By noticing which formulas only contain the operations of addition, subtraction, multiplication, and non-negative integer exponents, the polynomials may be located. Expressions with additional operations are considered non-polynomial expressions.
Expressions are polynomials, but expressions that equal zero are polynomial equations.
A polynomial may be written as the sum of a finite number of terms, where each term is the product of one or more variables raised to a positive integer exponent and a constant coefficient (or power).
An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
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Make q the subject of the formula 2(q + p) = 1 + 5q Give your answer in the form ap-b where a, b and c are all positive integers.
[tex]2(q+p)=1+5q\implies 2q+2p=1+5q\implies 2q+2p-5q=1 \\\\\\ 2q-5q=1-2p\implies q(2-5)=1-2p\implies -3q=-2p+1 \\\\\\ q=\cfrac{-2p + 1}{-3}\implies q=\cfrac{2}{3}p-\cfrac{1}{3}[/tex]
Answer:
Step-by-step explanation: 2(q+p)=1+5q
2q+2p=1+5q
2q-5q=1-2p
-3q=1-2p/:(-3)
q=-1/3+2/3 p
What is the range of the data set please help out!
4 is the range of the data set in the given set.
What is range data set?The space between the highest and lowest values in a data collection is known as the range. Similar units to the data are used to quantify variability. Variability is increased with larger values. The range has several limitations but is the most straightforward statistical measure of dispersion to compute and comprehend.
This means that the range might alternatively be described as the distance between the highest and lowest observation.
In the given data set,
range = maximum frequency - minimum frequency
range = 5 - 1
range = 4
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Are parallel algorithms always faster than sequential algorithms?
Answer:
Step-by-step explanation:
Parallel algorithms are not always faster than sequential algorithms. In general, the speed of an algorithm depends on a variety of factors, including the complexity of the algorithm, the hardware it is running on, and the specific problem it is trying to solve.
There are some cases where a parallel algorithm can be faster than a sequential algorithm. For example, if an algorithm can be easily divided into smaller subproblems that can be solved independently and then combined to get the final result, it may be possible to speed up the overall computation by using a parallel algorithm to solve the subproblems in parallel. This can be particularly effective if the subproblems are large and can be solved using multiple processor cores or distributed across multiple computers.
However, there are also cases where a sequential algorithm may be faster than a parallel algorithm. For example, if the problem is relatively small and can be solved efficiently using a single processor, it may not be worth the overhead of dividing the problem into smaller subproblems and coordinating their solution in parallel. In addition, some algorithms may be more difficult to parallelize, or may not lend themselves well to a parallel solution, in which case a sequential algorithm may be a better choice.
Overall, it is important to carefully consider the specific problem and available hardware when deciding whether to use a parallel or sequential algorithm.
Help me pleaseeeeeeeee!!!
0.08/0.2 and 0.2/0.8 are not proportional.
What is proportionality?A proportion is an equality of two ratios. We write proportions to help us establish equivalent ratios and solve for unknown quantities.
Given are two numbers, 0.08/0.2 and 0.2/0.8
Checking for if they are proportional or not,
0.08/0.2
Multiplying denominator and numerator by 100,
8/20 = 2/5
And,
0.2/0.8 = 1/4
Since, 0.08/0.2 ≠ 0.2/0.8
Hence, 0.08/0.2 and 0.2/0.8 are not proportional.
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A bag contains 10 pieces of paper, numbered 1 through 10with a different number on each piece of paper. A second bag contains 8 pieces of paper, numbered 20 through 27with different number on each piece of paper. One piece of paper is drawn random from each bag. What is the expected value of the sum of the numbers on the two selected pieces of paper
To find the expected value of the sum of the numbers on the two selected pieces of paper, we need to calculate the probability of each possible outcome and then multiply that probability by the value of the outcome. The expected value of the sum of the numbers on the two selected pieces of paper is 6.1625.
Therefore the answer is 6.1625.
The possible outcomes for the first bag are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, each with a probability of 1/10.
The possible outcomes for the second bag are 20, 21, 22, 23, 24, 25, 26, 27, each with a probability of 1/8.
The possible outcomes for the sum of the numbers on the two selected pieces of paper are:
(1,20) ,(1,21) ,(1,22) ,(1,23) ,(1,24) ,(1,25) ,(1,26) ,(1,27)
(2,20) ,(2,21) ,(2,22) ,(2,23) ,(2,24) ,(2,25) ,(2,26) ,(2,27)
(3,20) ,(3,21) ,(3,22) ,(3,23) ,(3,24) ,(3,25) ,(3,26) ,(3,27)
...
(10,20) ,(10,21) ,(10,22) ,(10,23) ,(10,24) ,(10,25) ,(10,26) ,(10,27)
The expected value of the sum of the numbers on the two selected pieces of paper is the sum of the products of each possible outcome and its corresponding probability.
The probability of each outcome is (1/10) * (1/8) = 1/80
So the expected value of the sum of the numbers on the two selected pieces of paper is
(1 + 21)×(1/80) + (1 + 22)×(1/80) + (1 + 23)×(1/80) + (1 + 24)×(1/80) + .... + (10 + 27)×(1/80) = (21 + 22 + 23 + 24 + ... + 37)/80
= (20×17 + 1 + 2 + ... + 17)/80
= (340 + 17×(17 + 1)/ 2)/ 80
= (340 + 17×9)/ 80
= 6.1625
So the expected value of the sum of the numbers on the two selected pieces of paper is 6.1625
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Is 0 Infinity closed interval?
Thus, 0 itself is the sole position at which [0,∞] and (0,∞] are separated. Since it is in [0,∞] the set is closed. Given that it is not in (0,∞), the set is open interval.
A (real) interval in mathematics is a collection of real numbers that includes all real numbers that fall within any two of the collection's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 x 1. The collection of numbers such that 0 x 1 and the collection of all real numbers are other examples of intervals.
the empty set, any singleton, the set of positive real numbers, the set of nonnegative real numbers, and (set of one element).
Because they are the most basic sets whose "length" (or "measure" or "size") is straightforward to define, real intervals are crucial in the theory of integration. The Borel measure and finally the Lebesgue measure result from extending the notion of measure to more intricate sets of real numbers.
Interval arithmetic is a broad numerical computing technique that automatically generates assured enclosures for arbitrary formulas, even in the presence of uncertainties, mathematical approximations, and arithmetic roundoff. Intervals are at the centre of this technique.
Therefore, 0 itself is the sole place at which [0,∞] and (0,∞] have a boundary. Due to its location in [0,∞] the set is closed. Since it is not in (0,∞), the set is unclosed.
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What i the invere of f(x) = 3/(x 1) f ^ - 1 * (x) = (3 - 1)/x f ^ - 1 * (x) = 3 x f ^ - 1 * (x) = x^ 1 2 f ^ - 1 * (z) = 3/x - 1
The inverse of f(x) = 3/(x-1) is f^-1(x) = 3/x - 1.
So the correct answer is f ^ - 1 * (x) = 3/x - 1
The inverse of a function, denoted f^-1(x), is a function that "undoes" the original function. To find the inverse of a function, we need to switch the roles of x and y and then solve for x.
Given the function f(x) = 3/(x + 1), we can find its inverse by:
y = 3/ (x + 1)
Multiply with (x + 1) and divide by y
y(x + 1)/ y = (3/ (x + 1))×(x + 1)/ y
x + 1 = 3/ y
x = 3/ y - 1
Switching the roles of x and y:
y = 3/ x - 1
Thus f^(-1)(x) = 3/ x - 1
It's worth noting that in order for a function to have an inverse function it must be a one-to-one function. This means that for every y value there is only one x value.
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The cot c in pound of hiring a van for d day i given by the formula c=1045d work out the cot for 5 day
The cost of hiring a van for 5 days is $235.
In this question, we have been given an equation c = 10 + 45d that represents the cost in pounds of hiring a van for days.
here c = cost in pounds
d = number of days
We need to find the cost of hiring a van for 5 days.
Substitute the value d = 5 in given equation.
c = 10 + 45d
c = 10 + (45 × 5)
c = 10 + 225
c = 235 dollars
Therefore, the cost for 5 days is 235 dollars
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There are 3.5 loaves of bread, each weighing 1.5 lbs. Anton's family eats 2.5 loaves of bread. What is the total weight of the loaves of bread that are left?
The total weight of the loaves of bread remaining is 1.5 lbs
How to find the total weight of the loaves of bread leftFrom the problem it can be deduced that'
There are 3.5 loaves of bread
each weighing 1.5 lbs
Anton's family eats 2.5 loaves of bread
the total weight of the loaves of bread that are left = ?
The loaves of bread that are left
= 3.5 loaves - 2.5 loaves
= 1 loaf
Since 1 loaf weighs 1.5 lbs the weight of the left over bread is 1.5 lbs
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which expression is equivalent to
The provided expression can be simplified in the form 2y4/x4 option ( B) Using the integer exponent characteristics, = [x[tex]^\frac{1}{8}[/tex] . y⁸] is the right answer.
What is defined as an integer exponent?In mathematics, integer exponents are exponents that fall under the integer category. It's possible for the number to be either positive or undesirable. The positive integer exponents in this example dictate how many times that base number must be multiplied by itself.
It's possible for the number to be either positive or undesirable. The positive integer exponents in this example dictate how many instances the base number must be multiplied by itself.
According to the given information:= [x[tex]^\frac{1}{4}[/tex] . y¹⁶][tex]^\frac{1}{2}[/tex]
= [x[tex]^\frac{1}{8}[/tex] . y⁸]
The provided expression can be simplified in the form 2y4/x4 option ( B) Using the integer exponent characteristics, = [x[tex]^\frac{1}{8}[/tex] . y⁸] is the right answer.
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What does the ∑ symbol mean in statistics?
The symbol ∑ (sigma) is used to represent the sum of a set of numbers. This is very important notation in statistics.
What is uses of sigma symbol in statistics?If a hypothesis is correct, a set of data's standard deviation serves as a gauge of how rare it is. Standard deviations are expressed in units called sigma, or, by physicists. The findings are progressively inconsistent with the hypothesis as the number of sigma increases. The word's derivation is derived from the Greek letter "sigma," which is used in statistics to measure how much a process deviates from its mean or goal.
To express the total of a set of data or the total of a function over a specified range, it is frequently used in statistics and probability. For instance, if X is a collection of numbers, the term ∑X would stand for the collection's total. The symbol is typically followed by a variable, such as I indicating the range of the sum, for example, ∑i=1 to n for the summing from i=1 to i=n. The index I is frequently used to identify the individual components of the set.
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A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly. After
11
11
11
11
months, he weighed
140
140
140
140
kilograms. He gained weight at a rate of
5.5
5.5
5.5
5, point, 5
kilograms per month.
Let
y
y
y
y
represent the sumo wrestler's weight (in kilograms) after
x
x
x
x
months.
Complete the equation for the relationship between the weight and number of months.
The equation of line is given by y = 13.45x - 7.95 where the slope of the line is m = 13.45 and y is the weight in kilograms , x is the number of months
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
The weight in kilograms = y
The number of months = x
Let the first point be represented as P = P ( 11 , 140 )
Let the second point be represented as Q = Q ( 1 , 5.5 )
Now , the slope of the line is given by
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 140 - 5.5 ) / ( 11 - 1 )
Slope m = 134.5 / 10
Slope m = 13.45
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 140 = 13.45 ( x - 11 )
On simplifying the equation , we get
y - 140 = 13.45x - 147.95
Adding 140 on both sides of the equation , we get
y = 13.45x - 7.95
when x = 11 months
y = 13.45 ( 11 ) - 7.95
y = 147.95 - 7.95
y = 140 kilograms
Therefore , the value of A is y = 13.45x - 7.95
Hence , the equation is y = 13.45x - 7.95
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Solve.
7 Jordan shoots 100 3-point shots per basketball practice.
She makes 44 of these shots. What decimal represents the
number of shots she makes?
8 At a county fair, 9 people out of 1,000 earned a perfect score
in a carnival game. What decimal represents the number of
people who earned a perfect score?
Answer:
7. .44
8. .009
Step-by-step explanation:
7. 44 ÷ 100 = .44
8. 9 ÷ 1000 = .009
11. Solve the inequality.
g-6> -1
Answer:
g>5
Step-by-step explanation:
Simply add 6 to both sides to get g>5
A class is learning about proportions and ratios, so the teacher decides to use the data about students in the local high school. There are 500-600 students and 29 - 32% of the student body participates in athletics. Which of the following is the most reasonable estimate of the number of students who are considered athletes
Using the provided data, We should consider the mid-value for the number of students and take the average of percentage to find the estimate number, The answer is 168.
What is statistics?Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It is used to make decisions, predictions and gain knowledge from data. It involves using statistical methods to collect, summarize, and draw conclusions from data. It is used in various fields such as business, economics, social science, engineering, and medicine. It helps to make sense of complex data and make informed decisions.
What do you mean by estimate?In statistics, an estimate is a value that is calculated from a sample of data in order to approximate a population parameter. The most common examples of estimates are sample mean, sample proportion, sample standard deviation, and sample variance. These estimates are used to infer information about the population from which the sample was drawn. For example, an estimate of the population mean is calculated by taking the average of a sample of data and using that value to infer the value of the population mean.
mid-value of 500-600 = 550
average % = 30.5%
Athletes number = 30.5% of 550
=168
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b) Sita had 50 sweets. She ate 10 sweets and gave 8 sweets to her brother. If she divided the rest of them among her 8 friends equally, how many sweets would each friend get
Answer:
4 sweets per friend
Step-by-step explanation:
so first you want to minus 10 sweets since she ate 10 leaving her with 40 sweets. then she gives 8 sweets to her brother leaving her with 32 sweets left. If you divide the remaining sweets ( 32 ) by 8 you get 4 sweets per friend
What is the slope of a logarithmic graph?
The slope of a logarithmic graph depends on the type of logarithm used.
For a logarithmic function in the form y = log(b,x) where b is the base of the logarithm, the slope of the graph is undefined for x=0 and for x<0 because logarithmic functions are not defined in those cases.
For a natural logarithm, the slope is negative infinity at x=0 and positive for x > 0. As x increases, the slope becomes closer to zero.
For a common logarithm, the slope is negative infinity at x=0 and positive for x > 0. As x increases, the slope becomes closer to zero.
It's important to note that logarithmic functions are not linear functions, and therefore they do not have a constant slope, the slope of a logarithmic graph will change throughout the graph.
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Stacy wants to buy a tree to decorate her apartment. Her living room has 8 foot high ceilings. The height of each tree she is interested in buying is given below. Which tree(s) can she buy so that they fit in her living room? Choose all that apply
A. 108 inches
B. 114 inches
C. 94 inches
D. 79 inches
or other you can type what you got
Answer:
C And D
Step-by-step explanation:
94 Inches Is 7.8 Feet Tall & 79 Inches is 6.5 Feet Tall
Answer:
C and D
Step-by-step explanation:
You should start by changing the inches to feet
(there are 12 inches in foot [ 12 inch = 1 foot ])
A. 9 foot
B. 9.5
C. about 7 feet
D. about 6 feet
C and D are correct. Hope this helps!
50PTS 50 PTS (DONT explain just answer please)
Answer: 17
Step-by-step explanation:
Answer:
x = 17°
Step-by-step explanation:
The given angles are,
→ 6x + 8
→ 4x + 2
Now we have to,
→ find the required value of x.
Forming the equation,
→ (6x + 8) + (4x + 2) = 180°
{As two angles in a straight line is 180°}
Then the value of x will be,
→ (6x + 8) + (4x + 2) = 180°
→ 6x + 4x + 8 + 2 = 180°
→ 10x + 10 = 180°
→ 10x = 180° - 10
→ x = 170/10
→ [ x = 17° ]
Hence, the value of x is 17°.
x + 2y = -18
-8x + 5y = -24
substitution method
To solve many simultaneous linear equations, use the substitution method in algebra.
What is substitution method ?The algebraic technique for resolving multiple linear equations at once is called the substitution method. As the name implies, this method involves substituting a variable's value from one equation into another.
The first stage in the substitution approach is to determine any variable's value in terms of the other variable from one equation. If there are two equations, x+y=7 and x-y=8, for instance, we can deduce from the first equation that x=7-y. The substitution approach is applied in this manner as the first stage.
There are three steps in the substitution technique:
For each variable, solve a single equation.Solve the other equation by substituting (plugging in) this expression.Find the corresponding variable by substituting the value back into the original equation.Therefore, the answer is x= -2 and y= -8.
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How do you graph a logarithmic curve?
Logarithmic Functions
In mathematics, the logarithmic function is an inverse function to exponentiation
Domain and range of logarithmic functions
We know that is defined only when >0. So the domain is the set of all positive real numbers. We can see that can be either a positive or negative real number (or) it can be zero as well. Thus, can take the value of any real number.
Note:
The domain of function = is >0 (or) (0,∞).
The range of any log function is the set of all real numbers ().
Logarithmic graph
We know that exponentials and functions are inversely proportional to each other, and so their graphs are symmetric concerning the line =. Also, note that =0 when =0 as =(1)=0 for any . Thus, all such functions have an -intercept of (1,0). A logarithmic function doesn’t have a -intercept as 0 is not defined.
Properties of logarithmic graph
>0 and ≠1.
The logarithmic graph increases when >1 and decreases when 0<<1.
The domain is obtained by setting the argument of the function greater than 0.
The range is the set of all real numbers.
Graphing logarithmic functions
Before plotting the log function, just have an idea of whether you get an increasing curve or decreasing curve as the answer. If the >1 then the curve is increasing, and if 0<<1, then the curve is decreasing.
Here are the steps for graphing logarithmic functions:
Find the domain and range.
Find the vertical asymptote by setting the argument equal to 0. Note that a function doesn’t have any horizontal asymptote.
Substitute some value that makes the argument equal to 1 and use the property (1)=0. This gives us the -intercept.
Substitute some value that makes the argument equal to the base and use the property ()=1 This would give us a point on the graph.
Connect the two points (from the last two steps) and extend the curve on both sides relative to the vertical asymptote.
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During a science experiment, a chemist boils a liquid and then sets it on the lab table and records the temperatures as it cools. The graph shows , the temperature in degrees Centigrade, and is the number of after the liquid is set on the table. Liquid Temperature Time () Which equation is the best model for this data?
The exponential function that best models this data is given as follows:
C. y = 80(0.75)^x + 20.
How to define the exponential function?An exponential function, considering it's asymptote, is defined as follows:
y = a(b)^x + c.
In which the parameters are given as follows:
a is used to define the initial value.b is the rate of change.c is the horizontal asymptote.From the graph, the horizontal asymptote is at y = 20, hence the parameter c is defined as follows:
c = 20.
When x = 0, y = 100, hence the parameter a is obtained as follows:
100 = a(b)^0 + 20
a + 20 = 100
a = 80.
When x = 5, y = 40, hence the parameter b is obtained as follows:
40 = 80b^5 + 20
80b^5 = 20
b^5 = 1/4
b = (1/4)^(1/5)
b = 0.75. (approximately).
Hence the function is defined as follows:
y = 80(0.75)^x + 20.
Meaning that the correct option is given by option C.
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4. Determine the type of triangle with the given set of side lengths. Show your work. A. a = 8, b = 15, c = 17 B. a = 6, b= 15, c = 18 C. a = 7, b = 10, c = 12
So A is a triangle, and B is a triangle, and C is a right triangle (or a right-angled triangle)
Define Pythagoras Theorem.The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in standard algebraic notation, a2 + b2, are equal to the squares on the legs.
What is right angle triangle?A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.
A. a = 8, b = 15, c = 17
We can use the Pythagorean theorem to determine the type of triangle:
c² = a² + b²
17² = 8² + 15²
289 = 64 + 225
289 ≠ 289
Therefore, this is not a right triangle.
B. a = 6, b= 15, c = 18
We can use the Pythagorean theorem to determine the type of triangle:
c² = a² + b²
18² = 6² + 15²
324 = 36 + 225
324 ≠ 324
Therefore, this is not a right triangle.
C. a = 7, b = 10, c = 12
We can use the Pythagorean theorem to determine the type of triangle:
c² = a² + b²
12² = 7² + 10²
144 = 49 + 100
144 = 144
Therefore, this is a right triangle.
So A is a triangle, and B is a triangle, and C is a right triangle (or a right-angled triangle)
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What y-intercept means?
A line's x-intercept as well as y-intercept are the points at which the x- and y-axes, respectively, are crossed.
Now, According to the question:
Let's know:
Definition of Intercept
The term "intercept" refers to the location where a line and curve crosses an graph's axis. The x-intercept would be the point at which the x-axis gets crossed. The y-intercept would be the point at which the y-axis becomes crossed.
The x- as well as y-axis intersection point gets what is meant when a line has an intercept. The y-axis was often taken into account if indeed the axis is also not stated. The letter "b" can be typically used to represent it.
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Here are six number cards.
-4 -2 -1 5 6 8
Arrange the cards into three pairs with the same total
Arranging cards with number -4, -2, -1, 5, 6, 8 making pair with the same total. Therefore, the pairs are (8,-4), (6,-2), (5,-1).
What are card pairs?A pair is a hand that has two cards of same rank and three other cards that do not match any of these or each other. When comparing two similar hands, the hand with the higher pair wins – therefore 6-6-4-3-2 defeats 6-6-4-3-2. 5-5-A-K-Q.Some things, such as a pair of pants or a pair of scissors, contain two major sections that are the same size and form.
A 55-card deck with one 1, two 2s, three 3s, and so on up to ten 10s is used in the game. Shuffle the deck at the start of the game, then remove five cards from play without looking. Give each player one face-up card.
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Given: 3ab = 7ad and 3ac = 7ae prove: δabc ~ δade triangles a b c and a e d are connected at point a. complete the steps of the proof. ♣: ♦:
The given problem has been proved below using the rules of Congruence.
The given problem can be solved easily if we apply the basic rules of Congruence on the question properly as they are required. Congruence is when two given figures have the same shape and size.
Given that,
3AB=7AD
3AC=7AE
So, by re-arranging them we get the same ratio that is,
AB/AD=7/3
AC/AE=7/3
Hence, we can conclude that,
AB/AD=AC/AE
Also, we can show that ∠BAC and ∠DAE by the property of vertical angles.
But ∠BAC ≌ ∠DAE is also true by the vertical angle theorem in this diagram.
So, SAS property ∆ABC~∆ADE is proved in the end.
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The circumference of a circle B is 80% of the circumference of circle A.
a) Find the ratio of the area of circle A to the area of circle B, giving your
answer in the form 100:n
100 :
(2)
Square E has sides of length e cm.
Square F has sides of length fcm.
The area of square E is 69% greater than the area of square F.
b) Work out the ratio of e:f
Your final line should say, Ratio of e:f is
(2)
The area of circle A to the area of circle B ratio is 100: 64, and the ratio of e: f is 13: 10.
The area of the circle is equal to the multiplication of the square of the circle's radius and π.
A = πr²
where 'r' is the radius
Circumference of circle A × 0.8 = circumference of circle B
So, taking r as the radius of A,
2πr = circumference of circle A
2πr × 0.8 = circumference of circle B
So the radius of B is r × 0.8.
Now we can substitute that in the area equations :
Area of A = π×r²
Area of B = π × (r × 0.8)² = π × r² × 0.64
The circumferences of the A to B ratio is
Circumference of A : Circumference of B = (2 × π × r)/(2 × π × r × 0.8)
= 1: 0.8 = 100: 80,
The areas of circle A to circle B ratio is
Area of A : Area of B = (π × r²)/(π × r² × 0.64) = 1: 0.64 = 100: 64
e² = f² × 1.69
69% larger shows that f² is the 100% to which we must add 69% to obtain e². 100% + 69% Equals 169%, obtaining a factor of 1.69.
We have this equation:
e² = f² × 1.69
Apply the square root on both sides.
e = f × √(1.69) = f × 1.3
e/f = 1.3 = 1.3/1 = 13/10
the ratio e:f = 13: 10
Thus, the ratio of circle A's area to circle B's area is 100: 64 and the ratio of e: f is 13: 10.
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A high school coach wants to buy new athletic shorts for the 15 members of the basketball team. The coach must spend less than $200 on the shares. Which inequality represents the maximum cost of each pair, s, the coach can buy
What is a plot point example?
A plot point example contains a point in a story that defines the turning point in the story.
What is a plot point?A story's plot point is a crucial turning moment that occurs during the narrative. The tale and the characters may be developed and advanced using these ideas.
Why are plot points necessary in stories?Plot points offer your tale movement by advancing the plot and dragging the reader along. 'A particularly crucial portion of a storyline of a work of fiction,' according to the definition of a plot point. Never undervalue the significance of your framework, even if your book is contemplative or literary.
An example of plot point is :
In a story about a young girl who is trying to save her village from an impending monster attack, the plot point may occur when the girl discovers an ancient artifact that gives her the power to defeat the monster. This event marks a significant turning point in the story, as it sets the stage for the girl to take on the monster and potentially save her village.
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A rectangle has a perimeter of 36 cm and an area of 72 cm2.
What is the length of the rectangle's shorter side?
O 2 cm
O 3 cm
04 cm
6 cm
8 cm
What is the length of the rectangle's longer side?
06 cm
O 8 cm
O 9 cm
O 12 cm
18 cm
The length of the rectangle's shorter side is 6cm and the of the rectangle's longer side is 12cm.
What is perimeter?
The total length of a shape's boundary, as used in geometry, is referred to as the shape's perimeter. Adding the lengths of all the sides and edges that surround a shape yields its perimeter. It is calculated using linear length units like centimeters, meters, inches, and feet.
Given:
A rectangle has a perimeter of 36 cm and an area of 72 cm^2.
Let the length of the rectangle's shorter side is 'a' and
the length of the rectangle's longer side 'b'.
As the perimeter is 36 cm.
⇒ Perimeter = 2(a + b)
36 = 2(a + b)
18 = a+ b
a = 18 - b
Now the area of rectangle is 72cm^2.
⇒ Area = ab
72 = (18 - b)*b
72 = 18b - b^2
b^2 - 18b + 72 = 0
b^2 - 12b - 6x + 72 = 0
b(b - 12) - 6(b - 12) = 0
(b - 12)(b - 6) = 0
(b - 12) = 0, (b - 6) = 0
b = 12, b = 6
When b = 12 ⇒ a = 18 - 12 = 6
When b = 6 ⇒ a = 18 - 6 = 12
Hence, the length of the rectangle's shorter side is 6cm and the of the rectangle's longer side is 12cm.
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