a division to find the number of times that Bertha submerges with respect to Vernon.
We have then:
Bertha's dive ended = -32 m
Vernon's dive ended -4 m
N = (Bertha's dive ended) / (Vernon's dive ended)
N = (- 32) / (- 4)
N = 8
Answer:
Bertha's dive was 8 times farther than the end of Vernon's dive

Jordan is calculating the slope of the trend line in the scatterplot below.
How can Jordan use the plot to check the reasonableness of his answer?
His slope should be positive because the coordinates of all the plotted points are positive.
His slope should be positive because the trend line is slanted up to the right.
His slope should be negative because there are plotted points not on the line.
His slope should be negative because the x-coordinate of each plotted point is less than the y-coordinate.

Answers

Answer: B

His slope should be positive because the trend line is slanted up to the right.

Step-by-step explanation:

from left to right the line is increasing upward so it is positive so this means both of the bottom answers are wrong. answer A. is wrong because even slopes that are negative have all points positive sometimes so this is not a valid reason. therefore this leaves us with the answer B, which is correct.

His slope should be positive because the trend line is slanted up to the right. which is the correct answer would be an option (B).

What is the Scatter plot?

The variables in the scatter plot made from the data are described by the independent variable, time, which is graphed along the horizontal axis.

Jordan is calculating the slope of the trend line in the given scatterplot.

As per the given scatter plot, the required solution would be as:

Take two points (1,24) and (8,96)

So, slope = (96-24)/(8-1) = 72/7 = 10.28

The line is moving upward from left to right, hence it is positive, implying that both of the bottom solutions are incorrect. Answer A. is incorrect since even negative slopes can have all points positive at times, hence this is not a legitimate argument.

As a result, we are left with solution B, which is accurate.

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