The balance of the account will be 1500 in a period of 8.31 years.
What is Compound Interest?Compound interest is defined as the amount of interest which has been calculated on the principal amount as well as the amount accumulated over the previous period is also included.
(a) The final amount in a compound interest is,
A = P(1 + [tex]\frac{r}{n}[/tex] )^ (nt), where,
A : Final amount
P : Principal amount
r : Rate of interest
t : Time in years
n : number of times compounded in a year
Given A = $1500, P = $1000, r = 0.05, n = 1
The equation is,
1500 = 1000 (1 + 0.05)^t
(b) 1500 = 1000 (1 + 0.05)^t
1500 / 1000 = (1.05)^t
1.5 = (1.05)^t
Taking logarithm on both sides,
㏒ (1.5) = t ㏒ (1.05) [since ㏒ (a)ᵇ = b ㏒ (a)]
t = ㏒ (1.5) / ㏒ (1.05)
t = 8.31 years
Hence the amount will be $1500 in 8.31 years.
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there are 50 586 757 people in south Africa and 44% live in rural areas. How many people live in rural areas
The number of people that live in the rural areas is 22 258 173
What is Percentage?
Percentage is a number or ratio that can be expressed as a fraction of 100.
How to determine this
44% live rural areas when there are 50 586 757 people in South Africa
i.e 44/100 * 50 586 757
= 22 258 173.08
which is approximately 22 258 173 people live in rural areas of South Africa
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Lou went shopping for a piano at our ST store a piano originally priced at $860 had a price reduction of 65% what was the reduced price
The reduced price of the piano is $301 if Lou went shopping for a piano at our ST store a piano originally priced at $860 had a price reduction of 65%
What is percentage ?
Percentage can be defined as the product of ratio of given value, total value and hundred.
To find the reduced price of the piano, we need to multiply the original price by the discount percentage (65%) and then subtract the result from the original price.
The amount of the discount is:
65% of $860 = 0.65 x $860 = $559
So, the reduced price of the piano after the discount is:
Reduced price = Original price - Discount
Reduced price = $860 - $559
Reduced price = $301
Therefore, the reduced price of the piano is $301.
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Iker runs laps on the track each week and increases what he runs by the same amount each Saturday. He began by running 24 laps and on the next Saturday he ran 35. A) How many laps did he start running?
b) How many more laps did he run each week?
c) Write the equation for this situation that models this type of growth:
A) Iker started running 24 laps on the track each week. This is mentioned in the question.
B) Iker ran 11 more laps each week.
C) The equation for this situation would be: y = 11x + 24
Determine the number of lapsTo find out how many more laps he ran each week, we can subtract the number of laps he ran on the first week from the number of laps he ran on the second week: 35 - 24 = 11 So, Iker ran 11 more laps each week.
To write an equation that models this type of growth, we can use the following formula: y = mx + b
Where y is the number of laps he runs, m is the number of additional laps he runs each week, x is the number of weeks, and b is the number of laps he started running.
In this case, m = 11 (the number of additional laps he runs each week) and b = 24 (the number of laps he started running).
So the equation for this situation would be: y = 11x + 24 This equation shows that the number of laps Iker runs each week (y) is equal to 11 times the number of weeks (x) plus the number of laps he started running (24).
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Function (f) is defined by the equation f(x)=3x-7. Find the value of c so that f(c) =20 is true.
The required value of c is 9 so that [tex]f(c) =20[/tex] is true, where the function is defined by the equation f(x)=3x-7.
What is the solution to the equation?A solution to an equation is a number that can be substituted for the variable to provide a true number statement.
To determine the value of c such that [tex]f(c) = 20[/tex], we can simply substitute in the given equation and solve for c.
So, we have:
[tex]f(c) = 3c - 7[/tex]
And, we know that [tex]f(c) = 20[/tex], so we can substitute to get:
20 = 3c - 7
Adding 7 to both sides, we get:
27 = 3c
Dividing both sides by 3, we get:
c = 9
Therefore, the value of c that satisfies the equation [tex]f(c) = 20[/tex] is 9.
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name the point of concurrency of the angle bisectors
The point of concurrency of the angle bisectors is called the incenter. The incenter is the center of the incircle of a triangle, which is the largest circle that can be inscribed within the triangle.
The center present in the largest circle that can be inscribed in the triangle is defined as incircle. It is in the equal distance from all the sides present in the triangle , which makes it unique comparing to others.
The line that bisects the angle which is also called as angle bisector is one of the method to find the incenter. It divide the entire triangle into three triangles of same area and length. The triangle includes three bisectors to each angle.
These bisectors are intersected at the same point in the triangle , which is also termed as incenter of the triangle. This is because the incenter is in equal distance from each of the every side of the triangle, and this makes the angle bisectors to divide the triangle into parts which makes the incenter equidistant from all three sides of the triangle.
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Which function represents g(c) a reflection of f(c)=6(1/3)^x across the y axis?
The function represents g(c) a reflection of ff(c) = 6 (1/3)ˣ across the y axis is g(c) = -6(1/3)⁻ˣ and option B is the correct answer.
What is reflection of a function?A function can be transformed by flipping its graph around an axis, which is known as a reflection function. Reflecting or reflection in mathematics, and more precisely in geometry, refers to flipping. Hence, a function's reflection is essentially the mirror image of the supplied function or graph. As a result, reflecting functions are a common name for them.
The given function is: f(c) = 6 (1/3)ˣ.
When a function is reflected along the y-axis the coordinates of the graph change as follows:
(x, y) → (-x, y)
The function f(c) = 6 (1/3)ˣ when reflected will have the function g(c) as:
g(c) = -6(1/3)⁻ˣ
Hence, the function represents g(c) a reflection of ff(c) = 6 (1/3)ˣ across the y axis is g(c) = -6(1/3)⁻ˣ and option B is the correct answer.
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Need help, please! *With step-by-step answer, thanks!
$3,600
Step-by-step explanation:Simple interest is the amount of money earned based on the initial amount invested.
Simple Interest Formula
The formula for simple interest is A = P(1 + rt). Let's define each of these variables.
A is the total amount of money in the accountP is the principal or the initial amount depositedr is the interest rate expressed as a decimalt is time in yearsTo solve for simple interest, we need to plug in the information we are given.
Solving Simple Interest
In the question, we're told that $3000 is the initial amount deposited, so P = 3000. The rate is 2%, which means that r = 0.02. Also, this interest is earned over 10 years, thus t = 10. Now, plug this into the formula above.
A = 3000(1 + 0.02*10)Then, just simplify the right side of the equation.
A = 3000(1 + 0.2)A = 3000 * 1.2A = 3600This means that after 10 years, there will be a total of $3600 in the account.
find the surface area of a Sphere of diameter
36 cm. tak x=22 7
Answer: The surface area of a sphere can be calculated using the formula:
A = 4 * π * r^2
Where r is the radius of the sphere.
The diameter of the sphere is 36 cm, so the radius can be found by dividing the diameter by 2:
r = 36 cm / 2 = 18 cm
Now that we have the radius, we can plug it into the formula:
A = 4 * π * r^2 = 4 * π * (18 cm)^2 = 4 * π * 324 cm^2 = 1296 * π cm^2
Since π is approximately equal to 3.14, we can get an approximate answer:
A ≈ 1296 * 3.14 = 4071.84 cm^2
So the surface area of the sphere with a diameter of 36 cm is approximately 4071.84 square centimeters.
Step-by-step explanation:
Assume that we have two events, A and B, that are mutually exclusive. Assume further that we know P(A) = 0.30 and P(B) =0.40.
1. What is P(A B)?
2. What is P(A | B)?
3. Is P(A | B) equal to P(A)?
4. A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent. Is this statement accurate?
5. What general conclusion would you make about mutually exclusive and independent events given the results of this problem?
1) The value of P(A∩B) = 0.
2) The value of P(A|B) = 0.
3) P(A|B) is not equal to P(A). A and B are independent events.
4) The statement "Mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent." is not accurate.
5) We can conclude that mutually exclusive events have a probability of intersection of zero and are not independent.
1) Since A and B are mutually exclusive, they cannot occur at the same time, so P(A∩B) = 0.
2) The conditional probability of A given B is defined as the probability of A occurring given that B has occurred. Since A and B are mutually exclusive, if B has occurred, then A cannot occur. Therefore, P(A|B) = 0.
3) No, P(A|B) is not equal to P(A). Since B has occurred, the sample space has been reduced to only those outcomes in which B has occurred. Therefore, the probability of A given that B has occurred can only be determined from the portion of the sample space in which both A and B occur.
However, since A and B are mutually exclusive, this probability is zero. Therefore, P(A|B) ≠ P(A).
4) The statement is not accurate. Mutually exclusive events and independent events are different concepts. Two events are mutually exclusive if they cannot occur at the same time, whereas two events are independent if the occurrence of one event does not affect the probability of the other event.
If two events are mutually exclusive, they are not independent because the occurrence of one event precludes the occurrence of the other event.
5) Mutually exclusive events have a relationship where if one event occurs, the other cannot. In contrast, independent events are events where the occurrence of one event does not affect the probability of the other event occurring.
Therefore, we can conclude that mutually exclusive events and independent events are not the same concept, and we must be careful not to confuse them.
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Question 9
Jamal's parents borrow $2900.00 from the bank for new appliances for their kitchen. The simple interest rate is 9% per year. How much
interest will they have to pay if it takes them 2 years and 3 months to repay the loan?
The amount of interest after 2 years and 3 months to repay the loan will be $587.25.
What is simple interest?Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.
The formula for interest is written as,
I = (PRT)/100
Where P is the principal, R is the rate of interest, and T is the time.
Jamal's parents borrow $2900.00 from the bank for new appliances for their kitchen. The simple interest rate is 9% per year.
The amount of interest after 2 years and 3 months is given as,
I = [$2,900 x 9 x (2 + 3 / 12)] / 100
I = $2,900 x 0.09 x 2.25
I = $587.25
The amount of interest after 2 years and 3 months to repay the loan will be $587.25.
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I know that the first term of the sequence is -2, and the fifth term is -1/8. What do you know?Type of sequence : Common ratio or difference : Explicit equation : Recursive equation :
Answer:
Type of sequence: Geometric
Common ratio: [tex]\mbox{\large \dfrac{1}{2}}[/tex]
Explicit equation:
[tex]a_n = a_1 \cdot \left(\dfrac{1}{2}\right)^{n-1 }[/tex]
Recursive Equation:
[tex]\mbox{\large a_n = \dfrac{1}{2} \cdot a_{n-1}}[/tex]
Step-by-step explanation:
Looking at the first and fifth terms it appears to be a geometric sequence where each successive term is r x previous term
r is referred to as the common ratio = aₙ/aₙ₋₁ where aₙ is the nth term and aₙ₋₁ the previous term
The nth term can be found by using the formula
aₙ = a₁ x rⁿ⁻¹
where a₁ is the first term
We have a₁ = -2
a₅ = - 1/8
Plugging these into the general equation for a geometric sequence we get
[tex]-\dfrac{1}{8} = -2 \cdot r^{5-1}\\\\\\-\dfrac{1}{8} = -2 \cdot r^{4}\\\\r^4 = -\dfrac{1}{8} \div -2\\\\\\r^4 = \dfrac{1}{16}\\\\\\r = \sqrt[4]{\dfrac{1}{16}} \\\\r = \dfrac{1}{2} \;\;\;\;\textrm(since \; 2^4 = 16)[/tex]
Recursive equation relates the nth term to the (n-1)th term and is
[tex]a_n = \dfrac{1}{2} \cdot a_{n-1}[/tex]
If we start at the first term
a₁ = -2
a₂ = 1/2 x (-2) = - 1
a₃ = 1/2 x (-1) = - 1/2
a₄ = 1/2 x (-1/2) = -1/4
a₅ = 1/2 x (-1/4) = - 1/8
So everything pans out fine
what is the area of a kite calculator?
The area of the kite is 40 square meters, calculated by using the area of a kite formula.
To calculate the area of a kite, you need to know the lengths of both the diagonals. Once you have those values, you can use the following formula to find the area:
Area = (d1 x d2) / 2
where d1 and d2 are the lengths of the diagonals.
Here is an example of how to use this formula:
Let's say you have a kite with diagonals of 8 meters and 10 meters. To find the area, you would use the formula:
Area = (8 x 10) / 2
Area = 40 square meters
So the area of the kite is 40 square meters.
There are also many online calculators available that can help you find the area of a kite if you enter the values of the diagonals.
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I've been having trouble figuring out trigonometry and I really could use somebody who knows this kind of stuff to help me out. Can anyone answer this by showing me how to do it and what the answer would be?
Answer: The positive acute angle between the x-axis and the angle's terminal side, or the angle's terminal side wherever it is, measured so that the reference angle is positive and less than 90° (or 2) is known as the reference angle for a given angle in trigonometry.
This is all I know I don't have a class like this sorry hope this helps you!
HELPPP PLEASE WILL GIVE BRAINLIEST
Answer: look at the images for the answers and solutions
Step-by-step explanation:
Collin did the work to see if 10 is a solution to the equation StartFraction r Over 4 EndFraction = 2.5.
StartFraction r Over 4 EndFraction = 2.5. StartFraction 10 Over 4 EndFraction = 2.5. 2.5 = 2.5.
Is 10 a solution to the equation?
Yes, because 10 and 4 are both even.
Yes, because if you substitute 10 for r in the equation and simplify, you find that the equation is true.
No, because 10 is not divisable by 4.
No, because if you substitute 10 for r in the equation and simplify, you find that the equation is not true.
Answer:
Yes, because if you substitute 10 for are in the equation and simplify, you find that the equation is true.
Step-by-step explanation:
Yes, because if you substitute 10 for are in the equation and simplify, you find that the equation is true.
Solve for a.
Set up your equation using the
Pythagorean Theorem.
a² + b² = c²
a² + [?]²=
12
Hint: Plug in the given leg
length for b.
12
a
9
Enter help
Answer: a²+ 9² = 12² (look at the image for the solution)
Step-by-step explanation:
what is the equation i need to write
The rate of change is $3 per mile and y=3x is the equation which represents the total cost to travel x miles.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
From the given table the rate of change or slope is m=8-5/2-1
m=3
The ride cost $3 per mile.
The equation which show the total cost to travel x miles is y=3x.
Hence, the rate of change is $3 per mile and y=3x is the equation which represents the total cost to travel x miles.
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Solve the system of equations using elimination: -2x+3y=-10 and -7x+3y+25
The solution to the system of equations is x = 35/9 and y = -20/27.
What is an expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.
I assume the second equation is supposed to be equal to zero, so the system of equations is:
-2x + 3y = -10
-7x + 3y = -25
To solve this system of equations using elimination, we can add the two equations together. This will eliminate the y variable and give us an equation in terms of x:
-2x + 3y + (-7x + 3y) = -10 - 25
-9x = -35
x = 35/9
Now that we know x, we can substitute it into either equation to solve for y. Let's use the first equation:
-2x + 3y = -10
-2(35/9) + 3y = -10
-70/9 + 3y = -90/9
3y = -20/9
y = -20/27
Therefore, the solution to the system of equations is x = 35/9 and y = -20/27.
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[tex] \frac{y }{8} + \frac{y}{4} [/tex]
Simplify.
I don't know how to do this, could someone please explain this for me.
y/8 + y/4
Algebraic Fractions
The expression of fractions y/8 + y/4 can be simplify as 3y/8.
How can the expression be simplified?Given that the expression is y/8 + y/4
Then we can find the number number that both 8, and 4 can go in, which is 8. and this will serves as the LCM. then we will start from the first value, 8 will divide 8 in just one times, then times y( numerator) which equals to y. for the right hand side values, 4 will divide 8 in two times which is 2, then times y equalos 2y.
y +2y/8
=(y+2y)/8
= 3y/8
Hence the simplification is 3y/8
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Less variables: What is the value of the expression 5a - 7b + c when a =5 , b =3, and c = 1?
3
24
5
39
Answer:
5
Step-by-step explanation:
5(5) - 7(3) + 1 = 5
⚠️PLEASE HELP⚠️ URGENT (all separate questions) (middle school math) not advanced I will give everyone who answers this everything good that you can possibly give⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️
. You get scores of 85 and 91 on two history tests. Write and solve an
inequality to find the scores you can get on your next history test to have
an average of at least 90.
. You and a group of friends wait hour to ride an amusement park ride. You
go on the ride a second time and wait hour. You want to go on a third
time. Write and solve an inequality to find how many minutes you can wait
for your average waiting time to be at most hour. (Hint: Convert the
waiting times to minutes.)
Write and solve an inequality to find the possible
values of x so that the rectangle has an area of more
than 130 square units.
The rectangle is 5 on the left side and
3x + 2 on the bottom
Answer:
8>x
Step-by-step explanation:
A>L×B
where A=area of rectangle,L=length,B=breath
A=>130,L=51,B=3x+2
130>(5)(3x+2)
130>15x+10
130-10>15x
120>15x
8>x
L=3(8)+2=24+2=26
I need help please and thank you
Solve for X
Answer:
12
Step-by-step explanation:
The large triangle is 4 times the size of the smallest one.
17*4=68, 8*4=32, and 15*4=60.
We know what the side length is now, so we set up an equation.
60=4x+12
Subtract 12 from both sides.
60-12=4x+(12-12)
48=4x
Divide
48/4=4x/4
12=x
Your job in a company is to fill quart-size bottles of oil from a full
150-gallon oil tank. Then you are to pack
24 quarts of oil in a case to ship to a store. How many full cases of oil can you get from a full
150-gallon oil tank?
you can get 25 full cases of oil from a full 150-gallon oil tank.
What are quarts?Quarts (abbreviated as "qt") is a unit of measurement commonly used for volume in both the US customary and British imperial measurement systems. One quart is equal to 32 fluid ounces, 2 pints, or 0.25 gallons.
given by the question: -
There are 4 quarts in a gallon, so a 150-gallon oil tank contains:
150 gallons * 4 quarts/gallon = 600 quarts of oil
To pack a full case of oil, we need 24 quarts of oil. So, the number of full cases of oil that can be obtained from a 150-gallon oil tank is:
600 quarts of oil / 24 quarts per case = 25 cases of oil
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Given AXYZ, find the length of XZ.
Y
8
X
6
N
Answer:
WJENW
Step-by-step explanation:
what is 1 usd to thai baht?
Answer: 1 usd to thai baht is 33.44 thai baht or 33 thai baht
Step-by-step explanation:
There's no need for an explanation for this as you can just search this on the internet.
find the size of the angle xyz
give you answer to 1 decimal point
hypotenuse is 15cm and the adjacent is 6
Answer:
Step-by-step explanation:
no
The point G( – 5, – 1) is rotated 180° counterclockwise around the origin. What are the coordinates of the resulting point, G'?
Answer:
the coordinates of the resulting point G' are (5, 1).
Step-by-step explanation:
When a point is rotated 180° counterclockwise around the origin, it is reflected across the x-axis and y-axis. This means that the x-coordinate and y-coordinate of the point are both negated.
So, for the point G(-5, -1), the x-coordinate becomes -(-5) = 5 and the y-coordinate becomes -(-1) = 1.
Answer:
(5,1)
Step-by-step explanation:
Rotating 180 degrees about the origin means that there is a reflection against the y-axis and x-axis. Therefore, the x and y values will change their signs.
Hence, the new coordinate would be (5,1)
What are the first four terms of an arithmetic. Sequence if the first term is -3 and the common difference is 7
The first four terms of the arithmetic sequence are -3, 4, 11, 18.
How to find the termsIf the first term of an arithmetic sequence is -3 and the common difference is 7, then we can use this formula to find the nth term of the sequence:
Un = a + (n - 1)d
Where
Un is the nth term
a is the first term
d is the common difference, and
n is the position of the term in the sequence.
To find the first four terms of the sequence, we can substitute n = 1, 2, 3, 4 into the formula and solve for Un:
n = 1:
U1 = -3 + (1 - 1)7 = -3
n = 2
U2 = -3 + (2 - 1)7 = 4
n = 3
U3 = -3 + (3 - 1)7 = 11
n = 4
U4 = -3 + (4 - 1)7 = 18
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How do you find the determinant of a 4x4 matrix?
The determinant of a 4x4 matrix is calculated using the Laplace Expansion method, which involves expanding the determinant along one row or column.
The formula for the determinant of a 4x4 matrix is:det(A) =[tex]a11 * a22 * a33 * a44 – a11 * a22 * a34 * a43 + a11 * a23 * a34 * a42 – a11 * a23 * a32 * a44 + a12 * a23 * a32 * a44 – a12 * a23 * a34 * a41 + a12 * a21 * a34 * a43 – a12 * a21 * a33 * a44 + a13 * a21 * a33 * a44 – a13 * a21 * a34 * a42 + a13 * a22 * a34 * a41 – a13 * a22 * a31 * a44 + a14 * a22 * a31 * a43 – a14 * a22 * a33 * a41 + a14 * a23 * a33 * a42 – a14 * a23 * a31 * a42[/tex]To calculate the determinant of a 4x4 matrix, take the sum of the products of the elements in each row/column and its corresponding minor, then multiply each product by the sign of the term (+ or -). For example, if A is a 4x4 matrix, then the determinant is: det(A) =[tex]a11 * |A11| - a12 * |A12| + a13 * |A13| - a14 *[/tex]|A14|.The minors A11, A12, A13 and A14 are the 3x3 matrices obtained by deleting the first row and first column from A. The values of the minors are calculated by applying the Laplace Expansion method to each minor.
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1) Chelsea and Matt each improved their yards by planting daylilies and ivy. They bought their
supplies from the same store. Chelsea spent $81 on 1 daylily and 8 pots of ivy. Matt spent $189
on 10 daylilies and 11 pots of ivy. Find the cost of one daylily and the cost of one pot of ivy.
Answer:
One daylily costs $9, and one pot of ivy costs $9.
Step-by-step explanation:
Step 1: Write a System of Algebraic Equations
We are given 2 different variables, or "unknowns", that we need to find the value of here - the cost of one daylily, and the cost of one pot of ivy. We know that the cost of each plant remains constant (doesn't change), and we are given the following information:
1 daylily and 8 pots of ivy cost $81.10 daylilies and 11 pots of ivy cost $189.We can see that we have a system of equations in the making. The first thing to do when writing a system is assign letters to variables. Let's let the cost of one daylily be denoted as [tex]d[/tex], and the cost of one pot of ivy be denoted as [tex]i[/tex] (in dollars for each). From the above information, we can write the system:
[tex]d+8i=81 \hspace{0.8cm} (1)\\10d+11i=189 \hspace{0.1cm} (2)[/tex]
Step 2: Solve the System (with Substitution)
Now that we have a solution, let's use it to solve for the value of each variable. There are many ways to do this (addition, subtraction, etc), but it seems that the quickest way to solve this particular system is using the substitution method. This is where you write one variable in terms of the others by manipulating one equation, and then substituting that expression in for the isolated variable in the other equation. It's easy to do this here because we already have a [tex]d[/tex] in (1).
Isolating [tex]d[/tex] in (1) by subtracting [tex]8i[/tex] from both sides, we get:
[tex]d+8i=81\\d=81-8i\hspace{0.5cm} (3)[/tex]
Substituting (3) into (2) and solving for i, we get:
[tex]10d+11i=189\\10(81-8i)+11i=189\\810-80i+11i=189\\810-69i=189\\-69i=-621\\\bf i=9[/tex]
Substituting this value into (3), we get:
[tex]d=81-8i\\=81-8*9\\=81-72\\=\bf9[/tex]
Therefore, one daylily costs $9, and one pot of ivy costs $9.