The measure of the sides 'b' and 'c' will be 5.7 units and 8.2 and angle C will be 55°.
What is the sine law?The Law of Sines The law of trigonometric functions, sine law, sine formula, or sinusoidal rule is a trigonometric equation that relates the sizes of any triangle's edges to the sines of its orientations.
The sine law in the triangle ΔABC is given as,
AB / sin C = BC / sin A = CA / sin B
The measure of the third angle is given as,
∠A + ∠B + ∠C = 180°
35° + 90° + ∠C = 180°
∠C = 55°
Then the measure of the side c (AB) is calculated as,
AB / sin C = BC / sin A
c / sin 55° = 10 / sin 90°
c = 8.2
Then the measure of the side b (AB) is calculated as,
AC / sin B = BC / sin A
b / sin 35° = 10 / sin 90°
b = 5.7
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What is the relationship of the volume of the pyramid to the volume of prism the volume of a pyramid is blank the volume of a prism with the same base area and height?
The relationship of the volume of the pyramid to the volume of prism: The volume of a pyramid is 1/3 the volume of a prism with the same base area and height.
In this question we need to find the relationship of the volume of the pyramid to the volume of prism.
The volume of a pyramid is ________ the volume of a prism with the same base area and height.
We know that the formula for the volume of pyramid.
V1 = 1/3 * base area * height
And the formula of the volume of prism is:
V2 = base area * height
We have been given a pyramid and prism have the same base area and height.
So, volume of pyramid = 1/3 * volume of prism
Consider a ratio the volume of the pyramid to the volume of prism.
(the volume of the pyramid) / (the volume of prism) = 1/3
Therefore, the volume of a pyramid is 1/3 the volume of a prism with the same base area and height.
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What is the median of 7 3 5 8 6 10 9 12?
For a given collection of data, the median is 7.
What is median?The median is the value in the center of a data collection, which means that 50% of the data points have a value less than or equal to the median, and 50% of the data points have a value greater than or equal to the median. The median is the value in the center of a group of numbers. The median corresponds to the 50th percentile of the collection of numbers. In other terms, the median is the value in the center of a group of numbers where half of the values are less than the median and half are more than the median.
Here,
First we have to arrange the numbers in ascending order.
3,5,6,7,8,9,10,12
There are 8 terms.
8 is an even number
So the median term is 8÷2=4th term
4th term =7
The median for given set of observations is 7.
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There is a proportional relationship between a volume measured in cups and the same volume measured in tablespoons. 3 cups is equivalent to 48 tablespoons, is plotted in the graph. For which value y is (1,y) on the line you just drew?
Since there is a proportional relationship between a volume measured in cups and the same volume measured in tablespoons, the value of y in the ordered pair (1, y) is 16.
How to determine the volume measured in tablespoons?Mathematically, a proportional relationship or direct variation can be represented by the following equation:
y = kx
Where:
k is the constant of proportionality.y represents volume measured in tablespoons. x represents the volume measured in cups.In order to have a proportional relationship and equivalent ratios, the variables x and y must have the same constant of proportionality. Next, we would determine the constant of proportionality (k) based on the given parameters:
Constant of proportionality (k) = y/x
Constant of proportionality (k) = 48/3
Constant of proportionality (k) = 16.
Therefore, a linear equation that relates the volume measured in tablespoons (y) and volume measured in cups (x) is given by;
y = kx
y = 16x
When x = 1 cups, the value of y is given by;
y = 16(1)
y = 16 tablespoons.
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What property is 4x7 4x3 4x4?
The number sentence 4x7 = (4x3) + (4x4) is an example of distributive property of multiplication.
According to the distributive property of multiplication, the product of a number and sum of two numbers is equal to the sum of product of the first number and other two numbers separately.
It can be expressed as,
a × (b + c) = (a × b) + (a × c)
Here, the given number sentence is 4x7 = (4x3) + (4x4).
It can be written as,
4 x (3 + 4) = (4 x 3) + (4 x 4)
Taking L.H.S of the equation,
4 x (3 + 4) = 4 × 7 = 28
Taking L.H.S of the equation,
(4 x 3) + (4 x 4) = 12 + 16 = 28
Therefore, the given number sentence represents the distributive property of multiplication.
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(10 points) a ferry will safely accommodate 66 tons of passenger cars. assume that the mean weight of a passenger car is 1.7 tons with standard deviation 0.5 tons. if a random sample of 36 cars are loaded onto the ferry, what is the probability that the maximum safe weight will be exceeded? hint! think about the average safe weight g
the probability that the maximum safe weight will be exceed is 0.054844.
What is z-score in statistics and probability?A z-score is a statistical measurement that express the relationship among standard deviation, mean value and actual value of a sample. Probability is the possibility of occurring a certain event regarding one or more conditions given in a statistical report.
What is mean and standard deviation?Standard deviation is a statistical term that express how the available data differ from mean value.
we calculate z -value from the following equation.
Given, mean weight of passengers, μ= 1.7 tons
standard deviation,σ = 0.5 tons
number of samples, n= 36 cars
the ferry will safely accommodate 66 tons of passenger cars
The maximum safe weight will be exceeded as total 36 cars are loaded
X=g = 66/36 =1.8333
now we estimate the Z value from the following formula,
Z= (X-μ)/(σ/√n)
Z = (1.8333-1.7)/(0.5/√36)
Z= 1.5996
as the Z value is 1.5996, X>Z so
the p value is 0.054844
hence, probability is 0.054844
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What is the mode of 1234?
There is no mode in the given data.
To find: Mode of the given data.
Given data is 1, 2, 3, 4
Mode: The mode of data is the observation having the highest frequency in a set of data. There is a possibility that more than one observation has the same frequency, i.e. a data set could have more than one mode. In such a case, the set of data is said to be multimodal.
The data is already arranged in ascending order. Therefore, there is no need to arrange the data in increasing order.
Constructing the frequency for given data:
Number: 1 2 3 4 5
Frequency: 1 1 1 1 1
Since the frequency of all the numbers are same, therefore, there is no specific mode for the given set of data distribution.
Conclusively, if no numbers in the data distribution are repeated, then there is no mode for such observation.
Therefore, there is no mode for given data.
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What is the surface area of 6 cube?
Answer: 216 cm3
Step-by-step explanation: 6*6*6=216 cm3
help me pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
From above graph
(A) The domain can be best described using
Interval notation
The domain is
-infinity , infinity
(a) The range cambe best described wing
Interval notation
The range is [4, infinity )
How do you know △ ABC ≅ △ DEF explain?
The property of congruence illustrated in the statement is the transitive property.
The transitive property states that if A is congruent to B and B is congruent to C, then A is congruent to C. In other words, if two things are congruent to a third thing, they are also congruent to each other.
In the statement "If AB ≅ DE, EF ≅ DE then AB ≅ EF," AB is congruent to DE, and EF is congruent to DE, so AB must also be congruent to EF according to the transitive property.
The other properties you listed are not applicable in this case. The symmetric property states that if A is congruent to B, then B is congruent to A. The reflexive property states that every object is congruent to itself. And multiplication is not a property of congruence.
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The question is -
How do you know AB ≅ DE, EF ≅ DE then AB ≅ EF explain?
What are the 4 type of a function?
Linear, quadratic, polynomial, and exponential functions are the four different types of functions.
There are several types of functions in mathematics, but four common types are:
Linear functions: An equation with the form f(x) = mx + b, where m and b are constants, is said to be linear. Linear functions have a constant slope and always produce a straight line when graphed.
Quadratic functions: A quadratic function is a function of form f(x) = ax^2 + bx + c, where a, b, and c are constants. Quadratic functions have a parabolic shape when graphed.
Polynomial functions: A polynomial function has the following formula: f(x) = a nxn + a (n-1)x (n-1) +... + a 1x + a 0, where n is a positive integer and a n, a (n-1),..., a 1, and a 0 are constants. Polynomial functions can have a variety of shapes when graphed, depending on the value of n and the constants.
Exponential functions: An exponential function is a function of form f(x) = a^x, where a is a constant and a > 0. Exponential functions have a constantly increasing or constantly decreasing slope when graphed.
These are just a few examples of the many types of functions that exist in mathematics. There are many other types of functions, such as logarithmic functions, trigonometric functions, and so on.
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The revenue over 30 weeks for a small landscaping company is modeled by the graph shown. Which of the following is true?
The True statement from the Graph is
The range from the graph is [0, 300].
What is Graph?The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.
In a line graph, the information or data is represented as a series of markers, or dots, and is then connected to one another by a straight line.
Usually, data that varies over time is represented with a line graph.
Given:
From the graph we can see that,
The domain is the Input value. So, the domain is [0, 30]
and, the Range is the output value.
So, the range from the graph is [0, 300]
Also, the function is increasing over [0, 15) and decreasing over (15, 30].
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Robert record the number of page he read each day. 27,54,81,108. What i the total number of page Robert will have read after 8 day?
The number of pages Robert reads each day form an arithmetic sequence 27, 54, 81, 108,... After 8 days he has read 216 pages.
The n-th term of an arithmetic sequence is given by:
a(n) = a0 + (n - 1) d
Where:
a0 = first term
d = common difference
In the given problem, the number of pages form an arithmetic sequence:
27, 54, 81, 108, ....
with:
first term = a0 = 27
common difference = d = 54 - 27 = 27
Hence, for n = 8
a(8) = 27 + (8 - 1) x 27
= 27 + 7 x 27 = 216
Hence, after 8 days he has read 216 pages.
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Which situation best represents causation?
A. As the weight of a dog increases, the length of its tail decreases.
B. As the number of miles driven increases, the amount of gas used increases.
C. As the number of siblings a student has increases, the grade in the student’s class increases.
D. As the sale of winter coats increases, the amount of hot chocolate sold decreases.
The best represents causation is D, As the sale of winter coats increase the amount of hot chocolate sold decreases.
What is causation?Causation can be defined as the capacity of one variable to influence another. The first variable may bring the second into existence.
There are two types of causation:
factual cause is often established using the but for testProximate causation refers to a cause that is legally sufficient to find the defendant liableTherefore the correct option is D because the best way to represent causation is when a sale of winter coat increases the amount of hot chocolate sold decreases.
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help me out on this please
We need to use the concept of Finding zeros of the polynomial function. The zeros of the function are 1/2,1+2i,1-2i.
How do you find the zeros of the polynomial?The values of x that fulfill the formula f(x) = 0 are the zeros of a polynomial. The polynomial's zeros are the x values for which the function's value, f(x), equals zero in this case. The degree of equation f(x) = 0 determines how many zeros a polynomial has. The zeros of the polynomial are all such domain values of the function for which the range is zero.
The locations where the graph of y = f(x) crosses the x-axis are known as the polynomial's zeros graphically. In the information that follows, we will learn more about how to express a polynomial's zeros on a graph.
Calculation:Take f(x)=2x^3 -5x^2+12x-5
So in the question he mentioned that (2x-1) is factor of the polynomial.
So take out (2x-1) from the polynomial function
f(x)=(2x-1)(x^2-2x+5)
We know that zeros of a polynomial can be found when f(x)=0
⇒(2x-1)=0
∴x=1/2
⇒(x^2-2x+5)=0
By using the concept of finding roots of a quadratic equation
(-b±√b2-4ac)/2a
⇒(2±4i)/2
∴x=(1+2i) and (1-2i)
∴1/2,(1+2i),(1-2i) are the zeros.
We need to use the concept of Finding zeros of the polynomial function. The zeros of the function are 1/2,1+2i,1-2i.
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5. The equation y = 1/3(x-6)² + 6 is shifted 3 units to the left and 7 units up.
What is the value of h in the new equation?
A.-6
B. -3
C. 13
D. 3
Answer:
D. 3
Step-by-step explanation:
Initially, the vertex is at [tex](6,6)[/tex]. After the transformation, the vertex moves to [tex](3,13)[/tex].
So, [tex]h=3[/tex].
Is quadrilateral DEFG congruent to quadrilateral MNOP? Explain.
The quadrilateral DEFG is congruent to the quadrilateral MNOP.
What is a quadrilateral?The quadrilateral has four sides and four angles. The sum of internal angles is 360 degrees.
In triangles ΔFED and ΔONM, we have
FE = ON (Given)
∠FED = ∠ONM (Given)
∠EDF = ∠NMO (Given)
The triangles ΔFED and ΔONM are congruent to each other by ASA postulates. Then the measure of the side FD is equal to MO.
In triangles ΔGFD and ΔPOM, we have
DF = MO (Defined)
∠GFD = ∠POM (Given)
∠FDG = ∠OMP (Given)
The triangles ΔGFD and ΔPOM are congruent to each other by ASA postulates.
Then the quadrilateral DEFG is congruent to the quadrilateral MNOP.
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How do you find the altitude of a triangle on a calculator?
The altitude of the triangle is determined by, a = √(c² - b²)
Given,
Altitude of triangle;
A triangle's altitude is determined by drawing a perpendicular line from its vertex to its opposite side. The altitude, sometimes referred to as the triangle's height, forms a right-angle triangle with the base.
Here,
The simplest way is to use the Pythagorean theorem if you are aware of two additional right triangle sides:
a² + b² = c²
Where,
a is the altitude, b is the base and c is the hypotenuse
Then,
If leg a is the missing side, change the equation such that a is on one side and compute the square root of that number:
a = √(c² - b²)
That is,
We can find the altitude of the triangle by, a = √(c² - b²)
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As a pharmacist, you are responsible for knowing about medication dosage, and how long a dose stays in the patient's system. Let's look at an example of a common medication, called ibuprofen. When a patient takes a 400 mg dose of ibuprofen, it releases into the bloodstream at a certain rate, and then decreases over time. The function that models this concentration of medicine over time is complex and looks like this:
P(t) = 0.5t++3.45t³ - 96.65t² + 347.7t, when 0 ≤ t ≤ 6 . In this function above, P(t) is the amount of medication (in mg) in the blood stream at time t (in hours). When put into a graphing software, it looks like this
1.How long does it take for the medicine to hit its peak concentration in the bloodstream?Using graphing calculator
(Must be exact values)
2. What is the peak concentration of the medicine in the bloodstream?
The graph peaks at t=2 hours and the peak concentration is 337.4mg
What is a polynomial?A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division.
Given here, P(t) = 0.5t++3.45t³ - 96.65t² + 347.7t, when 0 ≤ t ≤ 6
Clearly from the graph the medicine peaks at t=2 hours and the peak concentration therefore is = 0.5×2++3.45×2³ - 96.65×2² + 347.7×2
= 1+27.6-386.6+695.4
= 337.4mg
Hence, The graph peaks at t=2 hours and the peak concentration is 337.4mg
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How do you know which graph is greater?
To determine which graph is greater, you need to compare the y-values of the two graphs at the same x-values or look at the overall shape of the graphs.
You can compare the y-values of the two graphs at the same x-values to determine which graph is greater if one graph has a higher y-value than the other graph at a particular x-value, then the first graph is greater at that x-value.
For example, suppose you have two graphs: one is a straight line with a slope of 2 and the other is a straight line with a slope of -3. If you compare the two graphs at the same x-values, you will see that the graph with the slope of 2 has a higher y-value than the graph with the slope of -3 for all x-values. This means that the graph with the slope of 2 is always greater than the graph with the slope of -3.
You can also compare the graphs by looking at the overall shape of the graphs. For example, if one graph is always above the other graph, then it is clear that the first graph is greater. On the other hand, if one graph crosses over the other graph, then there may be some x-values for which one graph is greater and some x-values for which the other graph is greater.
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, if "y varies directly as x", find the constant of variation and write an equation of direct variation that
relates the two variables.
y = 0.4 when x = -1
Answer:
k = - 0.4 , y = - 0.4x
Step-by-step explanation:
given y varies directly as x then the equation relating them is
y = kx ← k is the constant of variation
to find k use the condition y = 0.4 when x = - 1 , then
0.4 = - k ( multiply both sides by - 1 )
- 0.4 = k
then constant of variation is k = - 0.4
y = - 0.4x ← equation of variation
Ursula pours equal volumes of vinegar into five separate containers. The total volume of vinegar in the five containers is one liter. What is the volume of vinegar in each container? 0. 02 milliliters 0. 20 milliliters 20 milliliters 200 milliliters.
The volume of vinegar in each container is 200 milliliters.
Since the total volume of vinegar in the five containers is one liter, and a liter is equal to 1000 milliliters, the volume of vinegar in each container is 1000/5 = <<1000/5=200>>200 milliliters.
The amount of space a container encloses, or how much room is inside of it, is measured by its volume. The volume of a box is easily calculated using the following formula: Volume of a box with dimensions H, W, and L is equal to L×W×H. Many different units can be used, however because of the way this formula is stated, the volume would have length to the third power dimensions. For instance, if the container's measurements are given in meters, the capacity of the box will be given in meters cubed, or m³.
The volume of vinegar in each container is 200 milliliters.
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Since the total volume of vinegar in the five containers is one liter, and a liter is equal to 1000 milliliters, the volume of vinegar in each container is 1000/5 = <<1000/5=200>>200 milliliters.
A container's volume is a measure of how much space it contains or how much space is inside of it. The following formula makes calculating a box's volume simple: LWH is the volume of a box having the dimensions H, W, and L. Although many various units can be used, the volume would have length to the third power dimensions due to the way this formula is written. For instance, the capacity of the box will be specified in meters cubed, or m3, if the container's dimensions are given in meters.
The volume of vinegar in each container is 200 milliliters.
What must be added to 2x² 5x 6 to get X³ 3x² 3x 5?
To obtain xA³ + 3xA² + 3x + 5 we msut add xA³ + xA² - 2x - 1 to
2xA² + 5x + 6.
What is a polynomial?A polynomial is an algebraic expression.
A polynomial of degree n in variable x can be written as,
a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.
Given, A polynomial 2xA² + 5x + 6.
Now, We know we can do arithmetic operations on like terms.
So to obtain xA³ + 3xA² + 3x + 5 we must subract 2xA² + 5x + 6.
Therefore, ( xA³ + 3xA² + 3x + 5) - (2xA² + 5x + 6).
= xA³ + xA² - 2x - 1 should be added to obtain xA³ + 3xA² + 3x + 5.
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What is the 4 step plan in math?
The 4 step plan in math:
1. Identify the problem: Break down the problem into individual parts and identify what needs to be solved.2. Gather information: Research the topic and gather any necessary tools or resources.3. Plan a solution: Develop a plan to solve the problem by drawing diagrams, making charts or lists, and/or writing out equations.4. Solve the problem: Use the plan and information gathered to solve the problem and check the answer.Math Problem Solving: A 4 Step PlanMath problem solving can be a daunting task, but it doesn't have to be. By following a simple four-step plan, anyone can approach and solve math problems in an organized and efficient manner. The four steps to successful math problem solving are identifying the problem, gathering information, planning a solution, and solving the problem.
Identifying the problem is the first step to successful math problem solving. This step involves breaking down the problem into its individual parts and understanding what needs to be solved. It is important to be thorough and get a good grasp of the problem before moving on to the next step.
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If you have dimes, quarters and 1-dollar bills, in how many ways can you make up $2? THIS IS URGENT PLS HELP
Answer:
9 ways
Step-by-step explanation:
2 × $1
1 × $1 + 4 × $0.25
1 × $1 + 2 × $0.25 + 5 × $0.10
1 × $1 + 10 × $0.10
8 × $0.25
6 × $0.25 + 5 × $0.10
4 × $0.25 + 10 × $0.10
2 × $0.25 + 15 × $0.10
20 × $0.10
I count 9 ways.
Given that a = 6i- 3j, find:
a the unit vector in the same direction of a
b the angle that a makes with the positive x-axis.
The unit vector in the same direction will be equal to (6 i/5.1 - 3 j/5.1).
What is a Vector?A vector is a quantity with both magnitude and direction in physics. It is often depicted by an arrow with the same direction as the amount and a length proportionate to the size of the quantity.
A vector lacks position, but has magnitude and direction. A vector is therefore unaffected by displacement parallel to itself as far as its length is unaltered.
As per the given data in the question,
The unit vector is calculated as:
[tex]\vec u_a=\frac{\vec a}{||\vec a||}[/tex]
[tex]\vec a= x \vec i+y \vec j[/tex]
Now, calculate the magnitude of the vector,
[tex]\vec a[/tex] = √(x² + y²)
[tex]|\vec a|[/tex] = √6² - 3²
= √36 - 9
= 5.1
So, the unit vector will be,
[tex]\vec u_a[/tex] = (6 i - 3 j)/5.1
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Scenario 2
A test has__total questions for a total of __
points. There are two question types: a true/false question is worth __ points and a multiple choice question is worth __ points.
a. What is the system of equations that represents the scenario you created?
Continue on the following page.
B. Show your solution graphically
C. Prove your solution correct
a. The system of equations that represents the scenario created is given as follows:
x + y = 10.2x + 4y = 30.b. The graphic solution is the intersection of the two functions, on the image given at the end of the answer.
c. Replacing the solution on the equations, we have that:
5 + 5 = 10. (true).2(5) + 4(5) = 10 + 20 = 30(true).How to model the system of equations?The variables of the system are given as follows:
Variable x: number of true/false questions.Variable y: number of multiple choice question.A test has 10 total questions, hence:
x + y = 10.
The test is worth 30 points. A true/false question is worth 2 points, while a multiple choice question is worth 4 points, hence:
2x + 4y = 30.
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PLEASE HELP!!!!!!
This visual representation shows the sets of real numbers. Which statement is true regarding the number sets? Responses Integers and rational numbers have no numbers in common. Integers and rational numbers have no numbers in common. Some integers are also rational numbers, but not all integers are rational numbers. Some integers are also rational numbers, but not all integers are rational numbers. All rational numbers are also integers. All rational numbers are also integers. All integers are also rational numbers. All integers are also rational numbers.
All integers are also rational numbers.
How do you identify a rational number?Integers, fractions, decimals, and more are all included in the set of rational numbers. The term "rational numbers" refers to all numbers that may be written as ratios with a non-zero denominator.We attempt to express an integer as a ratio of two numbers in order to determine whether it is a rational number. Writing it as a fraction with one as the denominator is a simple approach to accomplish this. All integers are rational numbers because any integer may be expressed as the ratio of two other integers.Any number that cannot be stated as a fraction for any integers is considered to be irrational. The decimal expansions of irrational numbers are neither periodic nor do they come to an end.To learn more about rational numbers refer,
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for any positive numbers a, b, and d, with b ≠ 1, logb(a)+logb(d)
For any positive numbers a, b, and d, with b ≠ 1, logb(a)+logb(d) = logab²d.
What are positive numbers ?
The numbers that are greater than zero are considered positive numbers. Zero has no positive or bad aspects.
We've, logb(a)+logb(d)
it can be written as, logb +loga + logb + logd ( ∵ logxy = logx +logy )
= 2 logb + loga + logd
= logb² + loga + logd ( ∵ a logx = log x² )
= logab²d.
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How do you tell the difference between a hole and an asymptote?
As per the concept of the function, the difference between a hole and an asymptote is explained below
The term function in math is known as the special relationship where each input has a single output.
Here we need to find the the difference between a hole and an asymptote.
In order to find the difference, here we must know the definition is asymptote.
The term asymptote is defined as a straight line that constantly approaches a given curve but does not meet at any infinite distance.
Based on the definition of asymptote we have identified the difference between these are that the holes occur when factors from the numerator and the denominator cancel. Where as when a factor in the denominator does not cancel, it produces a vertical asymptote.
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What does plotting the points tell us about the relationship between x and y?
Plotting the points x and y tells us that the points has positive correlation
What is correlation?A statistical measure known as correlation expresses how closely two variables are related linearly (meaning they change together at a constant rate).
It's a typical technique for describing straightforward relationship without explicitly stating cause and consequence.
When two variables behave in unison, rising or falling in lockstep with one another, there is a positive correlation.
When two variables move in opposition to one another—for example, when one rises, the other falls—this is referred to be a negative correlation.
The variables are increasing in the sense that as x increases, y increases
also the graph is not a straight line graph
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