the rectangle shown has a perimeter of 56 cm and the given area. it's length is 8 more than three times it's width. write and solve a system of equations to find the dimensions of the rectangle.
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's solve ~
Assume width of rectangle be " x ", length = 3×width + 8 = 3x + 8 ~
Now, Perimeter of rectangle is :
[tex]\qquad \sf \dashrightarrow \:2(l + w) = 56[/tex]
[tex]\qquad \sf \dashrightarrow \:2(3x + 8 + x) = 56[/tex]
[tex]\qquad \sf \dashrightarrow \:2(4x + 8) = 56[/tex]
[tex]\qquad \sf \dashrightarrow \:4x + 8 = 56 \div 2[/tex]
[tex]\qquad \sf \dashrightarrow \:4x + 8 = 28[/tex]
[tex]\qquad \sf \dashrightarrow \:4x = 28 - 8[/tex]
[tex]\qquad \sf \dashrightarrow \:x = 20\div 4[/tex]
[tex]\qquad \sf \dashrightarrow \:x =5 \: cm[/tex]
Hence, width = x = 5 cm
[tex]\qquad \sf \dashrightarrow \:l = 3w + 8[/tex]
[tex]\qquad \sf \dashrightarrow \:l = 3(5)+ 8[/tex]
[tex]\qquad \sf \dashrightarrow \:l = 15+ 8[/tex]
[tex]\qquad \sf \dashrightarrow \:l =23 \:cm[/tex]
And, length = 26 cm
Related Questions
Ayan has $48 andis saving $10 per week and Gemma has $300 and is spending $8 per week. When will they both have the same amount of money?
Answers
Answer:
14 weeks
Step-by-step explanation:
First, write as an equation with x the number of weeks Ayan and Gemma's money:
-> Ayan's money: 48+10x because every week he wins 10 more dollars
-> Gemma's money 300-8x
Finally just solve the equation for x where ayan's money = gemma's money so :
48+10x=300-8x
add 8x on both side: 48+18x=300
substract 48 on both side to isolate x : 18x =252
devide by 18 on both side : x=14
Can someone explain this to me?
Answers
If you turn 1/2 into a decimal it would be 0.5
Tripling 0.5 would just be multiplying it by 3
0.5 x 3 = 1.5
The answer would be A) 1.5x
1. Suppose that a theater charges a school group $4.50 per student to show a special film. Suppose that the theater's operating expenses include $130 for the staff and a film rental fee of $1.25 per student.
a. What equation relates the number of students x to the theater's income I?
b. What equation relates the theater's operating expenses E to the number of students x?
c. Copy and complete the table below.
Theater Income and Expenses
Number of Students, x 0 10 20 30 40 50 60 70
Income, I ($) box box box box box box box box
Expenses, E ($) box box box box box box box box
d. On the same set of axes, graph the theater's income and operating expenses for any number of students from 0 to 100.
e. Describe the patterns by which income and operating expenses increase as the number of students in a group increases.
f. Write and solve an equation that you can use to answer the question “How many students need to attend the movie so that the theater's income will equal its operating expenses?”
g. Write an equation that represents the theater's profit. Compare your equation to those your classmates wrote.
h. Find the number of students that make each of the following inequality statements true.
i. E < 255
ii. I > 675
Answers
The functions I(x) and E(x) of the theatre's income and expenses are illustrations of linear functions.
The equation of the theatre's incomeThe theatre charges $4.50 per student.
Assume the number of students is x, the equation of the theatre's income would be:
I(x) = 4.5x
The equation of the theatre's expensesThe theatre expense per student is $1.25, and the operating cost on the staff is $130
The equation of the theatre's expenses would be:
E(x) = 1.25x + 130
Complete the tableUsing the formulas I(x) = 4.5x and E(x) = 1.25x + 130, the complete table is:
Students, x 0 10 20 30 40 50 60 70
Income, I 0 45 90 135 180 225 270 315
Expenses, E 130 142.5 155 167.5 180 192.5 205 217.5
The graph of the theatre's income and expensesSee attachment
The pattern by which theatre's income and expenses increaseThe functions I(x) and E(x) are linear functions.
So, the pattern with which the functions increase is a linear pattern.
The number of students when the theatre's income and expenses are equal
This means that:
I(x) = E(x)
So, we have:
4.5x = 1.25x + 130
Subtract 1.25 from both sides
3.25x = 130
Divide both sides by 3.25
x = 40
Hence, the number of students is 40
The theatre profitThis is the difference between the theatre expenses and their income.
So, we have:
P(x) = E(x) - I(x)
This gives
P(x) = 1.25x + 130 - 4.5x
Simplify
P(x) = 130 - 3.25x
Solution to the inequalitiesWe have:
E(x) < 255
This gives
1.25x + 130 < 255
Subtract 130 from both sides and divide by 1.25
x < 100 students
Also, we have:
I(x) > 675
This gives
4.5x > 657
Solve for x
x > 146 students
Hence, the number of students for the inequalities are less than 100 and greater than 146
Read more about linear equations and inequalities at:
https://brainly.com/question/11234618
What is the measure of arc XZ if the angle equals 135 and the radius is 17 km
Answers
now, let's make the assumption that the arcXZ has a central angle of 135° and a radius of 17.
[tex]\textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=17\\ \theta =135 \end{cases}\implies s=\cfrac{(135)\pi (17)}{180}\implies s=\cfrac{51\pi }{4}\implies s\approx 40.06[/tex]
The following shape has 1 pair of parallel sides
Answers
Planes Q and R are parallel planes. Plane Q contains line a. Plane R contains line b.
Planes Q and R are parallel. Plane Q contains line a and plane R contains line b. Both lines are going the same direction.
If a third plane could be drawn which contains both lines a and b, then
lines a and b must be parallel.
lines a and b cannot be parallel.
lines a and b must be skew.
lines a and b must be perpendicular.
Answers
Answer:
lines a and b must be parallel
Step-by-step explanation:
if lines a and b are parallel in plane r and q, then the lines must always be parallel.
Answer:
A
Step-by-step explanation:
on e2020
on thursday and friday last week miss kelly rode her snowmobile 249 miles. ON friday she rode 35 more miles than she did on thursday. Howmany milesdid she ride each day? Write a system of eqautions for this situation and solve.
Answers
Step-by-step explanation:
x = miles ridden on Thursday
y = miles ridden on Friday
x + y = 249
y = x + 35
we can use the identity of the second equation in the first equation and solve :
x + (x + 35) = 249
2x + 35 = 249
2x = 214
x = 107 miles
y = x + 35 = 107 + 35 = 142 miles
on Thursday she rode 107 miles.
on Friday 142 miles.
the following shape has 1 pair of parallel sides 2, 7, 3, 8
Answers
Answer:
I think it's 8
Step-by-step explanation:
because if you think of an octagon it has eight sides and the only parallel sides is pn the top of the octagon and the bottom of the octagon
10 people each wants 3 slices but a box has 8 slices
Answers
Answer:
you need 30 slices
a minimum of 4 boxes of pizza
Step-by-step explanation:
very easy math do you know whats the answer?
Answers
3 is less than w , 7 is greater than or equal to w
[tex]3 < w \\ 7 \geqslant w[/tex]
Answer:
3 < w = 7 ≥ w
Step-by-step explanation:
Less than= "<"
Greater than or equal to = ≥
Rewrite without absolute value for the given condition: y=|x−3|+|x+2|−|x−5|, if 3 < x < 5
Answers
Answer:
x>3 but x<5 so x=4
4-3=1
+
4+2=6
-
4-5=-1
but |-1|=1
so
1+6-1=6
Helen wrote and solved the equation.
x minus 17 = 56. x minus 17 + 17 = 56 minus 17. x = 39.
What was Helen’s error?
Helen only needed to add 17 to the left side of the equation.
Helen should have added 17 to both sides of the equation.
Helen’s work is correct.
Helen made a subtraction error when subtracting 17 from 56.
Answers
Answer:
x-17=56
x-17+17=56+17
x=56+17
x=73
Step-by-step explanation:
Do mark BRAINLIEST
Answer:
d
Step-by-step explanation:
An electrician has an income of $41,500. The income tax the electrician has to pay is 12%. What is the amount of income tax that the electrician has to pay? A) $3,840 B) $4,164 C) $4,980 D) $5,210.
Answers
Answer:
he has to pay 4980$ in tax So its C) 4,980
The amount of income tax that the electrician has to pay is $4980. Then the correct option is C.
What is the percentage?The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.
An electrician has an income of $41,500.
The income tax the electrician has to pay is 12%.
Then the amount of income tax that the electrician has to pay will be
Amount of income tax = 0.12 × $41500
Amount of income tax = $ 4980
Thus, the amount of income tax that the electrician has to pay is $4980.
More about the percentage link is given below.
https://brainly.com/question/8011401
Researchers are recording how much of an experimental medication is in a person's bloodstream every hour. they discover that half-life of the medication is about 6 hours.
Answers
By using the known half-life, we can see that if the initial dose is 500mg, after 4 days the medication will be 0.0076 mg.
What is the half-life?
We define half-life as the time such that the initial amount is reduced to its half.
So, if a given substance has a half-life T, then the amount of substance as a function of time, we have:
S(t) = A*e^{-t*ln(2)/T}
Where t is the variable in time units.
We know that T = 6 hours, and A, the initial dose, is 500 mg, so the formula is:
S(t) = 500mg*e^{-t*ln(2)/6h}
Then after 4 days (or 4*24h = 96h) the amount of medication is:
S(96h) = 500mg*e^{-96h*ln(2)/6h} = 0.0076 mg.
If the initial dose was 750mg, after 4 days the person would have:
S(96h) = 750mg*e^{-96h*ln(2)/6h} = 0.0114 mg
So the person would have:
0.0114 mg - 0.0076 mg = 0.038 mg more of medication.
If you want to learn more about the half-life, you can read:
https://brainly.com/question/11152793
Rachel's starting salary was $45,000 per year.
Rachel received a 3.7% raise every year after her first
year. How much is Rachel making now, & years later?
Answers
Answer:
After 1 year $46,665
Vf = Vi ( 1 + r/m) ^ tm
Step-by-step explanation:
Vf = Final Value
Vi = Initial Value ($45,000)
r = Interest Rate (3.7%, put in decimal form so .037)
m = Compound Rate (amount of times it increases every year, for this it would be 1)
t = Amount of years you are forecasting
45000 * (1 + .037)²
45000 * (1.037)²
45000 * 1.075369
$48,391.605 in 2 years
Question Find the cube root. -125 divided by 3
Answers
Answer:
First of all multiply 5 in three times
Express 6 m as a percentage of 16 m.
Answers
Answer:
37.5%
Step-by-step explanation:
the percentage is calculated as a fraction of the quantities multiplied by 100% , that is
[tex]\frac{6}{16}[/tex] × 100% = 0.375 × 100% = 37.5%
Answer:
37.5%
Step-by-step explanation:
6/16×100
37.5%
brainiest please
The temperature in the freezer is -15°C. The temperature outside the freezer is 10°C. Find the difference between these two temperatures.
Is the answer 25? Just checking :)
Answers
Answer:
Yes it is 25
Step-by-step explanation:
10 - 25 = -15
-15 + 25 = 10
Help me solve this please
Answers
There are 372 children, I hope my answer will be of use to you.
Possible or impossible?
The difference is 3.
The difference is also
-3.
Answers
So
x -(3) = x - 3
But
x -(-3) = x + 3
They are not equal
Impossible
base radius of 7cm and height of 35cm what is the cylinder's volume
Answers
Answer:
5390 cm³Step-by-step explanation:
It is given that the base radius of a cylinder is 7cm and the height is 35cm and we are asked to find the volume of the cylinder.
We must know this formula :
⇒ Volume(Cylinder) = πr²hWe will take the value of π as 22/7Now substituting the values :
⇒ Volume(Cylinder) = 22/7 × (7)² × 35
⇒ Volume(Cylinder) = 22/7 × 49 × 35
⇒ Volume(Cylinder) = 22 × 7 × 35
⇒ Volume(Cylinder) = 22 × 245
⇒ Volume(Cylinder) = 5390
Therefore,
The volume of the cylinder is 5390 cm³A national survey is conducted to assess the association between hypertension and stroke in persons over 75 years of age with a family history of stroke. Development of stroke is monitored over a 5 year follow-up period. The data are summarized below and the numbers are in millions. Compute the RELATIVE RISK of stroke in hypertensive as compared to non-hypertensive persons.
Answers
The relative risk of stroke in hypertensive as compared to non-hypertensive persons will be 1.8367.
How to calculate relative risk?From the complete information, those with hypertension that had strike is 12. Those with no hypertension but had stroke is 4.
Also, those with hypertension but don't have stroke is 37 while those with no hypertension but had stoke is 26.
Therefore, the relative risk will be:
= (12/12 + 37) / (4/4 + 26)
= 12/49 / 4/30
= 1.8367
In conclusion, the correct option is 1.8367.
Learn more about relative risk on:
https://brainly.com/question/25264302
Please help answer the attached question
Answers
Answer:
angle BCD = 108
Step-by-step explanation:
opposite angles in a cyclic quadrilateral add to 180
so angle BDC is 180 - 72 = 108
what are the angles 32 and 114 there for??
Ashley predicts that 92% of the people she invites to her party will come. If she wants to have at least 23 guests, how many people should she invite to her party?
Answers
Answer:
25 people
Step-by-step explanation:
So, you're trying to find how many she needs to invite since only 92% show up. With this problem, you need to figure out 92% of what number is 23. An equation for this is:
92/100 = 23/x
1. Cross multiply to get 92x=2300
2. Divide both sides to get x by itself. You should get x= 25
3. So, she should invite 25 people
A rental car company charges $36.39 per day to rent a car and $0.09 for every mile
driven. Miguel wants to rent a car, knowing that:
He plans to drive 225 miles.
• He has at most $480 to spend.
Which inequality can be used to determine x, the maximum number of days Miguel
can afford to rent for while staying within his budget?
Answers
Answer:
12 days
Explanation:
480 >/= 36.39x + 20.25
The inequality to determine x, the maximum number of days Miguel
can afford to rent while staying within his budget is
202.5 + 36.39x ≤ 480
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
Charges per day = $36.39
Charges per mile = $0.90
Total miles = 225
Total charges for 225 miles.
= 225 x 0.90
= $202.5
The maximum amount to spend = $480
The inequality for the maximum number of x days.
202.5 + 36.39x ≤ 480
Thus,
The inequality to determine x, the maximum number of days is
202.5 + 36.39x ≤ 480
Learn more about inequalities here:
https://brainly.com/question/20383699
#SPJ2
Literacy
Fill in the missing letters to make Maths related words:
Venn
Set
Diagram
Universal
S_r_i_g
Event
Probability
Not
Answers
Answer:
Sorting
Step-by-step explanation:
Tom knows that in his school 10 out of every 85 students are left-handed.
There are 391 students in Tom's school.
how many students in Tom's school are left handed?
Answers
Answer:
46 are left handed
Step-by-step explanation:
divide 10 by 85 and you get 0.11764705882352941176470588235294 then multiply that by 391 and you get 46
i don't understand this at alllll :(
Answers
Answer:
300
Step-by-step explanation:
volume of rectangle formula:
HEIGHT*WIDTH*LENGHT*
12*10(1/2)*20(1/4= 300
Answer:
2551.5in³
Step-by-step explanation:
this is easy if you know the formula.
volume = l*w*h
= 20.25*10.5*12= 2551.5in³
A circular counter top has a radius of 5 feet.
Enter the area, in square feet, of the counter top. Round your answer to the nearest tenth.
Answers
Answer:78.6[tex]ft^{2}[/tex]
Step-by-step explanation:
Area=π[tex]r^{2}[/tex]
Area=[tex]\frac{22}{7}[/tex] x [tex]5^{2}[/tex]
=[tex]\frac{22}{7}[/tex] x 25
=78.6[tex]ft^{2}[/tex]
Helen is having a birthday
party. Her friends arrive at
her house at 8:15 p.m. They
leave three hours later. What
time do Helen's friends leave?
Answers
Answer: 11:15 p.m 5:15 p.m.
Step-by-step explanation: