Mathematics High School

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

Jake rewrites the expression 81x4 – 1 as a difference of squares so he can factor it. Which answer choice shows how Jake could rewrite the expression?

Answers

Answer: (9x^2)^2 -1^2

Step-by-step explanation:

Jake rewrite the expression as,

⇒ (3x - 1) (3x + 1) (9x² + 1)

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 81x⁴ - 1

And, Jake rewrites the expression as a difference of squares so he can factor it.

Now, We can rewrite the expression as;

⇒ 81x⁴ - 1

⇒ (9x²)² - 1²

⇒ (9x² - 1) (9x² + 1)

⇒ ((3x)² - 1²) (9x² + 1)

⇒ (3x - 1) (3x + 1) (9x² + 1)

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ6

Enter your answer and show all the steps that you use to solve this problem in
the space provided.


The two figures shown above are congruent. Identify the corresponding sides and
angles.

Answers

Answer:

Step-by-step explanation:

they're the same figure but turned 90 deg

congruent sides:

AD and RQ

BA and SR

BC and SP

PQ and CD

congruent angles:

D and Q

R and A

B and S

C and P

haven't done this in a minute sorry if this is wrong

how will rational numbers help in future

Answers

Answer:

They are used to share something among friends , Like if there are four friends and they want to divide a cake equally among themselves , then the quantity of cake that each friend will get will be one-fourth of the cake , That is a rational number 1/4.

Step-by-step explanation:

short answer it won't trust me

What type of triangle is this

Answers

Answer:

isosceles

Step-by-step explanation:

Answer:

An isosceles

use the quotient rule to find the derrivatives of 3/x^2

With full process ​

Answers

Answer:

[tex]\displaystyle \frac{d}{dx} \Big [ \frac{3}{x^2} \Big ]=-\frac{6}{x^3}[/tex]

Step-by-step explanation:

We can use either the Power Rule or the Quotient Rule to find the derivative of 3/x².

Power Rule: [tex]\displaystyle \frac{d}{dx}[ x^n] = nx^n^-^1[/tex]  

Rewrite [tex]\displaystyle \frac{3}{x^2}[/tex] as [tex]\displaystyle 3\cdot \frac{1}{x^2}[/tex] which is equivalent to [tex]3\cdot x^-^2[/tex].

Now we can apply the power rule to 3x⁻². Subtract 1 from the exponent and multiply the coefficient by -2.

3(-2)x⁻³ = -6x⁻³

This can be rewritten as [tex]\displaystyle -\frac{6}{x^3}[/tex].

Quotient Rule: [tex]\displaystyle \frac{d}{dx} \Big [ \frac{f(x)}{g(x)} \Big ]=\frac{g(x)f'(x)-f(x)g'(x)}{[g(x)]^2}[/tex]

Substituting 3 for f(x) and x² for g(x), we get:

[tex]\displaystyle \frac{(x^2)(0)-(3)(2x)}{(x^2)^2}[/tex]

Simplify.

[tex]\displaystyle \frac{-6x}{x^4}[/tex]

Using exponent rules, we can rewrite this as:

[tex]-6x^1^-^4 = -6x^-^3[/tex]

This can be rewritten as [tex]\displaystyle -\frac{6}{x^3}[/tex], which is the same as what we got using the product rule.

Answer:

[tex]\displaystyle \frac{d}{d x}\left[\frac{3}{x^2}\right] = -\frac{6}{x^{3}}[/tex].

Step-by-step explanation:

Let [tex]f(x)[/tex] and [tex]g(x)[/tex] denote two functions of [tex]x[/tex]. Assume that [tex]g(x) \ne 0[/tex]. The quotient rule states that:

[tex]\displaystyle \frac{d}{d x}\left[\frac{f(x)}{g(x)}\right] = \frac{{f}^\prime(x) \cdot g(x) - f(x) \cdot g^{\prime}(x)}{{(g(x))}^2}[/tex].

In this question:

The numerator of the fraction is [tex]f(x) = 3[/tex] (a constant function.)The denominator of the fraction is [tex]g(x) = x^{2}[/tex].

Find [tex]{f}^{\prime}(x)[/tex] and [tex]{g}^{\prime}(x)[/tex].

Notice that the value of [tex]f(x)[/tex] is constantly [tex]3[/tex] regardless of the value of [tex]x[/tex]. By the constant rule, [tex]{f}^{\prime}(x) = 0[/tex].

For [tex]{g}^{\prime}(x)[/tex], consider the power rule:

if [tex]m[/tex] represents a rational number (such as [tex]2[/tex],) then by the power rule, [tex]\displaystyle \frac{d}{d x}\left[{x}^{m}\right] = m\, {x}^{m-1}[/tex].

Apply this rule to find [tex]{g}^{\prime}(x)[/tex].

[tex]\begin{aligned}{g}^{\prime}(x) &= \frac{d}{d x} \left[x^{2}\right] \\ &= 2\, x^{2 - 1} \\ &= 2\, x\end{aligned}[/tex].

Substitute [tex]f(x) = 3[/tex], [tex]{f}^{\prime}(x) = 0[/tex], [tex]g(x) = x^{2}[/tex], and [tex]{g}^{\prime}(x) = 2\, x[/tex] into the quotient rule expression to find [tex]\displaystyle \frac{d}{d x}\left[\frac{3}{{x}^{2}}\right][/tex]:

[tex]\begin{aligned}&\; \frac{d}{d x}\left[\frac{3}{{x}^{2}}\right] \quad \genfrac{}{}{0em}{}{\leftarrow f(x) = 3}{\leftarrow g(x) = {x}^{2}} \\ =&\; \frac{d}{d x}\left[\frac{f(x)}{g(x)}\right]\\ =&\; \frac{{f}^\prime(x) \cdot g(x) - f(x) \cdot g^{\prime}(x)}{{(g(x))}^2} \\ =& \; \frac{0 \, x^2 - 3\, (2\, x)}{\left({x}^{2}\right)} \\ =&\; -\frac{6}{x^{3}}\end{aligned}[/tex].

Therefore, [tex]\displaystyle \frac{d}{d x}\left[\frac{3}{{x}^{2}}\right] = -\frac{6}{x^{3}}[/tex].

I NEED HELP PLEASE I DON’T WANT TO FAIL PLEASE PLEASE HELP ME

Answers

The slope is 4/3 because when the y axis increases by four, the x axis increases by three. The y intercept is -2 because the line intercepts the y axis at -2. This means that it’s equation would be y=4/3-2. I hope this helps :)

Will mark as brainliest

Answers

Answer:

p = 1

Step-by-step explanation:

Δ JKH ≅ Δ JIH

therefore KJ corresponds with IJ so you can set both sides equal to each other

10p = p+9

9p = 9

p = 1

34.23 times one year is ....

Answers

Answer:

410.76

Step-by-step explanation:

34.23 * 12= 410.76

1 year = 12 months

410.76

34.23 times 12, because there are 12 months in one year, and the calculator shows 410.76!

What is a simpler form of the following expressions?
(7m2 - 5)(7m2 + 5)
(This is a rushed one so pls help?)

Answers

Answer:

49m^4 - 25

Step-by-step explanation:

The simpler expression can simply be found by expanding

The kind of expansion we have here is the difference of two squares

(a + b)(a-b) = a^2 - b^2

Thus, we have it that;

(7m^2-5)(7m^2 + 5)

=

49m^4 - 25

Help quick!!!

What is the distance between the following points:

A ( 25,20 ) B ( 5, 20 )

Answers

Answer:

(20,0)

Step-by-step explanation:

I think that's it sorry if I am wrong:(

simplify 3 to the 2nd power + 1 x 2

Answers

18 i’m pretty sure (:

Factor each polynomial: 9x-6

Answers

Answer:

3(3x−2)

Step-by-step explanation:

Find:-
1) Complement of 75 degree
2) Complement of 40 degree
3) Complement of 71 degree
4) Complement of 101 degree ​

Answers

Given :

Some angles in degree.

To Find :

1) Complement of 75 degree

2) Complement of 40 degree

3) Complement of 71 degree

4) Complement of 101 degree ​

Solution :

We know, two angles are complement when their sum is 90 degree.

1) Complement of 75 degree is, 90 - 75 = 15 degree.

2) Complement of 40 degree is, 90 - 40 = 50 degree.

3) Complement of 71 degree is, 90 - 71 = 19 degree.

4) Complement of 101 degree is, 90 - ( -101 ) = 191 degree.

Hence, this is the required solution.

Please answer!! I added a screenshot

Answers

Answer:

S + 2.5S + (2.5S - 3.3)

Step-by-step explanation:

To get the perimeter of ANY shape, simply add up all the sides.

Find the volume of the cube in inches3 below. Then select the correct units
when entering your answer.
7 in.
7 in.
7 in
Answer here
cu. cm
cu, in
sq. in

Answers

Answer:

21 cubic inches (or cu. in)

Step-by-step explanation: Multiply 7 by three

what is the slope of the line?

Answers

Slope:0
Y intercept: -2
Do you still need help my guy?

PLEASE HELP ASAP!!!!!!!

Answers

Answer:

[tex]\frac{9}{16}[/tex]

Step-by-step explanation:

[tex]\frac{1 \frac{1}{2} * \frac{3}{4}}{2}=\frac{9}{16}[/tex]

Can you guys help meh pls

Answers

16500, 1650, ?, 0.165
This pattern is to move the the number to the right by 2 decimal places.
So pattern number 3 is 16.50

Which calculation will ALWAYS give a result greater than 1? A.8/9 × a number less than 1 B.1 2/5 − a fraction less than 25 C. 7 × a number less than 1 D.3/7 + a fraction less than 1/2

Answers

Answer: B.1 2/5 − a fraction less than 2/5

Step-by-step explanation:

Question was not formatted properly and in the proper format, the above is the answer.

1²/₅ - ²/₅ = 1

Any number therefore that is lower than ²/₅ will when subtracted from 1²/₅ give an answer greater than 1 because when ²/₅  was subtracted from  1²/₅, it gave 1 as an answer.

Which statement about the dilation of these triangles is true?

The scale factor is
The scale factor is 2
The scale factor is 3.
The scale factor is 4.

Answers

Answer

when 2 triangle scales are similar the ration reduces and become a scale factor

Answer:

The scale factor is 2

Step-by-step explanation:

I’m begging please help me with this

Answers

one solution i think it has one solution

What is the difference between a system of equations and a system of inequalities?

Answers

The graph of linear inequalities include a dashed line if they are greater than or less than but not equal to. Linear equations, on the other hand, include a solid line in every situation. Moreover, linear inequalities include shaded regions whereas linear equations do not.

Expressions can be expressed as equations or as inequalities.

The difference is that the variables in a system of equation have one solution each, while in a system of inequalities, the variables have a range of values.

Let the system of equation be:

[tex]\mathbf{ax + by = c}[/tex]

[tex]\mathbf{dx + ey = f}[/tex]

Let the system of inequality be:

[tex]\mathbf{ax + by < c}[/tex]

[tex]\mathbf{dx + ey > f}[/tex]

Both systems can be solved using the same method, such as: graphs, substitution and elimination.

However, the difference is that:

In a system of equation, the variables can have one solution each, while in a system of inequalities, the variables have a range of values.

Read more about system of equations and inequalities at:

https://brainly.com/question/11476486

An angle measures 72.2° less than the measure of its complementary angle. What is the
measure of each angle?
º and°

Answers

Answer:

We have the angles as;

8.9 and 72.2

Step-by-step explanation:

When two angles are complementary, they add up to 90

Let the first angle be x , the second angle is 72.2 degrees less and it is x-72.2

Thus, mathematically;

x + x - 72.2 = 90

2x = 90+ 72.2

2x = 162.2

x = 81.1

x = 81.1

The other will be

81.1 - 72.2 = 8.9

The table below shows the number of peaches and cups of water used to make fruit punch according to a certain recipe. Peaches Water (cups) 64 96 56 84 How many cups of water are needed for every 1 peach? Note: Your answer may be exact or rounded to the nearest hundredth. label optional​

Answers

Answer:

fhyedGFYUSEGCFUEGFCYU

Step-by-step explanation:

pay back

Solve.
3.5 x (5.8 - 7.09) =

Answers

Answer:

-4.515

Step-by-step explanation:

3.5 times 5.8 is 20.3 and then 3.5 times -7.09 is -24.815 added together to get -4.815 so technically its none of those but they might have miss typed so i think probably -4.515

Will Mark Brainliest

Solve each system by elimination. Show your work

3х – 10 y = 14
3х – 9y = 15

Answers

Answer:

subtracting both equations

3x-10y=14

3x-9y=15

- - =-

_________

0-y=-1

y=1

then putting the value of y in first eqn

3x-10×1=14

3x=24

x=8

so x is 8and y is 1

A car travels 2 5/8 miles in 3 1/2 minutes at a constant speed. How far did the car travel in 5 minutes?

Answers

Answer:

3.75 as a decimal

Step-by-step explanation:

Giving 5 stars and brainlist to whoever answers this correct!!!!
The table shows the number of animals in the most popular exhibit at the zoo.

Flamingo - 12
Crocodile - 4
Elephants - 3
Monkeys - 11

If an animal is selected at random to be fed in front of an audience, which expression can be used to determine the probability the animal will NOT be an elephant?

A. 1/10
B. 9/10
C. 3/10
D. 3/3

Answers

Answer:

its A because it can't be B or D obviously, and since there are the least amount of elephants, its gonna be the one will less of a percentage. So its A.

Step-by-step explanation:

jabsbabsbavvsbabs

Let u=-4i-5j and v=3i-6j

Answers

The answer is 2244. Because ghgfgggggffgfhfghfgh

Jasmine sold half of her Barbie doll Collection
and then bought 9 dolls. She now has 13 dolls.
Barbie dolls did she begin with?
How many

Answers

Answer: 8 dolls.

Explanation: 13 - 9 = 4, 4 x 2 = 8.

Work the equation backwards... she has bought 9 extra dolls to add on the the half of her original amount. Without the extra 9 dolls (13 - 9), Jasmine has half of her original amount left (4) and so to find the original amount of dolls, think that if 4 is half the amount, what is 4 half of? 4 is half of 8 and so 8 is the original amounting dolls she had.
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