The inverse of the logarithmic function f x log9x is f-1(x)=9^x.
The inverse of a logarithmic function is the exponential function. To find the inverse of the logarithmic function f x log9x, we can use the following equation: f-1(x)=9^x. This equation states that the inverse of the logarithmic function f x log9x is the exponential function f-1(x)=9^x.
The inverse of the logarithmic function f x log9x is f-1(x)=9^x, which is the exponential function.This means that for any value of x, the inverse of the logarithmic function f x log9x is equal to 9 raised to the power of x. For example, if x=2, then the inverse of the logarithmic function f x log9x is 9^2, or 81. Similarly, if x=3, then the inverse of the logarithmic function f x log9x is 9^3, or 729. In general, the inverse of the logarithmic function f x log9x is 9 raised to the power of x, for any value of x.
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Answer: f –1(x) = 9x
Step-by-step explanation:
A cone whose apex lies along its center axis and whose axis is perpendicular to its base is called a __________ cone.
A right cone is a cone whose apex is located along its center axis and whose axis is perpendicular to its base.
What is meant by right cone?When the line connecting the vertex to the circular base's midpoint forms the cone's axis, the cone is said to be right circular. In other words, the apex of the cone and the centre point of the circular base meet and form a right angle. Having a circular base and an apex or vertex, a cone is a three-dimensional solid. The cone whose axis line is parallel to the base is referred to as the right circular cone. In mathematics, a cone is a recognizable three-dimensional geometric shape having a smooth and curving surface pointing upward. The word "cone" comes from the Greek word "konos," which denotes a peak or a wedge.To learn more about right cone, refer to:
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How do you find the ordered pair?
On a Cartesian (or "coordinate") plane in which each point is represented by an ordered pair (x , y) belongs to x coordinate , y coordinate .
An ordered pair is a set of numbers in which it gives the location of a point on a coordinate plane.
The ordered pair is always expressed exactly the same way (x , y).
The first number in an ordered pair represents the x coordinate on the plane while the second number in an ordered pair represents the y coordinate.
The x-coordinate shoes that how far away the point is horizontally from the x-axis.
The y-coordinate shows that how far away the point is vertically from the x-axis.
Quadrant I: the upper-right quadrant of the plane in which all points in this quadrant have the positive x coordinates and positive y coordinates as { (+,+)} , {(+,+)}
Quadrant II: the upper-left quadrant of the plane in which all points in this quadrant have negative x coordinates and positive y coordinates
{ (+,-)}{ (+,-)}
Quadrant III: the lower-left quadrant of the plane in which all points in this quadrant have negative x coordinates and negative y coordinates
{ (-,-)}{(-,-)}
Quadrant IV: the lower-right quadrant of the plane in which all points in this quadrant have positive x coordinates and negative y coordinates
{(+,-)}{ (+,-)}
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Where is the x-intercept in a quadratic formula?
The x-intercept in a quadratic formula is where the graph of the function crosses the x-axis.
An x-intercept is a point on the graph of a function where the y-coordinate is equal to zero. In other words, it's a point on the graph where the function intersects the x-axis. The x-intercepts of a quadratic formula can be found by setting the y-value equal to zero and solving for x.
The quadratic formula is typically in the form of ax^2 + bx + c =0, thus by setting y=0 we get x = -b/2a and x = -b/2a, these are the x-intercepts where the graph of the function will cross the x-axis. The x-intercepts are also known as the roots or zeroes of the function, and are important for understanding the overall shape of the graph.
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Make
x
the subject of the formula
a = bx + c
Answer: x = a/b - c
Step-by-step explanation:
First divide by b on each side to get the x by itself.
Then subtract c from both sides to make x the subject of the formula.
Step-by-step explanation:
a = bx + c
the goal is to get to a form with "x = ...".
a - c = bx
(a - c)/b = x
done.
ACTIVITY 6: Modeling Real Life
A company is loading recliners and sofas onto a trailer that has a volume of about 3800 cubic feet. Each recliner takes up about 40 cubic feet and each sofa takes up about 80 cubic feet. The company wants the shipment to have at least 30 recliners and more than 25 sofas. Write and graph a system that represents the situation. Give one example of the numbers of recliners and sofas the company can have in the shipment.
The equation is 80x + 1200 = 3800. And the numbers of at least 30 recliners and 32 sofas the company can have in the shipment.
What is linear equation?Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.
Given:
A company is loading recliners and sofas onto a trailer that has a volume of about, 3800 cubic feet.
Each recliner takes up about 40 cubic feet and each sofa takes up about 80 cubic feet.
The company wants the shipment to have at least 30 recliners and more than 25 sofas.
The equation that represents the situation is,
80x + 40y = 3800,
where x is the volume of a sofa and y is the volume of a recliner.
If y = 30 then,
80x + 1200 = 3800
80x = 2600
x = 2600/80
x = 32.5
x ≈ 32
Therefore, 30 recliners and 32 sofas.
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-(4-7)
How do you do this?
I got -4+7
(Is that right)
Jack spends a total of $16.50 on one bag of popcorn and three drinks.
Jill spends a total of $29.75 for two bags of popcorn and five drinks.
Write a system of equations. Determine and state the price of a bag of popcorn and the price of a drink, to the nearest cent.
Answer:
Sure! Here's a system of equations we can set up to represent this situation:
Let x be the price of a bag of popcorn and y be the price of a drink.
Then we can set up the following system of equations:
x + 3y = 16.50 (equation for Jack's purchases)
2x + 5y = 29.75 (equation for Jill's purchases)
To solve this system of equations, we can use the substitution method.
First, we can solve for x in equation 1:
x = 16.50 - 3y
Then, we can substitute this expression for x into equation 2:
2(16.50 - 3y) + 5y = 29.75
Simplifying this equation, we get:
33 - 6y + 5y = 29.75
Combining like terms, we get:
33 - y = 29.75
Subtracting 29.75 from both sides, we get:
33 - 29.75 - y = -y
Simplifying, we get:
3.25 - y = 0
Subtracting 3.25 from both sides, we get:
-y = -3.25
Dividing both sides by -1, we get:
y = 3.25
So, the price of a drink is $3.25.
Now we can substitute this value for y back into equation 1 to solve for x:
x + 3(3.25) = 16.50
Simplifying, we get:
x + 9.75 = 16.50
Subtracting 9.75 from both sides, we get:
x = 6.75
So, the price of a bag of popcorn is $6.75.
To the nearest cent, the price of a bag of popcorn is $6.75 and the price of a drink is $3.25.
Step-by-step explanation:
What is quadrant 1 2 3 and 4?
The explanation of four quadrant are explained below.
In the coordinate plane the first coordinate or the x-coordinate will refer to the number which corresponds with the point's horizontal location as determined by the number on the x-axis.
And the second coordinate known as the y-coordinate, will refer to the number which corresponds with the point's vertical location as determined by the number on the y-axis.
By using these x and y values, we have divide the graph, into four part such as Quadrant I, Quadrant II, Quadrant III and Quadrant IV.
Here we want to know that each quadrant contains certain directions.
=> Quadrant 1 placed on 0 to 90 degrees.
=> Quadrant 2 placed on 90 to 180 degrees.
=> Quadrant 3 placed on 180 to 270 degrees.
=> Quadrant 4 placed on 270 to 360 degrees.
And the value in the quadrant are like as follows:
Quadrant I had both x and y-coordinate are positive.Quadrant II had x-coordinate is negative and y-coordinate is positive.Quadrant III had both x and y-coordinate are negative.Quadrant IV had x-coordinate is positive and y-coordinate is negative.To know more about Quadrant here.
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L) simplify
sin²x ( cot²x + 1 )
Answer: 1.
Step-by-step explanation:
[tex]\displaystyle\\sin^2x(cot^2x+1)=\\\\sin^2x(\frac{cos^2x}{sin^2x}+1)=\\\\\frac{sin^2xcos^2x}{sin^2x}+sin^2x=\\\\cos^2x+sin^2x=\\\\1.[/tex]
carman has saved 80% of the money she needs to buy a new video game. if she saved$36 how much does the video game cost
Carman buy the video game in the cost of $45.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
We have to given that;
Carman has saved 80% of the money she needs to buy a new video game.
And, she saved the cost $36.
Let total cost of the video game = x
So, We can formulate;
⇒ 80% of x = $36
⇒ 80/100 × x = 36
⇒ 8x = 360
⇒ x = $45
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A financial advisor has recommended two possible mutual funds for investment: Fund A and Fund B. The return that will be achieved by each of these depends on whether the economy is good, fair, or poor. A payoff table has been constructed to illustrate this situation:
STATE OF NATURE
INVESTMENT GOOD ECONOMY FAIR ECONOMY POOR ECONOMY
Fund A $10,000 $2,000 –$5,000
Fund B $6,000 $4,000 0
Probability 0. 2 0. 3 0. 5
Draw the decision tree to represent this situation.
Perform the necessary calculations to determine which of the two mutual funds is better. Which one should you choose to maximize the expected value?
Suppose there is a question about the return of Fund A in a good economy. It could be higher or lower than $10,000. What value for this would cause a person to be indifferent between Fund A and Fund B (i. E. , the EMVs would be the same)?
$21,500 this would be cause a person to be indifferent between Fund A and Fund B (i. E. , the EMVs would be the same)
EMV 1 = 0.2*10,000 + 0.3*2,000 + 0.5*-5,000 = $100EMV 2 = 0.2*6,000 + 0.3*4,000 + 0.5*-0 = $2,400.
Comparing both funds based on EMV calculations, Fund B shows a higher EMV. Therefore, to maximize expected value, we should invest in Fund B with an expected value of $2,400. First, his EMV for Fund A is not the same as Fund A's return being higher or lower in good economic conditions. Therefore, the EMC can also be higher or lower. But obviously the economy changes quickly sometimes. You don't always get the same return. So relying solely on returns is risky. Relying heavily on favorable economic conditions makes Fund A vulnerable to change and increases investor risk, so investors need to be more diversified. We can do the calculation:
Fund A return in good economy = Difference between A and B: EMV (Fund A) = EMV (Fund B) 0.2*X + 0.3(2,000) + 0.5(- 5,000) = 2 4,000.2X = 4,300X = $21,500.
Therefore, if the economy is good, Fund A's return should be $21,500 for there to be indifference between Fund A and the fund B.
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21
Kinza goes on holiday to South Africa.
Kinza wants to change £950 into South African rand.
She wants to get as many 200 rand notes as possible.
The exchange rate is £1 = 18.53 rand.
Work out the greatest number of 200 rand notes that Kinza can get for £950
A lost tourist arrives at a point with 2 roads A and B. Road A leads to the city and takes either 4 or 8 hours, depending on traffic, with equal probability. Road B brings him to the city after 7 hours on average. Since there are no signs on the road, the tourist chooses a road with equal probability; what is the expected time until the tourist arrives to the city
The expected time until the tourist arrives in the city is 4.75 hours.
The expected time until the tourist arrives at the city can be calculated by using the formula for the expected value:
Expected value = (probability of outcome 1) x (value of outcome 1) + (probability of outcome 2) x (value of outcome 2) + ...
In this case, there are two possible outcomes: the tourist takes road A or road B.
If the tourist takes road A, the expected time until he arrives in the city is the average of the two possible travel times (4 hours and 8 hours). The probability of this outcome is 0.5 (the tourist has an equal chance of choosing either road). So, the expected value for this outcome is (0.5) x (4 + 8)/2 = 6 hours.
If the tourist takes road B, the expected time until he arrives in the city is 7 hours. The probability of this outcome is also 0.5. So, the expected value for this outcome is (0.5) x 7 = 3.5 hours.
To find the overall expected time until the tourist arrives in the city, we add up the expected values for each outcome:
Expected time = (0.5) x 6 + (0.5) x 3.5 = 4.75 hours
So the expected time until the tourist arrives in the city is 4.75 hours.
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What is the correct equation for a slope of 2 and a y-intercept of -7
Answer:
y=2x-7
Step-by-step explanation:
y=mx+b ==> m is the slope and b is the y-intercept
y=(2)x + (-7) ==> plugin 2 for m=slope and -7 for b = y-intercept
y=2x-7 ==> simplify
A simple random sample of 10 people were asked how many first cousins they have. The results are listed below.
10, 19, 20, 13, 13, 2, 10, 8, 25, 10
What is the mean number of first cousins for this sample?
10
11.5
13
13.5.
answer is 13
Answer:
13
Step-by-step explanation:
mean= (10+19+20+13+13+2+10+8+25+10)/10=130/10=13
The mean number of first cousins for the given sample is 13. Thus, Option C is correct.
Mean is the arithmetic average of the given set of observations.
Mean for ungrouped or raw data is obtained by adding all the observations and dividing it by the number of observations.
Mean = Sum of all the observations/ Total number of observations.
Mean = ∑( x1 + x2 + x3 .... xn /n)
Where X bar represents mean, n is no. of observations and ∑ denotes sigma i.e. sum of all the values.
No. of observations (n) =10
Mean = ∑ (10 + 19 + 20 + 13 + 13 + 2 + 10 + 8 + 25 + 10) / 10
Mean = 130 / 10
= 13
Therefore, Option C is the correct answer.
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F(x)=Sin2x ,x0=pi:3
f(x)=3x-x^2 ,x0=-1
Pleae help and if omeone ha dicord erver to help olve math problema pleae give me invite
The given equation 1 value of F(x) is 0.109 and in equation 2 F(x) is -4 respectively.
What in mathematics is trigonometric?Trigonometry is one of the important branches in the history of mathematics that deals with the study of the relationship between the sides and angles of a right-angled triangle. This concept is given by the Greek mathematician Hipparchus.
Trigonometry is the study of angles and the angular relationships between planar and three-dimensional figures. The cosecant, cosine, cotangent, secant, sine, and tangent are among the trigonometric functions (also known as the circular functions) that make up trigonometry.
if x⁰=π in eq1
then [tex]f(x)= sin\ 2 \pi[/tex]
[tex]f(x) = 0.109[/tex]
if x⁰= -1 in eq2
then [tex]f(x)=3(-1)-(-1)^2[/tex]
[tex]f(x) = -4[/tex]
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Which is the definition of a ray?
a part of a line that has one endpoint and extends indefinitely in one direction
the set of all points in a plane that are a given distance away from a given point
lines that lie in the same plane and do not intersect
a part of a line that has two endpoints
Definition of Ray:
'A part of a line that has one endpoint and extends indefinitely in one direction'.
The correct statement is A.
What is a ray?A ray is a part of the line having one fixed point and the other point does not have an end. It means that a ray has one terminating end and the other end is extending infinitely.
Given definitions of ray:
A. a part of a line that has one endpoint and extends indefinitely in one direction.
B. the set of all points in a plane that are a given distance away from a given point.
C. lines that lie in the same plane and do not intersect.
D. a part of a line that has two endpoints.
Only statement A satisfies the definition of ray.
Hence, the definition of ray is described by statement A.
A part of a line that has one endpoint and extends indefinitely in one direction.
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A quadrilateral
is a polygon with four sides. Consider
the quadrilateral and the dashed segment. What is the sum
of the measures of the four interior angles of this quadrilateral?
Draw a different quadrilateral. Can you guess the sum
of the measures of its angles? Is it possible to generalize about
the angles of a quadrilateral?
Whatever the case a quadrilateral has always a sum of interior angles = 360°.
What is quadrilateral?A quadrilateral is a closed shape in geometry that is created by connecting four points, any three of which cannot be collinear. A quadrilateral has four sides, four angles, and four vertices. The word "quadrilateral" is derived from the Latin words "quadra" (four) and "latus" (sides). A quadrilateral may or may not have equal lengths on each of its four sides.
A quadrilateral is a polygon with four sides, four angles, and four vertices. The arrangement of the vertices must be considered whenever a quadrilateral is named. For instance, the following quadrilateral should be referred to as ABCD, BCDA, ADCB, or DCBA. Since they alter the order of vertices in which a quadrilateral is formed, it cannot be called ACBD or DBAC.
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On Monday, Lexi rode 3 miles on a bike. On Tuesday, she rode 3 times more than she did Monday. On Wednesday, she rode an additional 4 miles.
How many miles has Lexi ridden so far this week?
Answer:
she has rode 16 miles this week
Step-by-step explanation:
3 miles on monday 3 times that many on tuesday plus 4 miles one wensaday add them all up
3 times 3 is 9 plus 3 is 12 plus 4 is 16 there fore 16 miles in totale
sorry for my speling erros
She rode a total distance of 16 miles this week.
An expression in mathematics is a combination of terms both constant and variable. For example, we can write the expressions as -
2x + 3y + 5
2z + y
x + 3y
The distance rode by Lexi per day is mentioned below -
Monday - Lexi rode 3 miles on a bike.
Tuesday - Lexi rode 3 times more than she did Monday.
Wednesday - Lexi rode an additional 4 miles.
We can write the expression to find the total distance in miles covered by Lexi as -
d = d{M} + d{T} + d{W}
d = 3 + (3 + 3) + 4
d = 3 + 6 + 4
d = 13 miles
Therefore, she rode a total distance of 16 miles this week.
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Zachary's art club ordered a giant sub sandwich for a party. It was 5 feet long! When the sandwich arrived, Zachary cut it into 16 equal pieces.
How long was each piece?
The length of each piece of the sandwich is 0.3125 feet.
What is a unitary method?A unitary approach is a mathematical technique for finding the value of a single unit and then multiplying it by any number of other units to derive the value of the given units.
Given, Zachary's art club ordered a giant sub sandwich for a party.
Therefore, t6o obtain the length of each piece we have divide the total length of the sandwich by the total number of pieces which is,
= (5/16) feet.
= 0.3125.
So, The length of each piece is 0.3125 feet.
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in a school, students either study french, german or spanish. They study one language each. 11 percent of students study french 27percent students study spanish. what fraction of the students study German
Answer:
62%
Step-by-step explanation:
First, you got the formulate: 1-27%-11%
Second, calculate the difference: 0.73-0.11
Third, the sum is 0.62
Then you multiply 0.62 ×100\100
Write a single fraction: 0.62×100\100
Calculate the product or quotient: 62\100
100% to a percentage: 62%
That is your answer 62%
What do the following two equations represent? y+1= -4(x - 2) 2x8y = 16
On solving the provided question, we can say that the values of the equation here will be y +1 = 8X 8y = 16 => y = 9.455
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
y+1= -4(x - 2) 2x8y = 16
x = 0
y +1 = 8X 8y = 16
y = 9.455
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A third-grade student is asked to find the best estimated answer for the problem below by rounding to the nearest ten. 162 287 395 The student gets an answer of 840. Which of the following best describes the student's error
The error is that the student rounded off the outcome after combining the numbers.
What is rounding off?When a number is rounded off, its value is maintained but is brought closer to the next number, simplifying the number.
For entire numbers as well as decimals at different places of hundreds, tens, tenths, etc., it is done.
So, we have:
162 + 287 + 395 = 840
The error:
After adding the numbers, the student rounded the result.
If the learner had added the numbers first and then rounded the result, they would have received the correct answer of 850 instead of 840.
When estimating totals, students should be taught to round numbers first before adding them.
Therefore, the error is that the student rounded the outcome after combining the numbers.
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Correct question:
A third-grade student is asked to find the best-estimated answer for the problem below by rounding to the nearest ten.
162 + 287 + 395
The student gets an answer of 840. Which of the following best describes the student's error?
5.
4.2 cm
4.2 cm
square centimeters
The total area of triangle in square centimeters is 56.7cm squared .The three angles of the triangle add up to 180 degrees.
what is triangle ?The term "trigon" is occasionally (though not frequently) used to refer to a triangle, a 3-sided polygon. Every triangle consists of a set of three angles and three sides, some of which may be the same. The three angles of the triangle add up to 180 degrees. With three sides and three vertices, triangles are a specific type of polygon in geometry. The two-dimensional figure displayed here has three straight sides. A triangle is a type of 3-sided polygon.
here
Area of each triangles is 4.2 x 8.2 or 34.44.
There are two triangles, thus you don't need to divide by two.
In addition, 8.2 is obtained by deducting the top length from the overall length. (13.5-5.3)
rectangle: 22.26 x 5.3
56.7 square meters is the entire area.
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The correct question is
What is the area, in square centimeters, of the triangles are?
a) 5.3 cm
b) 4.2 cm
c) 13.5 cm
Ellen has a bag with 333 red marbles and 222 blue marbles in it. She is going to randomly draw a marble from the bag 300300300 times, putting the marble back in the bag after each draw. 3 red marbles and 2 blue marbles What is the best prediction for the number of times that Ellen will draw a blue marble? Choose 1 answer:
The probability best prediction for the number of times that Ellen will draw a blue marble is 200.
Number of blue marbles: 222
Number of red marbles: 333
Total number of marbles: 555
Probability of drawing a blue marble:
222/555
= 0.4
Number of times drawing a blue marble:
300300300 x 0.4
= 120,120,120
Rounded to nearest whole number:
120,120
Ellen has a bag with 333 red marbles and 222 blue marbles in it. She is going to randomly draw a marble from the bag 300300300 times, putting the marble back in the bag after each draw. The best prediction for the number of times that Ellen will draw a blue marble is 200. This prediction is based on the fact that there are more red marbles than blue marbles in the bag. To calculate this, we first need to determine the probability of drawing a blue marble; there are 222 blue marbles out of 555 total marbles, so the probability is
222/555
= 0.4.
Multiplying this by the total number of draws (300300300) gives us 120,120,120. Rounding this to the nearest whole number gives us our prediction of 200 times.
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The roof on a house is 6 metres wide peaks at at a height of 3 metres above the top of the walls. Find the length of the sloping side of the roof.
HELP THIS IS MY LAST PROBLEM
A store bought a set of speakers for $82.86
and sold it for $195.82. What was the markup percentage? Round your answer to the nearest tenth.
Answer:
142%
Step-by-step explanation:
How I got this solution is made it as a ratio, "82.86:195.82".
I then simplified the balance by dividing 82.86 into both sides.
It then equaled around 0.42 (or 42%). Including itself, it got a markup percentage of 142%
A farmer plants corn and wheat on a 180-acre farm
The farmer needs to sow 135 acres of corn and wheat, and 45 acres of wheat.
What is linear equation ?A linear equation is the algebraic expression y=mx+b. B is the y-intercept, and m is the slope. A "linear equation in two variables" is the term used to describe the previous sentence, where y and x are variables. Two variables make up bivariate linear equations. Examples include the linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is said to be linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.
given
180 acres total land area
The corn acres should be C.
The wheat acres should be W.
A 180-acre property is planted with wheat and corn by a farmer.
Equation 1: C + W = 180
Corn is grown on three times as many acres as wheat:
Equation 2 is created by substituting C = 3W into Equation 1. The result is:
45 acres is W.
For corn, 135 acres equals C.
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slope of a line parallel to the line whose equation is x - 2y = -8
Answer:
Step-by-step explanation:
slope is the coefficient of x when the coeficient of y is 1.
we need change the form.
2y=x+8
y=[tex]\frac{1}{2}[/tex]x+4
so, the slope of a line parallel to the line is 1/2
Which of the following will cause a logical error if you are attempting to compare x to 5?
Answers:
a. if (x >= 5)
b. if (x = 5)
c. if (x == 5)
d. if (x <= 5)
Logical Error: In computer programming language, a logic error is a bug or in a program or code that causes it to operate incorrectly, but not to terminate abnormally (or crash).
A logic error developed unintended or undesired output or other behavior, although it may not immediately be recognized as such.
For example, assigning a value to the wrong variable may cause a many of unexpected program errors.
These errors can be programmer mistakes or sometimes machine less memory to load the code.
if(x>=5) {
// program
}
else if(x==5) {
//program
}
else(x<=5) {
//program
}
they all do not give any error.
x=5 gave an error because it is value assigning to 5.
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