Dylan, Alan, Bruce, and Cecil are brothers. Dylan weighs d pounds. Alan weighs 3 pounds more than twice what Dylan weighs. Bruce weighs 12 pounds less than three times what Dylan weighs. If Cecil weighs the same as the combined weight of Bruce and Alan, what is Cecil’s weight in terms of Dylan’s weight (d)?

Part A
Alan weighs 3 pounds more than twice what Dylan weighs. Write an expression to represent Alan’s weight in terms of Dylan’s weight.

Part B
Bruce weighs 12 pounds less than three times what Dylan weighs. Write an expression for Bruce's weight in terms of Dylan's weight

Part C
Cecil weighs the same as the combined weight of Bruce and Alan. Use the expressions you found in parts A and B to write an expression for Cecil's weight in terms of Dylan’s weight.

Part D
Assume that Dylan weighs 45 pounds. Use the expression from part C to calculate Cecil’s weight.

Part E
Recall the linear expression for Cecil’s weight in part D. Before plugging values into it, could you have simplified the expression? If yes, explain how.

Part F
Simplify the expression (2d + 3) + (3d − 12).

Part G
Dylan weighs 45 pounds. Use the simplified expression you found in Part F to recalculate Cecil’s weight. Show your work.

Part H
Did you get the same answer for Cecil’s weight in parts D and G? What can you conclude about the expressions you developed in parts D and G?

Part I
Let's try something a bit different. The four brothers know that Bruce weighs more than Alan. Write an expression to represent how much more Bruce weighs than Alan. Write the in terms of Dylan’s weight, d.

Part J
Dylan weighs 45 pounds. Use the expression you derived in part I to calculate how much more Bruce weighs than Alan.

Part K
Now simplify the expression (3d − 12) − (2d + 3) you wrote in part I.

art L
Dylan weighs 45 pounds. Use the simplified expression you found in part K to recalculate how much more Bruce weighs than Alan. Did you get the same answer as in part J? If not, be sure to check your work, particularly the positive and negative signs.

PLEASE HELP I WILL DO YOUR WORK IF YOU DO THIS FOR ME PLZZZZZZZZZZZZZZZ

Answers

Answer 1

Answer:

PART A- 3+D POUNDS

PARTB- 3D-12

Step-by-step explanation:

dylan-d pounds

alan-3+d pounds

bruce-3d-12

Answer 2

Answer:

Alan = A

Bruce = B

Cecil = C

Dylan = D

Part A     A = 2 x D + 3

Part B     B= 3 x D - 12

Part C    C= A+B     A = 2 x D + 3       B= 3 x D - 12

Part D    Cecil weighs 216 pounds

Part E     Yes, the expression can be simplified by using the Associative and Commutative Properties of addition and by combining the like terms in the expression.

Part F      5d-9

Part G      Cecil’s weight in terms of Dylan’s weight is 5d – 9.  Find Cecil’s weight by substituting Dylan’s weight (d = 45) into the expression above:

(5 × 45) − 9  = 225 − 9  = 216.

If Dylan weighs 45 pounds, then Cecil weighs 216 pounds.

Part H   Yes, the answers are the same. The expression from part D is equivalent to the expression from part G.

Part I       Bruce's weight in terms of Dylan’s weight is 3d − 12.  Alan's weight in terms of Dylan’s weight is 2d + 3.

So, the expression (3d − 12) − (2d + 3) represents how much more Bruce weighs than Alan.

Part J      The expression is (3d − 12) − (2d + 3).  Evaluate the expression by substituting Dylan’s weight (d = 45) into it:  (3 × 45 − 12) − (2 × 45 + 3)  = (135 − 12) − (90 + 3)  = (123) − (93)  = 30.

Bruce weighs 30 pounds more than Alan weighs.

Part K   (3d − 12) − (2d + 3).

First remove the parentheses:

3d − 12 − 2d − 3.

Then group the like terms:

3d − 2d − 12 − 3.

Finally, subtract the like terms:

d − 15.

The expression (3d − 12) − (2d + 3) simplifies to d − 15.

Part L    The expression is d − 15.  Evaluate the expression by substituting Dylan’s weight (d = 45) into it:  45 − 15 = 30.

Bruce weighs 30 pounds more than Alan. This is the same answer as in part J.

Step by step explanation:

So you basically want to focus on Alan and Bruce they will help you get the rest of your answers

Note:

Some of these are direct answers from Edmentum


Related Questions

Identify the slope and y-intercept. If the equation is in standard form, you may need to switch it to slope-intercept form. Sketch the graph of each line.
4x + 3y = -9

Answers

vertical intercept: (0, -3)

a. Find the amplitude.
b. Find the period.
c. Find the vertical shift.
d. Find the horizontal shift.
e. Find the number of cycles between 0 and 2π.
f. Find the equation of the graph.

You must show all of your work to receive credit.

Answers

Answers:

a) Amplitude = 2b) Period = pic) Vertical shift = -2, which means it has been shifted down 2 units.d) Horizontal shift = 3pi/8, this shifting is to the right.e) There is  one   cycle between 0 and 2pi.f) The equation of the graph is y = 2*sin(2(x-3pi/8))-2

========================================================

Explanations:

Part (a)

The highest point is when y = 0 and the lowest point is when y = -4. The vertical distance between the peak and valley is 4 units, which cuts in half to 2. This is the amplitude. It's the vertical distance from the center to either the peak or valley.

Note: Amplitude is always positive as it measures a distance.

---------------------

Part (b)

For x > 0, the first valley or lowest point occurs between 0 and pi/4. It appears to be the midpoint of the two values. So that would be (0+pi/4)/2 = pi/8.

The next valley occurs between pi and 5pi/4. Compute the midpoint to get (pi+5pi/4)/2 = (4pi/4+5pi/4)/2 = (9pi/4)/2 = 9pi/8

So we have the graph go from one valley x = pi/8 to the next valley over x = 9pi/8. This is a distance of pi units because 9pi/8-pi/8 = 8pi/8 = pi

The graph repeats itself every pi units, so the period is pi.

---------------------

Part (c)

The midline is normally through y = 0, aka the x axis. However, the graph shows the midline is through y = -2. This means the graph has been shifted down 2 units.

---------------------

Part (d)

This will depend on whether you use sine or cosine. This is entirely because cosine is a phase-shifted version of sine, and vice versa. I'll go with sine.

The parent sine function y = sin(x) goes through the origin (0,0)

However, as part (c) mentioned, we shifted the graph 2 units down. So we have y = sin(x)-2. But plugging x = 0 into this leads to the point (0,-2)

This doesn't match what the graph says. The graph shows the point (3pi/8, -2) on the red curve. The x coordinate 3pi/8 is the midpoint of pi/4 and pi/2

This must mean we need to shift the sine graph 3pi/8 units to the right.

---------------------

Part (e)

Start at the lowest point when x = pi/8. If you start the cycle here, then it ends when x = 9pi/8. See part (b).

So far we've completed one cycle. If we start at x = 9pi/8, then the next valley or lowest point is slightly beyond or to the right of x = 2pi. This means we run out of room and we haven't completed a full cycle.

Overall, one full cycle is between 0 and 2pi.

---------------------

Part (f)

Again I'm going to use sine instead of cosine. Refer back to part (d).

The general sine curve equation is

y = A*sin(B(x-C))+D

where

|A| = amplitudeB handles the period, specifically T = 2pi/B where T is the period. We can solve for B to get B = 2pi/TC = horizontal phase shiftD = vertical shift, and ties together with the midline equation

In this case, we found that

|A| = 2T = pi leads to B = 2pi/T = 2pi/pi = 2C = 3pi/8D = -2

So,

y = A*sin(B(x-C))+D

will update to

y = 2*sin(2(x-3pi/8))-2

which is one way to express the equation of the red curve. Optionally you can distribute the 2 through to (x-3pi/8).

30% of what distance is 5.8 mi?

Answers

Answer: 1.74 mi

Step-by-step explanation:

30% = 0.3

5.8 × 0.3 = 1.74

12-(x-3)=8
what is the value of x

Answers

Answer: 7

Step-by-step explanation: First distribute the subtraction sign (negative one) to x and -3. Now we have 12 -1x + 3 = 8. Now combine 12 and 3 then subtract 15 from both sides to get -1x = -7. Now divide both sides by -1 to get x = 7.

Hope this helps!

Answer:

Step-by-step explanation:

12-(x-3) =8

12 -x +3 = 8

15 - x = 8

- 15.    -15

-x = -7

x = 7  

Make x the subject of the formula 3 b ( 2 x − a 2 ) = 5 d − 7 g x

Answers

Answer:

[tex]x=\frac{5d+6ba}{6b+7g}[/tex]

Step-by-step explanation:

Answer:

x = (3a²b + 5d) / (6b + 7g)

Step-by-step explanation:

Given:

3b( 2x − a² ) = 5d − 7gx

Solving for x:

6bx - 3a²b = 5d - 7gx6bx + 7gx = 3a²b + 5d(6b + 7g)x = 3a²b + 5dx = (3a²b + 5d) / (6b + 7g)

What is the simplified expression in the box by combing like terms and removing zero pairs?

-4 ( 2x+ 4) + 5

Answers

9514 1404 393

Answer:

  -8x -11

Step-by-step explanation:

Use the distributive property to eliminate parentheses. Then combine the constant terms.

  -4(2x +4) +5

  = -8x -16 +5

  = -8x -11

[tex]\sf \longmapsto-4 ( 2x+ 4) + 5[/tex]

[tex]\sf \longmapsto(−4)(2x)+(−4)(4)+5[/tex]

[tex]\sf \longmapsto−8x+−16+5[/tex]

[tex]\sf \longmapsto(−8x)+(−16+5)[/tex]

[tex]\sf \longmapsto−8x+−11[/tex]

[tex]\sf \longmapsto - 8x - 11[/tex]

The dance committee at Jefferson High School decides to charge students different prices for dance tickets depending on whether they are a student at Jefferson or at another school. A student attending Jefferson pays $5, whereas a student attending a different school pays $10. The dance committee didn't make different kinds of tickets, and they lost track of how many of each kind of ticket they sold. They know they sold a total of 500 tickets and they brought in $3,135. How many Jefferson and non-Jefferson students came to the dance?

Answers

Answer:

30

Step-by-step explanation:

The number of Jefferson students and the number of non-Jefferson students if A student attending Jefferson pays $5, A student attending a different school pays $10 is 373 and 127 respectively.

What is the equation?

Equation: A declaration that two expressions with variables or integers are equal. In essence, equations are questions and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.

Given:

A student attending Jefferson pays $5,

A student attending a different school pays $10,

The total number of tickets = 500,

The total money earned = $3135,

Write the equation of the given statement as shown below,

x + y = 500

5x + 10y = 3135

Here, x is the number of Jefferson students and y is the number of non-Jefferson students,

Solve the equation by elimination method as shown below,

y = 127,

x = 500 - 127 = 373

Thus, the number of Jefferson students is 373 and the number of non-Jefferson students is 127.

To know more about equation:

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Brainliest to right answer

Answers

I think it would be neither, sorry if I’m wrong-

will got 17 out of 25 questions correct on his driving test what percent correct did he get on the test?

Answers

Answer:

68%

Step-by-step explanation:

[tex]\frac{17}{25} = \frac{68}{100}[/tex]  [tex]\frac{68}{100}[/tex] = 68%

I hope this helps!

Answer: 68%

Explanation: divide 17/25 and get 0.68 which would be 68% have a nice day (:

Given a triangle ABC has angles of A = 30 and B = 70, what is the smallest side?

Answers

Answer:

A=30 is the smallest side

Step-by-step explanation:

A+B+C= 180

30+70+C=180

100+C=180

C=180-100

C=80

Therefore, A=30 is the smallest side of the triangle...

Which of the following equations has a solution that is negative?





a. – 0.4x + 4 = – 1.6



b. – 0.4(x + 1.6) = 1.6



c. – 0.4(– x + 1.6) = 1.6



d. – 0.4x – 4 + 1.6x = – 1.6

Answers

Answer:

b. – 0.4(x + 1.6) = 1.6

Step-by-step explanation:

The equation with negative solution is -

- 0.4(x + 1.6) = 1.6

What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given are the equations as shown in the question.

The equation with the negative solution are -

- 0.4(x + 1.6) = 1.6

- 0.4x - 0.64 = 1.6

- 0.4x = 1.6 + 0.64

- 0.4x = 2.24

x = - (2.24/0.4)

Therefore, the equation with negative solution is -

- 0.4(x + 1.6) = 1.6.

To solve more questions on algebraic expressions, visit the link below-

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Diego is on a diet. He has lost 10% of his weight this month. If he started with 75 kg (THAT'S THE 100%), how much weight did he lose?

Answers

Step-by-step explanation:

10% of 75 is the total kg he lost this month

So 10/100 x 75 = 7.5

So Diego lost 7.5 kg this month

True or False, The value pi/12 is a solution for the equation 4 cos^2(4x)-3=0

Please explain

Answers

Answer:

Yes, π/12 is a solution.

Step-by-step explanation:

Calculator --> sin(π12)=sin15∘=0.26 . √2−√32=√0.272=0.522=0.26 .  Uhmm... i dont rlly know how to explain it.. its complicated for me to word it without making it non confusing.

The statement 'The value [tex]\frac{\pi}{12}[/tex]  is a solution for the equation [tex]4~cos^2(4x)-3=0[/tex] ' is True.

What is an equation?

"It is a mathematical statement which consists of equal symbol between two algebraic expressions."

For given question,

We have been given an equation [tex]4~cos^2(4x)-3=0[/tex]

We need to check whether [tex]\frac{\pi}{12}[/tex]  is a solution for the equation.

Substitute [tex]x=\frac{\pi}{12}[/tex] in equation [tex]4~cos^2(4x)-3=0[/tex]

[tex]\Rightarrow 4~cos^2(4\frac{\pi}{12} )-3=0\\\\\Rightarrow 4~cos^2(\frac{\pi}{3} )-3=0\\\\\Rightarrow 4~cos^2(\frac{\sqrt{3} }{4} )-3=0\\\\\Rightarrow 4~\frac{3}{4}-3=0\\\\ \Rightarrow 3-3=0\\\\\Rightarrow 0=0[/tex]

This means,  [tex]\frac{\pi}{12}[/tex]  is a solution of the equation [tex]4~cos^2(4x)-3=0[/tex]

Therefore, the statement 'The value [tex]\frac{\pi}{12}[/tex]  is a solution for the equation [tex]4~cos^2(4x)-3=0[/tex] ' is True.

Learn more about the equation here:

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10/9 in simplest form pls

Answers

[tex]1\frac{1}{9}[/tex]

Write an equation that passes through (0, 20) and (4, 80) ??

Answers

Answer:

M= 15

Step-by-step explanation:

Hope it’s right

write 103 as a series of products

Answers

Answer:

10*10*10

Step-by-step explanation:

Given the expression 10^3

We are to write this as a series of products as as shown;

10^3 means the product of 10 in 3 places. Multiplying 10 in 3 places will give the required series of product.

10^3 = 10 * 10 * 10

Hence the series of product of 10^3 is 10*10*10

PLEASE HELP!! GIVING BRAINLIST TO WHOEVER ANSWERS

Answers

Does represent , like dividing or multiplying by 2

Please help me answer this

Answers

Answer: 7/8

10-2/12-4= 7/8

Step-by-step explanation:

Answer:

the answer might be number 3

2x - 3y = 3 solve y

Answers

Answer:

Y=-1+2x/3

Step-by-step explanation:

Move all the terms that don't contain y to the right side and solve. Hope this helps!

what is the ordered pair to y=7x-2

Answers

It would be (0,-2) I believe

OH MY GOD HELPPPPPPPPPPPPPP

Answers

Answer:

? = -36

Step-by-step explanation:

When you raise an exponent to an exponent, the resulting power is a product of the two exponents.

For this problem, you can solve for the missing value by writing:

[tex]?*1/3=-12[/tex]

Divide both sides by 1/3 to isolate the missing value.

[tex]?=\frac{-12}{1/3}[/tex]

Solve for ?.

[tex]?=-36[/tex]

I have 2 dice. If I roll both dice, what is the probability of rolling a 5 and then an even number

Answers

Answer:

1/6 and 1/2 or 3/6

Step-by-step explanation:

there's a 1 in 6 chance that u would roll a 5 but there's a higher chance of getting an even number as 3 out of 5 of those numbers are even so that would be 3/6 or simplify to 1/2

A fitness club charges its members a one time fee of 40$ and a monthly rate of 25$ what is this in q expression

Answers

y = 25x + 40 is the expression.

Can y’all please help me because my teacher assign a lot of work

Answers

Answer: okay just try your best to do it

Step-by-step explanation:

Got it?

You are running in a 26-mile race.
You have run 17 miles so far.
What is the ratio of the miles you have left to the total number of miles in the race?

Answers

Answer:

17:26

Step-by-step explanation:

You can't simplify 17 therefore it would be 17:26 ratio.

I hope this helps! Please give me brainllest!

never mind i forfeit

Bro what happened my brainliest is gone

Jessica borrows $1500 at 7% simple interest per week. If she ends up owing $2235, how may weeks did it take her to pay back the loan?
a. 6
b. 7
c. 8
d. 9
e. 10

Answers

Answer:

7 Weeks

Step-by-step explanation:

Each week is 105 because 1500*.07=105

Then through the process of elimination I found it would take 7 weeks.

Your answer is going to be 7 weeks

can you help me with this

Answers

Answer:

C.

Step-by-step explanation:

HELP!!
ASAP
Worth 10 points

Answers

Answer:

integers

Step-by-step explanation:

they wouldnt be whole numbers because there are opposites involved, but they wouldnt be just classified as rational because they have the requirements to be classified as integers

The answer is an integer.

An integer is any whole number (negative or positive) that is not either a decimal or a fraction.
A whole number is all the positive whole numbers including 0.
A Rational Number can be made by dividing two integers.
(An integer is a number with no fractional part.)


For khan academy. Need help . Explain if you can

Answers

Answer:

y = 2/3x + 1.5

Step-by-step explanation:

The Formula for that is

y = mx + b

m = slope

b =  y -intercept

so to find the slope I would do y/x or rise over run

So your slope is 2/3 ( it goes up 2 and right 3 times)

Since the line is going up and not down, it is a positive slope

y = 2/3x + b

we need to find where the line crosses the  vertical / y-axis and it's at the point.... (0,1.5)

y = 2/3x + 1.5

Hope this helped a little!

find the value of x and y

Answers

Answer: y is 40 x is 60

Step-by-step explanation:

Answer:

x=40 and y =5

Step-by-step explanation:

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