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.
Answers
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:
https://brainly.com/question/15656646
Related Questions
The perimeter of a rectangle is 39.2 km, and its diagonal length is 14 km.
Find its length and width
Answers
Using the formulas to find its length =
P= 2 ( l + w )
d= w² + l²
There are 2 solutions for,
l = P / 4 + 1 / 4 √8d² - p²
= 39.2 / 4 + 1 / 4 × √8 × 14² - 39²
= 11. 2 km answer.
Using the formula to find its width =
w = p / 2 - l
= 39.2 / 2 - 11.2
= 8.4 km answer.
≈ the length of a rectangle is 11.2 km and the width is 8.4 km
which inequality matches the graph?
A. x>4
B. x<4
C. x=4
D. x >4
Answers
Answer:
B
Step-by-step explanation:
The line goes left which means its going to be less than 4.
Answer:
[B] x < 4
Step-by-step explanation:
First you must know the following:
> ⇒ greater than
< ⇒ less than
≥ ⇒ greater than or equal to
≤ ⇒ less than or equal to
= ⇒ equal
When going to the left it means less than
Thus, we can conclude that
x < 4
Kavinsky
fnd the highest common factor of -8xy and 20y
Answers
Answer:
[tex]\huge\boxed{\boxed{2}\cdot\boxed{2}\cdot\boxed{y}=4y}[/tex]
Step-by-step explanation:
[tex]-8y=-2\cdot\boxed{2}\cdot\boxed{2}\cdot \boxed{y}\\\\20y=\boxed{2}\cdot\boxed{2}\cdot5\cdot\boxed{y}[/tex]
A hybrid car can go 400 miles on 8 gallons of gas. How far can the car take you with 1 gallon of gas?
Answers
Answer:
50 miles
Step-by-step explanation:
Take the number of miles and divide by the number of gallons
400 miles / 8 gallons
50 miles per gallon
Answer:
50 miles
Step-by-step explanation:
if for each 8 gallons it can go to 400 miles
so the 8 will be divided to 8 and get 1
and also divide the 400 into 8 you will get 50 miles per 1 gallon
What is 8 hours and 37 minutes converted into minutes?
Answers
Answer:
517 minutes
Step-by-step explanation:
Hope this helps:))
Answer:
517 mins
Step-by-step explanation:
1hour=60min
8hour=480min
37min is the same because it is already in minutes
480+37=517mins
Please help me solve this math problem
Answers
Answer:
(b)
Step-by-step explanation:
A suitable calculator or spreadsheet can find the matrix product for you. Here, the answer choices differ in their upper left term, so we can determine the correct choice by finding the value of that term. It is the dot product of the first row of B and the first column of A.
(5)(3) +(7)(3) +(3)(2) = 15 +21 +6 = 42
This matches choice B.
factorise
18p+6
please im so bad
Answers
Helppppppppppppp helppppppppppppp
Answers
Answer:
Should be the first answer, x=5
Step-by-step explanation:
This would flip the graph and the square would land on top of where it currently is.
2 FOR 2.20 UNIT RATE
Answers
Answer: (if your asking for the unit rate of that)
the unit rate is 1.10
Answer:
1.10
Step-by-step explanation:
2 /2 = 1
20/ 2 = 10
1.10 is the unit rate
Jose and Gavin are reading the same book. At the beginning of the month, Jose was
on page 10 and Gavin was on page 37. Jose will read 17 pages per day and Gavin will
read 14 pages per day. Let J represent the page of the book that Jose is on at the end
oft days into the month, and let G represent the page of the book that Gavin is on at
the end oft days into the month. Write an equation for each situation, in terms of t,
and determine what page Jose and Gavin will be on on the day they are both on the
same page.
Answers
Using linear functions, it is found that:
Jose's equation is: [tex]J = 17x + 10[/tex].Gavin's equation is: [tex]G = 14x + 37[/tex].They will be on the same page on the 9th day.Linear function:A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
m is the slope, which is the rate of change.b is the y-intercept, which is the value of y when x = 0.Jose:
Initially, he was on page 10, hence [tex]b = 10[/tex].He reads 17 pages per day, hence [tex]m = 17[/tex].Hence, Jose's equation is: [tex]J = 17x + 10[/tex].Gavin:
Initially, he was on page 37, hence [tex]b = 37[/tex].He reads 14 pages per day, hence [tex]m = 14[/tex].Hence, Gavin's equation is: [tex]G = 14x + 37[/tex].The day they will both be on the same page is x for which:
[tex]J = G[/tex]
Hence:
[tex]17x + 10 = 14x + 37[/tex]
[tex]3x = 27[/tex]
[tex]x = \frac{27}{3}[/tex]
[tex]x = 9[/tex]
They will be on the same page on the 9th day.
To learn more about linear functions, you can take a look at https://brainly.com/question/16302622
Which of the equations will be a true statement if p = 10 3 ? Select the two choices that apply.
A. 3.4 ÷ p = 0.034
B. 437 ÷ p = 0.437
C. 53.45 ÷ p = 53.45
D. 6,340 ÷ p = 6.34
E. 2,458.2 ÷ p = 24.582
Answers
Answer:A
Step-by-step explanation: make me brainlist if correct
Write five demicals that round to 0.96?
Answers
Answer:
0.964
0.959
0.961
0.958
0.963
Step-by-step explanation:
Anything below 5 can be rounded down, anything above 5 can be rounded up.
You can have a decimal after 0.96 to be less than 5, or a decimal after 0.95 to be greater than 5.
Here's some I picked:
0.964
0.959
0.961
0.958
0.963
?/5 =8/10 type the missing number that makes this fraction equal
Answers
Answer:
[tex]?=4[/tex]
Step-by-step explanation:
[tex]\frac{?}{5}=\frac{8}{10}[/tex]
[tex]\frac{2?}{10}=\frac{8}{10}[/tex]
[tex]2?=8[/tex]
[tex]?=4[/tex]
Evaluate.
(jk−1)÷j when j=−4 and k=−0.7
Enter your answer as a decimal in the box.
Answers
Answer:
(jk - 1) / j
jk = (-4 x -0.7) = 2.8
(2.8 - 1) / - 4
1.8 / -4 = -0.45
Answer is -0.45 when j = -4 and k = -0.7
What are the coordinates of the point (-4, 2) after a translation 2 units left and 2 units up?
A (-2, 0)
B (-6,0)
C (-2, 4)
D (-6, 4)
Answers
Answer:
the answer you're looking for is D. when you move to the left the -4 becomes -6 and when you move up 2 becomes 4.
Mrs. Baca uses a phone card to call a relative in Colombia, It cost her 45 cents to talk for 15 minutes. Choose True or False for each statement.
A. For 45 cents, Mrs. Baca can talk for 3 minutes. True or False.
B. The call rate is 3 cents per minute. True or False.
C. The call rate can represent by the ratio 445:15. True or False.
D. Divide 75 by 15 to find the number of minutes Mrs. Baca can talk. True or False.
Answers
Answer:
A: False
B: True
C: False
D: False
Hope This Helps!!!
For the following equation, find a solution for the variable. Show all of your work and use complete sentences to explain the solving process that you used to find a solution for the equation. Be sure to include at least two terms from the word bank. 4+ x = 7
Answers
Answer:
x=33
Step-by-step explanation:
you move the 4 to the other side
x=7-4
so
x=3
Answer:
x=3
Step-by-step explanation:
This should be easy.
4+x=7
-4 -4
x=7-4
x=3
Word explanation:
Here, we're solving for the variable x, first, we need to isolate x and therefore subtract 4 on both sides, 7 minus 4 is 3, so x is equal to 3.
If you spend 3/5 of your $40 gift card, how much money will be left on it?
Answers
Answer:
$16
Step-by-step explanation:
1-⅗=⅖
40×⅖=16
Here's the answer
x+3x+3y+3z=21
Find the value of X.
Answers
Answer:
[tex] x = \frac{21 - 3y - 3z}{4} [/tex]Step-by-step explanation:
Question:-To find value of xEquation:-x + 3x + 3y + 3z = 21Solution:-=> x + 3x + 3y + 3z = 21
[On adding like terms x and 3x]=> 4x + 3y + 3z = 21
[On subtracting both sides with 3y]=> 4x + 3y + 3z - 3y = 21 - 3y
[On Simplification]=> 4x + 3z = 21 - 3y
[On subtracting both sides with 3z]=> 4x + 3z - 3z = 21 - 3y - 3z
[On Simplification]=> 4x = 21 - 3y - 3z
[On dividing both sides with 4][tex] = > \frac{4x}{4} = \frac{21 - 3y - 3z}{4} [/tex]
[On Simplification][tex] = > x = \frac{21 - 3y - 3z}{4} (ans)[/tex]
Given :
x + 3x + 3y + 3z = 21To Find :
The value of xSolution :
[tex]\qquad { \dashrightarrow \: { \sf{x + 3x + 3y + 3z = 21}}}[/tex]
Adding the like terms :
[tex]\qquad { \dashrightarrow \: { \sf{4x + 3y + 3z = 21}}}[/tex]
Transposing 3y to the other side which then becomes negative :
[tex]\qquad { \dashrightarrow \: { \sf{4x + 3z = 21 - 3y}}}[/tex]
Now, Transposing 3z to the other side which then becomes negative :
[tex]\qquad { \dashrightarrow \: { \sf{4x = 21 - 3y - 3z}}}[/tex]
Dividing both sides by 4 :
[tex]\qquad { \dashrightarrow \: { \sf{ \dfrac{4x}{4} = \dfrac{21 - 3y - 3z}{4} }}}[/tex]
[tex]\qquad { \dashrightarrow \: { \sf{{x} = \dfrac{21 - 3y - 3z}{4} }}}[/tex]
Therefore, the value of x = 21 – 3y – 3z/4
What is the domain of the absolute value function below?
(will give brainless)!!!!
Answers
Answer:
D <----last option Domain is set of real numbers or (-∞,+∞)
help me plsss! need help
Answers
Is 6.32332333... a rational or irrational number? a Choose the correct answer below. O rational number O irrational number
Answers
Answer:
Irrational number because it cannot be written in fraction form a/b where b is not supposed to be 0
i need help fast plz
Answers
Answer:
27/16
Step-by-step explanation:
[tex]12 \div \left(2 + \dfrac 23 \right)^2\\\\\\=12 \div \left(\dfrac 83 \right)^2\\\\\\=12 \div \dfrac{64}9\\\\\\=12 \times \dfrac{9}{64}\\\\\\= \dfrac{3 \times 9}{16}\\\\\\=\dfrac{27}{16}\\\\\\=1\dfrac{11}{16}[/tex]
Harry has $10 in his bank account, and he adds $2 every week. based on this information, which representation best shows the relationship between the amount of money harry has in his bank account ,y, and the number of weeks that have passed, x? (im testing....)
Answers
Answer:
y= (2x)+10
Step-by-step explanation:
if harry has an initial balance of $10 in his bank account, he will have something +10 for the initial 10.
If he adds $2 to his bank account every week, then the amount of money in his bank account (y) can be modeled by the equation
y = (2x)+10
where y represents how much money he has in his bank account and x represents the amount of weeks he is adding $2.
What is the answer to the equation?
Answers
the slope is negative because the line is going down from left to right
the y-intercept is 5 because that’s where the line crosses the y-axis
Quantity is proportional of 40/8
Answers
40/8=5
(100 points will award brainliest)
In the image below, the m
Answers
Answer: 67°.
Step-by-step explanation:
1) m∠PMR=m∠LMN=3x+19°;
2) m∠LMN+m∠LMP=180°, it can be written as 3x+19+9x-31=180;
3) if to solve the equation 3x+19+9x-31=180, then x=16;
4) m∠PMR=3x+19=48+19=67°.
A linear function and an exponential function are shown below.
Over which interval does the growth rate of the exponential function exceed the growth rate of the linear function?
Answers
Answer:
x >2
Step-by-step explanation:
*The exponential function gets steeper when x is greater than 2
Answer:
D. x>2 is the answer got it right
solve for x. 2/x-3=x/12-4x
Answers
Answer:
x= 47 18+2 201 i ≈0.382978723+0.603295612i x= 47 −2 201 i+18 ≈0.382978723−0.603295612i Hopefully this makes just the same amount of sense as this question
Use the order of operations to simplify 4(3.5 - 1.5) - 1/2.
a. 19 1/2
b. 7 1/2
c. 12
d. -4
Answers
[tex]\huge\textbf{Hey there!}[/tex]
[tex]\mathbf{4(3.5 - 1.5) - \dfrac{1}{2}}\\\\\mathbf{\rightarrow 4(2) - \dfrac{1}{2}}\\\\\mathbf{\rightarrow 8 - \dfrac{1}{2}}\\\\\mathbf{\rightarrow \dfrac{15}{2} \approx 7.5 \approx \boxed{\bf 7 \dfrac{1}{2}}}\\\\\\\\\huge\boxed{\textbf{Therefore, your answer is: \boxed{\mathsf{Option \ B. \ 7 \dfrac{1}{2}}}}}\huge\checkmark[/tex]
[tex]\huge\textbf{Good luck on your assignment \& enjoy}\\\huge\textbf{your day!}[/tex]
~[tex]\frak{\bf Amphitrite1040:)}[/tex][tex]\huge \bf {Question}:—[/tex]
[tex] \boxed{\bf \: 4(3.5 - 1.5) - 1/2}[/tex]
[tex]\bf\huge Solution:—[/tex]
[tex] \sf \longmapsto \: 4*(3.5-1.5)-1/2[/tex]
[tex] \boxed{\bf \: Convert \: 1/2 \: i nto \: Decimal:—}[/tex]
[tex]\sf \longmapsto \: 4*(3.5-1.5)-0.5[/tex]
[tex] \boxed{\bf \: Subtract \: 3.5-1.5 :—\: (2 \: is \: the \: result)}[/tex]
[tex]\sf \longmapsto \: 4*(2) - 0.5[/tex]
[tex] \boxed{\bf Multiply \: 4 \: and \: 2:—(8 \: is \: the \: result)}[/tex]
[tex]\sf \longmapsto8-0.5[/tex]
[tex] \boxed{\bf \: Simply \: Subtract:—}[/tex]
[tex]\sf \longmapsto7.5[/tex]
[tex]\boxed{\bf Convert \: to \: Fraction, \: And \: Fraction\:to\:Mixed \:Fraction:—}[/tex]
[tex]\sf\longmapsto 15/2[/tex]
[tex] \boxed{\bf \: Mixed \: Fraction:—}[/tex]
[tex]\boxed{\sf\longmapsto 7 \dfrac{1}{2} }[/tex]
________________________________
[tex]\boxed{\bf Solving \: in \: another \: way:—}[/tex]
[tex]\sf \longmapsto4*2-1/2[/tex]
[tex]\sf \longmapsto4*(2)-1/2[/tex]
[tex]\sf \longmapsto8-1/2[/tex]
[tex]\sf \longmapsto \: 15/2[/tex]
[tex] \boxed{\bf \: Mixed \: Fraction:—}[/tex]
[tex]\boxed{\sf \longmapsto \: 7 \dfrac{1}{2} }[/tex]
________________________________
[tex] \boxed{\bf \: \: Answer \: i s \: Option \: B}[/tex]
[tex] \boxed{\huge\sf \: (B) \: \bf \: 7\dfrac{1}{2}} [/tex]