ANSWER
It will take 18 months before the company starts making a profit.
STEP-BY-STEP EXPLANATION
Given information
[tex]P(x)\text{ = }\frac{1}{3}x^2\text{ - 6x}[/tex]Where x is the number of months.
Step 1: Make P(x) = 0
[tex]\begin{gathered} \text{ p(x) = }\frac{1}{3}x^2\text{ - 6}x \\ 0\text{ = }\frac{1}{3}x^2\text{ - 6}x \end{gathered}[/tex]Step 2: Find x from the above equation
[tex]\begin{gathered} 0\text{ = }\frac{1}{3}x^2\text{ - 6x} \\ \text{Add 6x to the both sides} \\ 0\text{ + 6x = }\frac{1}{3}x^2\text{ - 6x + 6x} \\ 6x\text{ = }\frac{1}{3}x^2 \\ \text{cross multiply} \\ 6x\text{ }\times3=x^2 \\ 18x=x^2 \\ \text{Divide both sides by x} \\ \frac{18\cancel{x}}{\cancel{x}}\text{ = }\frac{\cancel{x^2}}{\cancel{x}} \\ x\text{ = 18 months} \end{gathered}[/tex]Therefore, it will take 18 months before the company starts making a profit.
use a combination of inverse operations to solve the following equations.2(x-1) = -6
Given the following question:
[tex]2(x-1)=-6[/tex][tex]\begin{gathered} 2(x-1)=-6 \\ \text{ Divide by two} \\ -6\div2=-3 \\ \frac{2(x-1)}{2}=(x-1) \\ (x-1)=-3 \\ -1+1=0 \\ -3+1=-2 \\ x=-2 \end{gathered}[/tex]Your answer is x = -2.
In the diagram, RSTU ~ ABC D. Find the ratio of their perimeterA А.24BR18S36TDCThe ratio of their perimeters is
The ratio of the perimeters of two similar shapes is equal to the ratio of their corresponding sides, then, by taking the top sides of these figures we can express the following ratio
18 : 24
by dividing both numbers by 2, we get:
9 : 12
Dividing by 3:
3 : 4
Then the ratio of their perimeters equals 3 : 4
help meeeeeeeeee pleaseee !!!!!
For the given functions, we can write the sum as:
(f + g)(x) = 9x + 1
How to find the sum between functions?Here we want to find the sum between functions f(x) and g(x), and in this case, we have:
f(x)= x - 8
g(x) = 8x + 9
The sum can be written as:
(f + g)(x) = f(x) + g(x)
Replacing the functions there we get:
(f + g)(x) = f(x) + g(x)
(f + g)(x) = (x - 8) + (8x + 9)
(f + g)(x) = x + 8x - 8 + 9
(f + g)(x) = 9x + 1
That is the sum of the functions.
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4.) explain clearly in your own words why the triangles and figure 12.3 to have area 1/2 (b•h) for the given choice of base B and height h
The area of the right angled triangle as well as that of the isosceles triangle is calculated as
Area = 1/2 (b * h)
The explanation is logical, observe the right angled triangle (the one on the left) and you'll see that the length covered by the height (labelled as h) is not the entire width covered by the base (labelled as b) unlike what you have in a rectangle or square. Its only logical to multiply the base by half of the height, otherwise you might end up calculating the area of a rectangle.
That applies to all triangles in general, the area is calculated as
[tex]A=\frac{1}{2}bh[/tex]The function y=f(x) is graphed below. Plot a line segment connecting the points on ff where x=-1 and x=0. Use the line segment to determine the average rate of change of the function f(x) on the interval −1≤x≤0
Answer:
Aveage Rate of cCanege = 40
Explanation:
The line segment is drawn in the function below:
Using the line segment:
[tex]\begin{gathered} \Delta x=0-(-1)=1 \\ \Delta y=40-0=40 \end{gathered}[/tex]Therefore, the average rate of change will be:
[tex]\text{ Average Rate of Change}=\frac{\Delta y}{\Delta x}=\frac{40}{1}=40[/tex]The average rate of change is 40.
In one hour, you can earn 350 points in your favorite video game. You already have 1050 points. a) Write an inequality where y is the total number for points and x is the number of hours. b) Your goal is 2450 points. What is the least number of hours to reach this goal?
SOLUTION
The initial points is 1050
The points earned per hour is 350
The total point y earned in x hours is:
[tex]y\ge350x+1050[/tex]Substitute y=2450 into the inequality
[tex]2450\ge350x+1050[/tex]Solve for x
[tex]\begin{gathered} 2450-1050\ge350x \\ 1400\ge350x \\ x\le4 \end{gathered}[/tex]Therefore the lease number of hours is 4.
Tickets at the carnival cost 35 each.on Friday night the carnivals earned a total of 12,425 in ticket sales on Saturday night the ticket sales tripled sales from the night before many people attended To the carnival on both nights
ticket sale on Saturday night is triple the ticket sale on Friday night.
Therefore
ticket sales on Saturday night = 3 x 12425 = 37275
Then
ticket sales for both nights = 12425 + 37275 = 49700
A ticket costs 35.
Let the number of people that attended the carnival on both nights be n.
Then, we have
[tex]\begin{gathered} 35n=49700 \\ \Rightarrow n=\frac{49700}{35}=1420 \end{gathered}[/tex]Therefore 1420 people attended the carnival on both nights
y varies directly as x, y = 7 when x = 21. Determine x when y = 5.
y varies directly as x, y = 7 when x = 21. Determine x when y = 5.
Step 1
Let
y varies directly as x, it is y depends on x, in math terms
f(x)=y
y = 7 when x = 21
f(21)=7
Determine x when y = 5. f(?)=5
Step 2
there is a proportion, this must be equal, make a rule of three to find the value
so
x y
[tex]\begin{gathered} 21\leftrightarrow7 \\ x\text{ }\leftrightarrow5 \\ \text{the relation is} \\ \frac{21}{7}=\frac{x}{5} \\ \text{solve for x} \\ x=\frac{21\cdot5}{7} \\ x=\frac{105}{7} \\ x=15 \end{gathered}[/tex]so , when y=5, x=15
Write the expression as a complex number in standard form.
(-2+6i)-(2-3i)=
Answer:
-4 +9i
Step-by-step explanation:
complex number in standard form.
(-2+6i)-(2-3i)=
Combine like terms
-2 -2 +6i +3i
Standard form is a+bi
-4 +9i
a machine can stamp 36 bottle caps in 10 seconds copy and complete the table. At this rate, how many bottle caps can the machine stamp in 5 minutes? At this rate, how many minutes will it take to stamp 24,408 bottle caps?
SOLUTION
1. From the question the machine stamps 36 caps in 10 seconds
In 5 minutes it will cap
[tex]\begin{gathered} 5\text{ minutes = 5 }\times\text{ 60 seconds } \\ =300\text{ seconds } \\ 36\text{ }\rightarrow\text{caps in 10 seconds } \\ x\text{ }\rightarrow\text{caps in 300 seconds } \\ \text{cross multiplying we have } \\ 36\times300=10\times x \\ 10800=10x \\ x=\frac{10800}{10} \\ x=1080 \end{gathered}[/tex]So in 5 minutes, it would stamp 1080 bottle caps
2. Minutes it would take to stamp 24,408 bottle caps?
[tex]\begin{gathered} 1080\text{ }\rightarrow\text{caps in 5 minutes } \\ 24,408\rightarrow caps\text{ in }x\text{ minutes } \\ \text{cross multiplying we have } \\ 1080\times x=24,408\times5 \\ 1080x=122040 \\ x=\frac{122040}{1080} \\ x=113\text{ minutes } \end{gathered}[/tex]Hence it would take 113 minutes to stamp 24,408 bottle caps
Choose the algebraic description that maps ΔABC onto ΔA′B′C′ in the given figure.Question 7 options:A) (x, y) → (x + 4, y + 8)B) (x, y) → (x + 8, y + 4)C) (x, y) → (x – 4, y – 8)D) (x, y) → (x + – 8, y – 4)
Step 1
Given the triangle, ABC translated to A'B'C'
Required to find the algebraic description that maps triangle ABC and A'B'C'
Step 2
The coordinates of points A, B,C are in the form ( x,y)
Hence
[tex]\begin{gathered} A\text{ has a coordinate of ( -3,-2)} \\ B\text{ has a coordinate of (-6,-5)} \\ C\text{ has a coordinate of (-1,-4)} \end{gathered}[/tex]Step 3
Find the algebraic description that maps triangle ABS TO A'B'C'
[tex]\begin{gathered} A^{\prime}\text{ has a coordinate of (5,2)} \\ B^{\prime}\text{ has a coordinate of ( 2,-1)} \\ C^{\prime}\text{ has a coordinate of ( 7, 0)} \end{gathered}[/tex]The algebraic description is found using the following;
[tex]\begin{gathered} (A^{\prime}-A^{})=(x^{\prime}-x,\text{ y'-y)} \\ OR \\ (B^{\prime}-B)=(x^{\prime}-x,\text{ y'-y)} \\ OR \\ (C^{\prime}-C)=(x^{\prime}-x,\text{ y'-y)} \end{gathered}[/tex]Hence,
[tex]\begin{gathered} =\text{ ( 5-(-3)), (2-(-2))} \\ =(8,4) \\ \text{Hence the algebraic description from triangle ABC to A'B'C' will be } \\ =(x,y)\Rightarrow(x\text{ + 8, y+4)} \end{gathered}[/tex]Hence the answer is option B
A paper airplane contest is being held. The following results are found: 80% of the participants used a triangle shape. The triangle shaped planes only won their trials 16% of the time. The other shaped planes won their trials 36% of the time. Create a tree diagram for this situation: What is the probability that a triangle plane won overall?Out of 100 planes, which shape has the most winners?A winning plane is selected at random, what is the chance it is triangle shaped?
Given:
Percent of participants that used triangles shape = 80% = 0.80
The triangles shaped won their trials 16% of the time = 0.16
The other shaped plane won their trials 36% of the time = 0.36
Thus, we have:
Percent of participants who used other shapes = 100% - 80% = 20% = 0.20
Amount of time the triangle shaped plane lost = 100% - 16% =84% = 0.84
Amount of time the other shaped plane lost = 100% - 36% = 64% = 0.64
Let's solve for the following:
• (a) Create a tree diagram for this situation.
We have the tree diagram below:
• (b) What is the probability that a triangle plane won overall?
To find the probability that a triangle plane won overall, we have:
[tex]P(\text{triangle)}=\frac{0.8\times0.16}{(0.8\times0.16)+(0.2\times0.36)}=\frac{0.128}{0.128+0.072}=0.64[/tex]• (c) Out of 100 planes, which shape has the most winners?
Given that 80% used triangle, the number of planes with triangle shape will be:
0.8 x 100 = 80 planes
Number of planes with other shape:
0.2 x 100 = 20 planes
Number of winners for traingles:
0.16 x 80 = 12.8
Number of winners for other shape:
0.36 x 20 = 7.2
Therefore, the shape with the most winners is the triangle shape.
• (d),. A winning plane is selected at random, what is the chance it is triangle shaped?
To find the probability a winning plane selected at random is triangle shaped, wehave:
[tex]P(\text{triangle)}=\frac{12.8}{12.8+7.2}=\frac{12.8}{20}=0.64[/tex]ANSWER:
(b) 0.64
(c) Triangle shape
(d) 0.64
If y varies directly as x, and y is 6 when x is 72, what is the value of y when x is 8?
1/9
2/3
54
96
Answer:
2/3
Step-by-step explanation:
y = xk
6 = 72K Solve for k Divide both sides by 72
[tex]\frac{1}{12}[/tex] = k
y = xk
y = [tex]\frac{8}{1}[/tex] x [tex]\frac{1}{12}[/tex]
y = [tex]\frac{8}{12}[/tex] I can simplify by dividing the numerator and denominator by 4
y = 2/3
What is the area of this triangle?
Pls help :(
Hi could you help me find out the correct answer to this?
Given:
There are given two triangles.
Explanation:
According to the question:
We need to find the tall of Ariadne.
So,
To find the value, we need to use triangle proportion properties.
So,
Suppose the value of tall is x.
So,
[tex]\frac{x}{6}=\frac{15}{18}[/tex]We need to find the value of x.
Then,
[tex]\begin{gathered} \frac{x}{6}=\frac{15}{18} \\ x\times18=15\times6 \\ x=\frac{15\times6}{18} \\ x=5 \end{gathered}[/tex]Final answer:
Hence, the solution is 5 ft tall.
I need help with geometry!
Basic geometry are formulars and properties of basic shapes like rectangle, square, circle, triangle, and solid shapes like cuboid, cube cylinder etc.
The area, perimeter and volume of solid shape are properties that can be determined from this shape.
Perimeter is the sum of the whole side of the figure. Example the perimeter of a rectangle with 2 length and 2 width can be calculated by adding the whole 2 length and width.
The perimeter of the rectangle above is by adding all the sides.
perimeter = 4 + 4 + 2 + 2 = 12 cm
The area of the figure below is the amount of space of the boundary. The area of the rectangle below is length * width = 4 * 2 = 8 cm squared.
HELP PLEASE!!!!!!!!!!! ILL MARK BRAINLIEST
Answer:
skill issue
Step-by-step explanation:
skill issue
Which expression is equivalent to (m−5n−3)−3?
m−15n−9
m15n9
m−8n−6
1 over the quantity m raised to the eighth power times n raised to the sixth power end quantity
The expression (m⁻⁵n⁻³)⁻³ has an equivaent of m⁻¹⁵n⁹
How to determine the equivalent expressionFrom the question, the expression is represented as
(m−5n−3)−3
Rewrite the expression properly
This is done as follows;
(m⁻⁵n⁻³)⁻³
Open the brackets
So, we have the following equation
(m⁻⁵n⁻³)⁻³ = (m⁻⁵)⁻³ x (n⁻³)⁻³
Evaluate the products
So, we have the following equation
(m⁻⁵n⁻³)⁻³ = (m⁻¹⁵) x n⁹
This gives
So, we have the following equation
(m⁻⁵n⁻³)⁻³ = m⁻¹⁵n⁹
Hence, the solution is (m⁻⁵n⁻³)⁻³ = m⁻¹⁵n⁹
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The given expression (m⁻⁵n⁻³)⁻³ has an equivalent to the m⁻¹⁵n⁹
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The expression is represented as (m−5n−3)−3
Rewrite the expression as follows;
(m⁻⁵n⁻³)⁻³
Open the brackets , we have
(m⁻⁵n⁻³)⁻³ = (m⁻⁵)⁻³ x (n⁻³)⁻³
Evaluate the products, we have;
(m⁻⁵n⁻³)⁻³ = (m⁻¹⁵) x n⁹
(m⁻⁵n⁻³)⁻³ = m⁻¹⁵n⁹
Hence, the solution will be; (m⁻⁵n⁻³)⁻³ = m⁻¹⁵n⁹
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Solve 3 (4x - 7) * 7x - 10 0 12x - 7 12x - 21 12x + 21
Answer:
12x-21
Explanation:
Given the expression
3 (4x-7)
On expanding using distributive law;
3(4x-7)
3(4x) - 3(7)
12x - 21
Hence the result required is 12x-21
Which quadrilateral has diagonals that are both congruent and perpendicular?ParallelogramRectangleRhombusSquare
The quadrilateral has diagonals that are both congruent and perpendicular is square.
The correct option is (d)
Answer:
Its A
Step-by-step explanation:
Evaluate the expression for r = –31, s = 4, and t = –16.
Answer:
st - r = -33
Explanation:
We need to replace r by -31, s by 4 and t by -16, so the expression is equal to
st - r = 4(-16) - (-31)
st - r = - 64 + 31
st - r = -33
So, the answer is
st - r = -33
A park in a subdivision is triangular shaped. Two adjacent sides of the park are 533 feet and 525 feet. The angle between the sides is 53 degrees. To the nearest unit, what is the area of the park in square yards?A. 27,935B. 24,831C. 37,246D. 12,415thank you ! :)
Given:
Length of the two adjacent sides = 533 feet and 525 feet
Angle between the two sides = 53 degrees
Let's find the area of park.
Let's make a sketch representing this situation:
Let's first find the length of the third side.
Apply the cosine rule.
We have:
[tex]\begin{gathered} a=\sqrt{533^2+525^2-2(533)(525)cos53} \\ \\ a=\sqrt{284089+275625-336805.7777} \\ \\ a=\sqrt{222908.2223} \\ \\ a=472.13\text{ ft} \end{gathered}[/tex]Now, apply the Heron's formula to find the area:
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]Where:
a = 472.13
b = 533
c = 525
Let's solve for s:
[tex]\begin{gathered} s=\frac{472.13+533+525}{2} \\ \\ s=\frac{1530.13}{2} \\ \\ s=765.1\text{ } \end{gathered}[/tex]• Therefore, the area will be:
[tex]\begin{gathered} A=\sqrt{765.1(765.1-472.13)(765.2-533)(765.1-525)} \\ \\ A=\sqrt{765.1(292.97)(232.1)(240.1)} \\ \\ A=111738.81\text{ ft}^2 \end{gathered}[/tex]The area in square feet is 111,738.81 square feet.
Now, let's find the area in square yards.
Apply the metrics of measurement.
Where:
1 square yard = 9 square feet
Thus, we have:
111,738.81 square feet =
[tex]\frac{111738.81}{9}=12415.4\approx12415\text{ square yards}[/tex]Therefore, the area of the park in square yards is 12,415 square yards.
ANSWER:
12,415 square yards.
Patrick is buying a new car. He can choose the body style, color and engine type. If there are 54 ways he can select a car, with there body styles and two engine choices , his many colors are available
Given:
Total Number of ways = 54
Number of body styles = 3
Number of engine choices = 2
Let's find the number of colors available.
To find the number of colors available, we have:
Number of ways = Number of body styles x Number of engine choices x Number of colors
54 = 3 x 2 x c
Where c represent the available number of colors.
Let's find c.
54 = 3 x 2 x c
54 = 6c
Divide both sides by 6:
[tex]\begin{gathered} \frac{54}{6}=\frac{6c}{6} \\ \\ 9=c \\ \\ c=9 \end{gathered}[/tex]Therefore, there are 9 colors available to select from.
ANSWER:
9
P. The Shah family basement floor is shaped like a trapezoid. The basement has sides of and 24 feet and two sides of 21 feet. They are going to carpet the basement. The carpeting will cost $35 per square yard. A. What is the area, in square feet, of the basement foor? Show your work. B. What is the cost to carpet the basement floor? Explain how you found your answer
A.
In order to calculate the area of the trapezoid, we need to calculate its height:
Using the Pythagorean Theorem, we have:
[tex]\begin{gathered} 21^2=h^2+6^2 \\ 441=h^2+36 \\ h^2=441-36 \\ h^2=405 \\ h=20.12 \end{gathered}[/tex]Now, calculating the area:
[tex]\begin{gathered} A=\frac{(B+b)h}{2} \\ A=\frac{(36+24)20.12}{2} \\ A=60\cdot10.06 \\ A=603.6 \end{gathered}[/tex]B.
If each square yard is $35, first let's convert the area from ft² to yd² (1 yard = 3 feet, 1 yd² = 9 ft²):
[tex]A=603.6\text{ ft}^2=\frac{603.6}{9}\text{ yd}^2=67.07[/tex]So the total cost is:
[tex]\text{cost}=67.07\cdot35=2347.45[/tex]So the cost is approximately $2347.45.
What is the measure of ZTVU shown in the diagram below?VSV12°R120°TO A. 132O B. 66 °C. 54D. 108
The external angle formed by the secants equals one-half the difference of the intercepeted arcs. Therefore:
How many -digit even numbers are possible the digit cannot be zero?
Answer:
45,000
Step-by-step explanation:
Hey! Let's help you with your question here!
So, let's think about this logically. The only limit we have here is that the leftmost digit cannot be zero. This makes sense because there would be no five-digit number if the leftmost is zero. In order to find the possible amount of even numbers, we need to take the possible numbers of each digit and have them multiplied to each other to get the total. (I will explain this soon).
First Digit:
Since, the rules state that the leftmost digit cannot be zero, this would be the digit that the rule affects. From here, we can have a possibility of the numbers 1 through 9 here. So, for the first digit, we have the possibility of 9 numbers that can be here.
Second, Third, Fourth Digit:
Now you're probably wondering as to why I've grouped up these 3 digits and not the last or the first one. We'll get to the last one in the next explanation, but we exclude the first digit because the rule that affects the first digit, does not affect these digits nor the last digit. With these 3 digits, we don't have that rule of it cannot be zero, so now our possibilities for what the numbers can be is 0 through 9. If we include 0 as a number too, then we have a possibility of 10 numbers that can be within these digits.
Fifth (Last) Digit:
For this last digit, there is an implicit rule being stated for the last digit. The question asks how many five-digit even numbers are possible if the leftmost digit cannot be zero. This rule affects the last digit only as that allows the whole five-digit number to be even and zero is included in this. So, the even numbers are 0, 2, 4, 6, and 8. In this case, we only have 5 possible numbers to choose from for the very last digit.
Answer Explanation:
Before I begin answering, back in the very first paragraph, I said we need to take the possible numbers of each digit and multiply them altogether to get the total amount of possible values. Why do we do this? This is the idea of possibility combination. We multiply because we are taking in account all of the possible values whereas if we just add, we're only taking in account the maximum possible value of each possibility. So, let's calculate the answer now! For the first digit, we have a possibility of 9 numbers being there (1-9). For the Second, Third, and Fourth digit, we have a possibility of 10 numbers being there (0-9). And finally for the last digit, we have a possibility of only 5 numbers (0, 2, 4, 6, and 8). So, the total possible combination is:
[tex]9*10*10*10*5[/tex]
[tex]=45,000[/tex]
Therefore, we get 45,000 total possible five-digit even numbers where the leftmost digit cannot be zero.
There are two machines that produce aluminum cans. The newer machine can produce 5700 cans in 190 minutes. It takesthe older machine 285 minutes to produce that many cans. If the two machines work together, how long will it take them to produce 5700 cans?
114 minutes
Explanation
Step 1
find the rate of production of each machine (cans per minute)
so
a)The newer machine:
[tex]\begin{gathered} rate=\frac{cans\text{ }}{time} \\ rate_1=\frac{5700\text{ cans}}{190\text{ minutes}}=30\text{ }\frac{cans}{minute} \end{gathered}[/tex]b)the older machine:
[tex]\begin{gathered} rate=\frac{cans\text{ }}{time} \\ rate_2=\frac{5700\text{ cans}}{285\text{ minutes}}=20\text{ }\frac{cans}{minute} \end{gathered}[/tex]Step 2
Add the rates together to determine their combined
[tex]\begin{gathered} rate_{total}=rate_1+rate_2 \\ rate_{total}=30\text{ }\frac{cans}{minute}+20\frac{cans}{m\imaginaryI nute} \\ rate_{total}=50\text{ }\frac{cans}{minute} \end{gathered}[/tex]so, the total rate( both machine working ) is 50 cans per minute
Step 3
finally, to find the time to produce 5700 cans, divide the total cans by the rate, so
[tex]\begin{gathered} time=\frac{number\text{ of cans}}{rate} \\ time=\frac{5700\text{ cans}}{50\frac{cans}{minute}}=114minutes \\ time=\text{ 114 minutes} \end{gathered}[/tex]therefore, the answer is 114 minutes
I hope this helps you
WW Solve the system by substitution. -10x + 4y = -18 and x= y Submit Answer
Substitute second expression (x=y) in the first expression.
[tex]\begin{gathered} -10x+4y=-18 \\ -10\times y+4y=-18 \\ -6y=-18 \\ y=\frac{-18}{-6} \\ y=3 \end{gathered}[/tex]Substitute the above value of y in the expression number 2.
[tex]\begin{gathered} x=y \\ x=3 \end{gathered}[/tex]Thus, the value of x=3 and the value of y=3.
Convert: 1200 liters =kiloliters
We have from the question 1200 liters, and we need to convert it into kiloliters.
To find the equivalent in kiloliters to 1200 liters, we can proceed as follows:
1. Find the equivalent between these two measures:
[tex]1\text{ kiloliter=}1000\text{ liters}[/tex]2. Then we have:
[tex]\begin{gathered} 1200liters*\frac{1kiloliter}{1000liters}=\frac{1200}{1000}\frac{liters}{liters}kiloliters=1.2kiloliters \\ \\ \end{gathered}[/tex]Therefore, in summary, we can conclude that 1200 liters are equivalent to 1.2kiloliters.
I need help figuring out how to solve the length
We have the parallel sides of the rectangle are equal, therefore:
[tex]\begin{gathered} RS=QP=4x+3 \\ \text{and} \\ SP=RQ=5x \end{gathered}[/tex]The perimeter is the sum of all sides, then:
[tex]RS+QP+SP+RQ=222[/tex]Substitute the given data:
[tex](4x+3)+(4x+3)+5x+5x=222[/tex]And solve for x:
[tex]\begin{gathered} 4x+3+4x+3+5x+5x=222 \\ 18x+6=222 \\ 18x+6-6=222-6 \\ 18x=216 \\ \frac{18x}{18}=\frac{216}{18} \\ x=12 \end{gathered}[/tex]Next, we find the length of side RS:
[tex]RS=4x+3=4(12)+3=48+3=51[/tex]Answer: RS = 51 units