a line ray or segment that divides a segment into two congruent parts at a 90° angle
A line, line segment, or ray that divides an angle into two congruent angles is called an angle bisector.
What are supplementary angles example?
Supplementary angles are those angles that sum up to 180 degrees. For example, angle 130° and angle 50° are supplementary angles because sum of 130° and 50° is equal to 180°. Similarly, complementary angles add up to 90 degrees.
What do you mean by angle bisector?
If the angle is divided by the line and the angle is divided such that the angles are equal to each other then the line is called the angle bisector.
The word congruent means equal of the things. In this, the angles are congruent to each other which means the angles are equal to each other.
Thus, the black space is to be filled by the angle bisector.
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Most Algebra 1 Formulas for needed for CST
The below would be most important Algebra 1 Formulas for CST.
Linear Equation:
[tex]Ax + By + C = 0[/tex]
Equation of Straight Line or Slope:
[tex]y = mx+b[/tex]
Point-slope form:
[tex]y-y_{1} = m(x-x_1)[/tex]
Slope when 2 points are given:
[tex]m = \frac{(y_2 - y_1)}{(x_2-x_1)}[/tex]
Quadratic Equation:
[tex]Ax^2 + Bx +C = 0[/tex]
When lines are parallel:
Slope of both lines are equal. [tex]m_1 = m_2[/tex]
When lines are perpendicular:
Slope of perpendicular lines are opposite reciprocals, meaning if the slope of a line [tex]l_1[/tex] is [tex]\frac{1}{2}[/tex]. The line [tex]l_2[/tex] perpendicular to [tex]l_1[/tex] is [tex]-\frac{2}{1}[/tex].
Work Formula:
Total Work Done = Number of Days [tex]\times[/tex] Efficiency
where Efficiency is inversely proportional to Time Taken.
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__________________energy that comes from the movement of particles.
Thermal energy that comes from the movement of particles.
What is meant by thermal energy ?The energy present in a system that determines its temperature is referred to as thermal energy. Thermal energy flows as heat. Thermodynamics is a whole field of physics that studies how heat is transmitted between various systems and how the procedure is carried out (see the first law of thermodynamics).
The energy that results from a substance's temperature is known as thermal energy. The amount of molecular vibration increases with temperature, increasing thermal energy.
Heat energy is another name for thermal energy. A moving object's kinetic energy is its energy. Thermal energy is a type of kinetic energy because it is produced by moving particles.
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How do you draw an inverse function?
Over the line y = x, a function and its inverse are reflected. It only takes one step to graph a function and its inverse: first, graph the function, then, to graph the inverse, switch all x and y values at each point.
Given,
Inverse function;
A function that can reverse into another function is known as an inverse function or anti function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. When a function is written as "f" or "F," its inverse is written as "f-1" or "F-1."
Here,
To graph the inverse, you only need to alter the x and y values in each point on the function graph. Just take a look at all the numbers that are being reflected along the line y = x as they move from the f(x) function to its inverse g(x) and back again.
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What is mean median and mode 7th grade?
The three statistical measures of central tendency are mean, median, and mode. While describing a set of data, we point out its primary location. This is referred to as the central tendency measure.
The arithmetic mean of a given data is the sum of all observations divided by the number of observations.
The data set's median is the value in the center. Put all the numbers in ascending or descending order, and then choose the middle number to determine the median. There will only be one middle integer if the number of data points is odd. If the number of data points is even, you must choose the middle two numbers, add them together, and divide by two. Your median will be that value.
A mode is defined as the value that has a higher frequency in a given set of values. It is the value that appears the most number of times.
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Why is the slope called M?
In the equation y = mx + b, m is the slope of the line and b is the intercept.
What does the m represent in slope intercept form?The letter m is frequently used to represent slope; the reason for this usage is unclear, but it can be found in O'Brien's (1844) and Tod hunter's (1888) formulations of the equation for a straight line as "y = mx + b" and "y = mx + c," respectively.m is the line's slope and b is its intercept in the equation y = mx + b. The letters x and y stand for the line's separation from the x- and y-axes, respectively. When x = 0, the value of b equals y, and m indicates how steep the line is. The gradient of a line is another name for its slope.To learn more about slope intercept equation refer to:
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Help Please :> Its for my homework I don't understand it :p
Answer:
>
Step-by-step explanation:
81 is greater than 64
What is the slope of the line represented by the equation y − 3x 1?
Applying the derivative to the provided line with respect to "x," using the equation of the given line, The response is 3.
Why do you use the word "derivative"?In mathematics, the derivative of a function of a real variable measures the sensitivity of the function's value to changes in its argument. The derivative is the fundamental tool in calculus. a function's rate of evolution in respect to a variable Problems involving calculus and differential equations need the use of derivatives.
By slope, what do you mean?The slope or gradient of a line in mathematics is a numerical representation of the steepness and direction of the line. Calculate the percentage by dividing the elevation difference between two places by their separation. slope, then multiply the result by 100. The term "rise" refers to the difference in elevation between two sites. The run is the separation between the points. Percent slope is therefore equal to (rise / run) x 100.
y(x) = 3x +1
derivate y(x) with respect to x. we get,
= 3
slope =3
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In a survey, one out of three people named blue as their favorite color. Two out of seven named red. If 1,092 people were included in the survey, how many named neither blue nor red as their favorite color?
By using fraction, it can be calculated that 416 people choose neither blue nor red as their favorite color.
What is fraction?
Suppose there is a collection and a part of the collection has to be taken. The part which is taken is called fraction. In other words, part of a whole is called fraction.
The upper part of the fraction is the numerator and the lower part of the fraction is called denominator.
This is a word problem on fraction.
Fraction of people choose blue as their favorite color = [tex]\frac{1}{3}[/tex]
Fraction of people choose red as their favorite color = [tex]\frac{2}{7}[/tex]
Fraction of people choose neither red nor blue as their favorite color =
[tex]1- (\frac{1}{3}+\frac{2}{7})\\\\1 - (\frac{7 + 6}{21})\\\\1-\frac{13}{21}\\\\\frac{21-13}{21}\\\\\frac{8}{21}[/tex]
Total number of people surveyed = 1092
Number of people choose neither red nor blue as their favorite color =
[tex]\frac{8}{21}\times 1092[/tex]
= 416
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what is the slope if all y's are 5 in a table of data
Answer: 0 slope; horizontal line
In Angle abc and angle pqr ab:pq=4:5 and a(angle pqr)=125cm² then find a(angle abc)
Answer:
Therefore, the measure of angle ABC is 55 cm².
Step-by-step explanation:
In order to solve this problem, we need to use the property of angles in a linear pair, which states that the measures of the two angles in a linear pair add up to 180 degrees.
If angle ABC and angle PQR form a linear pair, then the measure of angle ABC is 180 degrees minus the measure of angle PQR.
Since the measure of angle PQR is 125 cm² and the measure of angle ABC is 180 degrees minus the measure of angle PQR, the measure of angle ABC is:
180 degrees - 125 cm² = 55 cm²
Let [tex]\displaystyle f(x)= \lim_{n\to \infty}\left( \dfrac{n^n (x+n)\left(x+\dfrac{n}{2}\right) \dots \left(x+\dfrac{n}{n}\right)}{n! (x^2+n^2)\left(x^2+\dfrac{n^2}{4}\right)\dots \left( x^2+\dfrac{n^2}{n^2}\right)}\right)^{\dfrac{x}{n}}[/tex] for all x > 0 , then;
[tex] A ) \ f\bigg(\dfrac{1}{2}\bigg) \geq f(1) \\\\ B)\ f\bigg(\dfrac{1}{3}\bigg) \leq f\bigg(\dfrac{2}{3}\bigg) \\\\ C) \ f'(2)\leq 0 \\\\ D) \ \dfrac{f'3(3)}{f(3)}\geq \dfrac{f'(2)}{f(2)} [/tex]
The solution is Option C.
The equation f'( 2 ) ≤ 0 is true
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
[tex]f ( x ) = \lim_{n \to \infty} [ \frac{( n^{n} ( x + n ) ( x + \frac{n}{2} ) ....( x + \frac{n}{n} )}{n! (x^{2}+n^{2}) ( x^{2} + \frac{n^{2}}{4} ) ....( x^{2} +\frac{n^{2}}{n^{2} } ) } ]^{\frac{x}{n} }[/tex]
Taking logarithm on both sides of the equation , we get
[tex]ln f ( x ) = \lim_{n \to \infty} \frac{x}{n} [\sum _{r=1}^nln\frac{1}{r/n} + \sum _{r=1}^nln\frac{(x + \frac{1}{r/n} )}{(x^{2} + (\frac{1}{r/n})^{2} ) }[/tex]
On simplifying the derivatives of the equation , we get
[tex]ln f ( x ) = x [\int\limits^1_0 {ln ( 1/t )} \, dt + \int\limits^1_0 {ln \frac{( x+1/t )}{(x^{2} + 1/t^{2} ) } } \, dt][/tex]
Now , substituting the limits in the equation , we get
[tex]ln f ( x ) = x [ \int\limits^1_0 {( - ln t+ ln (tx+1)-lnt-ln(t^{2} x^{2}+1)+lnt^{2}] } \, dt[/tex]
Substitute the value of tx = z in the equation , we get
[tex]ln f ( x ) = \int\limits^1_0 {ln\frac{(1+z)}{1+z^{2} } } \, dz[/tex]
Taking exponential on both sides of the equation , we get
[tex]f ( x ) = e^{\int\limits^x_0 {{ln\frac{(1+z)}{1+z^{2} } } \, dz} \, }[/tex]
Differentiating with respect to x , we get
[tex]\frac{f' (x ) }{f ( x ) } = ln\frac{1+x}{1+x^{2} }[/tex]
Now , on further simplification of the equation , we get
f ( x ) > 0 for x > 0
And , f' ( x ) > 0
[tex]ln\frac{1+x}{1+x^{2} } > 0[/tex]
And ,
x > x²
0 < x < 1
Therefore , f ( x ) is increasing ∀ x ∈ ( 0 , 1 )
Hence , the equation f' ( 2 ) ≤ 0 is true
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Explanation:
[tex] \rm f(x) = \lim \limits_{n \to \infty } \left( \dfrac{ \displaystyle \rm \prod \limits_{r = 1}^n \left(1 + \dfrac{rx}n \right ) }{\displaystyle \rm\prod \limits_{r = 1}^n \left(1 + \bigg(\dfrac{rx}n \bigg)^{2}\right )} \right)^{ \dfrac{x}{n} }[/tex]
[tex] \large \rm = {e}^{ x \int \limits_{0}^{1} ln(1 + xy)dy - ln(1 + (xy {)}^{2} ) dy }[/tex]
[tex]\rm f'(x)=f(x) \ln \bigg( \dfrac{1 + x}{1 + {x}^{2} } \bigg)[/tex]
[tex]\rm For \: x \in(0,1) \: it \: i s \: increasing \: function[/tex]
[tex]\rm f'(2) = f(2) \ln( \frac{3}{5} ) < 0[/tex]
[tex]\rm \dfrac{f'(3)}{f(3)} =ln \bigg( \dfrac{2}{5} \bigg), \dfrac{f'(2)}{f(2)} = ln \bigg( \dfrac{3}5 \bigg) [/tex]
What represents a function on a graph?
Use the vertical line test to determine whether a graph accurately represents a function. If a vertical line is moved across it and only ever touches it at one point, the graph is said to be a function. If the vertical line crosses the graph more than once, the graph is not a function.
What do we mean by a Graph of a function?Equations that have been solved for y are graphed as functions! In this instance, the graph of f(x) is the graph of y = x² - 3.
Making points for the graph is simple.
Select a value for the first coordinate, then calculate the second coordinate by evaluating f at that value
To establish if a graph reflects a function, use the vertical line test.
The graph is a function if a vertical line drawn across it is moved and only ever touches it at one point.
The graph is not a function if the vertical line crosses it at more than one location.
Therefore, use the vertical line test to determine whether a graph accurately represents a function. If a vertical line is moved across it and only ever touches it at one point, the graph is said to be a function. If the vertical line crosses the graph more than once, the graph is not a function.
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Using the diagram, find GT and TA:
Answer:
GT: 10
TA: 6
Step-by-step explanation:
use the ratio of GR:RE to find GT:TA
since the ratio of GR:RE is 5:3, the ratio of GT:TA=5:3. The total length of GT+TA=16.
5x+3x=16, 8x=16, x=2.
By plugging in the x value, it is shown that GT=10 and that TA=6
Let x^{3}-5 x^{2}-17 x+21=0x
3
−5x
2
−17x+21=0 be a polynomial equation.
a) Find all potential rational solution(s) using the Rational Root Theorem. Separate multiple solutions with commas if necessary.
Preview
b) Find all the distinct, actual rational solution(s). Separate multiple solutions with commas if necessary. If no solutions exist, enter \text{None}None.
By Rational Root Theorem, all rational roots of the polynomial equationx³-5x²-17x+21 = 0x is (x−3)(x+1)(x+7).
How do you find rational solution using Rational Root Theorem?The rational root theorem, also known as the rational root test, is an algebraic theorem that states that for a polynomial equation with integer coefficients to have a solution (root) that is a rational number, the leading coefficient (the coefficient of the greatest power) must be divisible by the fraction's denominator and the constant term (the one without a variable) must be divisible by the fraction's denominator.
It is given that,
x³-5x²-17x+21 = 0x
Factor the left side of the equation,
(x−1)(x−7)(x+3)=0
If any of the factors on the left side of the equation equals 0, the entire expression equals 0.
x−1=0
x−7=0
x+3=0
Set, x−1equal to 0 and solve for x.
x−1 equal to 0.
x−1=0
Add 1 to both sides of the equation.
x=1
Set, x−7 equal to 0 and solve for x
Set x−7equal to 0.
x−7=0
Add 7 to both sides of the equation.
x=7
Set x+3 equal to 0and solve for x.
Set x+3 equal to 0.
x+3=0
Subtract 3 from both sides of the equation.
x= −3
The final solution is all the values that make (x−1)(x−7)(+3)=0 true.
x=1,7,−3.
Hence, By Rational Root Theorem, all rational roots of the polynomial equationx³-5x²-17x+21 = 0x is (x−3)(x+1)(x+7).
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What is the nature of the roots of x² − 3x 4 0?
The roots of the equation are x = (3 + iÂ√7)/2 and x = (3 - iÂ√7)/2.
The equation x^2 - 3x + 4 = 0 can be factored as (x - 4)(x - 1) = 0.
Therefore, the roots of the equation are x = 4 and x = 1.
To calculate this, we can use the Quadratic Formula:
x = [-b ± Â√(b^2 - 4ac)]/2a
In this equation, a = 1, b = -3, and c = 4
x = [-(-3) ± Â√((-3)^2 - 4(1)(4))]/2(1)
x = [(3) ± Â√(9 - 16)]/2
x = (3 ± Â√(-7))/2
x = (3 ± iÂ√7)/2
Therefore, the roots of the equation are x = (3 + iÂ√7)/2 and x = (3 - iÂ√7)/2.
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Sienna has 534 pounds of grapes. She eats 18 pound and gives 212 pounds to her brother.
How many pounds of grapes does Sienna have left?
Answer: 304 Pound of Grapes
Step-by-step explanation:
Sienna has 534 grapes. She eats 18 pounds of grapes.
[tex]534-18[/tex]
[tex]=516[/tex]
She gives 212 pounds of grapes to her brother.
[tex]516-212[/tex]
[tex]=\fbox{304 grapes left}[/tex]
the graph at right shows the situation after the u.s. removes a tariff on imports of canned tuna.
The supply-demand curve after US removed tariff on imports is provided. The customer surplus is denoted by area A+B+C+D, loss in producer surplus by A and government loss in revenue by C.
When supply is equal to the demand we get the equilibrium quantity produced and equilibrium price.
The initial price P0 is less than the equilibrium price and thus there is excess demand of the product and thus there is import. When tariff is removed price again drops increasing the excess demand and thus more product is imported.
Consumer surplus is the amount the customer saves as price set by the supplier is less than the amount the consumer is ready to pay. As the customer is ready to pay at P0, the customer surplus when price drop to P1 is given by area A+B+C+D.
The loss in producer surplus is denoted by the area A. As the tariff is removed, the loss in revenue for government is denoted by the area C.
--The question is incomplete, answering to the question below--
"The graph at right shows the situation after the U.S. removes a tariff on imports of canned tuna.
Which areas show the gain in consumer surplus?
A. C
B. A+B+C+D
C. A
D. B+C+D
Which area shows the loss in producer surplus?
A. B+C+D
B. A + B
C. A
D. A+B+C+D
Which area shows the loss in government tariff revenue?
A. A
B. C
C. A+B+C+D
D. B+C+D"
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The ratio of trees to flowering plants in Marsha’s backyard is shown on the ratio table. What number completes the ratio table to make an equivalent ratio? [Type your answer as a number.]
trees 2 12
plants 5 ?
The ratio of trees to flowering plants in Marsha’s backyard is shown on the ratio table.
30 numbers complete the ratio table to make an equivalent ratio.
What is equivalent ratio?When we compare two ratios, they are said to be equivalent. To determine if two or more ratios are comparable, they can be compared to one another.
Equivalent ratios are two ratios with the same value. By multiplying or dividing the two amounts by the same number, you may get the corresponding ratio. Finding comparable fractions follows the same procedure.
Here in this case,
for trees: 2: 12 [ 2 to 12, 6 times more ]
for plants: 5: 30 [ 5 to 30, it is also 6 times more]
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4. lisa wants to make a larger bandana similar to the bandana shown. if the shorter leg of the larger bandana is 15 inches, how long is its hypotenuse? a 10 in. c b 8 in.
Answer: 6 square root 23
Step-by-step explanation:
10^3 + 8^2
subtract ( – 8r–2)–( – 5r–9)
Answer:[tex]-3r+7[/tex]
Step-by-step explanation:
given the equation
[tex](-8r-2)-(-5r-9)[/tex]
Distribute the negative
[tex]-8r-2+5r+9[/tex]
Combine like terms
[tex](-8r+5r)+(-2+9)[/tex]
[tex](-3r)+(7)=[/tex]
[tex]-3r+7[/tex]
Hope this helps!
What are the 4 graphs called?
The four basic graphs used in statistics include bar, line, histogram and pie charts.
What is meant by graphs?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph. Charts and graphs come in a variety of styles. Line graphs, bar graphs and histograms, pie charts, and Cartesian graphs are likely the four most popular types. They serve quite diverse purposes and are best suited for very different uses.Intercepts, intervals where the function is rising, falling, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity are important characteristics. Data that is readily apparent. appropriate unit-specific labeling for each axis.To learn more about graphs refer to:
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when 110 is added to a certain number and the sum is divided by 3, the result is 4 times the original number.What is the original number.
Answer:
Step-by-step explanation:
Let X be the original number.
The problem can be written as the following equation:
(X + 110) / 3 = 4X
Multiplying both sides by 3 gives:
X + 110 = 12X
Subtracting X from both sides gives:
110 = 11X
Dividing both sides by 11 gives:
X = 10
Therefore, the original number is X = 10.
Answer:
(x + 110)/3 = 4x (multiple both side by 3)
x + 110 = 12x
110 = 11x
x = 10
CHECKING(x + 110)/3 = 4x
(10 + 110)/3 = 4(10)
120/3 = 40
40/40
Therefore the original number is 10.Step-by-step explanation:
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I don't see the picture. Can you send it in the message.
Answer:
x 0 2 4 6
y 3 4 5 6
Step-by-step explanation:
y = x/2 + 3
x = 0
y = 0/2 + 3 = 0 + 3 = 3
x = 2
y = 2/2 + 3 = 1 + 3 = 4
x = 4
y = 4/2 + 3 = 2 + 3 = 5
x = 6
y = 6/2 + 3 = 3 + 3 = 6
a new trendy restaurant is growing exponentially. after being open for 11 months the restaurant was serving an average of 310 customers a day. by month 15, the restaurant was serving about 456 customers a day. write an exponential function n(t) that models average number of customers, n, after t months of being open. if necessary, round any values to four decimal places (do not round on intermediate steps). write your answer in the form a(b)t
the exponential function is n(t) =n° (1+r)∧t, where t is the power refers the time in months after opening and n denotes average customer.
what means growing exponentially?when the rate of increases is occurred very rapidly. In this question, the trendy restaurant has earned reputation.
How will be the exponential function?Given, average number of customers after 11 months of opening = n(11) =310
average number of customers after 15 months of opening= n(15) =456
during this 4 month increases of customer =456 -310 =146
increasing rate of customer per month = 146/4 = 36.5
now increasing rate in percentages = 36.5 %
exponential growth rate, r= 0.365
let, n° is the initial number of customer while opening at t=0 month
now, the exponential function n(t) that model's average number of customers, n after t months of being open will be
n(t) = n° ( 1+r)∧t
we are given that after 11 months of opening average customer n(11) = 310
now, 310 = n° (1+ 0.365)∧11
n° = 10
hence, the exponential function = n(t) = 10(1+r)∧t
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Answer the question please
Answer:
81 degrees
Step-by-step explanation:
Because of exterior angles u=u-41+u-40
Solve:
u=2u-81
0=u-81
u=81
now let's look at the data from all the buffalo. if we calculate the 60% confidence interval for every buffalo's count (i.e. data sample), how many cis do we expect to contain the true mean? store your answer in theoretical hits. then we need to check our theoretical answer with our actual data. calculate the 60% confidence interval for each buffalo's count. then commpute how many of those cis contain the true mean. assume that the true mean is 25,000 . store this value in sample hits. does this value match the theoretical value?
For a 60% confidence interval, the number of cis that we expect to contain the true mean is of 60% of the total amount.
What is the interpretation of a x% confidence interval?The interpretation of a x% confidence interval it is x% likely that the population parameter(mean/proportion/standard deviation) is between a and b, which are the bounds of the confidence interval.
The bounds a and b of the confidence interval are given by the estimate plus/minus the margin of error.
The interpretation also means that out of n samples, the percentage which are expected to contain the true mean is of x, hence the percentage for this problem is of 60%, as it is the confidence level.
Missing InformationThe problem is incomplete, hence only the first part could be answered.
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How do you tell the end behavior of a graph from an equation?
The end behavior of a graph can be determined by looking at the leading term in the equation. If the leading term is a positive or negative power of x, then the end behavior of the graph will be either a horizontal asymptoteor an oblique asymptote. If the leading term is a constant, then the end behavior of the graph will be a horizontal line at that constant value.
To determine the end behavior of a graph from an equation, we first look at the leading term in the equation. If the leading term is a positive or negative power of x, then the end behavior of the graph will be either a horizontal asymptote (positive or negative infinity) or an oblique asymptote (slanted line). If the leading term is a constant, then the end behavior of the graph will be a horizontal line at that constant value. For example, if the leading term of an equation is 3x2, then the end behavior of the graph will be a horizontal asymptote at positive infinity. If the leading term of the equation is 4, then the end behavior of the graph will be a horizontal line at y=4. To determine the exact shape of the asymptote, we must look at the coefficient of the leading term. A positive coefficient will create a positive asymptote (sloping up), while a negative coefficient will create a negative asymptote (sloping down). Additionally, if the graph oscillates around a single point, then the end behavior of the graph is a limit cycle.
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A carpet cleaner charges $59 for the first room and $30 for each additional room. A customer does not want to spend no more than $125 for having the carpets in his house cleaned. If r represents the additional rooms, write an inequality that represents the situation
The inequality could be represented by 59 + 30r ≤ 125
According to the given information
Money charged for first room = $59
Money charged for per additional room = $30
The money that the customer could pay = $125
So
We need to write the inequality to determine the situation
Let the number of carpets be r
Firstly , determining an expression for the cleaner charges
59 + 30*r
Since
The customer cannot pay more than $125
Hence
According to the given situation
59 + 30r ≤ 125
30r ≤ 66
r ≤ 2.2
The inequality could be represented by 59 + 30r ≤ 125
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Mrs. Ortega paid $188 for some jeans and T-shirts. A pair of jeans cost $26, and a T-shirt was $16 cheaper than a pair of jeans. If Mr. Ortega bought 3 pairs of jeans, how many T-shirts did she buy?
Answer:
A pair jeans=26$
:. 3 pair jeans=78$
1 t-shirt=10$
No of t-shirt=188$-78$/10$=11