Answers
The slope of the line represented by 4x-7y=62 is 4/7. A line's steepness is measured by its slope. The mathematical expression for slope is "rise over run."
Option A is correct.
What is slope of line?In mathematics, a line's slope is the ratio of the change in the y coordinate to the change in the x coordinate. The net change in the y-coordinate and the net change in the x-coordinate, respectively, are denoted by the symbols delta y and delta x.
We are given equation as 4x-7y=62
First, let's write it in the slope-intercept form .In general, slope-intercept form is y=mx + b
where m is the slope
So, writing the equation in the form, we get
⇒-7y = 62-4x
⇒7y = 4x-62
⇒y = 4x/7-62/7
Now, matching the equation with the general form,
m = 4/7
Hence, the slope of the line represented by 4x-7y=62 is 4/7.
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Related Questions
PLEASE HELP ASAP??!!
What is the end behavior of the function f(x) = −x³ + 2x² +1
As a approaches infinity, f(x) approaches infinity. As approaches negative
infinity, f(x) approaches negative infinity.
As a approaches infinity, f(x) approaches negative infinity. As a approaches
negative infinity, f(x) approaches negative infinity.
As a approaches infinity. f(x) approaches negative infinity. As a approaches
negative infinity, f(x) approaches infinity.
As approaches infinity, f(x) approaches infinity. As a approaches negative
Answers
The end behavior of the function f(x) = −x³ + 2x² +1 is:
as x → ∞, f(x) → -∞
as x → -∞, f(x) → ∞
What is the end behavior of the function?Here we want to find the end behavior of the function below:
f(x) = −x³ + 2x² +1
Notice that the degree is odd, this means that the end behaviors are opposite in opposite values of x.
Because we have a negative sign on the term with the highest exponent, then as x tends to infinity, the function will tend to negative infinity.
And thus, because the degree is odd, the value of f(x) as x tends to negative infinity tends to positive infinity.
Thus we can write:
as x → ∞, f(x) → -∞
as x → -∞, f(x) → ∞
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In which direction must the graph of f(x) = 9x be shifted to produce the graph of g(x) = 9x + 7? a. up b. down c. left. d right
Answers
The translation or the graph must be shifted upwards by 7 units .
What are functions?Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given here: The graph f(x)=9x
The required graph is given by g(x)=9x+7
A graph is translated k units vertically by moving each point on the graph k units vertically. g (x) = f (x) + k; can be sketched by shifting f (x) k units vertically.
Thus two transform the given graph into g(x) we have to translate the graph vertically or upwards by 7 units i.e f(x)=9x+7
where k=7
Hence, The translation or the graph must be shifted upwards by 7 units .
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For each expression, circle any like terms and list any variables.
Answers
The final resultant expressions are 3.9 - 0.8 x , 1.5 + t+0.66 x ,
77/5 k - 3m.
What is Algebraic expression ?
Algebraic expression can be defined as the combination of variables and constants.
Given expressions,
-2.5x+3.9 + 1.7x
3.9 + 1.7x-2.5x
3.9 - 0.8 x
1 1/2 + t + 2/3 s
= (2+1) / 2 + t+ 2/3 s
= 3/2 + t + 2/3 s
= 1.5 + t+0.66 x
15k+2/5 k -3m
k(15+2/5 ) - 3m
k (75 + 2 / 5 ) - 3m
77/5 k - 3m
Hence, The final resultant expressions 3.9 - 0.8 x , 1.5 + t+0.66 x ,
77/5 k - 3m
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simplify [17-8] - [13-4]
Answers
Answer:
0
Step-by-step explanation:
First, you do 17 - 8, which is 9 and then you do 13 - 4, which is 9. Then, you subtract 9 from 9, which gives you 0.
15. write this problem in slop intercept form.
nick is given $50 to spend on a vacation. he decides to spend $5 a day. the amount nick has left and the number of days are related.
Answers
Answer: 10 I'm not sure ok
Step-by-step explanation: divide 50 and 5 you get 10
John is making apple pies and apple cobblers to sell at his stand at the Farmer's Market.
A pie uses 4 cups of apples and 3 cups of flour.
A cobbler uses 2 cups of apples and 3 cups of flour.
John has 16 cups of apples and 15 cups of flour.
When John sells the pies and cobblers at the Farmer's Market, he will make $3.00 profit per pie and $2.00 profit per cobbler.
Let x = the number of pies John makes.
Let y = the number of cobblers John makes.
Which inequality shows the constraint on the amount of apples John has to make pies and cobblers?
Let x = the number of pies John makes.
Let y = the number of cobblers John makes.
Answers
An inequality which shows the constraint on the amount of apple John has to make pies and cobblers is: D. 4x + 2y ≤ 16.
How to write an equation to model this situation?In order to write an equation that model this situation, we would assign a variable to the number of pies John makes and the total number of cobblers John makes respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of pies John makes.Let the variable y represent the total number of cobblers John makes.Since a pie uses 4 cups of apples and 3 cups of flour while a cobbler uses 2 cups of apples and 3 cups of flour, the constraint on the amount of flour is given by:
4x + 2y ≤ 16
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Write an equation in slope intercept form passing through the point (-10,1) and parallel to the line 10x+5y=15
Answers
Answer: y=-2x-19
Step-by-step explanation:
First, you should arrange the equation in the form of y=mx+c (that is the standard form of this type of equation)
10x+5y=15
5y=-10x+15
[tex]\frac{5y}{5} =\frac{-10x}{5}+\frac{15}{5}[/tex]
y=-2x+3 (now you got the equation in the simple form)
now you should substitute the given point (-10,1) into the simplified equation
y= 1 & x=-10
1=-2(-10)+c (the y-intercept must be taken as c )
c= 1 - 20
c= -19
therefore the equation will be : y=-2x-19
it will be the same gradient as the other line for this line too as the lines are parallel, you should only find the y-intercept. The gradient of the other line will stay the same as long as they are parallel lines.
Help please!! (5k + 2m)(3p + 4s)
Answers
7.Maddie performed a calculation on her calculator and received a result of 8E3.
What are the standard form and scientific notation for this value?
Select two answers: one for standard form and one for scientific notation.
Answers
The scientific notation of the given result is 8 x 10³
How does scientific notations work?The number is written in the form [tex]a \times 10^b[/tex] where we have [tex]1 \leq a < 10[/tex]
The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10. We can for a time, ignore the value of 'a' for two comparable quantities and only compare their orders(this type of comparison is useful when difference is too big, like size of human to size of a star etc sort of comparisons).
We are given that Maddie performed a calculation on her calculator and received a result of 8E3.
WE know that "E" means the power of ten
Therefore,
8E3 = 8 x 10³
This is the scientific notation.
For the standard form it should be 8,000.
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Emma wants to paint her house light pink. She adds 6 cans of white paint to every 4 cans of pink
paint to make the desired color. How many cans of white paint will she need to mixed with 12 cans of
pink?
Answers
To find out how many cans of white paint Emma will need to mix with 12 cans of pink paint, we can use the proportion of white paint to pink paint that she is currently using: 6 cans of white paint to every 4 cans of pink paint.
We can set up an equation using the proportion:
white paint/pink paint = 6/4 =3/2
We know that Emma wants to use 12 cans of pink paint, so we can use this information to solve for the number of cans of white paint she needs:
white paint/pink paint = 3/2
white paint = (3/2) * pink paint
white paint = (3/2) * 12 cans
white paint = 18 cans
So Emma will need 18 cans of white paint to mix with 12 cans of pink paint to get the desired color.
You toss two coins. In how many ways can they fall?
You toss three coins. In how many ways can they fall?
You throw two dice. In how many ways can they fall?
Answers
The ways they can fall are 4,8 and 36
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
P(E) = Number of favorable outcomes / total number of outcomes
Given;
Two coins, three coins and two dices are tossed
Probability of two coins;
=2x2=4
Probability of three coins;
=2x2x2=8
Probability of two dices;
=6x6=36
Therefore, the probability of coins and dice will be 4,8 and 36
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4. A 15-kg child is tossed up into the air by her parent. The child is 2.5 meters off the ground traveling 3 m/s.
Circle one: KE / GPE / both
Show your work for finding the values of each type of energy the object has:
Answers
The object has both kinetic energy and potential energy.
The values of each type of energy the object has are KE = 67.5 J
GPE = 367.5 J
How to find the energy of the object?Energy is the ability to do work. It can take many forms, such as kinetic energy (energy of motion), potential energy (stored energy) etc.
If a 15-kg child is tossed up into the air by her parent and the child is 2.5 meters off the ground traveling 3 m/s.
Then boy has kinetic energy due to his motion and also has potential energy due to his height.
Thus, M = 15-kg, h = 2.5 meters and V = 3 m/s
KE = 1/2(M)(V)² = 1/2 × 15 × 3² = 67.5 J
GPE = mgh = 15 × 9.8 × 2.5 = 367.5 J
KE + PE = 67.5 + 367.5 = 435 J
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Halla el FCM de 114, 138 y 234 usando el método de factorización prima
(escriba su respuesta)
Answers
The HCF of the numbers 114, 138 and 234 is 6.
The term HCF in math is also know as the greatest common factor or highest common factor of a set of whole numbers is the largest positive integer that divides evenly into all numbers with zero remainder.
Here we have given the numbers 114, 138 and 234.
And we need to find the HCF of the numbers.
By using the prime factorization method, here we have identified the factors of the numbers, and it can be written as
The factors of 114 are: 1, 2, 3, 6, 19, 38, 57, 114
The factors of 138 are: 1, 2, 3, 6, 23, 46, 69, 138
The factors of 234 are: 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234
While we looking into the given number we have identified that the the greatest common factor is 6.
Complete Question:
Find the HCF of the numbers 114, 138, and 234 by using the prime factorization method.
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Question 19
Luke invests 34000 into an account that pays 3. 4% compound interest per annum for the first two years, and 2. 3%
thereafter.
Given that the interest is paid into his account monthly (and calculated monthly), work out how much money Luke
will have in his account after 6 years and 3 months.
Answers
As per the formula of compound interest the amount in his account after 6 year 3 months is $40,085.307
In math the term called compound interest is defined as when you earn interest on both the money you've saved and the interest you earn.
Here we know that Luke invests 34000 into an account that pays 3. 4% compound interest per annum for the first two years and 2. 3% thereafter.
Here we need to find the amount in his account after 6 years and 3 months.
Then it can be calculated as,
FV = PV(1 + i)ⁿ
Here we know that PV = 34000 and i = 3.4% for two years,
Then the FV is value is calculated as,
=> FV = 34000(1 + 3.4/100)²
=> FV = 34000 ( 1 + 0.034)²
=> FV = 36351.304
Similarly, the FV value of 4 years 3 months is calculated as,
=> FV = 36351.304(1 + 2.3/100)⁴°³
=> FV = 36351.304(1 + 0.023)⁴°³
=> FV = 40085.307
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Use technology to find points and then graph the function
y
=
−
x
+
1
+
5
y=−
x+1
+5 following the instructions below.
done plotting points
Plot at least four points from the table of values with integer coordinates on the axes below. Click a point to delete it.
Answers
The graph and the points are added as an attachment
How to determine the graph?From the question, we have the following parameters that can be used in our computation:
y = -x + 1 + 5
Evaluate the like terms
y = -x + 6
Set x = values from 0 to 3
So, we have
y = -0 + 6 = 6
y = -1 + 6 = 5
y = -2 + 6 = 4
y = -3 + 6 = 3
So, the points are (0, 6), (1, 5), (2, 4) and (3, 3)
Next, we plot the graph and the points
See attachment
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An angle is two collinear rays with a common endpoint. Find an example that contradicts this definition. How would you change the definition to make it more accurate? Part B: Give an example of an undefined term and how it pertains to angles
Answers
For the definition "An angle is 2 collinear rays with a common endpoint" , then
(a) the contradictory example is "When two rays are collinear having a common end point; then the rays do not form an angle instead they form a line."
(b) the changed definition is , "An angle is formed at the intersection of two non-collinear rays that have the same endpoint " ;
(c) the example is "the Plane" .
The Angles are formed when the two straight lines or rays meet at a common endpoint.
Part(a) ;
An example which contradicts this definition of angles is "When two rays are collinear with a common endpoint; the rays do not form an angle ,instead they form a line" because when all the points of two lines are collinear then all the points of the two lines will be overlapping .
Part(b) ;
The change that need to be made in the definition of angle is "An angle is formed at intersection of two non-collinear rays which have same endpoint ".
Part(c) ;
The Example of the undefined term is :
Undefined terms do not have a formal definition; an example of this is "the plane" . The plane pertains to the angles because the plane determines the parameter to be measured.
The given question is incomplete , the complete question is
An angle is two collinear rays with a common endpoint.
(a) Find an example that contradicts this definition.
(b) How would you change the definition to make it more accurate ?
(c) Give an example of an undefined term and how it pertains to angles .
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2. Mark is trying to fit a circular tabletop with a diameter
of 88 inches through a door. The width of the door is 36
inches and the height of the door is 84 inches. Will the
tabletop fit through the door?
Answers
Answer: lol no it won't
Step-by-step explanation:
In order to determine if the circular tabletop with a diameter of 88 inches will fit through the door, we must compare the dimensions of the tabletop to the dimensions of the door.
The width of the door is 36 inches and the height of the door is 84 inches. The diameter of the tabletop is 88 inches. To fit through the door, the tabletop's diameter must be less than or equal to both the width and the height of the door.
88 inches > 36 inches and 88 inches > 84 inches
In this case, the tabletop will not fit through the door because its diameter is larger than both the width and the height of the door.
In each row decide whether the expression in column A is equivalent to the expression In column b. If they are not equivalent show how to change one expression to make them both equivalent. YAWL HELP URGENTLY IM GONNA CRY
Answers
I apologize for misunderstanding your question.
Regarding your new question, it depends on the specific expressions provided in column A and column B. Without knowing the exact expressions, I am unable to determine if they are equivalent or not. Additionally, if they are not equivalent, then to make them equivalent, you can use algebraic properties such as the commutative property, associative property, distributive property and simplification techniques to change one of the expressions so that it has the same value as the other expression for every input in their domain.
Please let me know the specific expressions you are working with and I will be happy to help you determine their equivalence and/or how to change one of the expressions to make them equivalent.
Answer:
SO bassically its is equivalent bc i seethat the dgene is really good
Step-by-step explanation:
1 + 1 =2w + 2x +2y = 3x and equiavelnt number
Complete the explanation of how you could use the work backward problem-solving strategy to solve the equation
x/5 − 3 = 2.
The equation says that a number was divided by 5 and that 3 was then subtracted from the quotient, giving the result 2. So, working backward, first add (blank)to 2, giving (blank). Then multiply that result by (blank), giving x = (blank)
Answers
The solution to the equation is described as follows:
The equation says that a number was divided by 5 and that 3 was then subtracted from the quotient, giving the result 2. So, working backward, first add 3 to 2, giving 5. Then multiply that result by 5, giving x = 25.
How to solve the equation?The equation for this problem is described as follows:
x/5 - 3 = 2.
We must isolate the variable x, hence the first step is adding 3 to 2, as follows:
x/5 = 2 + 3
x/5 = 5.
Then we apply cross multiplication, multiplying the result by 5, as follows:
x = 5(5)
x = 25.
Which is the solution to the equation.
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Your friend secretly chooses a number. She says that when you divide the number by 4, add 6, and then multiply by -3, the result is -27. What number did your friend choose?
Answers
Answer: 12
Step-by-step explanation:
Say that your friends number is x
She says that when you divide the number by 4, add 6, and then multiply by -3, the result is -27, so:
(x/4 + 6) * -3 = -27
We can solve the equation by first dividing by -3 on both sides:
x/4 + 6 = 9
Multiply both sides by 4:
x + 24 = 36
Subtract 24 from both sides:
x = 12
Double checking...
(12/4 + 6) * -3
= (3+6) * -3
= 9 * -3
= -27
Correct :>
So your friend chose the number 12
The path of a volleyball thrown over a net is modeled with the function
A(x) = -0.02x2 + 0.6x + 5, where x is the horizontal distance, in feet, from the
starting point, and A is the altitude of the ball in feet. Write an equation that can be solved to find out how far the ball travels horizontally before it hits the ground. Then find the distance to the nearest foot.
equation:
distance:
Answers
The ball travel horizontally 37 feet before it hits the ground.
What is Distance ?
Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.
we have;
A(x) = -0.02x2 + 0.6x + 5
where
The horizontal distance, x, is given in feet.
The ball's height is indicated by the symbol A ---> in feet.
The fact that
The ball's altitude was zero when it landed on the earth.
so,
For A(x)=0
-0.02x^2 + 6x +5 = 0
'
the quadratic equation to be solved
The equation solving formula for a quadratic equation of the type;
ax^2 + bx + c = 0
this equation is equal to ;
[tex]x = \frac{-b\pm \sqrt{b^{2}- 4ac } }{2a}[/tex]
we have ;
-0.02x^2 + 0.6x +5 = 0
So,
a = -0.02
b = 0.6
c = 5
Subsititue this values in the formula;
[tex]x = \frac{-0.6\pm \sqrt{0.6^{2} -4 *(-0.02)(5) } }{2*(-0.02)}[/tex]
[tex]x = \frac{-0.6\pm \sqrt{0.76 } }{-0.04}[/tex]
[tex]x = \frac{-0.6\pm \ 0.87 }{-0.04}[/tex]
[tex]x = \frac{-0.6\ + \ 0.87 }{-0.04}= -6.75[/tex]
[tex]x = \frac{-0.6\ - \ 0.87 }{-0.04}= 36.75[/tex]
therefore
The ball travel horizontally 37 feet before it hits the ground.
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1
Select all quadrilaterals for which a diagonal is also a
line of symmetry.
(Select all that apply. )
trapezoid
isosceles trapezoid
parallelogram
rhombus
rectangle
square
Answers
Correct answer is parallelogram and rhombus.
A parallelogram is a geometric object with sides that are parallel to one another in two dimensions. It is a form of polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length. A parallelogram has adjacent angles that add up to 180 degrees.
Rhombuses are a particular sort of quadrilateral in Euclidean geometry. It is a unique instance of a parallelogram in which the diagonals meet at a 90-degree angle and all sides are equal. This is a rhombus' fundamental characteristic. A rhombus has a diamond-shaped form. As a result, it is also known as a diamond.
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rectangle, rhombus
got it wrong on my test and was given the correct answers, so here they are.
On a trip to the mall Ziva spent 25% of her budget on shoes. Her total budget was $250. How much did she spend on shoes?
Answers
Answer:
$62.50
Step-by-step explanation:
We multiply 0.25(25% as a decimal) by $250 to get $62.50.
When isabella young received her bank statement, she noticed that her present balance was the same as her previous balance. Her deposits were 1/2 her present balance, her withdrawals were 1/3 her present balance, and her auto payments were 1/4 her present balance. Her direct deposit was 1/10 her present balance. The account had a $9. 29 service charge but no interest. What is isabella present balance?
Answers
According to Isabella transactions, her present balance in bank statement is -$9.45
The term called transaction in math is defined as a finalized agreement between a seller and a buyer for transferring goods, services, or financial assets in exchange for money
Here let us consider that Isabella's present balance be X.
According to the problem statements regarding her deposits, there is withdrawals, auto-payments, direct deposit and service charge are also done on the account.
Then those transaction values are calculated as,
=> (1/2)x - (1/3)x -(1/4)x +(1/10x) -$9.29 = x
Here by finding the LCM of common terms, then we get
=> (1/60)x - $9.29 = x
When we solve it for x, then we get the equation like the following,
=> 59x = -$9.29 × 60
=> 59x = -$557.4
Therefore the value of x is -$9.45.
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A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded. Number of Hours Total Number of Students 0 1 1 3 2 3 3 10 4 9 5 6 6 3 Determine the probability that a student studied for exactly 5 hours. Round to the nearest hundredth. 0.83 0.21 0.17 0.14
Answers
There is a 0.17 percent chance that a student spent 4 hours in class.
What is probability?Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty. Probability is a crucial subject since it teaches all the fundamental ideas of the subject. One is the probability of every event in a sample space.
To determine the probability.
The number of students that has 5 hours is 6
The total number of students are 35.
P(5 hours) = 6/35
P(5 hours) = 0. 17
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. eight times the quotient of 6 and 3
Answers
Answer: 16
Step-by-step explanation:
8 * (6/3)
= 8 * 2
= 16
There is 3/4 of a large cake left over from a party. Pedro eats 1/2 of the cake that was left. How much cake did he eat?
Answers
Pedro ate 3/2 of the cake that was left.
We know that the fraction is used to represent the portion or part of the whole thing.
The fraction has two parts: numerator and denominator.
The top part of fraction is numerator and the bottom part is denominator.
Consider a fraction 1/5.
Here, numerator is 1, denominator is 5
When certain thing is divided into 5 equal parts then each part of is represented by fraction 1/5
In this situation, there is 3/4 of a large cake left over from a party.
Pedro eats 1/2 of the cake that was left.
This means, Pedro eats half of the remaning cake.
We need to find the half of fraction 3/4
We divide fraction 3/4 by 2 in order to find the amount of cake he ate.
[tex]\frac{\frac{3}{4} }{2} \\\\=2\times \frac{3}{4} \\\\=\frac{3}{2}[/tex]
Thus he ate 3/2 of cake.
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An electronic store sells an average of 60 entertainment systems per month at an average of $800 more than the cost price. For every $20 increase in the selling price, the store sells one fewer system. What amount over the cost price will maximize revenue?
Answers
Let x be the cost price of an entertainment system.
The selling price is x+800
The number of systems sold is 60-((x+800-x)/20) = 60-((800)/20) = 60-40 = 20 systems
The revenue is the product of the number of systems sold and the selling price.
R = 20(x+800) = 20x+16000
To maximize the revenue, we need to differentiate the above equation with respect to x and set it to 0 and solve for x.
dR/dx = 20 = 0
20x = 0
x = 0
Therefore, the cost price of an entertainment system is 0 and the store should sell the system at x+800 = 800
This means that the store should sell the system at $800 more than the cost price to maximize the revenue.
Formulate a erie and how a proof by PMI to validate.
Give at leat one example each on the operation of function.
In at leat 50 word; What have you learned in GE4?
Answers
The student has learned that GE4 is an introduction to mathematical proof and problem solving, including basic algebra, functions, sets, and the different approaches to problem solving.
Example of operation of function:
1. f(x) = x^2 + 3x - 2
When x = 3, f(3) = 3^2 + 3(3) - 2 = 14
2. g(x) = x^3 + 3
When x = 4, g(4) = 4^3 + 3 = 67
I have learned that GE4 is an introduction to mathematical proof and problem solving. We have gone through a variety of topics such as basic algebra, functions, and sets. We have also learned about the different approaches to problem solving, such as working backwards, proof by cases, and proof by PMI. I have also been introduced to the basics of logic and proof writing.
This answer explains the proof by PMI for the erie that if n is an odd number, then n^2 is an odd number. Two examples of operations of functions are also given. The student has learned that GE4 is an introduction to mathematical proof and problem solving, including basic algebra, functions, sets, and the different approaches to problem solving.
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How many times as long as a THimble jellyfish is a Lion's Mane jellyfish? Thimble jellyfish = 1 inch, Lion's mane jellyfish = 7 feet
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84 inches times as long as a Thimble jellyfish is a Lion's Mane jellyfish.
Now, According to the question:
"Information available from the question"
A Thimble jellyfish is a Lion's Mane jellyfish.
Thimble jellyfish = 1 inch,
Lion's mane jellyfish = 7 feet
Convert feet into inches.
To calculate a value in feet to the corresponding value in inches, just multiply the quantity in feet by 12 (the conversion factor).
Here is the formula:
Value in inches = value in feet × 12
Formula: multiply the value in feet by the conversion factor '12'.
So, 7 feet = 7 × 12 = 84 inches.
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