Given the function p(x)=6x+2, p(-2) is -10 while p(4) is 26, this shows that value of p(-2) is smaller than the value of p(4). The correct option is B.
What is a function?A function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). It is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Let A & B be any two non-empty sets; mapping from A to B will be a function only when every element in set A has one end, only one image in set B.
p(x)=6x+2
for p(-2)
p(-2) = 6(-2) + 2
p(-2) = -12 + 2
p(-2) = -10
for p(4)
p(4) = 6(4) + 2
p(4) = 24 + 2
p(4) = 26
p(-2) < p(4)
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Answer:
(B) "The value of p(-2) is smaller then the value of p(4)" is True
Step-by-step explanation:
p(x)=6x+2
p(-2) = 6*(-2)+2
p(-2) = -12+2
p(-2) = -10
p(4) = 6*(4)+2
p(4) = 26
====
p(-2) = -10
p(4) = 26
===
(A) The value of p(-2) is larger then the value of p(4). False
(B) The value of p(-2) is smaller then the value of p(4). True
(C) The value of p(-2) is the same as the value of p(4). False
(D) The values of p(-2) and p(4) cannot be compared. False
what are the properties of rational exponents and how are they used to solve problems
The properties of the rational exponents are given and a rational equation is of the form b = aˣ
What are the laws of exponents?When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the rational exponent equation be A
Now , the properties of the exponent equations are
mᵃ×mᵇ = mᵃ⁺ᵇ
The powers of the exponents are added together
mᵃ / mᵇ = mᵃ⁻ᵇ
The powers of the exponents are subtracted together
( mᵃ )ᵇ = mᵃᵇ
The powers of the exponents are multiplied together
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
Any number raised to the power of 0 is 1
m⁻ᵃ = ( 1 / mᵃ )
Hence , the exponents are solved
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Suppose a historian wants to estimate the true mean number of children per household in New York City in 1900. The historian randomly selects 200 household census records from New York City. She records the number of children residing in each household. The historian then computes the mean number of children per household among these 200 households.
The data which is given by the historian is used to find the population, variable, parameter, sample, data, and statistic. He estimated the mean number of children per household in New York City in 1900.
Population - all of the households in New York City in 1900.
Variable - a quantity equivalent to the number of children in a randomly selected household
Parameter - the mean number of children per household in New York City in 1900
Sample - the 200 households selected by the historian
Data - the 200 records collected by the historian
Statistic - the mean number of children per household in the historian's sample.
Complete question:
Suppose a historian wants to estimate the true mean number of children per household in New York City in 1900. The historian randomly selects 200 household census records from New York City. She records the number of children residing in each household. The historian then computes the mean number of children per household among these 200 households. Classify each description as one of a parameter, variable, population, sample, data, or statistic.
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How do you find the two missing sides of an acute triangle?
Using the Pythagorean Theorem (a2 + b2 = c2), plug in the known side lengths to solve for the two unknown sides of an acute triangle.
1. Identify the two known side lengths of the triangle.
2. Plug the known side lengths into the Pythagorean Theorem equation (a2 + b2 = c2).
3. Solve for the two unknown sides of the triangle.
4. The two unknown sides are the lengths of the missing sides of the triangle.
5. To solve for the unknown side lengths, first, calculate the hypotenuse (the longest side) by finding the square root of the sum of the squares of the two shorter sides.
6. Then, calculate the shorter sides by subtracting the square of the hypotenuse from the sum of the squares of the two shorter sides.
7. Finally, use the Pythagorean Theorem to calculate the missing side lengths.
8. The two missing side lengths will be the unknown side lengths of the triangle.
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The foundation for a new high school building is rectangular in shape, and the area is [tex]5x^3 + 4x^2 - 10x - 8[/tex] square meters. Factor by grouping to find expressions for the dimensions of the building
The dimensions of the building are (x² - 2)(5x + 4). The result is obtained by using the expression for the dimensions.
How to factor by grouping?Grouping is a specific technique used to factor polynomial equations. You can use it with quadratic equations and polynomials that have four terms. The method is slightly different.
Here is how to factor by grouping:
Look at the equation and find the master product (ac).Find the factors of ac that the sum is equal to b.Split the center term into two factors.Group the terms to form pairs.Factor out each pair and factor out the shared parentheses.The area of the new high school building in a rectangular shape is 5x³ + 4x² - 10x - 8. Factor by grouping to find the dimensions!
Follow the steps on how to factor by grouping.
5x³ + 4x² - 10x - 8
= (5x³ + 4x²) - (10x - 8)
= x²(5x + 4) - 2(5x - 4)
= (x² - 2)(5x + 4)
Hence, the dimensions of the building are (x² - 2)(5x + 4).
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Which fraction is equivalent to -3/2
A) 3/-2
b) -(3/-2)
C) -3/-2
D) -(-3/2
HELP ASAP PLS
Answer: A
Step-by-step explanation: The other answer choices have 2 negatives which cancel and make a positive number.
Your colleague’s computer stops working, and no one from the IT department is available to fix it. You have basic knowledge of computer hardware. Which action should you take as an ethical employee?
A.
Initiate help by offering to check the computer.
B.
Start a conversation with your colleague and provide a distraction.
C.
Take a quick break and offer your computer for a short time.
D.
Ignore it because it is beyond your designated scope of work.
Since you have basic knowledge of computer hardware, an action which you should take as an ethical employee include the following: A. Initiate help by offering to check the computer.
What is a computer hardware?A computer hardware can be defined as a physical component of a computer system or an information technology (IT) that can be seen, touched and replaced.
In Computer technology, there are various examples of a computer hardware and these include the following:
Power supply unit (PSU).Hard-disk driveKeyboardMonitor (screen)MouseMotherboardCentral processing unit (CPU).Network interface card (NIC).Memory moduleBased on ethical principles, we can reasonably infer and logically conclude that an ethical employee should initiate help by offering to help check the colleague’s computer since he or she has basic knowledge of computer hardware.
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which system of equations has only one solution
4x+2y=8 -4x-2y=3
A wire 30 inches long is bent into a triangle with sides measuring 6 inches, 11 inches, and 13 inches Find the measure of the largest angle in the triangle.
The triangle's internal angles add up to 180 degrees. The biggest angle is then 95.22° in size.
What is trigonometry?
Trigonometry is the study of angles and the angular relationships between planar and three-dimensional shapes.
The cosecant, cosine, cotangent, secant, sine, and tangent are the trigonometric functions (sometimes known as the circle functions) that make up trigonometry.
These functions' inverses are designated by the notations csc(-1)x, cos(-1)x, cot(-1)x, sec(-1)x, sin(-1)x, and tan(-1)x.
Keep in mind that f(-1) here refers to the inverse function, not f to the -1 power.
According to our question-
the biggest angle on a wire that is 30 inches long and bent into a triangle with sides that measure 6 inches, 11 inches, and 13 inches.
cosine rule is given as
cosa= a^2 + b^2 + c^2/2ab
cosa = 36 + 121 - 169/132
a = 95.22°
Hence, The triangle's internal angles add up to 180 degrees. The biggest angle is then 95.22° in size.
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f(n) = 2n-1 find the arithmetic sequence ?
An arithmetic sequence is a sequence of numbers in which the difference between any two successive members of the sequence is a constant value. The general form of an arithmetic sequence is:
a, a + d, a + 2d, a + 3d, ...
where "a" is the first term of the sequence, and "d" is the common difference between successive terms.
Given the function f(n) = 2n - 1, we can see that the function outputs a sequence of integers, with a common difference of 2. So f(n) is not an arithmetic sequence.
Arithmetic sequence is a list of numbers in which each number is the sum of the previous number and a constant number.
Example: 1,3,5,7,9 is an arithmetic sequence because the constant difference is 2.
If you have any other question feel free to ask.
Which of the following is equivalent to 5 a) ²/3 + 2/1/1/0 4 b) 1/2 x 1/1/20 c) / x4 d) / x4 ÷ 4 ? Show your thinking.
Can someone help me find x for both
On solving the provided question, we can say that - the value of x in triangle ABD is = 60
What is triangle?Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is the name given to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.
here, in triangle ABD
x = 60
as its acute angle
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What is the name of a 3 4 5 triangle?
The right angle triangle is the name of the 3, 4, and 5 triangles.
A right-angled triangle is a triangle with one of the angles at 90 degrees. A 90-degree angle is called a right angle.
The formula states that in a right triangle:
The square of the hypotenuse is equal to the sum of the square of the base and the square of the altitude.
(Hypotenuse)² = (Base)² + (Altitude)²
c²=a²+b²
The three numbers which satisfy the above formula are the Pythagorean triplets
Properties of right angle:
The largest angle is always 90º and called the hypotenuse which is always the side opposite to the right angle.
The measurements of the sides follow the Pythagoras rule, which cannot have any obtuse angle.
consider c=5 a=3, b=4 substitute in above formula:
5²=3²+4²
⇒25=9+16
⇒25=25
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How do you know if a graph is wider or narrower than the parent function?
The parabola narrows as the quadratic coefficient increases. The parabola's width increases as the quadratic coefficient decreases.
Define the condition for wider graph of the parent function?The graphs' width and whether or not they slant upward or downward depend on the quadratic term's coefficient, a for the parent function.
The parabola ends point up when the quadratic coefficient is positive.The parabola's ends point down when the quadratic coefficient is negative.The parabola narrows as the quadratic coefficient increases.The parabola's width increases as the quadratic coefficient decreases.The axis of symmetry is moved away from the y-axis by the linear-term coefficient b. The quadratic coefficient's sign and the linear coefficient's sign both affect the shift's direction.The y-intercept is impacted by the constant term c. The intercept point just on y-axis increases higher the higher the number is.To know more about the parent function, here
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I
need to show work please help me its due tomorrow
Answer:
#1
Step-by-step explanation:
boxes apples
3 6
6 12
9 18
10 20
ratio of apples to boxes is 2:1. 2 apples each box. Divide the number of apples by 2 to get the number of boxes. multiply boxes by 2 to get apples.
#2
boxes cherries
3 12
5 20
6 24
7 28
if you divide cherrie by 4 you get the number of boxes.
Multiply boxes by 4 to get cherries.
Ratio of cherries to boxes is 4 to 1.
When Souta went to Sweden, 1 Swedish krona was worth about 0. 12 US
dollar. He took d dollars on the trip. Which equation could be used to find
the value in Swedish krona, k, of the dollars?
A
k = 0. 12d
B
d
k=
0. 12
с
0. 12
k=
d
D k= 1. 12d
If 1 Swedish krona was worth 0.12 US dollar , and if he took d dollars for the trip then the equation that is used to find the value in Swedish krona (k) of the dollars is option (a) [tex]k = 0.12\times d[/tex] .
The value of 1 Swedish krona is = 0.12 US dollar ,
the number of dollar that Souta took on the trip is = d dollars ;
we have to find the equation that can be used to find the equation in Swedish krona "k" of the dollars ,
According to the question ,
the equation for Swedish krona can be represented as [tex]k = 0.12\times d[/tex] ;
Therefore , the required equation is [tex]k = 0.12\times d[/tex] .
The given question is incomplete , the complete question is
When Souta went to Sweden, 1 Swedish krona was worth about 0.12 US dollar. He took d dollars on the trip. Which equation could be used to find the value in Swedish krona, k, of the dollars ?
(a) k = 0.12d
(b) dk = 0.12
(с) 0.12k = d
(d) k = 1.12d
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jacks meeting stared at 2:45 pm and ended at 5:25 pm how long did the meeting last
Jacks meeting lasted for 160 min or 2 hrs 40 min.
What is Time?Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future.
Given is that jacks meeting stared at 2:45 pm and ended at 5:25 pm.
The time for which the meeting lasted can be written as -
{i} = 2:45 pm
{i + 60 minutes} = 3:45 pm
{i + (2 x 60) minutes} = 4:45 pm
{i + (2 x 60 + 40) minutes} = 5:25 pm
{f} = 5 : 25 pm
The meeting lasted for -
2 x 60 + 40
160 minutes
or
2 hours 40 minutes
Therefore, Jacks meeting lasted for 160 min or 2 hrs 40 min.
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Mi Morgan i a cience teacher he found that 30% of her 120 tudent are athlete and Mr. Gregory i a math teacher he found that 27 or 15% of hi tudent are athlete
Of the part, the whole, and the percent, a. the exact number of students that are athletes is unknown to Ms. Morgan, which is 36, and b. the total strength of the students is unknown to Mr. Gregory which is 180.
Here we need to know 3 things- the total no. of students each teacher has, the percentage of athletes, and no. of students that are athletes.
a)
As we can see in the case of Ms. Morgan, we know the total strength of the students and the percentage of the students that are Athletes. Hence what we don't know here is the exact number of students that are athletes.
Hence we need to find 30% of 120
= 30/100 X 120
= 36 students.
b)
Here, in Mr. Gregory's case, we know the percentage and the actual number of students that are athletes. Hence, here we don't know the total strength of the students Mr. Gregory has.
Total strength = no. of athletes X 100/percent of athletes
= 27 X 100/15
= 180 students.
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Complete Question
Ms. Morgan is a science teacher. She found that 30% of her 120 students are athletes. Mr. Gregory is a math teacher. He found that 27, or 15%, of his students, are athletes. a. Of the part, the whole, and the percent, which information is still unknown to Ms. Morgan? Find this unknown value. b. Of the part, the whole, and the percent, which information is still unknown to Mr. Gregory? Find this unknown value.
If a coin is tossed 4 times, the odds of it coming up either heads every time or tails every time are 1:7.
What is the probability the coin comes up all heads or all tails after 4 tosses?
The probability the coin comes up all heads or all tails after 4 tosses is 12.5%.
What is probability?Probability refers to the ratio, chance, likelihood, or odds that an expected outcome is achieved when there are many possible outcomes.
Probability is a fractional value, especially when the odds of the occurrence of the expected event are not 100% uncertain or certain.
In this case, probability lies between zero and one.
Odds of a coin coming up either heads or tails every time = 1:7
The sum of ratios = 8 (1 + 7)
Thus, the probability of the coin coming up with all heads or all tails = 12.5% (1/8 x 100)
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Who can solve these equations?
let's hmmm hmmm multiply both sides by the LCD of all denominators, that way we do away with the denominators and see what "x" is
[tex]\cfrac{x+1}{2}+\cfrac{x+2}{3}=3-\cfrac{x+3}{4}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{12}}{12\left( \cfrac{x+1}{2}+\cfrac{x+2}{3} \right)=12\left( 3-\cfrac{x+3}{4} \right)} \\\\\\ (6x+6)+(4x+8)=36-(3x+9)\implies 10x+14=36-3x-9 \\\\\\ 10x+14=27-3x\implies 10x=13-3x\implies 13x=13 \\\\\\ x=\cfrac{13}{13}\implies x=1 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{1-4x}{10}-\cfrac{2x+1}{2}=\cfrac{5x+1}{5}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{10}}{10\left( \cfrac{1-4x}{10}-\cfrac{2x+1}{2}\right)=10\left( \cfrac{5x+1}{5} \right)} \\\\\\ (1-4x)-(10x+5)=10x+2\implies 1-4x-10x-5=10x+2 \\\\\\ -14x-4=10x+2\implies -4=24x+2\implies -6=24x \\\\\\ \cfrac{-6}{24}=x\implies -\cfrac{1}{4}=x[/tex]
What is the smallest positive multiple of $13$ that is greater than $500?$
Answer:
Step-by-step explanation:
The smallest possible multiple of 13 dollars greater than 500 dollars would be 507 which is 13*39 (i assume you mean whole numbers when you say positive numbers, if not the other answer would be 13*38.461)
Quadrilateral FGHI is similar to quadrilateral JKLM. Find the measure of side JK. Figures are not drawn to scale.
The measure of side KL in the given quadrilateral is 31.88 units.
What is a Quadrilateral?A quadrilateral is a four-sided polygon with four edges and four corners that is used in geometry.
The Latin words Quadri, a variation of four, and latus, meaning "side," are the source of the name.
A two-dimensional shape with four sides, four vertices, and four angles is referred to as a quadrilateral.
Convex and concave are the two main forms.
Convex quadrilaterals can also be divided into a number of subgroups, including trapezoids, parallelograms, rectangles, rhombus, and squares.
So, according to the given figure of FGHI and JKLM:
FG/JK = GH/KL = HI/LM = FI/JM
GH/KL = HI/LM
7/KL = 9/41
KL = 7*41/9 = 31.888
Therefore, the measure of side KL in the given quadrilateral is 31.88 units.
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Correct question with a diagram:
Quadrilateral FGHI is similar to quadrilateral JKLM. Find the measure of side KL. Round your answer to the nearest tenth.
Brigid has a 25-foot ladder she will use to paint the side of her house. What angle does the ladder need to make with house so she can reach 18 feet up the side of her house
The ladder needs to make an angle of approximately 54.7 degrees with the house in order for Brigid to reach 18 feet up the side of the house.
To determine the angle the ladder needs to make with the house, we can use the tangent function.
First, we'll need to determine the opposite side (the height that the ladder needs to reach) and the adjacent side (the distance from the base of the ladder to the house) of the triangle formed by the ladder and the house.
Opposite side = 18 feet
Adjacent side = 25 feet
We can then use the tangent function to find the angle:
tan(angle) = opposite / adjacent
Solving for the angle, we get:
angle = arctan(18/25) = approximately 54.7 degrees
Therefore, the ladder needs to make an angle of approximately 54.7 degrees with the house in order for Brigid to reach 18 feet up the side of the house.
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Find the ratio of the volume of the cone to the volume of the cylinder. Express your answer as a common fraction.
The ratio of the volume of the cone to the cylinder is 1:3.
A cone has a circular base and the base is made of a radius and diameter.
The volume of a cone is defined as the amount of space a cone occupies. The formula of the volume of a cone is given as one-third the product of the area of the circular base and the height of the cone. If the radius of the cone is "r" and the height is "h", the volume of a cone is given as V = (1/3)πr²h.A cylinder is a three-dimensional solid shape that makes of two parallel bases linked by a curved surface.
Thus, the volume (V1) of a right circular cylinder, using the above formula, is,V1= πr²h
Here,
'r' is the radius of the cylinder
'h' is the height of the cylinder
π is a constant whose value is 22/7.
The ratio of the volume of the cone to the cylinder is
= (1/3)πr²h : πr²h
= 1 : 3
So, the ratio is - 1:3.
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Which expression is modeled by this set of arrows on the number line?
On solving the provided question, we can say that - here in number line we jump fron 2 to 7 as we have added +5
what is number line?A number line is a visual representation of real numbers used in introductory mathematics. It is an image of a magnitude line. On the number line, each point represents a real number, and each real number is taken to represent a point. Increments on a number line are separated by equal distances. You can only respond to the numbers on a line in the manner indicated by those numbers. How the number is utilized is determined by the question that goes with it. B: Make a point.
here,
we have +5
so 2+(+5) = 7
we will jump to 7 from 2
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Radicals help please
Consequently, the answer to the above fraction problem comes out to be 1/2 .
What is fraction?An element of a fraction or ratio is a piece of a whole. The number of equally sized pieces into which the whole has been divided is represented by the denominator b, and the number of parts that are included is represented by the numerator a. The LCM of two fractions' denominators is the least common multiple (LCD) of those denominators.
Here,
Given here is: (4√(2) - √(2)) × √(2) / (2) (2) × √(18) (18)
The radical is then simplified in order to determine its value.
=> 3√(2) × √(2) / 2√(2) × 3√(2)
=> 3(2) / 6(2)
=> 3/6
=> 1/2 or 0.5
so,
after simplification, the answer is 1/2.
Consequently, the answer to the above fractional problem comes out to be 1/2 .
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Is the simplified form of 2 square foot 3. Square Foot 12 rational
The simplified form of the given radical expression is rational.
What is exponent ?Exponent can be defined as the method of expressing large numbers in terms of powers. Exponent refers to how many times a number multiplied by itself. For example, 6 is multiplied by itself 4 times, i.e. 6 × 6 × 6 × 6.
We are asked to determine whether the simplified form of 2√3.√12
To solve our given problem we will use exponent property for radicals
√m.√n = a√m.n
2√3.√12=2√3.12
2√3.√12=2√36
2√3.√12=2×6
2√√3.√12=12
The simplified form of the given radical expression is rational.
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Since our given radical expression simplifies to a rational, therefore, our answer is yes
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Please help asap people kept giving me wrong answers. Due tonight in a couple hours +25pts
ES = ___ units
Round your answer to the nearest tenth.
The value of ES will be;
⇒ ES = 10.63 units
What is Line segment?Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.
Given that;
The coordinate of E = (- 3, - 4)
The coordinate of S = (4, 4)
Now,
Since, The coordinate of E = (- 3, - 4)
The coordinate of S = (4, 4)
Hence, The value of ES is find as;
⇒ ES = √ (4 - (-3))² + (4 - (-4))²
= √ 7² + 8²
= √ 49 + 64
= √ 113
= 10.63
Thus, The value of ES = 10.63 units
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What type of lines will be presented by the system of equations 2x 3y 6 and 4x 6y 11?
The system of equations 2x+3y=6 and 4x+6y=11 will present two lines in the coordinate plane.
The linear equation is a mathematical expression that describes a straight line in a coordinate plane. It is of the form y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept (the point where the line crosses the y-axis). Linear equations can also be expressed in other forms, such as ax + by = c, where a, b, and c are constants.
Since each equation represents a line, and the system has two equations, it will have two lines. The lines will be in slope-intercept form (y = mx + b), with different slopes and y-intercepts. The lines will intersect at one point, which is the solution to the system of equations.
The system of equation will present the unique straight line as the solution in two-dimensional coordinate plane.
Two lines in the coordinate plane will present the system of equations 2x+3y=6 and 4x+6y=11 .
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How do you graph log functions with transformations?
required transformed function will be y = parent function+5⇒y=logx+5.
Since, given function y= logx
According to the graph, the transformed function is getting after shifting the function by 5 unit upward.
Thus, transformed function must be equals to parent function+5.
Therefore, required transformed function will be y = parent function+5⇒y=logx+5.
How to do logarithmic transformations?
Image result for How do you graph log functions with transformations?
Recall the general form of a logarithmic function is: f ( x ) = k + a log b where a, b, k, and h are real numbers such that b is a positive number ≠ 1, and x - h > 0. A logarithmic function is transformed into the equation: f ( x ) = 4 + 3 log
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How do you find the asymptotes and zeros of a function?
The process to find the asymptote and zeros of the function is explained below.
The term asymptote is referred as a horizontal/vertical/slant line to which the curve is very close to but the curve doesn't touch the asymptote.
Here we need to find the way to identify the asymptotes and zeros of a function.
The process of finding the asymptote is defined as,
If you want to find the horizontal asymptotes, then apply the limit x→∞ or x→ -∞.
Where as if you want to find the vertical asymptotes, then apply the limit y→∞ or y→ -∞.
Finally, if you want to find the slant asymptote, then divide the numerator by the denominator.
The process of finding the zero of the function is defined as the way to find the values of x where f(x) = 0.
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