The slope of the function may be found by differentiating it. Finding the derivative's maxima will show where the function is rising at the fastest pace as slope is defined as the rate of change.
What is Maxima and Minima ?The slope of the function may be found by differentiating it. Finding the derivative's maxima will show where the function is rising at the fastest pace as slope is defined as the rate of change.
The curve of a function has peaks and troughs called maxima and minima. A function may have any number of peaks and minima. Calculus allows us to determine any function's maximum and lowest values without ever consulting the function's graph. Maxima will be the curve's highest point within the specified range, while minima will be its lowest.
The curve of a function has peaks and troughs called maxima and minima. A function may have any number of peaks and minima. Calculus allows us to determine any function's maximum and lowest values without ever consulting the function's graph. Maxima will be the curve's highest point within the specified range, while minima will be its lowest.
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Is 3x² 4x 15 a polynomial in one variable?
The equation is 3x² - 4x + 15 is polynomial in one variable.
What are polynomial in one variable?An algebraic expression with one or more terms and a non-zero coefficient is called a polynomial. A polynomial is an expression composed of variables, coefficients, and constants connected by a mathematical operator. A polynomial is an expression connected by mathematical operations like addition, subtraction, multiplication, and division. An algebraic expression with only one variable is called a polynomial in one variable.
Given equation 3x² - 4x + 15
An algebraic expression with only one variable is a polynomial in one variable.
some examples of one variable polynomial
x + 2
y+ 5
x² + ax + b
ax³ + bx + c
all the equations that contain only 1 variables are polynomial in one variable.
Hence the expression is polynomial in one variable.
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What is domain simple answer?
A domain is a component of the nomenclature used in web addresses to identify your website or a particular page of your website online.
What is domain ?A function's authorized range of values is known as its domain. For a function like f, this set contains of the x values (x). The set of those values represents the possible range of values that a function can take as input. The function's response to our x value entry is this group of values.
here ,
A domain is typically a sphere of knowledge or an area under one's control.
Users find it much easier to recall and search for online because it is a string of text linked to a website's numerical IP address.
Both the internet's architecture and the way a company's network resources are set up fall under the umbrella term "domain."
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I can't seem to figure out what it means by characteristics for these equations, It might be more simple than I think, but I honestly don't know.
Explanation:
Characteristics about an equation are slope, intercepts, and things like that.
Part D of each problem is just referring to part a, b, and c
So, Part D is basically asking you to show your work, to explain slope-intercept equation, make observations about the problem, etc.
Hope I helped! :)
1800 ounces of a radioactive substance are stored in a radioactive container.
ounces, of the substance that is left after t years can be modeled by the equation y = 1800e-0.00052t
where y is the amount of the substance left after t years.
Approximately how many years will it take until 80 ounces of this substance remains?
According to the given statement 2.622 years will it take until 80 ounces of this substance remains.
How much does one ounce weigh?Use a test tube holder that has an ounce marker or can be converted quickly to ounces (like cups). As you take the measuring cup from the ingredient, let it overflow. You may try and reduce measurement afterwards. Use a knife to level the measuring cup.
Briefing:The equation may be used to predict how much of the chemical is still present after t years, measured in ounces.
y=1800e -0.00052t
In the equation above, we substitute y = 80 ounce to obtain the time.
80= 1800e -0.00052t
80/1800=e -0.00052t
2/45= e -000.52t
Considering both ends of the aforementioned equation
In(2/45)= In(e -000.52t)
In(2)-In(45)= In(e -000.52)
0.3010-1.653= -000.52t
-1.352= -000.52t
dividing by 000.52 on both side
1.352/000.52= t
t= 2.622 years
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Why is 1 not a square number?
According to square numbers , 1 is a square number while 2 is not .
What does Squaring mean ?
In mathematics, a square is the result of multiplying a number by itself. The verb "to square" is used to denote this operation. Squaring is the same as raising to the power 2, and is denoted by a superscript 2; for instance, the square of 3 may be written as 32, which is the number 9.
When you multiply an integer (a “whole” number, positive, negative or zero) times itself, the resulting product is called a square number, or a perfect square or simply “a square.” So, 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on, are all square numbers.
Thus , 1 is a square number while 2 is not .
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Algebra II 5.02: Solve Radical Equations
Radical Equations
Step 1
To demonstrate how to solve a radical equation, let's use the following equation as an example:
g what word is used to say the probability of an adverse outcome? question 12 options: risk variance random statistics none of the above
Risk is used to say the probability of an adverse outcome.
Option (a) (Risk) is the correct choice.
Through risk assessment, businesses, governments, projects, and investors may determine the likelihood that a bad occurrence will have a detrimental effect on their operations.
Risk assessment is crucial for figuring out the value of a particular project or investment and the appropriate process(es) to manage such risks.
Different methods may be used to evaluate the risk and reward tradeoff of a possible investment opportunity using the information provided by risk analysis.
A risk analyst begins by determining what may go wrong.
These drawbacks must be compared to a probability meter that assesses the chance that the event will occur.
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The correct question may be:
What word is used to say the probability of an adverse outcome?
(a) risk
(b) variance
(c) random statistics
(d) None of the above
Given:
CD CB CA CE and
Prove:
A E
You may use any style proof you prefer.
The alternate angles between two parallel lines are equal, therefore, ∠ A = ∠ E.
What is rectangle?An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel, opposite sides. Since a rectangle is a two-dimensional form, it has two dimensions: length and width. The rectangle's longer side is its length, while its shorter side is its breadth.
Given:
CD ≅ CB and CA ≅ CE
As you can see from the diagram, on joining BE and AD the figure will represent a rectangle ABED because the diagonals of the rectangle are equal and bisect each other.
Thus, DE || AB (Rectangle property)
∠ A = ∠ E, because the alternate angle of parallel lines is equal.
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What is the first step to graph an inequality?
Always begin by separating the variable y from the inequality's left side is the first step to graph an inequality.
What are the steps to graphing an inequality?The graph of a two-variable inequality is the set of points that describe all solutions to the inequality. The coordinate plane is split in half by a boundary line created by a linear inequality, with one-half representing the solutions to the inequality.
Step 1: Always begin by separating the variable y from the inequality's left side.
Step 2: Replace the symbol for inequality with that for equality.
Step 3: In the xy plane, graph the boundary line from step 2. You are creating the boundary line that would divide or cut the xy-plane into two sections in this stage.
Step 4: Shading one side or area of the boundary line is the final step.
Step 5: Use this optional step to check or confirm that you have shaded the boundary line's side appropriately.
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I need to know the unit price for both a and b and what’s the better buy
Answer:
Brand A Forks $0.08, Brand B Forks $0.06, Better Buy is Brand B
Step-by-step explanation:
Unit price is price per unit (in this case, forks)
You need to find the $ for 1 fork for Brand A and B, since they have different unit prices.
total price/units = price/unit
Brand A: $1.97/25 forks = $0.0788 (rounded up is $0.08)
Brand B: $2.98/48 forks = $0.06208 (rounded up is $0.06)
Better brand is Brand B because it is cheaper.
Where are the asymptotes for the following function located?
f (x) = startfraction 7 over x squared minus 2 x minus 24 endfraction
The asymptotes for the given function f(x) = 7/(x^2-2x-24) are located at
x = -3 and x = 8.
The asymptotes of a function are the lines that the graph approaches, but never touches as it continues to infinity. In the given function, f(x) = 7/(x^2-2x-24), the asymptotes are located at x = -3 and x = 8.
To find the asymptotes of a function, you first need to factor the denominator of the function. In this case, the denominator is[tex]x^2-2x-24,[/tex]which can be factored into (x+3)(x-8). This means that there are two potential zeroes in the denominator, x=-3 and x=8. These two points are the two asymptotes of the graph of the given function.
To explain further, the two asymptotes divide the x-axis into three intervals. On the interval (-infinity, -3), the graph of the function will approach negative infinity as x approaches -3 from the left. On the interval (-3, 8), the graph of the function will approach positive infinity as x approaches 8 from the right. On the interval (8, infinity), the graph of the function will approach negative infinity as x approaches 8 from the right.
In summary, the asymptotes for the given function f(x) = 7/(x^2-2x-24) are located at x = -3 and x = 8.
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passes through (6,3) and (14,-5)
Answer:
Slope: m = (y2 - y1)/(x2 - x1) = (-5 - 3)/(14 - 6) = -8/8 = -1
The equation of the line is y = -x + b
Substitute (6,3) into the equation:
3 = -6 + b
b = 9
Therefore, the equation of the line is y = -x + 9
Step-by-step explanation:
State a and d for the arithmetic sequence below:
1, 3, 5, 7...
a=
d=
Answer:a,9 b,11
Step-by-step explanation:
How do you determine the relationship between the volume of a rectangular prism and pyramid?
The relationship between the volume of a rectangular prism and pyramid is defined as that the pyramid takes up 1/3 of the volume of a prism.
Here we need to identify the relationship between the volume of a rectangular prism and pyramid.
As we all know that the volume of rectangle prism is written as,
=> Volume of a prism = (area of base) * height
Now, let us consider the volume of a pyramid that the pyramid takes up 1/3 of the volume of a prism when their bases and height are equal.
So, here the volume of a pyramid is 1/3 multiplied by the volume of a prism.
Then we get the volume of pyramid is written as,
Volume of a pyramid = 1/3 (area of the base) * height
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What is the horizontal asymptote of f/x )= 4 x?
The given equation of the horizontal asymptote is y=0
Because there is not a rational expression so there is no horizontal asymtotes.The given equation would be linear because degree of given function is 1.
what is an Asymptote?An asymtote is a line being approached by a curve but never touching the curve at any finite distance.It is a line that the graph approaches as either x or y in positive or negative infinity.
How do you find horizontal asymptotes?The horizontal asympototes of a function can be determined by looking at the degree of the numerator and denominator.if we say N is the degree of numerator and Dis the degree of denominator.So it will be N<D.Then horizontal asymptotes will be y=0
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Find the missing number in this proportion. ?/8=16/64
A.0
B.1
C.2
D.3
Evaluation:
We are required to find the equivalent fraction here. When simplifying 16/64, we divide both sides by 16:
16 ÷ 16 = 1
64 ÷ 16 = 4
16/64 in its simplest form is 1/4. When we multiply both the numerator and denominator by 2, we will find that:
1/4 = 2/8
Verification:
To verify this, we can multiply both parts of the fraction by 8:
2 × 8 = 16
8 × 8 = 64
Hence, we know our answer is correct.
Classifying Triangles Maze! Directions: Glven each set of side lengths, determine if the triangle is acute. obluse, night, or not a triangle. Use your solutions to navigate through the moze End! Start! Acute 6,10,17 Obtuse 26, 28, 38 Nota a 10, 17, 23 Obtuse Not a Right Not a A Obtuse Acute Right 13, 18, 29 Not a A 9,13, 20 Acute 15,19,25 Not A 4, 11, 13 Acute Right Obtuse Not a A Right Acute Obtuse 16,16, 22 Nota A 4,7,8 Acute 20, 21, 29 Obtuse 3,16,25 Obtuse Obtuse Right Not a Δ Not a Acute Not a A 5, 16, 24 Acute 19,24,39 Right 9,40,41 Obtuse 12, 35, 37 Right Not a A Acute Not a A Acute Right Acute 7,34,45 Not a 4,13,16 Right 23, 30, 37 Obtuse 14, 21, 37 on 1 Gino Won A Things Algebra LLC. 2016
Classifying triangles maze's path formed from the starting point is 3 - 10 - 17, 9 - 13 - 20, 4 - 7 - 8, 20 - 21 - 29, 15 - 19 - 25, 26 - 28 - 38, 4 - 11 - 13, 3 - 16 - 25, 12 - 35 - 37, 23 - 30 - 37, 9 - 40 - 41, 19 - 24 - 39, 16 - 16 - 22, and 13 - 18 - 29.
The full question is in the attachment. According to the Pythagorean theorem if there are three sides a, b, and c, where a ≤ b < c
a² + b² < c² an obtuse triangle is formeda² + b² = c² a right triangle is formeda² + b² > c² an acute triangle is formedBut if a + b < c then a triangle cannot be formed
From point start
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How do you know what method SSS SAS ASA AAS to use when proving triangle congruence?
We can find out which method SSS, SAS, ASA, and AAS can be used to prove similarity by observing what three components are given.
If it is given that three sides are equal then we will use side side side(SSS) postulate.
If it is given that two sides and one angle is given then we will use the side angle side(SAS) postulate.
If two angles and one side is given then we will use the angle side angle (ASA) postulate.
To find which postulate will suit for that we will have to observe which components are given that are equal.
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The m∠BOD = 46 and the m∠BOC = 26. What is the m∠COD?
The measure of the angle m∠COD is 20 degrees
How to determine the measure of the angle m∠COD?From the question, we have the following parameters that can be used in our computation:
The measures of the angles:
m∠BOD = 46 and m∠BOC = 26.
The measure of the angle m∠COD is the difference between of the above angles
Using the above as a guide, we have the following:
Measure of the angle m∠COD = Difference of angles m∠BOD and m∠BOC
Mathematically, this is represented as
Measure of the angle m∠COD = m∠BOD - m∠BOC
Substitute the known values in the above equation, so, we have the following representation
Measure of the angle m∠COD = 46 - 26
Evaluate the difference
Measure of the angle m∠COD = 20
Hence, the angle is 20 degrees
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12 pencils cost 1.80 pounds. How many pencils can be bought for 6 pounds?
Answer:
Step-by-step explanation:i think to answer is either 90p or 9p
Answer:
90p or 9p
Step-by-step explanation:
Determine the domain and range for the function below.
Answer:
Domain: (-∞, ∞); Range: [1, ∞)
Step-by-step explanation:
Domain is the set/interval of x-values that the function spans while the range is the set or interval of y-values that the function spans.
Domain
We can see that the arrows point towards negative and positive infinity for x and also see there are no holes or asymptotes for this graph. Therefore, the domain is (-∞, ∞) or {x | x is any real number}
Range
We can see that the arrows both point towards infinity for y-values and that the lowest y-value this graph touches is y = 1 (inclusive, meaning this y-value is included in the range). Thus, the range is [1, ∞) or {y | y ≥ 1}
1. Find the length of arc PRQ: Show your work.
Answer:
The length of arc PRQ is 16.7 in.
Step-by-step explanation:
Given;r = 8 inθ = 120°So,
arc length = 2πr × (θ/360)
arc length = 2(3.14)(8) × (120/360)
arc length = 2(3.14)(8) × (120/360)
arc length = 50.24 × (1/3)
arc length = 16.7 inches
Thus, The length of arc PRQ is 16.7 in.
In circle H with m/GHJ = 54°, find the m/GKJ.
Answer:
H
G
K
Submit Answer
DEVEL
attempt 1 out of 2
The measure of the angle ∠GKJ, m∠GKJ, at the circumference of the circle H, which is subtends the same arc GJ as the angle ∠GHJ at the center of the circle is 27°
What is an arc of a circle?An arc of a circle is a part of the circle's circumference.
The measure of angle ∠GHJ, m∠GHJ = 54°
The measure of angle ∠GKJ, m∠GKJ = Required
Please find attached a possible drawing of the circle H created with MS Word and based on a similar question posted online
The circle, Angle at the Center Theorem states that the angle subtended at the center by arc is twice the angle subtended by the arc at the circumference of the circle.
The question indicates that the angle subtended by the arc GJ at the center of the circle, ∠GHJ = 2 × The angle subtended by the arc GJ at the circumference, ∠GJK
Therefore;
m∠GHJ = 2 × m∠GKJ
54° = 2 × m∠GKJ
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Find the distance between two numbers on a number line -4 7/12 and -3 1/6
Answer: -17/12 or -1 5/12 or 1 5/12
Step-by-step explanation:
convert both equations into improper fractions
− 55/12 - (-19/6)
-55/12+19/6
find the common factor of the denominators
-55/12 + 38/12
-17/12
-1 5/12
Question 4 (1 point)
What is the product? (6.28x10^3) x 10,000
62,800
6,280,000
6,280
62,800,000
62,800,000 is the product of (6.28 x 10^3) x 10,000.
What is the product?It refers to the result of one or more multiplications.
Given number is (6.28 x 10^3) x 10,000.
6.28 x 10^3 = 6280
Therefore, 6280 x 10,000 = 628,000,00
Hence, the product of (6.28 x 10^3) x 10,000 is 628,000,00.
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What are the 4 tests of congruency?
The 4 tests of congruency are:
Side - Side - Side (S.S.S. congruency)
Side - Angle - Side (S.A.S. congruency)
Angle - Angle - Side (A.A.S congruency)
Right - Hypotenuse - Side (R.H.S. congruency)
Tests of congruency:
Side - Side - Side (S.S.S. congruency)
If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.
Side - Angle - Side (S.A.S. congruency)
If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.
Angle - Angle - Side (A.A.S congruency)
If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.
Right - Hypotenuse - Side (R.H.S. congruency)
If the hypotenuse and one leg of one right-angled triangle are equal to the corresponding hypotenuse and leg of another right-angled triangle, the two triangles are congruent.
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What mode of observation is 5'7 8?
The mode for a particular set of observations is 5 since it occurs the majority of the time.
What is mode?The mode formula is described in statistics as the formula for calculating the mode of a given collection of data. The value that occurs most frequently in a particular set is referred to as the mode, and the mode differs across grouped and ungrouped data sets. The mode may be calculated quite easily. Put all of the numbers in a given set in order, either lowest to highest or highest to lowest, and then count how many times each number appears in the set. The mode is the one that appears the most.
Here,
given set of observation:
5, 7, 8, 5, 7, 6, 9, 5, 10, 6
Mode is the number which occurs the highest time.
So here 5 occurs the highest times(3 times).
So,5 is the mode.
The mode for given set of observation is 5 as it occurs most time.
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What is equal to 3 minus square root of eight divided by square root of 3
Answer:
approximately 1.732
Step-by-step explanation:
To solve this expression, we need to start by performing the operations inside the parentheses first. The square root of 8 is equal to 2, so 3 minus 2 is equal to 1. Then, we can divide 1 by the square root of 3, which is equal to approximately 1.732. Therefore, the expression 3 minus square root of eight divided by square root of 3 is equal to approximately 1.732.
Clark's rule is a formula used to determine pediatric doses of over the counter medicine.
The formula says
The weight of a child divided by 150 multiplied by the adult dose is the same as the child dose
if an adult dose of acetaminophen is 1,000 mg and a child weighs less than 90 pounds, what is
the recommended range of doses?
A. x≤ 600
B. x ≥ 600
C. 500
D. 500 ≤x≤ 600
500 ≤x≤ 600 is the recommended range of doses. Typically, a phase I or early phase II clinical trial involves dose range.
How to calculate doses ?To solve this problem using Clark's rule, we need to determine the range of pediatric doses for a child who weighs less than 90 pounds and for whom the adult dose is 1,000 mg.
A mathematical formula known as Clark's rule is used in medicine to determine the right dosage of medication for patients aged 2 to 17 depending on their weight and the recommended adult dose.
First, we can use the formula provided to calculate the child dose:
Child dose = (Weight of child / 150) * Adult dose
Since the weight of the child is less than 90 pounds, we can set the weight of the child to the minimum value in the range, which is 50 pounds. This gives us:
Child dose = (50 / 150) * 1000 mg
= 333.33 mg
Next, we can set the weight of the child to the maximum value in the range, which is 89 pounds. This gives us:
Child dose = (89 / 150) * 1000 mg
= 593.33 mg
Therefore, the recommended range of doses for a child who weighs less than 90 pounds and for whom the adult dose is 1,000 mg is 500 mg ≤ x ≤ 600 mg.
So, the correct answer is D. 500 ≤x≤ 600.
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What is the median of the following data sample 2 7 4 8 9 10 6 12 13?
There are 9 values in the sample: 2, 4, 6, 7, 8, 9, 10, 12, and 13. Since there are an odd number of values, the median is the middle value. In this case, the median is the 5th value, which is 8.
The median is a measure of central tendency, which means it is used to describe the "typical" or "average" value in a sample of data. To find the median, we first need to arrange the data in numerical order. In this case, the data is already in numerical order, so we can proceed directly to finding the median.
There are 9 values in the sample: 2, 4, 6, 7, 8, 9, 10, 12, 13. Since there are an odd number of values, the median is the middle value. In this case, the median is the 5th value, which is 8. This means that 8 is the middle value, with 4 values smaller than it and 4 values larger than it.
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