Therefore, the only statement that is true is: "The new area is 6 times the original area."
What is area?Area is a measure of the size or extent of a two-dimensional surface or region, such as the surface of a square, rectangle, circle, triangle, or any other shape. It is expressed in square units, such as square meters, square feet, or square centimeters.
Here,
If the side lengths of a square are tripled, the new side length will be 2 mm x 3 = 6 mm.
The original area of the square is:
Area = side length x side length = 2 mm x 2 mm = 4 mm²
The new area of the square with tripled side lengths will be:
New area = new side length x new side length = 6 mm x 6 mm = 36 mm²
Therefore, the new area of the square will be 36 mm².
To determine which of the following statements about its area will be true, we need to see which statements are true for the new area of 36 mm²:
A. The new area is 6 times the original area. This statement is true because 36 mm² is 6 times larger than 4 mm².
B. The new area is 3 times the original area. This statement is false because 36 mm² is 9 times larger than 4 mm², not 3 times larger.
C. The new area is equal to the original area. This statement is false because the new area of 36 mm² is much larger than the original area of 4 mm².
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Complete question:
look at this square: 2 mm 2 mm if the side lengths are tripled, then which of the following statements about its area will be true?
The ratio of the new area to the old area will be 2:1
The ratio of the new area to the old area will be 6:1.
The ratio of the new area to the old area will be 1:2.
The ratio of the new area to the old area will be 4:1.
THE FIRST ANSWER GETS BRAINLIEST AND FIVE STARS!
Parallelogram ABCD is a rhombus with measure EBC = 36. What is the measure of DAE?
picture below
type the correct words in the blanks. two radicals are said to be radicals if they have the same and the radicand.
Two radicals are said to be radicals if they have the same indices and the radicand.
In mathematics, a radicand is an expression, a number, or a variable that is enclosed in a root symbol. The factor for which we are determining the root is quantity. As we study exponents and roots, the word "radicand" is utilised. Therefore, the radicand in 2 has a value of 2. Following are some radicand examples:
3√(pq) → pq is the radicand
√(a+b) → a + b is the radicand
4√15 → 15 is the radicand
A radical is a symbol used to represent a number's root. It is symbolised as. The word or phrase that appears after the radical symbol is known as the radicand. Hence, it may be claimed that the radical represents the radicand. Alternatively said, the radicand sign is √.
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Complete question:
Type the correct words in the blanks:
Two radicals are said to be radicals if they have the same and the radicand.
can anyone help me with this question triangles?
The missing side is 30.
What is a triangle?Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. The triangle's three line segments are referred to as its sides, and its three points of intersection as its vertices.
A triangle is a three-sided polygon formed by three line segments intersecting at three non-collinear points, and it can be classified based on the length of its sides and the measure of its angles.
Given figure, there are two lines ate parallel, that's why two triangles are similar triangle.
Assume that the missing side is x.
So that side ratio in similar triangle are equal;
14/20 = 21/x
So, x = 30.
Therefore, the missing side x is 30
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Triangle Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. According to the question the missing side is 30.
What is a triangle?Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. The triangle's three line segments are referred to as its sides, and its three points of intersection as its vertices. A triangle is a three-sided polygon formed by three line segments intersecting at three non-collinear points, and it can be classified based on the length of its sides and the measure of its angles.
Given figure, there are two lines ate parallel, that's why two triangles are similar triangle.
Assume that the missing side is x.
So that side ratio in similar triangle are equal;
14/20 = 21/x
So, x = 30.
Therefore, the missing side x is 30
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Complete the recursive formula of the arithmetic s -17,-8, 1, 10, .... a(1) = -17 a(n) = a(n − 1)+
Answer:
The common difference between consecutive terms in the sequence is 8 (since -17 + 8 = -9, -9 + 8 = -1, -1 + 8 = 7, and so on). Therefore, the recursive formula for this arithmetic sequence is:
a(1) = -17
a(n) = a(n-1) + 8 for n >= 2
This formula says that the first term in the sequence is -17, and each subsequent term is found by adding 8 to the previous term.
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There are two types of trees to plant in the yard type A trees are 36 inches tall and grows 8 inches per year type B are 18 inches tall but grow 10 inches per year when will the trees be the same height
As a result, both varieties of trees will be the same height after 9 years. We can change both equations to a = 9 to verify this: Height of the type A tree is 36 + 8(9) or 36 + 72 inches, whereas the height of the type B tree is 18 + 10(9) or 18 + 90 inches.
What function do height and distance serve in everyday life?Trigonometry includes heights and distances, and it has numerous uses in practical daily life. It utilised to compute height of towers, structures, mountains, etc., and distance between any two objects such celestial bodies others. ,sys,s tos.as to .... and.
Let's use "a" to denote the number of years after planting the trees.
A type A tree will reach the following height after "a" years:
Height of type A tree = 36 + 8a
After "a" years, the height of a type B tree will be:
Height of type B tree = 18 + 10a
We must set the two types of trees' heights equal to one another and solve for "a" to determine when they will reach the same height:
36 + 8a = 18 + 10a
Subtracting 8a from both sides, we get:
36 = 18 + 2a
Subtracting 18 from both sides, we get:
18 = 2a
Dividing both sides by 2, we get:
a = 9
Therefore, after 9 years, both types of trees will be the same height.
To check this, we can substitute a = 9 into both equations:
Height of type A tree = 36 + 8(9) = 36 + 72 = 108 inches
Height of type B tree = 18 + 10(9) = 18 + 90 = 108 inches
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Question:
You have two types of trees to plant in your yard: type A trees are 36 inches tall and grow 8 inches per year, while type B trees are 18 inches tall and grow 10 inches per year. At what point in time will the trees be the same height? How tall will the trees be at that time?
help plssss explainnn!!
Answer:
[tex]xy^8[/tex]
Step-by-step explanation:
Notice if you have the same base you can ADD the exponent, for example:
[tex]x^{-6} x^{7} =x^{-6+7}=x^{1 }=x[/tex]
[tex]y^{6} y^{2} =y^{6+2}=y^{8 }\\[/tex]
so the answer is
[tex]xy^8[/tex]
any point on the parabola can be labeled (x,y), as shown. a parabola goes through (negative 3, 3)
The correct standard form of the equation of the parabola is:
[tex]y = -x^2 - 1[/tex].
To find the standard form of the equation of the parabola that passes through the given points (-3, 3) and (1, -1), we can use the general form of the equation of a parabola:
[tex]y = ax^2 + bx + c[/tex] ___________(1)
Substituting the coordinates of the two given points into this equation, we get a system of two equations in three unknowns (a, b, and c):
[tex]3 = 9a - 3b + c[/tex]
[tex]-1 = a + b + c[/tex]
To solve for a, b, and c, we can eliminate one of the variables using subtraction or addition. Subtracting the second equation from the first, we get:
[tex]4 = 8a - 4b[/tex]
Simplifying this equation, we get:
[tex]2 = 4a - 2b[/tex]
Dividing both sides by 2, we get:
[tex]1 = 2a - b[/tex]___________(2)
Now we can substitute this expression for b into one of the earlier equations to eliminate b. Using the first equation, we get:
[tex]3 = 9a - 3(2a - 1) + c[/tex]
Simplifying this equation, we get:
[tex]3 = 6a + c + 3[/tex]
Subtracting 3 from both sides, we get:
[tex]0 = 6a + c[/tex]
Solving for c, we get:
c = -6a __________(3)
Substituting this expression for c into the second equation, we get:
[tex]-1 = a + (2a - 1) - 6a[/tex]
Simplifying this equation, we get:
[tex]-1 = -3a - 1[/tex]
Adding 1 to both sides, we get:
[tex]-3a =0[/tex]
Solving for a, we get:
[tex]a = 0[/tex]
Substituting this value of a into the equation(3) for c, we get:
c = 0
Substituting a = 0 into the equation(2) for b that we found earlier, we get:
[tex]1 = 0 - b[/tex]
Solving for b, we get:
[tex]b = -1[/tex]
Putting the values of a, b and c in (1), we get
[tex]y = -x^2 - 1[/tex]
Therefore, the equation of the parabola that passes through the given points (-3, 3) and (1, -1) is:
[tex]y = -x^2 - 1[/tex]
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Complete question:
A parabola goes through (-3, 3) & (1, -1). A point is below the parabola at (-3, 2). A line above the parabola goes through (-3, 4) & (0, 4). A point on the parabola is labeled (x, y).
What is the correct standard form of the equation of the parabola?
The figure is in the image attached below
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table.
In response to the stated question, we may state that As a result, the overall probability of an accurately picked drive-thru order across all chains is roughly 0.929, or 92.9%.
What is probability?Probability theory is an area of mathematics that calculates the likelihood of an occurrence or a proposition being true. A risk is a number in the range of 0 and 1, whereas 1 implies certainty and a probability of roughly 0 indicates how likely an event seems to be to occur. Probability is a mathematical expression of the chance or chances that a given event will occur. Probabilities can alternatively be stated as integers between 0 and 1 or as % from 0% to 100%. the ratio of occurrences among equally likely choices that result in a certain event in comparison to all other outcomes.
Using the data in the table, we can compute the likelihood of a correct drive-thru order for each fast food chain, as well as the overall chance of an accurate order across all chains.
Divide the number of accurate orders by the total number of orders to find the chance of a randomly picked order being accurate at each chain:
P(accurate order) = 1246 / 1300 = 0.958 for McDonald's
P(accurate order) = 1020 / 1100 = 0.927 Taco Bell
P(accurate order) = 708 / 800 = 0.885 for Burger King
P(accurate order) = 940 / 1000 = 0.94 for Wendy's
P(adequate overall order) = 0.3 * 0.958 + 0.25 * 0.927 + 0.2 * 0.885 + 0.25 * 0.94 = 0.929
As a result, the overall likelihood of an accurately picked drive-thru order across all chains is roughly 0.929, or 92.9%.
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Find any critical numbers of the function.
Answer:
(1, 2) and (-1, -2). or. (±1, ±2)
Step-by-step explanation:
[tex]{ \sf{f(x) = \frac{4x}{ {x}^{2} + 1 } }} \\ [/tex]
- Simply, a critical number or critical point is gotten by differentiating the function.
From Quotient rule;
[tex]{ \sf{ {f}^{l}(x) = \frac{4( {x}^{2} + 1) - (2x)(4x)}{ {( {x}^{2} + 1)}^{2} } }} \\ \\ { \sf{f {}^{l}(x) = \frac{ {4x}^{2} + 4 - {8x}^{2} }{ {( {x}^{2} + 1) }^{2} } }} \\ \\ { \sf{f {}^{l}(x) = \frac{4(1 - {x}^{2}) }{ {( {x}^{2 } + 1) }^{2} } }}[/tex]
Then equate this derivative to zero;
[tex]{ \sf{0 = \frac{4(1 - {x}^{2} )}{ {( {x}^{2} + 1) }^{2} } }} \\ \\ { \sf{4(1 - {x}^{2} ) = 0}} \\ \\ { \sf{4 - {4x}^{2} = 0}} \\ \\ { \sf{4 {x}^{2} = 4}} \\ \\ { \sf{x = \sqrt{1} }} \\ \\ { \sf{ \underline{ \: x = \pm 1 \: }}}[/tex]
Substitute for x in f(x)
For x = 1
[tex]{ \sf{f(1) = \frac{4(1)}{ {(1)}^{2} + 1} = \frac{4}{2} = 2 }} \\ [/tex]
For x = -1
[tex]{ \sf{f( - 1) = \frac{4( - 1)}{ {( - 1)}^{2} + 1 } = \frac{ - 4}{2} = - 2 }} \\ [/tex]
Therefore points are;
(1, 2) and (-1, -2)
generally, cold fronts move fast er than warm fronts generally, cold fronts have steeper slopes generally, precipitation cover s a much broader area with a cold front especially in winter, cumuliform clouds are more often associated with cold fronts
Cold fronts generally move faster than warm fronts because cold air is denser and thus, moves more quickly. Precipitation with a cold front typically covers a broader area, especially during the winter.
On the other hand, warm fronts move more slowly as they are characterized by the gradual lifting of warm air over colder air. Cold fronts also typically have steeper slopes than warm fronts. This is because the leading edge of a cold front is more abrupt.
With a steep rise in the cold air mass. In contrast, the leading edge of a warm front has a gentler slope as the warm air gradually rises over the colder air.
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Convert each number to scientific notation and perform the indicated operations. Express the result in ordinary decimal notation.
The result of the division in ordinary decimal notation is 300.
Scientific notation, also known as standard form or exponential notation, is a method of expressing very large or very small numbers in a compact and standardized way.
To perform the indicated operation, we need to divide 0.00036 by 0.0000012.
First, let's express both numbers in scientific notation
0.00036 = 3.6 x 10^(-4)
0.0000012 = 1.2 x 10^(-6)
Now we can divide the two numbers and simplify
3.6 x 10^(-4) / 1.2 x 10^(-6) = (3.6 / 1.2) x 10^(-4-(-6)) = 3 x 10^(2)
Finally, we can convert this result back to ordinary decimal notation
3 x 10^(2) = 300
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The given question is incomplete, the complete question is:
Convert each number to scientific notation and perform the indicated operations. Express the result in ordinary decimal notation. 0.00036/0.0000012
Help please! Appreciate the help
For the given statements for domain and range, option 3 and option 4 are correct answers.
What is domain and range?The sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively, are the domain and range of a relation. With functions, we enter various numbers, and the output is a new set of numbers. The two essential characteristics of functions are domain and range. A function's domain and range are its constituent parts.
The domain of the function are all the input values while the range are the output values of the function for the given input.
In the given options, option 3 and 4 are correct as the functions have the same input but not the same output.
That is, they have the same domain, all real numbers, but not the same range.
Hence, for the given statements for domain and range, option 3 and option 4 are correct answers.
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Letsha wants to produce 80 pages information books for school project. She can have this done at local printing company at R0.35 per page.
Answer:
if u want total price then,
=Rs.35×80=Rs.2800
Find the distance from Link to the Octorok so Link can attack
The distance from Link to the Octorok is 10.63 units.
How to find the distance?We know that the distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula below:
distance = √( (x₂ - x₁)² + (y₂ - y₁)²)
Here we want to find the distance from Link to the Octorok so Link can attack, so we need to get the distance between the points (-4, -5) and (3, 3).
The distance will be:
distance = √( (3 + 4)² + (3 + 5)²)
distance = √( (7)² + (8)²)
distance = √113
distance = 10.63
The distance is 10.63 units.
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Graph the function.
f(x) = 3/5x -5
Use the Line tool and select two points to graph.
Answer:
see attached
Step-by-step explanation:
You want to graph the function f(x) = 3/5x -5.
GraphFor graphing purposes, it is convenient to choose values of x that result in integer values of y. In this case, the multiplier of x (the slope) has a denominator of 5, so it is convenient to choose x-values that are multiples of 5.
For x = 0, y = 3/5·0 -5 = -5
For x = 5, y = 3/5·5 -5 = 3 -5 = -2
Suitable points for your plot are (0, -5) and (5, -2). These are shown in the attachment.
Let A and B be events with P(A) = 0.3, P(B) = 0.6, and P(A and B) = 0.03. Are A and B mutually exclusive? Explain why or why not.
Answer:
A and B are not mutually exclusive
Step-by-step explanation:
A and B are not mutually exclusive because P(A and B) > 0. If A and B were mutually exclusive, then they would have no outcomes in common and the probability of their intersection would be zero. However, in this case, they do share some outcomes, since P(A and B) is greater than zero.
can you help me to solve these two questions?
Case 1: The constant c of the piecewise function is equal to 1 / 7.
Case 2: The value of the constant b of the piecewise function with the greater absolute value is equal to 20.
How to determine the value of a variable such that a piecewise function is continuous
A piecewise function is function formed by two or more functions relative to intervals. A piecewise function is continuous if they do not have any jump on graph. For two functions, we must solve the following equation for the case of a piecewise function formed by two functions:
g(a) = h(a)
Case 1 - g(y) = c · y + 3, h(y) = c · y² - 3, a = 7
c · a + 3 = c · a² - 3
c · (a² - a) = 6
c = 6 / (a² - a)
c = 6 / (7² - 7)
c = 6 / 42
c = 1 / 7
The value of the constant c is equal to 1 / 7.
Case 2 - g(x) = b - 2 · x, h(x) = - 150 / (x - b), a = 5
b - 2 · a = - 150 / (a - b)
(b - 2 · a) · (a - b) = - 150
a · b - b² - 2 · a² + 2 · a · b = - 150
- b² + 3 · a · b - 2 · a² = - 150
b² - 3 · a · b + 2 · a² - 150 = 0
b² - 15 · b - 100 = 0
(b - 20) · (b + 5) = 0
b₁ = 20 or b₂ = - 5
The solution with the greater absolute value is b = 20.
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CAN SOMEONE PLEASE HELP thank you so so much please!!!
Step-by-step explanation:
try this option, all the details are in the attachment.
Is this figure a polygon dont answer if you don’t know the answer
Polygon - a plane figure with at least three straight sides and angles, and typically five or more.
Answer:
No
Step-by-step explanation:
Since a polygon has straight sides, with 3 or more, it cannot be a polygon since one side is curved.
can you help me to solve this question?
The asymptotes of the function f(x) = (2x² - 5x + 3)/(x - 2) are given as follows:
Vertical asymptote at x = 2.Oblique asymptote at: y = 2x - 3/2.How to obtain the asymptotes of the function?The function for this problem is defined as follows:
f(x) = (2x² - 5x + 3)/(x - 2)
The vertical asymptote is the value of x for which the function is not defined, hence it is at the zero of the denominator, and thus it is given as follows:
x - 2 = 0
x = 2.
The oblique asymptote is at the quotient of the two functions, hence:
(mx + b)(x - 2) = 2x² - 5x + 3
mx² + (b - 2m) - 2b = 2x² - 5x + 3.
Hence the values of m and b are given as follows:
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Curious about people's recycling behaviors, Sandra put on some gloves and sifted through some recycling and trash bins. She kept count of the plastic type of each bottle and which bottles are properly dispensed.
What is the probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle? Please show your work.
The probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle is 0.25 or 25%
What is Conditional probability?
Conditional probability is the probability of an event occurring given that another event has occurred or is known to have occurred. It is denoted by P(A|B), which reads as "the probability of A given B."
The formula for conditional probability is:
P(A|B) = P(A and B) / P(B)
where P(A and B) is the probability of both events A and B occurring, and P(B) is the probability of event B occurring.
The total number of Plastic #2 bottles is 8 (correctly placed) + 5 (incorrectly placed) = 13.
The total number of Plastic #4 bottles is 5 (correctly placed) + 2 (incorrectly placed) = 7.
The probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle is given by:
(number of Plastic #4 bottles correctly placed) / (total number of bottles)
So the probability is:
5/20 = 1/4 = 0.25
Therefore, the probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle is 0.25 or 25%.
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In an effort to figure out why application rates are slipping, your college decides to set up an experiment to determine why students who are interested in the college decide to enroll or not. The college decides to send out a questionnaire to everyone who submitted an application to the college in 2017. What's the population for this study, and what's the sample?
A. The population is all college students everywhere, and the sample is all college students interested in your school.
B. The population is all college students everywhere, and the sample is the individuals who responded to the survey.
C. The population is all students who applied to your college, and the sample is the individuals who responded to the survey.
D. The population is all college students interested in your school, and the sample is everyone who decided to enroll.
The population of interest is the group of students who submitted an application to the college in 2017.
What is sample?A sample is a subset of a population that is selected and studied in order to make inferences or conclusions about the population. The sample is usually selected to be representative of the population in some way, so that the conclusions drawn from the sample can be generalized to the population as a whole.
According to question:The correct answer is C.
The purpose of the study is to determine why students who are interested in the college decide to enroll or not. Therefore, the population of interest is the group of students who submitted an application to the college in 2017.
Option A is incorrect because the population is not all college students everywhere, only those who applied to the college in question.Option B is incorrect because the sample is not just the individuals who responded to the survey, but rather all students who submitted an application in 2017.Option D is incorrect because the sample is not just everyone who decided to enroll, but rather all students who submitted an application, regardless of whether they enrolled or not.To know more about sample visit:
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Consider two agents, Alice and Bob, who have utility functions 0.3x3 + 0.72A if xa > XB (0.314 +0.72B if XB > XA UA(2A, 2B) = UB(XA, XB) 4X A – 32B if XB > IA -0.32A + 1.3xB if x A > XB If Alice is the dictator in the dictator game with a $10 endowment, then she will offer Bob (A) $0; (B) $5; (C) $2; (D) $10.
The utility that maximizes the possible utility of both the agents Alice and Bob is equal to option D. $10.
Compare Alice's utility from each option and choose the one that maximizes her utility.
Let us consider each option,
If Alice offers Bob $0, her utility will be,
If XA > XB then
UA (XA , XB )= 0.3x3 + 0.72A
UA(10,0)
= 0.3(10)³ + 0.72(10)
= 307.2
If Alice offers Bob $5, Bob's utility will be,
UB(10,5)
= 0.314 + 0.72(5)
= 0.314 + 3.6
= 3.914
And Alice's utility will be,
UA(5,10)
= -0.32(5) + 1.3(10)
= 11.4
Total utility for both Alice and Bob will be,
UA(5,10) + UB(10,5)
= 11.4 + 3.914
= 15.314
If Alice offers Bob $2, Bob's utility will be,
UB(10,2)
= 0.314 + 0.72(2)
= 1.754
And Alice's utility will be,
UA(2,10)
= -0.32(2) + 1.3(10)
= 12.4
So the total utility for both Alice and Bob will be,
UA(2,10) + UB(10,2)
= 12.4 + 1.754
= 14.154
If Alice offers Bob $10, Bob's utility will be,
UB(10,10)
= 0.314 + 0.72(10)
= 7.514
And Alice's utility will be,
UA(10,10)
= 0.3(10)³ + 0.72(10)
= 307.2
So the total utility for both Alice and Bob will be,
UA(10,10) + UB(10,10)
= 307.2 + 7.514
= 314.714
Therefore, utility which maximizes the total utility for both Alice and Bob is given by option (D) $10.
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Which operation do you use to simplify a ratio after finding the greatest common factor (GCF)?
division
addition
multiplication
subtraction
Answer:
hey baby
Step-by-step explanation:
hi thwrw honey i love you lol
The operation we use to simplify a ratio after finding the greatest common factor (GCF) is division.
Option A is the correct answer.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To simplify a ratio after finding the greatest common factor (GCF), we use division.
We divide both terms of the ratio by the GCF.
This reduces the ratio to its simplest form.
Thus,
The operation we use to simplify a ratio after finding the greatest common factor (GCF) is division.
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Can someone actually see if I got this answer correct please
Instead of 2.00 as mentioned in the question, the semester GPA is 1.38. Please double-check your calculations or provide more details if you made an error when reporting your grades or computing your GPA.
How many credit hours are there in three?Students must devote approximately 135 hours (45 x 3) of class, instructional, and independent time to a three credit unit course. Students who enroll in a course for four credit hours must dedicate around 180 (45 x 4) hours to it, split between in-class and out-of-class work.
You must first translate each letter grade using the common 4.0 scale into its equivalent numerical number before you can determine your semester GPA:
A = 4.0
B = 3.0
C = 2.0
D = 1.0
F = 0.0
E = 0.0 (equivalent to F)
Then, you can use the formula:
(Total grade points) / GPA (total credit hours)
Using this formula, we can calculate your semester GPA as follows:
FYE 105: F (0.0) x 3 credit hours = 0.0 grade points
MAT 150: E (0.0) x 3 credit hours = 0.0 grade points
ENG 101: D (1.0) x 3 credit hours = 3.0 grade points
BIO 112: A (4.0) x 3 credit hours = 12.0 grade points
BIO 113: B (3.0) x 1 credit hour = 3.0 grade points
Total grade points = 0.0 + 0.0 + 3.0 + 12.0 + 3.0 = 18.0
Total credits earned is 13 (3 + 3 + 3 + 3 + 1)
GPA = 18.0 / 13 = 1.3846
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What is the smallest possible average of five distinct positive even integers?
A. 10
B. 8
C. 6
D. 4
E. 0
Answer:
The smallest possible average of five distinct positive even integers will occur if we choose the five smallest even integers. Since we want the integers to be distinct, we start with 2 and add the next four even integers:
2, 4, 6, 8, 10
The average of these five integers is:
(2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6
Therefore, the smallest possible average of five distinct positive even integers is 6, which is answer choice C.
Question 6
One gallon of water weighs 8.34 lb. How much weight is added to a fire truck when its tank is filled
with 750 gal of water?
Question 7
1
Answer
6255 pounds
8.34×750=6255lbs
-51+((-5+(-4)) all calculation
Answer:
the answer to that is -31
Simplify without calculator: (-5) (7)+4×5 (Show all calculations)
Step-by-step explanation:
this is the answerrr
without calculator
for autonomous equations, find the equilibria, sketch a phase portrait, state the stability of the equilibria.
Understanding the equilibria, sketching a phase portrait, and determining the stability of equilibria for autonomous equations are important tools for analyzing and understanding the behavior of systems over time.
Autonomous equations are differential equations that do not depend explicitly on time. To find the equilibria of an autonomous equation, we set the derivative of the function to zero and solve for the values of the independent variable that satisfy the equation. These values represent points at which the function does not change over time and are known as equilibrium points.
To sketch a phase portrait for an autonomous equation, we plot the slope field of the function and then draw solutions through each equilibrium point. The resulting graph shows the behavior of the function over time and helps us understand how the solutions behave near each equilibrium point.
The stability of an equilibrium point is determined by examining the behavior of nearby solutions. If nearby solutions move toward the equilibrium point over time, the equilibrium point is stable. If nearby solutions move away from the equilibrium point over time, the equilibrium point is unstable. Finally, if the behavior of nearby solutions is inconclusive, further analysis is needed.
Here is the sketch for [tex]dx/dt = x - x^3[/tex]
/ <--- (-∞) x=-1 (+∞) ---> \
/ \
<--0--> x=-1 x=1 0-->
\ /
\ <--- (-∞) x=1 (+∞) ---> /
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