a) 7 examples are:
[tex]2x + 3y\\(4a - 5b) / 2c\\(5 + 8) * 3\\8^2 - 6\\√(64)\\(1/3) * π * r^2\\2(3x + 4y) - 5z[/tex]
b) Fabric Larry will have left after using [tex]2\frac{2}{3}[/tex] yard out of [tex]5\frac{5}{6}[/tex] yard to make a bag for his computer is: [tex]3\frac{3}{6} yard[/tex]
What kinds of expressions are examples?Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
7 examples of mathematical expression are:
[tex]2x + 3y\\(4a - 5b) / 2c\\(5 + 8) * 3\\8^2 - 6\\√(64)\\(1/3) * π * r^2\\2(3x + 4y) - 5z[/tex]
For the second part of the question:
Larry had 5 3/6 yards of fabric. He used 2 2/3 yards to make a bag for his computer. Write an expression that will show how much of the fabric Larry will have left.
The mathematical expression that represents the amount of fabric Larry has left is:
5 3/6 - 2 2/3 = 2 7/18
You can simplify this further:
2 7/18 = 2 1/6
The amount of fabric Larry will have left is 2 1/6 yards.
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80 people were laying out on the beach. Clouds started forming, and it looked like it was going to rain. 42 people left. What is a reasonable estimate for the percentage of people that left the beach?
Select the best answer from the choices provided.
A. 10%
B. 25%
C. 50%
D. 75%
Answer:
C. 50%
Step-by-step explanation:
Since 40 is half of 80, and 50% means half, and 42 out of 80 is close to half, then 42 out of 80 is close to 50%.
Answer: C. 50%
Answer:
b25
Step-by-step explanation:
beacuse that is a rain and reasonable he percentage
Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set. y < c - 1 y > x -4
The graph of the inequality system is attached. The coordinate of a point in the solution set is (-1, 2).
In order to graph the system of inequalities graphically, consider the equation of each inequality.
y = x – 1
y = x - 4
Choosing a few values of x, plot the graph for each equation. Shade the area bounded by the line based on the inequality. If the inequality is less than, shade the area right to the line and if the inequality is greater than, shade the area left to the line. Hence, y < x – 1 is represented by red area and y > x – 4 is represented by blue area. The overlapping shaded area contains the coordinates that represent the solution of the inequality system. The coordinate of a point in the solution set is (-1, 2).
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Derek owns a snack shop where he sells tins of buttered and caramel popcorn. The table shows the number of each type of popcorn sold over w weeks.
Popcorn Sales
Popcorn Cost ($)
Number Sold
Over w Weeks
Buttered 11 8w+9
Caramel 11 6w−1
After 12 weeks, how much more will he have made in sales of buttered popcorn than the sales of caramel popcorn?
In the transaction, he will receive $374 more in sales of buttered popcorn than caramel popcorn.
What are mathematical operations?An operation, often known as an "operand" or "argument," is a function in mathematics that converts zero or more input values into a clearly defined output value. In mathematics, addition, subtraction, multiplication, division, and modular forms are the five basic operations.
Given, Derek owns a snack shop where he sells tins of buttered and caramel popcorn. The table shows the number of each type of popcorn sold over w weeks.
Popcorn Sales Popcorn Cost ($) Number Sold Over w Weeks
Buttered 11 8w+9
Caramel 11 6w−1
After 12 weeks of total buttered popcorn, he will make the sale
= $11 * (8*12 + 9)
= 11 * (96 + 9)
= $1,155
After 12 weeks of total caramel popcorn, he will make the sale
= $11 * (6*12 - 1)
= $11* (71)
=$781
In the sale, he will get more sales in buttered popcorn than sales in caramel popcorn by 1,155 - 781 = $374
Therefore, He will make $374 more in sales of buttered popcorn than caramel popcorn during the sale.
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Stella took a taxi from her house to the airport. The taxi company charged a pick-up
fee of $1. 20 plus $1. 50 per mile. The total fare was $29. 70, not including the tip. How
many miles was the taxi ride?
09
Equivalent fractions are those that, despite their visual differences, reflect the same value. we consumed half of a cake, for instance, if you have one, divide it into two equal pieces, and then eat one of the pieces.
what is fraction?Any number of equal portions, or parts of a whole, are described by fractions. Fractions in standard English indicate the number of pieces of a specific size. 8, 3/4 of .Part of an entire is a fraction. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. When a fraction is true, its numerator is smaller than its denominator.
If the denominators differ, similar fractions with a common denominator must be used. This requires figuring out the LCM of the two denominators. To be used as a denominator in fractions with various denominators, rename the fractions with a similar denominator.
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What is reflex angle class 9?
A reflex angle is an angle which measures more than 180 degrees and less than 360 degrees.
There are different types of angles in geometry, such as obtuse, acute and right angles, which all are under 180 degrees.
Assume, z is an acute or obtuse angle, and r is the reflex angle, then:
z + r = 360
r = 360 - z
Therefore, we can find the related reflex angle(r), if we know the value of the acute or obtuse angle(z).
A reflex angle equals the summation of 180 degrees and any of the primary angles (acute, right and obtuse angles). Therefore,
Reflex angle = 180° + Acute angle
Reflex angle = 180° + Right angle
Reflex angle = 180° + Obtuse angle
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16. A large waffle cone has a diameter of 3 inches and a height of 8 inches. Two scoops of
✓ ice cream have been stacked on top of the cone, after it was filled. The scoops are
completely round and have a diameter the same as the cone.
Find the volume of the two scoops of ice cream combined with the ice cream inside the
cone.
Answer:
(1/3) (44.5)π cm3.
Step-by-step explanation:
The volume of the two scoops of ice cream combined with the ice cream inside the cone can be calculated as follows:
Volume of cone = (1/3) π (3/2)2h = (1/3) π (4.5)8 = (1/3) (35.5)π
Volume of scoop = (1/6) π d3 = (1/6) (3)π
Total volume = (1/3) (35.5)π + 2(1/6) (3)π = (1/3) (44.5)π cm3.
Can you help me with this
Answer: 1/4
Step-by-step explanation:
Method 1
this method only works when there is a visual graph, but you can oick 2 points. then go to the point farthest to the left ide of the graph. then count up to be on the same y coordinate as the other point. then count over to be on the same x point, hence 1/4 (up 1 over 4)
Method 2
You can also pick 2 points, and put them into this formula to find slope ([tex]\frac{x2-x1}{y2-y1} }[/tex] then you plug in so the point farthest left would be x1 and y1 and the other point would be y1 and y2 so when you plug in and solve you get 1/4
Answer:
Step-by-step explanation:
rise/run
=1/4
Theoretically, if a fruit is chosen 300 times, how many times would you expect to pick an apple or banana?
The answer is 90 times to expect picking an apple or banana.
If the fruit is chosen 300 times, then it would be a 1:3 ratio of apple or banana to the other fruits. This means that 100 times out of the 300 times, you would expect to pick an apple or banana.
Predicting the outcome using the experiment results because 300 times is a sizable number.
8+4 is either an apple or a banana in 40 times.
Therefore, the solution would be x in 300 times.
[tex]x = \frac{300}{40}[/tex] x12
x = 90
Therefore, the probability of picking an apple or banana is 90 times.
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mary and max are playing a game with complex numbers. mary has a score of 3+2i. Wat must Max's score be so that the product of their score is one?
Since Mary and Max are playing a game with complex numbers, Max's score must be equal to 1/(3 + 2i), so that the product of their score is one.
What is a reciprocal function?A reciprocal function simply refers to a type of function which comprises a constant on its numerator and an algebraic expression or complex number in its denominator such as: f(x) = 2/3 + 7i.
In Mathematics, a reciprocal function is typically used when describing relationships that are inversely proportional to one other.
Let the variable n represent Max's score. Therefore, a mathematical expression which models the product of both Mary and Max's score is given by the following:
Product = 3 + 2i × n = 1
Making n the subject of formula, we have the following as Max's score;
n = 1/(3 + 2i)
Check:
3 + 2i × 1/(3 + 2i) = 1
(3 + 2i)/(3 + 2i) = 1
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math. f(x)=8x-7;f(x)=9
Answer:
65
Step-by-step explanation:
We are given f(x) = 9
Substitute 9 for x in f(x) = 8x - 7
f(x) = 8 (9) - 7
f(x) = 72 - 7
f(x) = 65
Thirty eight students are going on a field trip. Parents will drive. Each car can hold 4 students along with the driver. How many cars will be needed?
Answer: you will need 8 cars. 4 can go into 7 evenly so you will have to left over. So 8 cars will be necessary.
Step-by-step explanation: divide 30 by four which equals 7.5 so we can just round up and say we need 8 cars
To determine how many cars are needed to transport 38 students, we need to divide the total number of students by the number of students that can fit in each car.
According to the problem, each car can hold 4 students and a driver. Therefore, the total number of people that can fit in one car is 4+1 = 5.
To transport 38 students, we need to divide 38 by 4 to find the number of cars needed to transport all the students.
38 ÷ 4 = 9 remainder 2
This means that 9 cars can transport 36 students (9 cars x 4 students per car), but we still have 2 students left.
Therefore, we need an additional car to transport the remaining 2 students.
In total, we need 10 cars to transport all 38 students.
A traffic study has shown that the probability that 5 cars will pass over a small bridge in a 4-minute period is 0.16.
What are the odds against exactly 5 cars passing over the bridge in that time?
The odds against exactly 5 cars passing over the bridge in that time are given as follows:
5.25:1.
What is the relation between probabilities and odds?A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
An odd, conversely, is calculated as the division of the number of desired outcomes by the number of non-desired outcomes.
The probability(in favor) that 5 cars will pass over a small bridge in a 4-minute period is 0.16, hence the odds are given as follows:
0.16 : (1 - 0.16) = 0.16 : 0.84.
To obtain the odds against, we must exchange the desired and the non-desired outcomes, meaning that the odds against is then given as follows:
0:84 : 0.16.
As the quotient of 84 by 16 is of 5.25, the simplified odd is given as follows:
5.25 : 1.
Meaning that it is 5.25 times more likely that exactly 5 cars do not pass over the bridge over that time rather that they do pass.
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Adrian has $1 worth of nickels and dime. He has twice as many nickels as dimes. Write a system of equations that could be used to determine the number of nickels and the number of dimes that Adrian has. Define the variables that you use to write the system.
Answer: We can use two variables, x and y, to represent the number of dimes and nickels Adrian has, respectively.
We know that Adrian has twice as many nickels as dimes, so we can write the equation:
y = 2x
We also know that the total value of the coins is $1, and since nickels and dimes have different values, we can write the equation:
0.05y + 0.1x = 1
So the system of equations is:
y = 2x
0.05y + 0.1x = 1
These equations can be solved simultaneously to find the number of nickels and dimes that Adrian has.
Step-by-step explanation:
Answer: X+ywwiww asksn q9ru3
Step-by-step explanation:
88-2
How many dimes are in 4.72
Answer: 47
Step-by-step explanation:
4.72 / .1= 47
47
A family of 3 children and 2 adults visited a health club. The club charges sy an hour for each child and $x an hour for each adult. If the family does not want to spend more than $30 an hour at the health club, which of the following graphs best models the situation? Your answer: 16 14 12 10 O 2 2 8 10 12 14 14 12 4 2. + -2 -2 2 4 6 8 10 12 14 10 10 14 101214 a O 2 2 4 8 101214 -2
We have inequality. So, we have to take a test point (0,0) and as the statement is true therefore Graph will shade towards the test point (0,0).
2(0)+3(0) ≤ 30 => 0≤ 30
What is inequality?An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.
A family of 3 children and 2 adults visited a health club. The club charges $y an hour for each child and $x an hour for each adult.
First we make inequality according to question.
In a family number of children 3
Charge for 1 child = $y per hour
Charge for 3 children = 3y
Charge for 1 Adult = $x per hour
Charge for 2 adults = 2x
If the family does not want to spend more than $30 an hour at health club.
2x+3y≤30
Where, x and y should be greater than 0.
x≥0 and y ≥0
Now we make the graph of this inequality.
First we take equality of equation and then find x and y table.
2x+3y=30
x y
0 10
6 6
15 0
Here we have inequality. So, we have to take a test point (0,0)
2(0)+3(0) ≤ 30 => 0≤ 30
This statement is true. So, Graph will shade towards the test point (0,0)
Please see the attachment for graph:
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What value is X in math?
Answer:
Any value
Step-by-step explanation:
X is a variable, meaning it can be any number, and they are just using our variable, x, as a little mask to hide the exact value. In math, we will usually need to find x by solving different equations.
Examples:
x + 4 = 7
Know, x in this case is 3 because we just know 3 + 4 = 7, but x can be any value, and sometimes it gets more complicated than this. For example, we can have something like:
2x + 8 = 16
In this case, we need to have multiple steps to solve for x. First, we minus 8 from both sides:
2x = 8
Then we divide by 2:
x = 4
So, we know x = 4. In conclusion, x is a variable that is hiding a value, and you will need to either solve or substitute x. Meaning x can be any value.
Hope this Helped!
Amy operates a coffee kiosk and is blending her special house coffee. She is mixing Kenya beans that cost $9. 00 per pound with Colombia
beans that cost $7. 50 per pound to create a 30 pound blend that sells for $8. 50 per pound. How many pounds of Kenya beans and how many
pounds of Colombia beans does Amy need to use to create her blend?
So Amy needs to use 2 pounds of Colombia beans and 32 pounds of Kenya beans to create her blend.
Define Unitary Method.The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
What is direct and indirect variation in the unitary method?We are aware that an inverse variation or indirect variation occurs when two values are coupled in a way that a rise in one generates a corresponding reduction in the other, and vice versa.
Let x be the number of pounds of Kenya beans and y be the number of pounds of Colombia beans. We know that:
x + y = 30 (since the blend is 30 pounds)
We also know that the blend sells for $8.50 per pound, so the total cost of the blend is:
8.50(x + y) = 8.50(30) = $255
We know that the cost of the Kenya beans is $9.00 per pound and the cost of the Colombia beans is $7.50 per pound, so the total cost of the Kenya beans is:
9.00x and the total cost of the Colombia beans is 7.50y
We can set up the following equation:
9x + 7.5y = 255
We have 2 equations and 2 variables, we can solve this system of equation by different methods, one of them is substitution:
x + y = 30
9x + 7.5y = 255
We can substitute the first equation into the second equation
9(x + y) + 7.5y = 255
9(30) + 7.5y = 255
270 + 7.5y = 255
7.5y = -15
y = -2
So Amy needs to use 2 pounds of Colombia beans. We can substitute that value into the first equation to find the amount of Kenya beans:
x + (-2) = 30
x = 32
So Amy needs to use 32 pounds of Kenya beans.
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three cards are chosen from a pack of 52 cards. what is the probability that they are not all the same color
Three cards are chosen from a pack of 52 cards. what is the probability that they are not all the same color is 0.8824 or 88.24%
What is the definition of probability?The likelihood or chance that a specific event will occur is represented by a probability.
A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportion with a range of 0 to 1, or as percentages with a range of 0% to 100%.
Given that three cards are chosen from a pack of 52 cards.
There are 26 cards of each color (i.e. 26 cards are red color and 26 cards are of black color)
The probability of drawn first card of any one color is
P(1)= 26/52 = 1/2
The probability of drawn second card of same color is
P(2)= 25/51
The probability of drawn third card of same color is
P(3)= 24/50 = 12/25
The probability of having three cards are same color is
P = P(1)*P(2)*P(3)
P = 1/2 * 25/51 * 12/ 25
P = 6/51
So the probability that three cards are not all the same color is
P' = 1 - P
P' = 1 - 6/51
P' = (51-6)/51
P' = 45/51 = 15/17
P' = 0.8824
The likelihood that the three cards are not all red is roughly 0.8824, or 88.24%,
.
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ou have $54.75. You earn additional money by mowing lawns. Then you purchase a new pair of shoes for $79.99 and have $34.76 left. How much money do you earn mowing lawns
Answer: 60
Step-by-step explanation:
If you subtract how much money you already had(54.75) from what you spent(79.99) you get 25.24. You then add 25.24 to the koney you had left(34.76) to get you answer of 60
does the order of the quantities in an inequality matter
The order of the quantities in an inequality matters. Therefore, it is true.
How to illustrate the inequality?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The most frequent application is to size-compare two numbers on a number line.
When resolving an inequality, you can do one of the following: Add the same amount to each side; Subtract the same amount from each side; Multiply or divide each side by the same positive amount. You must flip the inequality symbol if you multiply or divide each side by a negative number.
Therefore, the order matters.
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Please help
VX is a midsegment of UWY
IF UY=13p-1 and VX=20p-95 what is UY
The length UY of the triangle is 90 units
How to determine the length UYFrom the question, we have the following parameters that can be used in our computation:
VX is a midsegment of triangle UWYUY = 13p - 1 and VX = 20p - 95This means that
UY = 2 * VX
Substitute the known values in the above equation, so, we have the following representation
13p - 1 = 2 * (20p - 95)
Evaluate the products
13p - 1 = 40p - 190
So, we have
40p - 13p = 190 - 1
So, we have
27p = 189
Divide by 27
p = 7
Substitute p = 7 in UY = 13p - 1
UY = 13 * 7 - 1
So, we have
UY = 90
Hence, the length is 90 units
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How do you explain irrational numbers to children?
The irrational numbers to children can be explained as the numbers that can be written as a nonrepeating or nonterminating decimal .
What are Irrational Numbers ?
The real numbers that can be represented as a nonrepeating or a nonterminating decimal but not as a fraction, and the decimal that goes on forever without repeating.
For Example : [tex]\sqrt{2} , \sqrt{5} , \sqrt{7}[/tex] are few example of irrational numbers .
In simpler words : the irrational number is a number that is not rational. which means It is a number which cannot be written as a ratio of two integers or cannot be written as fraction.
and If a fraction has a 0 in the denominator , it is an irrational number .
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Hundredths
2347
whole hundredths
:) How many tenths are in 2,347? How many whole tenths
tenths
whole tenths
D) How many tenths are in 234. 7? How many whole tenths
C) The whole hundredths of 2347 is 234700 hundredths. Zero-tenths are in 2,347. The whole tenth of 2347 is 2470tenth.
D) The tenth in 234. 7 are 7. The whole tenth of 234. 7 is 2347.
What is the tenth?
The tenth place is represented by the first digit following the decimal. The hundredth place is represented by the digit that follows the decimal.
Given number is 2347.
To find the whole hundredth, multiply the number by 100.
The whole hundredth in 2347 is 2347 × 100 = 234700.
The given number can be written as 2347.0.
Thus tenth of 2347 is 0.
To find the whole tenth, multiply the number by 10.
The whole tenth in 2347 is 2347 × 10 = 23470.
Thousand Hundred Ten decimal point Tenth
2 3 4 . 7
The tenth of in 234. 7 is 7.
The whole tenth in 234. 7 is 234.7 × 10 = 2347.
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Winston has a savings in a bank and was surprised that his money
accumulated to P 65. 000 after 3 years. He knew that the bank offered him 5%
interest rate compounded bimonthly. How much was his sayings at the start?
The initial saving of the Winston was $55952.48
Compound InterestCompound interest is when you receive interest on both your interest income and your savings.
According to the question given,
Let the initial savings amount be P
We know Compound interest =
[tex]A = P(1+\frac{r}{n} )^{nt}[/tex]
Where,
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest is applied per year
t = number of time periods elapsed
Given,
A = $65000
t = 3 years
r = 5% = 0.05
n = 2 *12 = 24
So
65000 = P(1 + (0.05/24))^72
P = $55952.48
Therefore the initial savings was $55952.48
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5. Step 4: Convert the number into decimal form rounded to the
nearest thousandth.
6.28=
O 6.284
O 6.280
O 6.283
O 6.282
Answer: 6.280
Step-by-step explanation:
Find the volume of the cone either enter an exact anwer in term of pi or ue 3. 14. For pie. R= 5 l=6
The volume of the cone is 50π cubic units .
What is a cone ?A cone is a three-dimensional geometric shape that tapers smoothly from a flat base to a point called the apex or vertex. A cone is formed by a set of line segments, half-lines, or lines connecting a common point, the apex, to all of the points on a base that is in a plane that does not contain the apex.
A cone has a circular base.
A cone has no edges, one face, and one vertex.
The length of the line segment from a cone's apex to any point around the circle of the cone's base is known as the slant height of the cone.
A right circular cone is a cone with its apex perpendicular to the base of the cone and directly above it.
An oblique cone is one that doesn't have its apex precisely over the base's circle.
Radius of the cone = 5
Height of the cone is 6
Volume of the cone = [tex]\frac{1}{3}\pi r^{2} h[/tex] = [tex]\frac{1}{3}\pi *5^{2}* 6 = 50\pi[/tex] cubic units.
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I WILL MARK BRAINLYIST
Describe a meal that you could put together that provides 4 servings of both a main
course and a side dish. Explain how you know that it will not exceed the weight limit of the box
A meal that you could put together that provides 4 servings of both a main
course and a side dish and not exceeding the weight limit is 4 servings of
chicken and 4 servings of baked beans.
What are the types of representing data?Data refers to the elements that make up persons, things, events, and ideas. It could be an integer, a title, or anycast. Data must be tabulated after collection in order to study their prominent characteristics. The presentation of data is the name given to such a configuration.
Bar Chart, Histogram, Line Graph, Pie Chart, Frequency Distribution Table.
Given, Each box can hold a maximum of 44 ounces.
By observing the given table we see 4 servings of chicken would weight
2×12.6 oz = 25.2 oz.
And 4 serves of baked beans weigh 14.2 oz.
Therefore, The total serving would weigh (25.2 + 14.2) oz.
= 39.4 oz.
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Mold has started to grow in
the bathroom. When I first
noticed it there was 3cm².
The next day there was 4.5
cm². I noticed each day it
grew by 50%.
The amount of mold after n days is 3 × (1.5)ⁿ⁻¹.
What is Geometric Progression?Geometric progression is a sequence of numbers such that the ratio of two consecutive numbers is the same for whole sequence.
This ratio is common ratio.
At first, mold was 3 cm², then 4.5 cm², and it was increasing each day by 50%.
a₁ = 3
a₂ = 4.5
a₃ = 4.5 + (4.5 × 50%) = 6.75
.............
Here the common ratio, r = a₂/a₁ = a₃/a₂ = ..... = 1.5
n th term of a GP = a rⁿ⁻¹, where a is the first term and r is the common ratio.
Area of mold after n days = 3 × (1.5)ⁿ⁻¹
Hence the mold at any time can be calculated by the formula 3 × (1.5)ⁿ⁻¹.
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What is elimination method example?
The elimination method is used for solving linear equations. Here we make use of the addition property of equality, that is when same number is added on both sides of equation, it still remains equal.
Lets look into some examples.
Example 1x + y = 10
x - y = 2
By adding both equations,
x + y + x - y = 10 + 2
+ y and - y are cancelled or y term is eliminated.
2x = 12
x = 6
Example 22x + 3y = 10
-3x + 3y = 15
Here to eliminate y, we have to add the additive inverse of second equation.
2x + 3y + 3x - 3y = 10-15
5x = -5
x = -1
Example 3x + 4y = 5
3x - y = 2
To equalize the y term we multiply the second equation by 4
12x - 4y = 8
Adding both equations,
x + 4y + 12x - 4y = 5 + 8
13x = 13
x = 1
So elimination method is used for solving linear equations.
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How do you find the nature of the roots of a given quadratic equation?
To find the nature of the roots of a given quadratic equation, use the quadratic formula, which is [tex]x= \frac{(-b±\sqrt{b^2-4ac} )}{2a}[/tex].
Finding the Nature of Roots of a Quadratic EquationSubstitute the values of a, b, and c from the given equation into the formula and solve for x. The nature of the roots can then be determined by examining the sign of the discriminant, b² - 4ac.
If the discriminant is positive, the quadratic equation will have two real roots; if the discriminant is zero, the quadratic equation will have one real root; and if the discriminant is negative, the quadratic equation will have two complex roots.
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