write the equations of all the circles in the design from smallest to biggest .( please help me )
Answers
The equation of a circle is given by the formula;
(x-h)² + (y-k)² = r²
r is the radius of the circle
(h,k) is the center of the circle
Smallest circle (Red circle)
r = 1
(h,k)= (0, 7)
substitute the values into the formular
(x - 0)² + (y-7)² = 1²
x²+ (y-7)² =1
Bigger circle (Blue circle)
r= 3 h=0 K=3
substitute the values into the formula
(x -0)² + (y-3)²= 3²
x² + (y-3)² = 9
Biggest circle ( Orange Circle)
r=5 h=0 K=-5
substitute the values into the formula and evaluate
(x-0)² + (y+5)² = 5²
x² +(y+5)² = 25
Related Questions
Which statement about this equatiin is true? 3+x=2-3x
1. The equation has no solution
2. The equation has one solution
3. The equation has infinitely many solutions
Answers
The equation has only one solution.
What is solution of equation?Equation solutions are numerical numbers that meet the requirements of the equation. When our answers are used to replace the variables in the equations, true assertions are obtained.
A mathematical equation proves the equality of two expressions. There is a mathematical formula: 4 + 4 = 8. A mathematical formula that has one or more variables is called an algebraic equation. Therefore, (2x + 5 = 35) is a linear equation with one variable. Its graph is a straight line, and its first-degree variable is (x).
Given
3+x = 2-3x
3-2 = -3x - x
1 = -4x
x = -1/4
Hence, x has only one value.
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the trapezoids shown below are similar. find Y
Answers
Since it is given that trapezoids are similar so,
[tex]\begin{gathered} \frac{y}{25}=\frac{12}{15} \\ y=\frac{4}{5}\times25 \\ y=20 \end{gathered}[/tex]So value of y is 20.
In 2000, the profit of Company A was $9,875,000. Each year after 2000, the profits fell by $29,532 on average. Construct a linear model for this scenario and use it to solve for profits in the year 2030.
Answers
Given:
In 2000, the profit of Company A was $9,875,000.
Each year after 2000, the profits fell by $29,532 on average.
So, the losses of the profit per year = $29,532
We will construct a linear model for this scenario
Let the number of years after 2000 = x
And the profit after the year 2000 = y
the linear model will be: y = mx + b
Where m is the slope which represents the losses per year and the b is the initial profit of the year 2000
So, the linear model will be:
[tex]y=-29,532x+9,875,000[/tex]now, we will use the equation to find the profit in the year 2030
so, x = 2030 - 2000 = 30
substitute x = 30 into the equation:
[tex]y=-29,532(30)+9,875,000=8,989,040[/tex]So, the answer will be:
The equation of the model: y = -29532x + 9875000
The profit in the year 2030 = 8989040
Maureen measured a house and its lot and made a scale drawing. The scale she used was
1 inch 8 feet. If the actual length of the house's driveway is 24 feet, how long is the
driveway in the drawing?
Answers
The most appropriate choice for unitary method will be given by-
Length of driveway in the drawing is 3 inch
What is unitary method?
Unitary method is the method in which value of a single unit can be calculated from the value of a multiple unit and value of a multiple unit can be calculated from the value of a single unit.
Sometimes value of single unit is less than value of multiple unit
For example - cost of food and quantity of food
Sometimes value of single unit is more than value of multiple unit
For example- Number of men and time taken by those men to do a work
Here,
Scale used by Maureen is 1 inch = 8ft
Actual length of house's driveway = 24 feet
8 ft of room is equal to 1 inch on scale
1 ft of room is equal to [tex]\frac{1}{8}[/tex] inch on scale
24 feet of room is equal to [tex]\frac{1}{8} \times 24[/tex] inch on scale
24 feet of room is equal to 3 inch on scale
Length of driveway in the drawing is 3 inch
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help meee
solve for system of equations with steps shown please
1.
x+4y=0
3x+2y= 20
2.
6x+3y=54
2x+y=18
3.
x-3y=-2
10x+8y=-20
4.
3x-y=-8
5x+2y=5
Answers
The solutions to the equations are :
1. x= 8 ; y = -2
2.infinitely many solutions.
3. x= - 2 ; y = 0
4. x= -1 ; y = 5
How are the equations solved?
1. x+4y=0 --(1)
3x+2y= 20 ---(2)
(1)*3
3x+ 12y =0 ---(3)
(3) - (2)
(3x+ 12y) -(3x+2y -20)
10y +20= 0
10 y = -20
y = - 2
Substituting y in equation(1)
x+ 4 (-2) = 0
x = 8
The solutions to the equations are x= 8 and y = -2
2. 6x+3y=54 --(1)
2x+y=18 ----(2)
(2)*3
6x+3y=54 --(3)
(3) = (1)
0 = 0
The equations have infinitely many solutions.
3. x -3y= -2 --(1)
10x+8y=-20 ---(2)
(1)*10
10x - 30y +20 = 0--(3)
(3) - (2)
(10x - 30y +20 )- (10x+8y +20)
-38y = 0
y = 0
Substituting y in equation(1)
x - 0 = -2
x = -2
The solutions to the equations are x= - 2 and y = 0
4.
3x-y=-8 ---(1)
5x+2y=5 ---(2)
(1)*2
6x -2y+16 =0---(3)
(3) +(2)
(6x -2y+16) +(5x+2y-5)
11x +11 = 0
11x = -11
x = -1
Substituting x in equation(1)
3(-1) -y = -8
-3- y = - 8
- y = -8+3
-y = -5
y = 5
The solutions to the equations are x= -1 and y = 5
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Richard Gaziano is a manager for Health Care, Inc. Health Care deducts Social Security, Medicare, and FIT (by percentage method) from his earnings. Assume a rate of 6.2% on $118,500 for Social Security and 1.45% for Medicare. Before this payroll, Richard is $1,000 below the maximum level for Social Security earnings. Richard is married, is paid weekly, and claims 2 exemptions.
What is Richard’s net pay for the week if he earns $2,200?
Answers
Richard’s net pay for the week if he earns $2,200 is equal to $1,797.65.
How to calculate net pay?Mathematically, net pay can be calculated by using this formula:
Net pay = Gross pay - Deductions.
First of all, we would determine Richard's Medicare tax and Social Security tax on $1,000 as follows:
Medicare tax = $2,200 × 1.45/100
Medicare tax = $31.9
Social Security tax = $1,000 × 6.2/100
Social Security tax = $62
Since Richard claims 2 exemptions and paid weekly, we would calculate the withholdings from his weekly pay by using the information provided in Table 1 (see attachment):
Two (2) exemptions = $76.9 × 2 = $153.8
Withholdings = $2,200 - $153.8
Withholdings = $2046.2
Since Richard claims to be married, we would calculate his federal tax withholdings by using the information provided in Table 1 (see attachment):
Over $1,606 = $198.40 plus 25%
= $2046.2 - $1,606 = $440.2
Federal tax withholdings = $198.40 + (25/100 × $440.2)
Federal tax withholdings = $198.40 + $110.05
Federal tax withholdings = $308.45
Now, we can calculate Richard's net pay as follows:
Richard's net pay = Gross pay - Medicare tax - Social Security tax - Federal tax withholdings
Richard's net pay = $2,200 - $31.9 - $62 - $308.45
Richard's net pay = $1,797.65
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I am trying to simplify a composition of functions.(f o g) (7.5)f(x) = -x + 7f(g) = -4x -2
Answers
There can be two methods that we can use to solve this problem. As per composition of the function, we substitute the function g(x) on the x's of f(x) o get fog. We have
[tex]\begin{gathered} (f\circ g)(x)=-(-4x-2)+7 \\ (f\circ g)(x)=4x+2+7 \\ (f\circ g)(x)=4x+9 \end{gathered}[/tex]We then substitute 7.5 on the resulting function above to evaluate (f o g) (7.5). We get
[tex]\begin{gathered} (f\circ g)(7.5)=4(7.5)+9 \\ (f\circ g)(7.5)=39 \end{gathered}[/tex]The other way around is to start evaluating g(x) for x = 7.5 and then the value that we got in g(x) will be substituted on f(x). We got
[tex]\begin{gathered} g(7.5)=-4(7.5)-2 \\ g(7.5)=-32 \\ \Rightarrow\Rightarrow f(-32)=-(-32)+7=39 \end{gathered}[/tex]3 cookies and 5 brownies cost $19; 2 cookies and 10 brownies cost $26. How much do 13 cookies and 6 brownies cost?
Answers
ANSWER
$51
EXPLANATION
Let the cost of one cookie be c.
Let the cost of one brownie be b.
3 cookies and 5 brownies cost $19. This means that:
3 * c + 5 * b = 19
3c + 5b = 19 ___(1)
2 cookies and 10 brownies cost $26. This means that
2 * c + 10 * b = 26
2c + 10b = 26 ____(2)
We have two simultaneous equations:
3c + 5b = 19 ___(1)
2c + 10b = 26 ____(2)
From (2):
2c = 26 - 10b
Divide through by 2:
c = 13 - 5b
Put this in (1):
3(13 - 5b) + 5b = 19
=> 39 - 15b + 5b = 19
Collect like terms:
-15b + 5b = 19 - 39
-10b = -20
Divide through by -10:
b = -20 / -10
b = $2
Remember that:
c = 13 - 5b
=> c = 13 - 5(2)
c = 13 - 10
c = $3
Therefore, one cookie costs $3 and one brownie costs $2.
Therefore, the cost of 13 cookies and 6 brownies is:
13 * 3 + 6 * 2
=> 39 + 12
=> $51
13 cookies and 6 brownies cost $51
If h(x) = 2x and k(x) =2x -k, what is h(k(x))?
Answers
If h(x) = 2x and k(x) =2x -k, then h(k(x)) would be:
h(k(x))= 2*(2x-k)
h(k(x))= 4x - 2k Using distributive property
Final answer is: h(k(x))= 4x - 2k
Which numbers are irrational numbers?
Select each correct answer.
Responses
110−−√
square root of fraction 1 over 10 end fraction
116−−√
square root of fraction 1 over 16 end fraction
14√
square root of fraction 1 over 4 end fraction
12√
square root of fraction 1 over 2 end fraction
18√
square root of fraction 1 over 8 end fraction
Answers
Answer:Here I hope this helps
1/10=irrational
1/16=rational
1/4=rational
1/2=irrational
1/8=irrational
Step-by-step explanation: you can go into desmos graphing calculator and plug in each number into the square root and it will tell you if its irrational or not.
Perform the indicated operation. 22 6/11 x 1 1/2
Answers
Multiplying the two fractions gives us the result 372/11
Here, we are given an expression- 22 6/11 x 1 1/2
To multiply these fractions, we first need to first convert the mixed fraction into an improper fraction. This can be done as follows-
22 6/11 = (22 * 11 + 6)/ 11
= (242 + 6)/ 11
= 248/ 11
similarly we have,
1 1/2 = (1*2 + 1)/2
= (2 + 1)/2
= 3/2
Thus, the given expression becomes-
248/ 11 x 3/ 2
= (248 * 3)/ (11 * 2)
= 744/ 22
= 372/ 11
We cannot simplify this fraction further.
Thus, multiplying the two fractions gives us the result 372/11
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Find the coordinate point for that would make ABCD a rhombus. Answer Choices: (3,5), (5,1), (1,1), (3,4)
Answers
A rhomus has te following shape:
therefore, the top part is missing, if we analyze, it should be 5 on the y axis and 3 on the x axis.
Answer: (3,5)
which number set(s) does -10 belong toirrational numberswhole numbersrational numbersintegersreal numberscounting or natural numbersNo number set describes this number.
Answers
Given:
The number is -10.
To describe the number:
Explanation:
Since 10 is a whole number and it has a minus sign.
So, -10 is an integer number.
Since it is an integer number.
So, it must be a rational number as well as the real number.
Therefore, -10 is a number that belongs to the sets
Integer numbers
Rational numbers
Real numbers
Final answer:
• Integer numbers
,• Rational numbers
,• Real numbers
Patsy’s pizza sells one 20-inch cheese pizza or two 12-inch cheese pizzas for 11.99. Determine which size gives more pizza (A= 3.14r^2)
Answers
Since 20-inch pizza, means it is a circle with a diameter of 20 inches
Since the diameter is twice the radius, then
The raduis = 20/2 = 10 inches
Then the area of it is
[tex]\begin{gathered} A_1=\pi(r)^2 \\ A_1=3.14(10)^2 \\ A_1=3.14(100) \\ A_1=314 \end{gathered}[/tex]The area of the first pizza is 314 square inches
Since the diameter of the other area is 12 inches, then
The radius = 12/2 = 6 inches
Then the area of it is
[tex]\begin{gathered} A_2=3.14(6)^2 \\ A_2=3.14(36) \\ A_2=113.04 \end{gathered}[/tex]Then the area of the second pizza is 113.04 x 2 = 226.08 square inches
Since the area of the first offer is greater than the area of the second offer, then
The first size gives more pizza
Represent the following sentence as an algebraic expression, where "a number" is the letter x. You do not need to simplify.2 minus twice a number.
Answers
Given the statement:
2 minus twice a number.
Let's represent the sentence as an algebraic expression where the number is the letter x.
To represent the statement as an algebraic expression, we have:
A number is the letter x ==> x
• 2 minus twice the number ==> 2 - 2x.
Therefore, the algebraic expression that represents the sentence is:
2 - 2x
ANSWER:
2 - 2x
Brad stands 30 feet from a tree. He estimates the angle of elevation from a point onthe ground 30 feet from the tree to the top of the tree to be 60° as shown below.60°30 feetWhich of the following is closest to the height of the tree?
Answers
To determine the height of tree using trigonometric ratio,
please answer this question
Answers
It's important to know that similar figures have equal angles, for example, if two triangles are similar, then their corresponding angles are congruent.
Having said that, D is true because all rectangles have equal angles.
If a full air container has a volume of 2.3 m3, and 78.1 % of that air is nitrogen, what is the volume of nitrogen in the container. Quote your answer to an appropriate number of significant figures.
Answers
The amount of nitrogen is 1.80 cubic meters if a full air container has a volume of 2.3 m³, and 78.1 % of that air is nitrogen.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
From the data given:
The total volume of the air container = 2.3 cubic meters
78.1 % is nitrogen.
The amount of nitrogen = 78.1 % of 2.3
= (78.1/100)x2.3
= 1.7963 cubic meters
The number 1.7963 to three Significant Figures is 1.80
The amount of nitrogen = 1.80 cubic meters
Thus, the amount of nitrogen is 1.80 cubic meters if a full air container has a volume of 2.3 m³, and 78.1 % of that air is nitrogen.
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I need help with my algebra
Answers
N 1
we have the ordered pairs
(1,1) and (4,2)
m=(2-1)/(4-1)
m=1/3
the slope is 1/3Which statement about the following equation is true?
2x2 – 9x + 2 = –1
The discriminant is less than 0, so there are two real roots.
The discriminant is less than 0, so there are two complex roots.
The discriminant is greater than 0, so there are two real roots.
The discriminant is greater than 0, so there are two complex roots.
Answers
Answer:
The discriminant is greater than 0, so there are two real roots.
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.2 cm}\underline{Discriminant}\\\\$b^2-4ac$ \quad when $ax^2+bx+c=0$\\\\If $b^2-4ac > 0 \implies$ two real roots\\If $b^2-4ac=0 \implies$ one real root\\If $b^2-4ac < 0 \implies$ no real roots\\\end{minipage}}[/tex]
Given equation:
[tex]2x^2-9x+2=-1[/tex]
Add 1 to both sides of the equation so that the equation equals zero:
[tex]\implies 2x^2-9x+2+1=-1+1[/tex]
[tex]\implies 2x^2-9x+3=0[/tex]
Compare the equation with ax²+bx+c=0:
a = 2b = -9c = 3Substitute the values of a, b and c into the discriminant formula and solve:
[tex]\begin{aligned}\implies b^2-4ac&=(-9)^2-4(2)(3)\\&=81-4(2)(3)\\&=81-8(3)\\&=81-24\\&=57\end{aligned}[/tex]
As 57 > 0, the discriminant is greater than zero, so there are two real roots.
Answer:
B on Edge 23
Step-by-step explanation:
trust me bro
Use the following figure and information to complete the proof. Given: m∠4=m∠2m∠5=m∠3m∠DBE=180∘ Prove: m∠1+m∠2+m∠3=180∘ Parallel lines m & n. Triangle A B C with A & C on n & B on m. A is to the left of C with angle 2 at A & angle 3 is at C. B is above A & C with angles 4 3 & 5 at C from left to right.© 2019 StrongMind. Created using GeoGebra. Match each numbered statement in the proof to its correct reason.
Answers
Explanation:
The given information is
m∠4 = m∠2
m∠5 = m∠3
m∠DBE = 180
The angle addition postulate says that the angle that the sum of the angles 4, 1, and 5 is equal to the angle DBE, so we can write the following equation
m∠4 + m∠1 + m∠5 = m∠DBE
But, we know that m∠DBE = 180, so by transitivity, we get:
m∠4 + m∠1 + m∠5 = 180
Then, we also know that m∠4 = m∠2 and m∠5 = m∠3, so we can substitute the angles to get
m∠2 + m∠1 + m∠3 = 180
Therefore, we can change the order by the commutative property to get
m∠1 + m∠2 + m∠3 = 180
Answer:
So, the answer is
2ax-b=cx+d solve for x
Answers
We have to solve the following equation for the variable x:
[tex]2ax-b=cx+d[/tex]For doing so, we assume that the variables a, b, c and d behave as normal numbers, and we will move the terms with x to the left side, and those who doesn't have it, to the right.
[tex]\begin{gathered} 2ax-b-cx=cx+d-cx \\ 2ax-cx-b=d \\ 2ax-cx-b+b=d+b \\ 2ax-cx=d+b \end{gathered}[/tex]Now, we will factor the variable x, as we want to have just one expression with x, thus:
[tex](2a-c)x=d+b[/tex]And lastly, we will divide both sides by 2a-c, and we obtain:
[tex]x=\frac{d+b}{2a-c}[/tex]Which is the asked expression for x.
Solve for the variable: 1 - p = 7
Answers
Given,
Solve for the variable,
[tex]1-p=7[/tex]Solution:
Take the variable on one side of the equation and the constant on another side of the equation.
[tex]\begin{gathered} -p=7-1 \\ -p=6 \\ p=-6 \end{gathered}[/tex]Thus, the value of p is -6.
How many times can 2/7 be subtracted from 6/7
Answers
Answer:
Exactly three times.
Step-by-step explanation:
(6/7) / (2/7) = (6/7) * (7/2) = 3/1 * 1/1 = 3
please help me I’m really not understanding this my answer was completely wrong
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
From the table, we can see that:
Gross profit for Q 1 = 85 x 1000= 85,000
Gross profit for Q 2= 94 x 1000 = 94, 000
Hence the increase in Gross profit = 94,000 - 85,000 = 9000
Then,
[tex]\begin{gathered} \text{Percentage change = }\frac{9000}{85000}\text{ x 100} \\ =\frac{900000}{85000} \\ =\text{ 10}.58823529 \\ \approx\text{ 10. 6 \% ( to the nearest tenth )} \end{gathered}[/tex]CONCLUSION:
The percent change = 10. 6 % ( to the nearest tenth)
1.Emily needs to make party hats in the shape of a cone. Shewants the hat to have a radius of 6 inches and a height of15 inches. What is the volume of the party hat?a) 565.2b) 94.2c) 2260.8d) 188.4
Answers
Emily needs to make party hats in the shape of a cone. She
wants the hat to have a radius of 6 inches and a height of
15 inches. What is the volume of the party hat?
a) 565.2
b) 94.2
c) 2260.8
d) 188.4
the volume of a cone is equal to
[tex]V=\frac{1}{3}\cdot\pi\cdot r^2\cdot h[/tex]we have
pi=3.14
r=6 in
h=15 in
substitute
[tex]\begin{gathered} V=\frac{1}{3}\cdot3.14\cdot6^2\cdot15 \\ V=565.2\text{ in3} \end{gathered}[/tex]answer is option A
The website for Company A receives 8 * 10 ^ 6 visitors per year. The website for Company B receives 4 * 10 ^ 3 visitors per year. Determine how many times more visitors per year the website for Company A receives than the website for Company B.
Answers
1) Let's find out how many times there are more visitors by dividing the number of visitors from A by B's visitors:
Dividing firstly 8 by 4, and then using the exponents pro
[tex]undefined[/tex]Heather is six years younger than her husband Ryan. Thesum of their ages is 52. How old is Ryan23293146
Answers
Let's begin by listing out the information given to us:
Ryan (r) = r
Heather (h) = r - 6
[tex]\begin{gathered} r+h=52 \\ h=r-6 \\ r+r-6=52 \\ 2r-6=52 \\ 2r=52+6 \\ 2r=58 \\ r=\frac{58}{2}=29 \\ r=29 \\ \\ \therefore Ryan^{\prime}s\text{ age is 29 years old} \end{gathered}[/tex]Therefore, Ryan is 29 years old
Answer:74
Step-by-step explanation:
Find all the missing elements.Round to the nearest tenth.aba = 5b = 2A C = 6BСA = [?]° B =[ 1°C = [ 1°Inter
Answers
Explanation:
Taking into account the law of cosines, we can write the following equation:
[tex]a^2=b^2+c^2-2bc\cos A[/tex]Then, replacing the values for a, b, and c, we get:
[tex]\begin{gathered} 5^2=2^2+6^2-2(2)(6)\cos A \\ 25=4+36-24\cos A \\ 25=40-24\cos A \end{gathered}[/tex]Solving for cos A, we get:
[tex]\begin{gathered} 25-40=40-24\cos A-40 \\ -15=-24\cos A \\ \frac{-15}{-24}=\frac{-24\cos A}{-24} \\ 0.625=\cos A \end{gathered}[/tex]Therefore, the value of angle A is:
[tex]\begin{gathered} \cos ^{-1}(0.625)=A \\ 51.3=A \end{gathered}[/tex]Now, we can use the law of sines, we can write the following equation:
[tex]\frac{\sin B}{b}=\frac{\sin A}{a}[/tex]So, replacing the values and solving for B, we get:
[tex]\begin{gathered} \frac{\sin B}{2}=\frac{\sin 51.3}{5} \\ \sin B=\frac{\sin 51.3}{5}\times2 \\ \sin B=0.3121 \\ B=\sin ^{-1}(0.3121) \\ B=18.2 \end{gathered}[/tex]In the same way, Angle C is equal to:
[tex]\begin{gathered} \frac{\sin C}{c}=\frac{\sin A}{a} \\ \frac{\sin C}{6}=\frac{\sin 51.3}{5} \\ \sin C=\frac{\sin51.3}{5}\times6 \\ \sin C=0.9365 \\ C=\sin ^{-1}(0.9365) \\ C=69.5 \end{gathered}[/tex]So, the answers are:
A = 51.3°
B = 18.2°
C = 69.5°
A motorcycle can be purchased for $9000 or leased for a down payment of $400 and $290 per month. Find a function that describes how the cost of the lease depends on time. Assuming that the monthly payments are made, how long can the motorcycle be leased before more than the purchase price has been paid?Question content area bottomPart 1The function that models the situation is p= enter your response here, where p is the amount paid on the lease in dollars and t is the time in months.(Simplify your answer.)
Answers
Let's find the function p that describes that situation, at the initial time we must pay 400, then
400 - 0
After one month we must pay 290, it will sum with the previous 400 that we have paid
400 - 0
690 - 1 month
In the third month, we must add 400, the previous 290 and 290 again, two times.
400 - 0
690 - 1 month
980 - 2 months
If we repeat that we will see that we will have 290*3 plus 400, in other words, more 290 per month. We can write an expression to do it, it's
[tex]p=400+290\cdot t[/tex]Where t is the time in months, verify that our expression is coherent with our previous logic, now we have our expression let's go to the next step. The lease will be equal to the purchase price when p = 9000, which means that the person paid 9000 on the lease, if we use it in our equation we can solve it for t
[tex]9000=400+290\cdot t[/tex]Let's solve it for t
[tex]\begin{gathered} 9000=400+290t \\ \\ 290t=9000-400 \\ \\ 290t=8600 \\ \\ t=\frac{8600}{290} \\ \\ t=29.65 \end{gathered}[/tex]Then, if we lease the motorcycle for 30 months, we will pay $9100, more than the purchase price, if we lease it for 29 months, we will pay $8810.
Final answer:
Expression:
[tex]p=400+290t[/tex]How long you can lease it before it costs more than the purchase price:
[tex]t=29[/tex]