A function increases if the output value of function increases on increasing the input value and the function decreses if the output value of function decreases on increasing the input value
As we know a function is nothing but a relation between input values and output values where each input has exactly one output.
Consider a function y = f(x)
For a given function if the value of y increases on increasing the value of x, then the function is an increasing function
If the y-value decreases on increasing the value of x, then the function is a decreasing function.
Another method is that if we need to determine whether a function f(x) is increasing or decreasing at point 'a'.
If a function is differentiable on an open interval, we calculate the derivative of function f(x)
If the derivative f′(x) > 0 on an open interval, then function f(x) is increasing on that interval.
If the derivative f′(x) < 0 on an open interval, then function f(x) is decreasing on that interval.
Therefore, if the output value of function increases on increasing the input value then the function is an increasing function and if the output value of function decreases on increasing the input value then the function is an decreasing function.
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what percent is 35 out of 45
Answer: The correct answer is 77.77 %
Step-by-step explanation: To calculate the percentage, number or ratio that can be expressed as a fraction of 100.
find the length of the arc of the curve from point p to point q. x2 = (y − 4)3, p(1, 5), q(8, 8)
The length of the arc of the curve from point p to point q of the equation x2 = (y − 4)3 as calculated is 8 units.
as to calculated the length of the arc we will differentiate the given equation x² = (y-4)³ with respect to y
=> 2x = 3( y - 4 )²
=> 2x = 3( y² -8y + 16)
=> 2x = 3 y² - 24y + 48
=> 3 y² - 24y + 48 - 2x = 0
now , x = 5 - 1 = 4
y = 8 - 1 =7
Therefore, length = 3 x 8² - 24 x 8 + 48 - 2x 4 = 0
=192 - 192 - 8 = -8
On taking modulus we get the length as 8 units.
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What is the arithmetic mean of the following numbers 3 5 6 7 9 6 8?
The mean for a given set of observations is 6.286.
What is mean?The mean is the average of a set of variables in mathematics and statistics. The mean may be calculated in a variety of methods, including the simple arithmetic mean (add the numbers and divide the total by the number of observations), geometric mean, and harmonic mean. A data set's mean (average) is calculated by summing all of the numbers in the set and then dividing by the number of values in the set. When a data collection is arranged from least to largest, the median is the midway value. The mode is the number that appears the most frequently in a data collection.
Here,
given set of observation,
=3,5,6,7,9,6,8
=(3+5+6+7+9+6+8)/7
=6.286
The mean for given set of observation is 6.286.
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8. Given f(x)= a(x-h)² + k is the vertex form of a parabola.
If a < 0, h> 0 and k < 0, then which of the following are true?
I. The vertex of f(x) Is In quadrant 2
II. The vertex of f(x) is in quadrant 4
III. f(x) has no x-intercepts
IV. f(x) has no y-intercepts
A. I and IV
B. II and IV
C. I and III
D. II and III
For the given statement f(x)= a(x-h)² + k is the vertex form of a parabola.
If a < 0, h> 0 and k < 0 Option B is correct.
Vertex of a Parabola
The vertex of a parabola is the point where the parabola crosses its axis of symmetry. If the coefficient of the x2 term is positive, the vertex will be the lowest point on the graph, the point at the bottom of the “ U ”-shape. If the coefficient of the x2 term is negative, the vertex will be the highest point on the graph, the point at the top of the “ U ”-shape.Given that:
f(x)= a(x-h)² + k
If a < 0, h> 0 and k < 0 then
f(x) = -1 (x - 1)^2 - 1
= -1([tex]x^{2} + 1^{2} - 2x[/tex]) - 1
= [tex]-x^{2} -1 + 2x[/tex] - 1
f(x) = -([tex]x^{2} - 2x + 2[/tex])
while making graph using the equation , we can find the vertex of f(x) is in quadrant 4 and has no y-intercepts.
Thus , the option B is correct.
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How do you solve a system of three equations in two variables?
Pick any two pairs of equations from the system. Eliminate the same variable from each pair using the Addition/Subtraction method. Solve the system of the two new equations using the Addition/Subtraction method. Substitute the solution back into one of the original equations and solve for the third variable.
In order to solve systems of equations in three variables, known as three-by-three systems, the primary goal is to eliminate one variable at a time to achieve back-substitution. A solution to a system of three equations in three variables (x,y,z) is called an ordered triple.
To find a solution, we can perform the following operations:
Interchange the order of any two equations.Multiply both sides of an equation by a nonzero constant.Add a nonzero multiple of one equation to another equation.Graphically, the ordered triple defines the point that is the intersection of three planes in space. You can visualize such an intersection by imagining any corner in a rectangular room. A corner is defined by three planes: two adjoining walls and the floor (or ceiling). Any point where two walls and the floor meet represents the intersection of three planes.
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How many cells in Excel 2022?
Number of Rows per Worksheet: 1,048,576. Number of Rows per Worksheet: 16,384. Total cells per Worksheet: 17,179,869,184.
Now, According to the question:
The specifications for Excel Worksheet current versions include: Number of Rows per Worksheet: 1,048,576. Number of Rows per Worksheet: 16,384. Total cells per Worksheet: 17,179,869,184.
How many sheets can Excel have?
Set default number of worksheets
It means you can set the number of how many worksheets initially be in a workbook. Inside the General options, you will find an option "Include this many sheets". You can change it to between 1 to 255. Step 1: First of all, open MS Excel and create a new workbook.
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An Olympic-sized pool, which holds 660,000 gallons of water,
is only 63% full. The pool maintenance company adds more
water, filling the pool to 90% full. How many gallons of water
did they add?
P
7.AR 3.1
a
244 200
178 200
B) 594 000
415.800
134
The amount of water added by the pool maintenance to make the pool 90% full is 178,200 gallons.
How much water, in gallons, did they add?The amount of water an Olympic-sized pool can hold is, 660,000 gallons.
The pool is 63% full at the moment
The of water in the pool now is:66% of 660,000 gallons
If the pool is 90% full then the amount of water in the pool is:
90% of 660,000 = 594,000 gallons
The amount of water added by the pool maintenance is:
Amount of water added = 90% of 660,000 - 63% of 660,000
594,000 - 415,800
= 178200
Thus, the amount of water added by the pool maintenance to make the pool 90% full is 178,200 gallons.
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The intersection of Beech Street and fourth Street is 150 yards east of the intersection of Fort Street and Clover Street how many yards south is it
The amount of yards south that the intersection of Fort Street and Clover Street is given as follows:
450 yards.
How to obtain the slope?The slope of an inclined object is obtained as the division of the vertical distance of the street by the horizontal distance of the object.
The distances are classified as follows:
Vertical: south is negative, north is positive.Horizontal: west is negative, east is positive.The slope of the street is given as follows:
-3.
The east distance is given as follows:
150 yards.
Thus the south distance can be identified applying the slope as follows:
-3 = S/150
S = -3 x 150
S = -450 yards.
The negative number represents that the direction is south, hence the distance is only of 450 yards.
Missing InformationThe problem is given by the image shown at the end of the answer.
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How do you find the base of a triangle with only the height?
The hypotenuse and the known leg are squared. Subtract the squared length of the hypotenuse from the squared length of the leg. Finally, compute the result's square root.
What is triangle?A triangle is a polygon having three vertices and three edges. It is a fundamental geometric figure. Triangle ABC represents a triangle with three vertices: A, B, and C. Any three non-collinear points constitute a unique triangle and, by extension, a unique plane in Euclidean geometry. Triangles are polygons with three vertices that have three sides. The triangle's angles are constructed by joining the three sides end to end at a point. The triangle's three angles add up to 180 degrees.
Here,
Square the hypotenuse and the known leg. Subtract the squared length of the leg from the squared length of the hypotenuse. Finally, compute the square root of the result.
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How to calculate the variance in R?
According to the distribution , The general formula for the variance varies, For the discrete and continuous probability distribution, The expected values formula varies. The variance is given by [tex]E(X^2)-(E(X))^2[/tex] .
What do you mean by random variable?The mathematical formalization of a number or object that is subject to chance events is known as a random variable. It is a function or mapping between a space of potential outcomes, commonly real numbers, to a space of measurement.
What is standard deviation?The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
If distribution is discrete , E(X) = x*P(x).
If distribution is continuous , E(x) = x *f(x).
Variance = [tex]E(X^2)-(E(X))^2[/tex]
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A line has a slope of. If one of the points on the
line is (-10, -16), which of the following could be
another point on the line? Show work.
a) (-5, -6) b) (4, 11) c) (0, 2)
d) (10, 22)
Which pair could be used
Another point on the line is (0,2).
The equation of a line, in point-slope form, is given by:
[tex]$$y-y_0=m\left(x-x_0\right)$$[/tex]
In which [tex]$\mathrm{m}$[/tex]is the slope and the point is [tex]$\left(x_0, y_0\right)$[/tex]
Slope of [tex]$9 / 5$[/tex] if one of the points on the line is [tex]$(-10,-16)$[/tex]
This means that [tex]$m=\frac{9}{5},\left(x_0, y_0\right)=(-10,-16)$[/tex]. So
[tex]$$\begin{aligned}& y-y_0=m\left(x-x_0\right) \\& y-(-16)=\frac{9}{5}(x-(-10)) \\& y+16=\frac{9}{5}(x+10)\end{aligned}$$[/tex]
Which of the following could be another point on the line?
We have to find a point for values of [tex]$x$[/tex] and [tex]$y$[/tex] which gives us an identity. So
x=-5, y=-6
Lets see
[tex]$$\begin{aligned}& -6+16=\frac{9}{5}(-5+10) \\& 10=\frac{9 * 5}{5} \\& 10=9 > \text { False }\end{aligned}$$[/tex]
So this is not the answer.
[tex]$$\begin{aligned}& x=4, y=11 \\& 11+16=\frac{9}{5}(4+10) \\& 27=9 * 14 / 5\end{aligned}$$[/tex]
False
Option C:
[tex]$$\begin{aligned}& \mathrm{x}=0, \mathrm{y}=2 \\& 2+16=\frac{9}{5}(x+10) \\& \frac{90}{5}=18 \\& 18=18\end{aligned}$$[/tex]
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isabella is making a huge flag of her country, the republic of seychelles, on a canvas 202020 by 101010 meters long. to do that, she has to draw a diagonal line that begins at the bottom-left corner and ends at the top side of the flag, 6.66.66, point, 6 meters to the right. since the ends of the diagonal line are too far to put a ruler between them, isabella wanted to find the angle of the diagonal and draw it using a protractor. what is the angle, in degrees, between the diagonal line and the left edge of the flag? round your final answer to the nearest tenth.
The angle, in degrees, between the diagonal line and the left edge of the flag is 67.8 degrees.
To find the angle between the diagonal line and the left edge of the flag, you can use the Pythagorean theorem to calculate the length of the hypotenuse (the diagonal line) and one of the legs (the horizontal distance from the bottom-left corner to the end of the diagonal line). The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
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does anyone know this?!?
The answers for the given proof of a parallelogram are explained below:
What is a parallelogram?A parallelogram is a straightforward (non-self-intersecting) quadrilateral in Euclidean geometry that has two sets of parallel sides. In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size. The Euclidean parallel postulate, or one of its equivalent formulations, is a necessary precondition for both the congruence of opposite sides and opposite angles, and neither condition can be demonstrated without using it. In contrast, a quadrilateral with just one set of parallel sides is referred to as a trapezoid or trapezium in British or American English. A parallelepiped is the parallelogram's three-dimensional counterpart.
1) CPCTC(corresponding parts of congruent triangles are congruent)
2) Reflexive property
3) Corresponding angles theorem converse(If corresponding angles are equal then the lines are parallel)
4) Alternative angles theorem converse(If alternative angles are congruent then the lines are parallel)
5) SSS
6) Given.
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Did 8 is a prime number?
A whole number higher than one that cannot be divided exactly by any other whole number than itself and one is a prime number, 8 is divisible by 2 and 4 other than itself and 1, so 8 is not a prime number.
What is a prime number?A whole number higher than one that cannot be divided exactly by any other whole number than itself and one is a prime number.
what is whole number?Complete numbers the range of numbers that includes zero and natural numbers. not a decimal or fraction.
factor of 8 = 2x2x2,
since 8 is divided by 2, so it is not a prime number.
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How do you find discontinuity?
There are a few ways to find discontinuities in a function. One way is to look for places where the function is not defined or where it produces an undefined result, such as division by zero. Another way is to look for places where the function exhibits a sudden change in behavior, such as a jump or a sharp turn.
To find discontinuities more formally, you can use mathematical techniques such as limits or derivatives. If you are familiar with these concepts, you can use them to identify discontinuities in a function.
For example, if you are trying to find the discontinuities of a function f(x), you can consider the limit of the function as x approaches a certain value, say x=c. If the limit of the function as x approaches c from both the left and the right is different, then there is a discontinuity at x=c. Similarly, if the derivative of the function is not defined at a certain value of x, then there is a discontinuity at that point.
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if you are trying to find the discontinuities of a function f(x), you can consider the limit of the function as x approaches a certain value, say x=c. If the limit of the function as x approaches c from both the left and the right is different, then there is a discontinuity at x=c. Similarly, if the derivative of the function is not defined at a certain value of x, then there is a discontinuity at that point.
What is the side included between the ∠ LMN and ∠ LNM of ∆ LMN?
Line MN is the side in between the 2 angles which are ∠LMN and ∠LNM in triangle △LMN.
What do we mean by sides in maths?An edge is a specific kind of line segment that connects two vertices of a polygon, polyhedron, or higher-dimensional polytope in geometry.
An edge, also known as a polygon side, is a line segment that forms the boundary of a polygon.
The sides of the angle are the two straight lines that unite to make it.
The intersection of two lines or rays that make an angle is known as its vertex.
So, according to the given figure, the side between ∠LMN and ∠LNM in triangle △LMN is side MN.
Therefore, line MN is the side in between the 2 angles which are ∠LMN and ∠LNM in triangle △LMN.
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The graph shown here is the graph of which of the following rational
functions?
Helpppp meeeeee. Merry Christmas!!
Answer:
Yup it the first one
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
Decide whether the triangles are similar. If they are, write a similarity statement and state the reason justifying the similarity.
What kind of problem is 3x 1?
This is a multiplication issue, as shown by the usage of the multiplication symbol. The multiplication issue is the solution.
What do math signs mean?When data is represented by symbols, mathematical statements are easier to comprehend. For all real numbers, the four fundamental arithmetic operations in mathematics are:
+ Addition
Subtraction (-) (-)
Multiplication (x) (x)
() Division
Why are you referring to my multiplication issue?As we proliferate, there are more elements in the group. The product, the two factors, and the product are all components of a multiplication problem. The numbers 6 and 9 are the factors in the multiplication equation 6 x 9 = 54, and 54 is the result. The multiplication formula is represented as Multiplicand x Multiplier = Product. The first figure is multiplicand (factor). the multiplier following figure (factor). The outcome of multiplying the multiplicand and multiplier is the product.
3 x 1 , shows a multiplication signs between them.
which signifies It is a multiplication problem with result 3.
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Amelie needs 2 3/8 cups flour for one recipe and 1 1/3 cups of flour for another recipe.
How many cups of flour does Amelie need in all?
Enter your answer as a mixed number in simplest form by filling in the boxes.
Answer:
2 3/8 + 1 1/3 (LCD is 24)
= 2 9/24 + 1 8/24
= 3 17/24 cups
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Answer:
3 17/24
Step-by-step explanation:
2 3/8 + 1 1/3
2 3/8 = 19 /8
1 1/3 = 4/3
The common factor is 24
57/24 + 32/24 = 89/24
89/24 = 3 17/24
Select the methodology that would result in a subjective probability....
Dividing the number of favorable events by the number of possible events.
Studying the fraction of times in the past a particular event has happened.
Weighing the available information and assigning a probability.
Weighing the available information and assigning a probability.
A sort of probability called subjective probability is one that is based on a person's subjective assessment or personal knowledge of the likelihood of a particular result. It solely represents the subject's thoughts and prior experience and does not include any formal computations. A "gut instinct" used when making a deal is an illustration of subjective probability.
So, as per the definition of subjective probability
Dividing the number of favourable events by the number of possible events and Studying the fraction of times in the past a particular event has happened, both can be determined through calculations mathematically accurate but for Weighing the available information and assigning a probability we might use a "gut instinct". Thus
Weighing the available information and assigning a probability.
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What type of symmetry does this graph have?
Answer:
Line
Step-by-step explanation:
You could draw a line up the center, and it would be symmetrical.
The odds in favor of an event are 3 to 4. What is the probability of the event?
37
The probability from the odds is 3/7
How to determine the probability?The value of the odds is given as
Odds = 3 to 4
Represent the odds as a fraction
So, we have the following representation
Odds = 3/4
To convert the odds to probability, we make use of the following equation
Probability = Odds/(1 + Odds)
Substitute the known values in the above equation, so, we have the following representation
Probability = (3/4)/(3/4 + 1)
Evaluate the sum
Probability = (3/4)/(7/4)
Evaluate the quotient
Probability = 3/7
Hence, the probability is 3/7
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A ball is thrown into the air. Its height in
feet after t seconds is given by the
function h(t) = −5t² + 20t. How high will
the ball be after 3 seconds?
Answer:
15 ft
Step-by-step explanation:
h(t) = −5t² + 20t (Given)We need to find: height of the ball after 3 seconds.So, plug t = 3 in the above equation, we find:h(3) = −5(3)² + 20(3)->h(3) = −5(3)² + 20(3)->h(3) = −5(9) + 60->h(3) = −45 + 60->h(3) = 15 feetThe vertex form of the quadratic function f(x) = x² + 10x + 1 is f(x) = a(x - h)² + k.
What is the value of a? |
What is the value of h?
What is the value of k?
Answer:
[tex]a=1, h=-5, k=-24[/tex]
Step-by-step explanation:
[tex]f(x)=x^2+10x+1 \\ \\ =x^2+10x+25+1-25 \\ \\ =(x+5)^2-24 \\ \\ \therefore a=1, h=-5, k=-24[/tex]
Paul pay the newpaper company 70% of what he collect how much would he keep for himelf in a month when he collected 450. 0
Answer:
£135
Step-by-step explanation:
70% of £450
=£315
£450-£315=135
What can good debt do to your credit score?
Responses
nothing
increase it
negatively affect it
decrease it
The effect of good debt to ones credit score is that is would increase it. That is option B.
What is a credit score?A credit score is defined as the expression that can be used to show a customer's worth regarding the payment of their debts.
A customer's credit score can be rated as follows:
BadFairGood orExcellent credit score.A good debt is the ability of a customer to quickly pay off their debt which has been noted as one of the qualities that raise their credit score.
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Solve for k.
k² - 19k - 20 =0
Answer:
k = -1, 20
Step-by-step explanation:
k² - 19k - 20 = 0
k² + 1k - 20k - 20 = 0 ==> 1 * (-20) = -20 and -20 + 1 = -19
k² + k - 20k - 20 = 0
k(k+1) - 20(k+1) = 0 ==> factor and simplify
(k-20)(k+1) = 0
k-20=0 ==> k=20
k+1=0 ==> k=-1
k = -1, 20
Answer:
k² - 19k - 20
(k-20) (k+1) = 0
k-20 = 0
k=20
k+1 = 0
k= -1
k= 20 and -1
what is the answer to the question
Answer: blah blah blah join my chatlet write join/johan chatlet with no spaes
Step-by-step explanation: