Yes, a hole in a function is considered a type of discontinuity. A hole occurs when a point is missing from the graph of a function, which causes the graph to have a break in it.
A discontinuity is a break or jump in the graph of a function. A hole in a function is a type of discontinuity where a point is missing from the graph, causing the graph to have a break in it. This type of discontinuity is usually caused by a function having a denominator that is equal to zero, as this creates an undefined point on the graph. This can also occur when two parts of the function are not connected, causing an open gap in the graph. In both cases, the graph is not continuous and has a discontinuity at the point where the hole is present.
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Yes, the function has a hole in discontinuity.
The term function in math is called as a rule that gives value of a dependent variable that corresponds to specified values of one or more independent variables.
Here we to identify is a hole in a function a discontinuity.
the term discontinuity is defined as is discontinuous at a point if it becomes undefined or the limit at that point does not exist. And whether this point is known as the point of discontinuity.
While we looking the hole on a graph looks like a hollow circle. And which represents the fact that the function approaches the point, here it is not actually defined on that precise value. Where the major reason why this function is not defined at is because is not in the domain of the function.
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Select the correct answer. point r divides in the ratio 1 : 5. if the coordinates of e and f are (4, 8) and (11, 4), respectively, what are the coordinates of r to two decimal places? a. (4.66, 7.62) b. (6, 6.86) c. (5.17, 7.33) d. (9.83, 4.67)
The coordinates of point R are (5.17, 7.33), which is answer choice C.
To find the coordinates of point R, we can use the formula for finding the coordinates of a point that divides a line segment into a given ratio:
R = [(1 - ratio) * A + ratio * B] / (1 + ratio)
In this case, the ratio is 1 : 5, which means that point R divides the line segment EF into a ratio of 1 : 5. The coordinates of points E and F are (4, 8) and (11, 4), respectively. Plugging these values into the formula, we get:
R = [(1 - (1/6)) * (4, 8) + (1/6) * (11, 4)] / (1 + (1/6))
= [(5/6) * (4, 8) + (1/6) * (11, 4)] / (6/6)
= [(20/6, 40/6) + (11/6, 4/6)] / (6/6)
= [(20/6 + 11/6, 40/6 + 4/6)] / (6/6)
= [(31/6, 44/6)] / (6/6)
= [(31/6)/(6/6), (44/6)/(6/6)]
= (31/6, 44/6)
= (5.17, 7.33)
Thus, the coordinates of point R are (5.17, 7.33), which is answer choice C.
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The coordinates of point r to be (5.17, 7.33) which is in option c.
To calculate the coordinates of point r, we must first determine the length of each section of the line segment. To do this, we can use the distance formula. The distance formula is given by d = √( (x2-x1)^2 + (y2-y1)^2 ). Using this formula, we can calculate the length of the line segment connecting points e and f to be 7 units.
We can then use the ratio of 1:5 to calculate the length of each segment. The length of the section starting at e is 1/6 of the total distance (7 units). The length of the section starting at f is 5/6 of the total distance (7 units).
To find the coordinates of point r, we can use the midpoint formula. The midpoint formula is given by (x, y) = ( (x1 + x2)/2, (y1 + y2)/2 ). Using this formula, we can calculate the coordinates of point r to be (5.17, 7.33). Therefore, the correct answer is c. (5.17, 7.33).
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Find the area of the region bounded by the hyperbola 9x2-4y2=36 and the line x=3.
Begin by solving the equation for y.
Sketch only the right half of the hyperbola.
Use symmetry to evaluate the trigonomic integral.
Draw a reference rectangle.
First, we will solve the equation of the hyperbola for y:
9x^2 - 4y^2 = 36
4y^2 = 9x^2 - 36
y^2 = (9/4)x^2 - 9
y = ±√((9/4)x^2 - 9)
In math, what is a parabola?
Any point on a parabola is at an equal distance from both the focus, a fixed point, and the directrix, a fixed straight line. A parabola is a U-shaped plane curve.
We only need to consider the right half of the hyperbola because of the symmetry,
the line x=3 is the vertical asymptote of the hyperbola, so we need to find the y-coordinates of the hyperbola when x=3
y = ±√((9/4)3^2 - 9)
y = ±√(9/49 - 9)
y = ±√(27 - 9)
y = ±√18
The area of the region is given by the definite integral of y with respect to x between the limits of x = 3 and x = infinity.
∫y dx = ∫√18 dx = 3/2 * √18 * x^(3/2) from 3 to infinity
The area of the region is infinite as the integral is evaluated from x = 3 to infinity.
It's important to note that the method of evaluating the definite integral is not valid in this case as the integral is of an improper kind and it does not converge to a finite value.
It's impossible to draw a reference rectangle for this problem as the area of the region is infinite.
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What does PQ = and m < C = how many degrees?
The side length of PQ = 5.6 unit and angle C = arc sin [sin A (0.70)]
What is sine rule for triangle?
The mathematical law that shows the relationship between the size of an angle and opposite side length of a triangle is called sine rule. It is an equation that express the ratio of the side length of a triangle to the sine of the opposite angle.
The laws can be shown as
a/ sin A = b /sin B = c /sin C
How to calculate the unknown angle and unknown side length in the given problem?Given, triangle ABC ≈ triangle PQR
for the triangle PQR, PR = 8
angle Q = 63 degrees
angle R = 38.5 degrees
we need to determine the length PQ
as per the sine rule for triangle PQR
PQ/ sin R = PR / sin Q
PQ = PR × sin R / sin Q
PQ = (8 × sin 38.5) / sin 63
PQ = 5.59
PQ = 5.6 unit
As triangle ABC ≈ triangle PQR
AB/PQ = BC/PR = AC / QR
and sin A / sin Q = sin B/ sin P = sin C /sin R
sin C = (sin A / sin Q) × sin R
sin C = sin A (0.70)
C = arc sin [sin A (0.70]
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What does it mean when an observational study is retrospective' When does it mean when an observational study is prospective? What does it moan when an observational study is retrospective? A retrospective study requires that individuals look back in three or require the researcher to look at existing records A retrospective study collects the data over time A retrospective study is a list of all individuals in a population along with certain characteristics of each individuals What does it mean when an observational study is prospective? A prospective study requires that individuals took hack in time or require the researcher to look at existing records A prospective study collects the data over time. A prospective study is a list of all individuals in a population along with certain characteristics of each individual.
A. Prospective observational studies involve collecting data from participants before an event or outcome occurs, while retrospective observational studies collect data after the event has already taken place.
A prospective observational study is a type of observational study that involves collecting data from participants before an event or outcome occurs. This type of study is used to predict and measure outcomes in the future.
In this type of study, the researcher can control the variables, such as when and how the data is collected, and can also observe the effects of any changes in the environment.
On the other hand, a retrospective observational study is a type of observational study that involves collecting data after an event or outcome has already taken place. This type of study is used to study the causes of a given outcome.
In this type of study, the researcher looks back in time and collects data from the past. This type of study is more limited than a prospective observational study, since the researcher cannot control the variables of the study or observe any changes in the environment.
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Pls help due tomorrow!!!
All the possible values of each expression is given as an inequality as;
0 < a - b < 4
How to solve Linear Inequalities?We are given the inequalities of the domain and range as;
2 < a < 5
1 < b < 2
Thus, we can say that the maximum value of a - b will be the difference between the maximum value of a and the minimum value of b to give;
(a - b)max = 5 - 1
(a - b)max = 4
Similarly, minimum value of a - b will be the difference between the maximum value of b and the minimum value of a to give;
(a - b)min = 2 - 2
(a - b)min = 0
Thus, all possible values would be expressed as;
0 < a - b < 4
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A line that includes the points (-10, W) and (10, 6) has a slope of I. What is the value of w?
Can someone please help me?
Thank you!
Step-by-step explanation:
(6 - W)/(10+10)= (6 - W)/20= 2
6 - W= 40
-W= 34
W= -34
Answer:
line can be described by the equation y = mx + b, where m is the slope of the line and b is the y-intercept, which is the point where the line crosses the y-axis.
Since we are given that the line has a slope of 1 and includes the point (10, 10), we can plug these values into the equation to solve for the y-intercept. We get:
10 = 1 * 10 + b
b = 10 - 10
b = 0
So the equation of the line is y = x + 0, or simply y = x.
Since we are also given that the line includes the point (u, 9), we can substitute this value for y in the equation of the line to solve for u. We get:
9 = x
x = 9
Therefore, the value of u is 9.
Uday Tahlan
line that includes the points (-10, W) and (10, 6) has a slope of I. What is the value of w?
Can someone please help me?
Thank you!
To find the value of W, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
Since we are given that the line includes the points (-10, W) and (10, 6) and has a slope of I, we can use these two points to find the value of W.
First, we can plug in the coordinates of one of the points and the value of the slope into the equation to solve for the y-intercept. Let's use the point (10, 6):
6 = I * 10 + b
b = 6 - 10I
Then, we can plug the values of the slope and y-intercept into the equation and solve for W using the coordinates of the other point (-10, W):
W = I * (-10) + (6 - 10I)
= -10I + 6 - 10I
= 6 - 20I
Therefore, the value of W is 6 - 20I.
The teacher gave a true and false quiz where P(true) = 0.8 for each question. Interpret the likelihood that the first question will be true.
Likely
Unlikely
Equally likely and unlikely
This value is not possible to represent probability of a chance event.
The interpretation that the likelihood that the first question will be true is (a) Likely
How to interpret the likelihood that the first question will be true.From the question, we have the following parameters that can be used in our computation:
Probability value
The value of the probability and the notation is given as
P(true) = 0.8
As a general rule of probability, we have
Range of probability value = 0 to 1 (inclusive)Unlikely = less than 0.5Equally likely and unlikely = 0.5Likely = greater than 0.5Using the above as a guide, we have the following:
The value of P(true) = 0.8 is greater than 0.5
This that the probability is likely
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Answer: A its that easy
Step-by-step explanation:
What is SSS congruence rules?
SSS congruence rules states that if three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.
The SSS (Side-Side-Side) congruence rule states that if three sides of one triangle are equal to the three sides of another triangle, equal, and the two triangles share the same dimensions then the two triangles are congruent. This means that all of the angles and sides of the two triangles are In order for two triangles to be congruent according to the SSS congruence rule, the lengths of the three corresponding sides of the two triangles must be equal. If all three of these conditions are met, then the two triangles are congruent and can be used to solve a variety of geometric problems.
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The SSS congruence rule is rule that is used to prove two triangles congruent . Its full form is Side-Side-Side Congruence .
The Two Triangles can be called as Congruent Triangles if their sides have same length and the angles also have the same measure.
One of the 4 rules in proving the triangles congruent is SSS .
The SSS Congruence Rules also called as (Side-Side-Side) Rule means that if all the three sides of one triangle are equal to the corresponding three sides in the other triangle ,
then we can say that the two triangles are congruent by SSS (Side-Side-Side) Rule .
Therefore , The SSS Congruence rule means Side-Side-Side Congruence .
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Find the value of x
The value of {x} in the given geometrical figure is 7.
What are angles?In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.When two or more lines cross each other in a plane, they are called intersecting lines. The intersecting lines share a common point, which exists on all the intersecting lines, and is called the point of intersection.Given is a pair of intersected lines.
We can write, as observed from the image that -
6x + 3 = 45 {Vertically opposite angles}
6x = 42
x = 7
Therefore, the value of {x} in the given geometrical figure is 7.
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please help and answer the question 2/3x=-1
Answer:
[tex]x=-\frac{3}{2}\\[/tex]
Step-by-step explanation:
We must isolate x in this equation. To do that, we can multiply both sides by [tex]\frac{3}{2}[/tex].
[tex](\frac{3}{2})(\frac{2}{3})x=-1(\frac{3}{2})[/tex]
[tex]x=-\frac{3}{2}[/tex]
−5.55− 8.55c+ 4.35c Combine like terms to simplify
The simplification of the expression −5.55− 8.55c+ 4.35c by combining the like terms is - 5.55 - 4.20c.
What are like terms?Like terms can be defined as terms which has the same variable and power.
For instance,
4a + 5a²
They are not like terms, though they have the same variable a but different power of 1 and 2 respectively.
So,
−5.55− 8.55c+ 4.35c
The like terms are - 8.55c and + 4.35c
−5.55− 8.55c+ 4.35c
= - 5.55 - 4.20c
Consequently, - 5.55 - 4.20c is the simplification of −5.55− 8.55c+ 4.35c.
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x/3 < -9 solve the inequality
Answer:
X/3 < -9
(x/3) 3 < -9(3)
x < -27
Step-by-step explanation:
Daren can run 8.55 kilometers in one hour. Umberto can run 9.5 kilometers in one hour. If Daren plans to run for 3.5 hours and Umberto plans to run for 3 hours who will run more kilometers assuming their running pace stays the same for the entire time? How do you know?
Answer: Daren
Step-by-step explanation:
The rate for Daren is 8.55 kph, while Umberto is 9.5 kph.
Find the total miles for Daren and Umberto:
8,55 x 3,5 = 29,925
9,5 x 3 = 28,5
Daren will run more kilometers than Umberto because the distance running is more than Umberto's.
Who is right, and why?
Neither Kurt nor Maria is right, because 3,500 should be used instead of 3,600.
Kurt is right, because finding One-fifth of 3,600 is not a good way to approximate 21% of 3,585.
Maria is right, because finding 10% of 3,600 and multiplying the result by 2 is not a good way to approximate 21% of 3,585.
Both Kurt and Maria are right, because 3,585 should be rounded up to 3,600, and 21% of this amount can be approximated by either finding 10% of 3,600 and multiplying the result by 2 or by finding One-fifth of 3,600.
The correct statement regarding the proportion is given as follows:
Both Kurt and Maria are right, because 3,585 should be rounded up to 3,600, and 21% of this amount can be approximated by either finding 10% of 3,600 and multiplying the result by 2 or by finding One-fifth of 3,600.
How to obtain the correct proportion?A proportion is a fraction of a total amount.
The total amount is of 3585, and 21% of the goal has been reached, hence the amount reached is obtained as follows:
0.21 x 3585 = $752.85.
Both Kurt or Maria took different routes, rounding the amount to 3600, and then obtaining 20% of it, which is equivalent to one-fifth. 20% can also be obtained as twice of 10%, hence both are correct, and the fourth statement is correct.
Missing InformationThe missing text is given as follows:
Kurt and Maria’s high school is having a newspaper drive.The goal is to collect 3,585 pounds of newspapers. So far, 21% of the goal has been reached.
Kurt estimated the number of pounds of newspapers collected by finding 10% of 3,600 and then multiplying the result by 2.
Maria estimated the number of pounds of newspapers collected by finding One-fifth of 3,600.
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Examine the equation and the table, each of which represent a different linear function. Function A: y=3x−6 Function B: Input (x) Output (y) 3 3 6 13 9 23 12 33 Which statement is true about the two functions? Responses Function B has a greater rate of change. Function B has a greater rate of change. - no response given Function B has a greater output when the input is 3. Function B has a greater output when the input is Function A has a greater rate of change. Function A has a greater rate of change. Function A has a greater output when the input is 6.
The statement which is true about the two functions include the following: A. Function B has a greater rate of change.
What is the rate of change?In Mathematics, the rate of change is sometimes referred to as slope or gradient and it can be calculated by using this formula;
Rate of change, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Rate of change, m = (y₂ - y₁)/(x₂ - x₁)
Next, we would determine the rate of change of the value of y with respect to the value of x in function B, which represents a line that is passing through the data points (3, 3) and (6, 13):
Rate of change, m = (13 - 3)/(6 - 3)
Rate of change, m = 10/3 or 3.33.
From function A (y = 3x - 6), we can logically deduce that the rate of change is equal to 3.
In conclusion, we can logically deduce that the rate of change of function B (m = 3.33) is greater than the rate of change of function A (m = 3).
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20 pionts
The graph shows three lines y1 = x + 3, y2 = 2x + 3, and y3 = 4x + 3. What does increasing the value of the coefficient in front of x do to the line?
Responses
A It makes the line become shallower.It makes the line become shallower.
B It makes the line change from increasing to decreasing.It makes the line change from increasing to decreasing.
C It makes the line become steeper.It makes the line become steeper.
D It moves the line down on the coordinate plane.It moves the line down on the coordinate plane.
E It moves the line up on the coordinate plane.
Answer:
C
Step-by-step explanation:
C It makes the line become steeper. When the coefficient in front of x is increased, the slope of the line becomes larger, so the line becomes steeper. The other responses are not correct.
George is planning a dinner party for three other couples, his wife, and himself. He plans to seat the four couples around a circular table for 8, and wants each husband to be seated opposite his wife. How many seating arrangements can he make, if rotations and reflections of each seating arrangement are not considered different
Seating arrangements that can be made, if rotations and reflections of each seating arrangement are not considered different is 24.
The combination is defined as “An arrangement of objects where the order in which the objects are selected does not matter.” The combination means “Selection of things”, where the order of things has no importance.
Total number of couples = 3
No. of seating in Circular table = 8
Total number of ways they can be seated =3*8 = 24
Thus, Seating arrangements that can be made, if rotations and reflections of each seating arrangement are not considered different is 24.
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The number of possible arrangements he can make = 24
Assume that George and his wife seated opposite to each other.
Then there would be six open seats for three other couples.
The first woman of them can be seated in six ways.
Using combination formula, we can write it as
6C1 = 6
And her husband sits opposite to her.
Now the next woman can be seated in six ways.
Using combination formula, we can write this as
4C1 = 4
And her husband sits opposite to her.
Now the last woman can be take any seat from the remaning 2 seats and her husband sits opposite to her.
Since rotations and reflections of each seating arrangement are not considered different, there are 6 × 4 = 24 possible seating arrangements.
Therefore, there would be 24 possible seating arrangements.
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80 pts PLEASE HELP ME ASAP!!!
- Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station. The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.
(1, 3), (2, 6), (3, 12), (4, 24)
Part A: Is this data modeling a linear function or an exponential function? Explain your answer.
Part B: Write a function to represent the data. Show your work.
Part C: Determine the average rate of change between station 2 and station 4. Show your work.
a) The data modeling in this problem is an exponential function.
b) The function is defined as follows: y = 1.5(2)^x.
c) The rate of change from x = 2 to x = 4 is of 4.
What is an exponential function?The general format for an exponential function is presented as follows:
y = a(b)^x.
For which the parameters are given as follows:
a is the value assumed by the exponential function when x = 0.b is the rate of change of the exponential function when x increases by one.From the data, when x increases by one, the output y is multiplied by two, hence the rate of change is given as follows:
b = 2.
Hence, when x increases by two, as is the case from x = 2 to x = 4, the rate of change is given as follows:
b² = 2² = 4.
When x = 1, y = 3, hence, applying the recursion of the rate of change, the parameter a is given as follows:
a = 3/2 = 1.5.
Meaning that the function is defined as follows:
y = 1.5(2)^x.
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42. How many lines of symmetry does the figure have? (1 point)
04
3
02
01
Answer:
yES, THIS IS CORRECT THE ANSWER IS 2
Step-by-step explanation:
F(x)=2+3x²; find f(3)
Answer:
29
Step-by-step explanation:
[tex]f(3)[/tex] represents the value of [tex]f(x)[/tex] when [tex]x=3[/tex].
[tex]f(3)=2+3(3)^2=29[/tex]
a carpenter has an AB wooden plank lengthening 252cm. He divides it into four parts by inserting the points C, D and E in such a way that: CD=3*AC, DE=2*CD, EB=4*AC. Calculate the measure of each of the four parts of the axis
The value of each part is AC = 18 cm, CD = 54 cm, DE = 108 cm, and
EB = 72 cm.
What are Mathematical operators?A collection of numbers and operations is an expression in mathematics. The following are the parts of a math expression that do a math operation:
Operands: Operands are the numbers that an operation uses. The terms that are given to the operands vary according to the kind of operation.
Operator: An operator is the symbol that denotes a math operation, such as: division, addition, subtraction, and multiplication.
Given length of wooden plank AB is 252 cm
divides it into four parts by inserting the points C, D and E
parts of plank are AC, CD, DE, EB
CD = 3AC,
DE = 2CD, and DE = 2(3AC) = 6AC
EB = 4AC
AB = AC + CD + DE + EB
substitute the values,
AB = AC + 3AC + 6AC + 4AC
252 = 14AC
AC = 252/14 = 18cm
CD = 3AC = 3(18) = 54 cm
DE = 6AC = 6(18) = 108 cm
EB = 4AC = 4(18) = 72 cm
Hence length of each part is AC = 18 cm, CD = 54 cm, DE = 108 cm, and
EB = 72 cm.
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A Small Publishing Company is planning to publish a new look. The Production Costs will include one-time fixed cost (such as edition) andVariable Casts (such as Printing). The One-time fixed Costs will total $10,300. The Vouciable Casts will be $12 per book. The Publisher Will Sell the finished froduct to bookstores at a price of $118.25 per bookHow Many books must the Publisher Produce and sell So that the producation Costs will equal the money from Sales?
Using the provided values and making an equivalent equation and equating the equation to solve for the number of books required to break even, The answer is 97 books should be produced and sold.
What do you mean by equations?An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A collection of one or more linear equations containing the same variables is known as a system of linear equations in mathematics. A set of two or more linear equations with two or more variables each constitutes a system of linear equations, all of which are taken into account simultaneously. Finding a numerical value for each variable in the system that will simultaneously satisfy all of the system's equations is necessary to identify the one and only solution to a system of linear equations.
What are the methods to solve system of equations?There are three ways to solve systems of linear equations :
GraphingSubstitution methodElimination methodrequired equation,
10300 + 12x = 118.25x
solving for x , we get,
106.25x = 10300
x=10300/106.25
=97
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Why is it called tangent function?
The tangent function is a trigonometric function used to calculate angles and the relationships between them.
This function is also known as the “slope of a curve” and measures the rate of change of the angle with respect to the x-axis. In its most basic form, the tangent function is expressed as tanθ, which is interpreted as the ratio between the length of the opposite side of angle θ and the length of the adjacent side. The graph of the tangent function is a periodic curve with a range of [-π/2,π/2]. It has many uses in mathematics and physics, such as the calculation of derivatives, integration, and interpolation.
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Which property will need to be used to solve the equation below? -5x = 15
The property that will be used to solve the equation given, is the Division Property of Equality.
What is the Division Property of Equality?According to the division property of equality, the quotients of an equation remain equal when both sides are divided by a common real integer that is not equal to 0.
An example is:
6 / 3 = 6 / 3
2 = 2
This means that to find the value of x in -5x = 15, the Division Property of Equality, allows us to divide both sides by - 5:
- 5 x / - 5 = 15 / - 5
x = - 3
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If f(x)=x^2 sin(2x), then dy/dx = ?
T Raiderlink Bb Blackboard SPC Blackboard TTU -/1 Points] DETAILS HARMATHAP12 9.4.011. Find the derivative of the function. w = 2? - 326 + 14 w= 1-/1 Points) DETAILS HARMATHAP12 9.4.014.MI. Find the derivative of the function. +(x) = 16x12 + 6x6 - 2x + 19x - 7 h'(x) = [-/1 Points] DETAILS HARMATHAP12 9.5.002.MI. Find the derivative and simplify. y = (8x + 5)(x2 – 3x).
The derivative of the function is
A) dw/dz=z^5 (7z-18)
B) dh/dx=192x^11+36x^5-6x^2+19
C) dy/dx=24x^2-38x-15
In mathematics, the derivative of a function measures the sensitivity to change of the function value with respect to a change in its argument. It is the rate of change of a function with respect to a variable.
A) w = z^7 – 3z^6 + 14
dw/dz=7z^6-18z^5
dw/dz=z^5 (7z-18)
B) h(x) = 16x^12 + 6x^6 – 2x^3 + 19x – 7
dh/dx=192x^11+36x^5-6x^2+19
C) y = (8x + 5)(x^2 – 3x)
dy/dx= d/dx [8x+5]*〖(x〗^2-3x)+(8x+5)*d/dx[x^2-3x]
dy/dx=(8* d/dx [x}+d/dx[5])*〖(x〗^2-3x)+(8x+5)*(d/dx[x^2]-3 d/dx[x])
dy/dx=(8*1+0)(x^2-3x)+(8x+5)(2x-3*1)
dy/dx=8(x^2-3x)+(2x-3)(8x+5)
dy/dx=24x^2-38x-15
Note: The question is incomplete. The complete question probably is: Find the derivative of the following function: A) w = z^7 – 3z^6 + 14 B) h(x) = 16x^12 + 6x^6 – 2x^3 + 19x – 7 C) y = (8x + 5)(x^2 – 3x).
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Evaluate the integral by interpreting it in terms of area. hint: sketch the region indicated by the integrand and limits of integration. You may also want to consider the fact that the integral of a sum is the sum of the integrals provided they exist.
To evaluate an integral by interpreting it in terms of area, one should first sketch the region indicated by the integrand and limits of integration. Once the region is visualized, the integral can be thought of as the total area under the curve of the integrand within the given limits. If the integrand is a sum, the integral is the sum of the areas under each individual curve, provided they exist.
EVALUATE AN INTEGRALTo evaluating an integral by interpreting it in terms of area is a powerful technique that allows you to visualize the problem and understand the meaning of the integral. By sketching the region indicated by the integrand and limits of integration, you can gain a better understanding of what the integral represents. The integrand is the function whose area is being calculated, and the limits of integration are the boundaries of the region over which the integral is being taken. The integral can be thought of as the total area under the curve of the integrand within the given limits.
For example, consider the definite integral of a function f(x) between the limits of a and b. This integral represents the area between the curve of the function f(x) and the x-axis, between the values of x = a and x = b. By sketching this region, you can visualize the area being calculated and understand the meaning of the integral. It's also important to note that when the integrand is a sum, the integral is the sum of the areas under each individual curve, provided they exist. This allows you to break down a complex function into simpler parts and evaluate them separately.
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Dregg guessed the answers to three multiple-choice questions on a test. If each questions had 5 different choices, how many different answer combinations were there?
There were 10 different combinations to the multiple choice questions.
What is Combination?Combination is defined as “An arrangement of objects where the order in which the objects are selected does not matter.” The combination means “Selection of things”, where the order of things has no importance.
It is a way of selecting items from a collection where the order of selection does not matter. Suppose we have a set of three numbers P, Q and R. Then in how many ways we can select two numbers from each set, is defined by combination.
[tex]C_{n,r} = \frac{n!}{(n-r)! r!}[/tex]
where n = 5
r = 3
[tex]C_{5,3} = \frac{5!}{(5-3)!3!} \\= \frac{5!}{2!3!}[/tex]
= [tex]\frac{5(4)(3!)}{2!3!}[/tex]
= 20/2
= 10 ways
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A designer wants to
place a fountain at the intersection of the
shortest paths from each side to the opposite
vertex. What mistake is made on her model?
At what point of concurrency should the
fountain be located?
The shortest path from a vertex to the opposite side is an altitude, but the designer used a median. The foundation should be located at the orthocentre.
What is the mistake and the point of concurrency?In order to obtain the shortest side, they actually want the shortest pathways from each side to the opposing vertex, as seen in the triangle below, which shows the medians drawn from each angle to the middle of the opposite side.
In its place, you would draw a straight line the shortest distance from the vertex to the opposite side, add a perpendicular, and then do the same thing here, draw a straight line out of a perpendicular, and then pulled down it, a perpendicular; this center, where they all come together, is referred to as the ortho center. In order to respond to the query, I will say that the point of concurrency would be the shortest route from the vertex to the opposite. Go precisely across to the side.
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10.
An athlete wants to run 52.6 miles in 1 week. She runs 8.5 miles on Sunday. If she runs the same distance on each
of the 6 remaining days, how many miles will she need to run each day?
Answer:
7.35 miles
Step-by-step explanation:
DivisionExample: [tex]\frac{66}{6} = 11[/tex]
SolutionGiven 1 week = 7 days.
Given the athlete has ran 8.5 miles on Sunday, the remaining distance to run is:
[tex]52.6-8.5\\=44.1 miles[/tex]
Distance to run each day for the remaining 6 days is:
[tex]\frac{44.1}{6} \\=7.35 miles[/tex]