A wire is first bent into the shape of a triangle. Each side of the triangle is 16 long. Then the wire is unbent and reshaped into a rectangle. If the length of the rectangle is 15 in, what is its width?

All cases rewritten in the form of difference expressions are listed below:

Equalities represent relationships between two expressions, in which one expression is equal to another. An equality (x = a) is equivalent to the following difference expression:  

x - a = 0   (1)

And inequalities represent relationships between two expressions, in which one expression is not necessarily to another. An inequality (x < a, x > a, x ≤ a, x ≥ a) is represented by the following difference expression:

x - a = b   (2)

Where b have the following cases:

Now we proceed to rewrite each case in term of difference expressions:

To learn more on inequalities, we kindly invite to check this verified question: https://brainly.com/question/19491153

Let's solve

[tex]\\ \rm\rightarrowtail -2.5(1.4+3.1)+6.9(-4.3)[/tex]

[tex]\\ \rm\rightarrowtail -3.5-7.75-29.67[/tex]

[tex]\\ \rm\rightarrowtail -11.25-29.67[/tex]

[tex]\\ \rm\rightarrowtail -40.92[/tex]

Both did error in signs

Answer:

Given expression:

-2.5(1.4+3.1) + 6.9(-4.3)

Student P

Step 1:  -3.5 + 7.75 + 6.9(-4.3)

Step 2: -3.5 + 7.75 - 29.67

Step 3: 7.75 - 3.5 - 29.67

Step 4: -25.42

Student P made an error in step 1.  When expanding the first part of the expression, they forgot the negative sign when multiplying -2.5 by 3.1.  

So Step 1 should be:  -3.5 - 7.75 + 6.9(-4.3).  

This error then impacted all following steps and gave an incorrect final solution.

Student Q

Step 1: -3.5 - 7.75 + 6.9(-4.3)

Step 2: -3.5 - 7.75 - 29.67

Step 3: -(3.5 - 7.75 - 29.67)

Step 4: -(-33.92)

Step 5: 33.92

Student Q made an error in step 3.  When placing the numbers in parentheses and placing a negative sign outside the parentheses, they should have changed the two negative signs inside the parentheses to positives.

So Step 3 should be: -(3.5 + 7.75 + 29.67).  

This error then impacted all following steps and gave an incorrect final solution.

Correct steps and solution

Step 1:  -3.5 - 7.75 + 6.9(-4.3)

Step 2: -3.5 - 7.75 - 29.67

Step 3: -(3.5 + 7.75 + 29.67)

Step 4: -(40.92)

Step 5: -40.92

Answer:

I don't understand

Step-by-step explanation:

You answer it.

Answer:

  $10,596.81

Step-by-step explanation:

The balance on an account earning 5% interest compounded quarterly can be found using the formula ...

  A = P(1 +0.05/4)^(4t)

where P is the principal invested and t is the number of years.

__

Here, we are investing $7500.00. After 2 years, the account balance will be ...

  A = $7500(1 +0.05/4)^(4·2) = $8283.65

After the $1500 withdrawal, the new balance will be ...

  $8583.65 -1500.00 = $6783.65

__

This is the amount earning interest for the next year, after which time the balance will be ...

  A = $6783.65·(1.0125)^(4·1) = $7129.24

When $2000 is added to the account, the principal earning interest for the last 3 years is ...

  $7129.24 +2000.00 = $9129.24

__

The final balance after 3 more years is then ...

  A = $9129.24·(1.0125)^(4·3) = $10,596.81

_____

These calculations are conveniently carried out by a spreadsheet, as in the attached. Since the account changes are all done at the end of the year, we don't have to keep track of the quarterly balances. The formula used to calculate the ending balance each year is shown.

The function N =1053(1.23)^m or 1053(1.23)^m = N is an illustration of an exponential function

The function is given as:

N =1053(1.23)^m

On April 1, 2016; the value of m is:

m = 0

So, we have:

N =1053(1.23)^0

N = 1053

Hence, there are 1053 deers on April 1, 2016

The function is given as:

N =1053(1.23)^m

On April 1, 2016; the value of m is:

m = 1

So, we have:

N =1053(1.23)^1

N =1295

Hence, there are 1295 deers on May 1, 2016

An exponential growth function is represented as:

y = a(1 + r)^x

Where r represents the growth rate

By comparison; the monthly growth rate (r) is calculated as:

1 + r = 1.23

Subtract 1 from both sides

r = 0.23

Express as percentage

r = 23%

Hence, the monthly growth rate is 23%

We have the monthly growth rate to be 23%

There are 12 months in a year.

So, the yearly growth rate is:

y = 23%^12

Evaluate

y = 0.00022%

Hence, the yearly growth rate is 0.00022%

We have the monthly growth rate to be 23%

There are 4 weeks in a months

So, the weekly growth rate is:

m = 23%^(1/4)

Evaluate

m = 69%

Hence, the weekly growth rate is 69%

Read more about exponential functions at:

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Answer:

Step-by-step explanation:

firstly the area for teh rectangle is 12 x 15 = 18are0

the area for the circle is 113.1 sq inches because  pi x r squared

The bucket that contains 2120 grams of sand and a cup that contains 438 grams of sand , the bucket of sand has 1682 grams of sand than the cup of sand in the cup.

A cup contains 438 grams of sand. A bucket contains 2120 grams of sand.

Therefore, the number of more grams of sand in the bucket than the cup is as follows:

mass of sand in cups = 438 grams

mass of sand in the bucket = 2120 grams

Therefore,

difference in mass = 2120 - 438

difference in mass = 1682 grams

Therefore, they are 1682 grams of sands in the bucket than the cup.

learn more on mass(grams) here: https://brainly.com/question/12843854

Answer:

Step-by-step explanation:

To get one portion of soup, each ingredient should be divided by 3

Quantity of onion required=  180 ÷ 3 = 60 g

Quantity of carrots required = 120 ÷ 3 = 60 g

Oil = 3 ÷ 3 = 1 table spoon

Quantity of tomatoes required = 600 ÷ 3 = 300 g

Vegetable stock = 1.2 ÷ 3 = 0.4 litres

Answer:

Step-by-step explanation:

Use FOIL method.

(x -2)(x+3) = x*x + x*3 + (-2)*x + (-2)*3

                 = x² + 3x - 2x -6  {Combinelike terms}

                  = x² + x - 6

(x² + x -6)*(2x + 1) = x²*2x + x²*1 + x*2x +x*1 + (-6)*2x + (-6)*1

                             = 2x³ + x² + 2x² + x -12x - 6

                             = 2x³ + 3x² - 11x - 6

I think it's 16.5lbs I'm sorry if I'm wrong I don't know for sure

Answer:

The answer is B.

Step-by-step explanation:

15÷3=5    15÷5=3

30÷3=10   30÷5=6

45÷3=15    45÷5=9

60÷3=20    60÷5=12

Answer:

see explanation

Step-by-step explanation:

look at the photo

Answer:

7x+4+2y is your answer

Tim covered 21.333 kilometers

Kilometers, km covered is distance, d

d = speed / time

d = 80 / 3 hours 45 mins

Converting 45 mins to hours we have

1 hour = 60 minutes

? Hours = 45 minutes

? = 45 / 60 = 0.75

So time is 3.75 hours

d = 80 / 3.75

= 64 / 3

= 21.333km

hope it helps

Answer:

300 km

Step-by-step explanation:

Tim drives 80 km in 1 hour or 60 minutes

Tim drives in 1 minute = 80/60 km

so, tim drives in 3 hours 45 minutes ( 225 minutes)

[tex] \frac{80 \times 225}{60} [/tex]

= 300 km

67,600 different passwords can be formed.

26 x 26 x 10 x 10 = 67,600 (26 letters in the alphabet and 10 from 0-9)

Answer: Fragment.

Step-by-step explanation:

A Fragment phrase can be defined as a sentence that resembles a sentence but lacks delivering a complete idea. This sentence serves as a dependent clause in a sentence.

The given sentence is an example of a fragment phrase or sentence. Though the phrase appears to be a sentence but it lacks complete idea because we don't know about which 'people' is it talking about.

Answer:

yes

Step-by-step explanation:

is there a specific question?

Answer: All children should be doing homework. But the amount and quality should change." His basic prescription.

Step-by-step explanation:

Answer:

nice handwriting

Step-by-step explanation:

Answer:

You may want to add more context to this question.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Equation

Part A

# Calculators = Total amount / Cost of 1 calculator

Givens

# Calculators = ?

Total amount of money = 195 dollars

Cost of one calculator = 6.50

Solution

# Calculators = 195/6.50

# Calculators = 30

Answer: He can buy 30 calculators.

Work Shown:

A = P*(1+r/n)^(n*t)

A = 1000*(1+0.07/4)^(4*10)

A = 2001.59734318603

A = 2001.60

This assumes that you do not withdraw any of the money over the course of the 10 years. Also, the interest rate must stay the same at 7%.

Answer:

the answer is; 68% of 7000 which gives 4760 football fans rooting for the home team

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Here's the solution ~

To write a quadrilatic function, we have to use its roots, like we have to subtract the roots from x and multiply them ~ then we will get our required function !

Since our only root is 11 here, we have to do t double

[tex]\qquad \sf  \dashrightarrow \:(x - 11)(x - 11)[/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} - 11x - 11x + 121 [/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} - 22x + 121[/tex]

That's our required function ~ I hope you understood the whole thing !

Answer:

A) 5x - 3= -39

B) 5x = -39 + 3

5x = -36

x = -36/ 5

x= -7.2

Answer:

A. 3.5

Step-by-step explanation:

The perimeter is just the sum of all of the side lengths. The sides of this triangle are n inches, (n + 5.2) inches, and (2n + 3.4) inches.

So, your equation is n + n + 5.2 + 2n + 3.4 = 22.6 inches.

You can combine like terms (adding together all of the n's and all of the numbers) to simplify your equation to 4n + 8.6 = 22.6 inches.

Subtract 8.6 from both sides of the equation to get 4n = 14, and divide both sides by 4 to get n = 3.5.

Hope this helps! :)

Answer:

A. True

B. True

C. False

D. False

Hey there!

Basically for all of your equations/questions you have to COMBINE the LIKE TERMS (if they are any in the particular equation you have)

/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\

QUESTION/EQUATION #1

x - 5 ÷ 3 + b

We pretty much CANNOT do anything to this equation because it doesn’t have that many like terms.

So, thus your answer will most likely be/

[b + x - 5 ÷ 3]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

QUESTION/EQUATION #2

6b + 15b ÷ 3

= 21b ÷ 3

= 7b

Thus, your answer is: [7b]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
QUESTION/EQUATION #3

c - 2c × 4

REWRITE

= 1c - 2c × 4

COMBINE the LIKE TERMS

= 1c - 7

= -7c
Thus, your answer is: [-7c]

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

By using Euler's notation, we will see that:

z^7 = 78,125*e^(-i*4.48)

We know that:

z = 4 - 3i

Remember that for a complex number:

w = a + bi

In Euler's notation, we can write this as:

w = √(a^2 + b^2)*e^(i*Atan(b/a))

Then, for z, we will get:

z =  √(4^2 + (-3)^2)*e^(i*Atan(-3/4))

z = 5*e^(-i*0.64)

Now, if we apply an exponent of 7 to this number, we will get:

z^7 = ( 5*e^(-i*0.64))^7

z^7 = 5^7*e^(-i*7*0.64) = 78,125*e^(-i*4.48)

If you want to learn more about complex numbers, you can read:

https://brainly.com/question/10662770