1. Use precise mathematical language to justify and explain each mathematical process.

Use the rectangle with side lengths 5.22 – 8x + 9 and x + 5 for the following two questions.

1. What is the perimeter of the rectangle? Write a summary of the process used to determine the expression.

2. What is the area of the rectangle? Write a summary of the process used to determine the expression.

1. Use Precise Mathematical Language To Justify And Explain Each Mathematical Process.Use The Rectangle

Answers

Answer 1

Mathematical processes are the steps used to determine the result of operations

The perimeter of the rectangle is [tex]10x^2 - 14x + 28[/tex]The area of the rectangle is [tex]5x^3 +17x^2 -31x + 45[/tex]

The dimension of the rectangle is given as:

[tex]Length = 5x^2 - 8x + 9[/tex]

[tex]Width = x + 5[/tex]

(1) The perimeter of the triangle

This is the sum of the side lengths of the rectangle.

So, we have:

[tex]Perimeter = 2 \times (Length + Width)[/tex]

This gives

[tex]Perimeter = 2 \times (5x^2 - 8x + 9 + x + 5)[/tex]

Collect like terms

[tex]Perimeter = 2 \times (5x^2 - 7x + 14)[/tex]

Open brackets

[tex]Perimeter = 10x^2 - 14x + 28[/tex]

Hence, the perimeter of the rectangle is [tex]10x^2 - 14x + 28[/tex]

(2) The area of the triangle

This is the product of the dimensions of the rectangle.

So, we have:

[tex]Area = Length \times Width[/tex]

This gives

[tex]Area = (5x^2 - 8x + 9) \times (x + 5)[/tex]

Open brackets

[tex]Area = 5x^3 - 8x^2 + 9x +25x^2 - 40x + 45[/tex]

Collect like terms

[tex]Area = 5x^3 - 8x^2 +25x^2+ 9x - 40x + 45[/tex]

[tex]Area = 5x^3 +17x^2 -31x + 45[/tex]

Hence, the area of the rectangle is [tex]5x^3 +17x^2 -31x + 45[/tex]

Read more about areas and perimeters at:

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Related Questions

What is 1,000 x 10,090g

Answers

Answer:

10,090,000 grams

Step-by-step explanation:

Just add three zeros to 10090g.

Choose the symbol that correctly compares the fractions below.

Answers

Answer:

[tex] \frac{1}{8} < \frac{2}{7} [/tex]

1/8 < 2/7

Answer: B

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Thank you for spreading this message! Very appreciated :D I’ve never encountered one but I hope not.
Thank for telling everyone about this!

Help help ASAP ASAP

Answers

Answer:

1

Step-by-step explanation:

y2 - y1 / x2 - x1

6 - 4 / 0 - -2

2 / 2 = 1

Help help help math math

Answers

Answer:

gradient M = 4

Step-by-step explanation:

pick any two pairs

M= change in Y / change in X

considering the last pairs

3--1/0--1=4✓

considering first pair

-1--5/-1--2 is also 4✓

I hope it helps

help me please ill mark as the brainiest if correct.

Answers

Answer:

14 minutes

Step-by-step explanation:

For every two minutes the temperature increases by 15 c. since 8 equals 55, 10 is 70, 12 is 85, and 14 is 100.

Answer:

14

Step-by-step explanation:

1. Find selling price in the following cases.
a) Market price = Rs 480,discount = Rs 40
b) Market price = Rs 870, discount = Rs 75.
2. Find cost price or selling price in the following cases.
a) cost price = Rs 120, profit = Rs 25
b) selling price = Rs 200, profit = Rs 20

Answers

Answer:

1) a. Rs 440.

1) b. Rs 795.

2) a.Rs 145.

2) b. Rs 180.

Step-by-step explanation:

1) a.

Given,

Marked Price = Rs 480

Discount Amount = Rs 40

Selling Price = ?

Now,

Selling Price = Marked Price - Discount Amount

= Rs 480 - Rs 40 = Rs 440.

1) b.

Given,

Marked Price = Rs 870

Discount Amount = Rs 75

Selling Price = ?

Now,

Selling Price = Marked Price - Discount Amount

= Rs 870 - Rs 75 = Rs 795.

2) a.

Given,

Cost Price = Rs 120

Profit = 25

Selling Price = ?

Now,

Selling Price = Cost Price + Profit

= Rs 120 + Rs 25 = Rs 145.

2) b.

Given,

Selling Price = Rs 200

Profit = Rs 20

Cost Price = ?

Now,

Cost Price = Selling price - Profit

= Rs 200 - Rs 20 = Rs 180.

Find the least common denominator for these fractions. Enter your answer in
the space provided.

Answers

Answer: 27

Step-by-step explanation: LCM of 3 and 27 is 27.



A notecard is 3 inches by 4 inches. How
long is its diagonal

Answers

Answer:

7. Is answer

Step-by-step explanation:

Because 3+4=7

what does it mean to square a value/ expression

Answers

Squaring a number means multiplying the same number by itself.

For example,

[tex]\\2 \cdot 2 =2^2\\\\a\cdot a =a^2~~ \\\\ (a+1)(a+1) =(a+1)^2 \\\\ (x^{10}+1)(x^{10}+1) =(x^{10}+1)^2[/tex]

Use the graph method to solve the system of linear equations:
2x + y = 3 and x + y = 3
A) (-1.5, 0)
B) (0, -1.5)
C) (0,3)
D) (3,0)

Answers

Answer:

C) (0,3)

Step-by-step explanation:

It would be that answer because I found the answer in a website. Its Math-way

Answer:

C) (0,3)

Step-by-step explanation:

Graph each line on the same plane and take the point of their intersection.

Given linear equations:

2x + y = 3 and x + y = 3

See the attached  to confirm the answer is the point (0, 3)

Please help my assignment

Answers

There is no solution since ln(0) is undefined

If 3 people share 5 pizzas , how much pizza does each person get

Answers

Answer:

1 2/3

Step-by-step explanation:

5 pizzas divided by 3 people = 1 2/3

Help me solveee this

Answers

A straight angle = 180 so you have the cute angle given so it would be x + 47 = 180 same as 180-47= 133. Therefore x=133°
Straight angel = 180
The angel given is 47 sooo x + 47=180
Orrrr you can do 180 - 47 = x which is better and then the answer will be 133

Alec invested $1500 in an account with annually compounded interest. The account earns 4% annual interest. How much will Alec have in his account after 4 years?

Answers

Answer:

He will have $1,754.79 in his account after 4 years

Step-by-step explanation:

We can use the compound interest formula to find how much money he will have after 4 years:

[tex]A = P(1 + \frac{r}{n})^{nt}[/tex] ;

where

A= final amount

P= initial amount

r= interest rate

n= number of times interest applied per time period

t= number of time periods elapsed,

so from the given information, we know that 1500 is our initial amount, so P= 1500.

Annual interest means once a year, so n= 1, and the interest rate is 4%, so r= 4% or 0.04

and we are asked to find the amount in his account after 4 years, so t= 4

Now, all we need to do is plug in these values for each of the variables and solve.

[tex]A= 1500(1+\frac{0.04}{1} )^{(1)(4)}[/tex]

and we get

A= $1,754.79

What are the common factors of 45 and 272
O A 1,36.9.15
0
B. 1.39
C 1.3.9.15
D. 1,3,5,9

Answers

Answer:

Step-by-step explanation:

they are prime to eachother.

There is only one common factor .i.e.,1

45=1×3×3×5

272=1×2×2×2×2×17

The solution to the following inequality:
-3(6-2g)>4g

Answers

Answer:

Solution: g > 9

Interval Notation: (9 , ∞)

Step-by-step explanation:

-3 * (6-2g) > 4g

-18 + 6g > 4g

6g - 4g > 18

2g > 18

g > 9

Which algebraic expression is equivalent to the expression below?

3/5x-7/5y

Answers

Answer:

455554444444555556555555554444

Can someone help me? Will make brainiest :)

Answers

Answer:

D

Step-by-step explanation:

BH is perpendicular to AC since an orthocenter is a point at which the three altitudes of a triangle intersect. The altitude of a triangle is that line that passes through its vertex and is perpendicular to the opposite side. Since you know that BH is an altitude due to Point H being an orthocenter, you know that BH is perpedendicular to AC.

I also agree that it is D

If 3(x - 2) = 6, then x

Answers

Answer:

8

Step-by-step explanation:

3(x - 2) = 6

3x - 6 = 6

x - 6 = 2

x = 8

hope it helps :)

mark brainliest!!

Hello could I please get a straightforward answer I need to catch up pelsse

Answers

Answer:

Step-by-step explanation:


I need help doing this

Answers

The answer is 3 because x is -7. I hope this helps!

find the value of 7u+7 given that -3u-5=4

Answers

Answer:

14

Step-by-step explanation:

-3u = 4+5

-3u = 9

u = -3

7u + 7

7(u +1) = 7(-3+1)

7(-2)

14

Amaya used these steps to solve the equation 8x+4=9+4(2x−1). Which choice describes the meaning of her result, 4=5?
A.Amaya made a mistake because 4 is not equal to 5.
B.No values of x make the equation true.
C.All values of x make the equation true.
D.The solution is x=4 or 5.

Answers

Answer:

B.

Step-by-step explanation:

4 is of course not equal to 5 so no values of x make the equation true.

There are no solutions to this equation.

6. If the net investment function is given by
I(t) = 100e0.11
calculate
(a) the capital formation from the end of the second year to the end of the fifth year
(b) the number of years required before the capital stock exceeds $100 000.

Answers

The capital formation of the investment function over a given period is the

accumulated  capital for the period.

(a) The capital formation from the end of the second year to the end of the fifth year is approximately 298.87.

(b) The number of years before the capital stock exceeds $100,000 is approximately 46.15 years.

Reasons:

(a) The given investment function is presented as follows;

[tex]I(t) = 100 \cdot e^{0.1 \cdot t}[/tex]

(a) The capital formation is given as follows;

[tex]\displaystyle Capital = \int\limits {100 \cdot e^{0.1 \cdot t}} \, dt =1000 \cdot e^{0.1 \cdot t}} + C[/tex]

From the end of the second year to the end of the fifth year, we have;

The end of the second year can be taken as the beginning of the third year.

Therefore,  for the three years; Year 3, year 4, and year 5, we have;

[tex]\displaystyle Capital = \int\limits^5_3 {100 \cdot e^{0.1 \cdot t}} \, dt \approx 298.87[/tex]

The capital formation from the end of the second year to the end of the fifth year, C ≈ 298.87

(b) When the capital stock exceeds $100,000, we have;

[tex]\displaystyle \mathbf{\left[1000 \cdot e^{0.1 \cdot t}} + C \right]^t_0} = 100,000[/tex]

Which gives;

[tex]\displaystyle 1000 \cdot e^{0.1 \cdot t}} - 1000 = 100,000[/tex]

[tex]\displaystyle \mathbf{1000 \cdot e^{0.1 \cdot t}}} = 100,000 + 1000 = 101,000[/tex]

[tex]\displaystyle e^{0.1 \cdot t}} = 101[/tex]

[tex]\displaystyle t = \frac{ln(101)}{0.1} \approx 46.15[/tex]

The number of years before the capital stock exceeds $100,000 ≈ 46.15 years.

Learn more investment function here:

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Captain Brewster captured a pack of aliens. The following data points represent the lengths of each of the aliens' big toes (in centimeters). 18, 16, 17, 17, 16, 15, 16. Using this date, create a dot plot where each dot represents a big toe.

Answers

Answer:

15 ·

16 ···

17 ··

18 ·

19

Step-by-step explanation:

There were 2 aliens that each have big toes measuring 17 cm long. So, the 17 would have 2 dots above it:

17 ··

Please help I don't understand

| X = 2 | Y = 3 | Z = 4 |

Evaluate the expression using the solutions above

5x + 6z + 2y

Answers

Answer:

The expression can be written as:

5(2) + 6(3) + 2(4).

if I'm wrong, please tell me

Using y = 1 − 2x, plot the ordered pairs from the table. Then graph the function represented by the ordered pairs and tell whether the function is linear or nonlinear.
Helppp plzz due in 20 min

Answers

I think therefore its a linear function

A shirt costing $34 is on sale for 30% off. What is the new price of the shirt after the discount?

Answers

Answer:

$23.80

Step-by-step explanation:

30% off means we take 30% off of the original price, or we calculate

(1-30%)=70% of the shirt's price

34*70%=23.8

The area of a trapezoid is 140 cm2 and the height is 20 cm. What is the sum of the bases?

A. 14 cm

B. 49 cm

C. 60 cm

D. 7 cm

Answers

Answer:

the answer is 14

Step-by-step explanation:

[tex]1 \div 2b \times h = 1 \div 2 \times 20 \times b = 140 \: so \: base \: = 14[/tex]

hope this helped

The sum of the bases of a trapezoid using height is 20 cm is 14 cm.

Thus, option (A) is correct.

The formula to calculate the area of a trapezoid is given by:

Area = 1/2 x height x sum of bases

Given that the area is 140 cm² and the height is 20 cm.

Now, rearrange the formula to solve for the sum of the bases:

Sum of bases =  (2 x Area) / (height)

Substitute the given values:

Sum of bases =  (2 x 140) / (20)

                       = 14

So, the sum of the bases is 14 cm.

Thus, option (A) is correct.

Learn more about area of Trapezium here:

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