Answers
The coefficient and constant in the system of linear equations are identified below
System of Linear EquationThe system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1.
In this question, we are given two equations to define the variables.
3x + 7y = 18 ...eq(i)
2x - 4y = 9 ..eq(ii)
In the equations above;
3 = The coefficient of x in the first equation7 = The coefficient of y in the first equation2 = The coefficient of x in the second equation-4 = The coefficient of y in the second equation18 = The constant in the first equation9 = The constant in the second equationLearn more on system of linear equation here;
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Related Questions
compare the y-intercept and the rate of change of the following items
Answers
Answer:
A) They have the same y intercept and the same rate of change
Step-by-step explanation:
Write the equation for the line passing through the points (2,4) and (12,7)
Slope [tex]\frac{7-4}{12-2}[/tex] = [tex]\frac{3}{10}[/tex] = .3
y intercept (b)
y = mx + b
Use 2 fox x, 4 for y and .3 for m
y=mx + b
4 = .3(2) + b
4 = .6 + b Subtract .6 from both sides
3.4 = b
The equation is
y = .3x + 3.4
The two equation are identical so the slope and y intercepts are the same.
compare the y-intercept and the rate of change of the following items. Option (d) The rates of change are the same, but the y-intercepts are different. is correct.
for rates,
we will find the slope of I and II
slope = dy/dx = change in y/change in x
for both of them when we compare the slope, it is 0.3.
for y-intercepts.
equation for II should be formed in order to compare with the y-intercept of I which is 3.4.
y-7=0.3(x-12) .................(i)
so, the y-intercept is 7 for II
thus, the y-intercepts of given eq are not equal.
A circular pond has a diameter of 30 feet. The City of Puebla wants to build a fence enclosing the pond. How many feet of fencing does the city need to enclose the pond?
Answers
The amount of fencing feet the city needs to enclose the pond is 94.29 feet.
What is perimeter?Perimeter can be defined the total distance around an object.
To calculate the amount of fencing the city needs to enclose the pond, we use the formula for the perimeter of a circle.
Formula:
P = πd............ Equation 1Where:
P = Perimeter of the pondd = Diameter of the pondπ = PieFrom the question,
Given:
d = 30 feetπ = 22/7Substitute these values into equation 1
P = 30×22/7P = 94.29 feet.Hence, the feet of fencing needed is 94.29 feet.
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Karen has a bag containing 423 rubber ducks.
If Karen gives 30 rubber ducks to every person she meets, then she will have enough for _____ people and she will have _____ extra ducks left over.
Answers
Answer:
karen will have enough for 14 people, and she will have 3 extra ducks left over
Step-by-step explanation:
divide 423 by 30
423/30 = 14
14 times 30 is 420, so subtract 420 from the total number of rubber ducks
423 - 420 = 3
so, karen will have enough for 14 people and 3 ducks will be left over !!
Answer:
Karen we'll have enough for 14 people and have 3 ducks left over.
If a student had homework 65 days out of 100, what fraction and what
percentage of days did the student not have homework? Choose two
answers.
A. 0.65%
B.
C.
35
100
40
100
D. 65%
E. 35%
65
OF. 100
Answers
Answer:
B and E
Step-by-step explanation:
100-65=35 so the number of days they didn't have homework was 35. 35/100 and 35% represent this.
examine the linear relationships. linear equation a: y=45xy=45x linear equation b is represented by this graph.
Answers
The correct option 1. the slope of Equation A is steeper because 4/5 is bigger than 2/5.
Explain the term slope of the line?A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (variation in y divided by change in x).The format of a linear function is as follows:
y = ax + b
That where:
The rate of change is represented by the slope, or a.The function is steeper the higher the slope:Given by: Linear equation A
y = 4/5 x.
Points (0, 2) and pass through linear equation B. (5, 4).
Given that changes in y divided by change in x determines the slope between two points, we have that:
m = (4 - 2)/(5 - 0)
m = 2/5
Equation A is steeper as it contains a higher slope, so the appropriate response is:
Due to the fact that 4/5 is greater than 2/5, Equation A has a steeper slope.
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The complete question is-
Linear equation A: y=45x
Linear equation B is represented by this graph.
A line that passes through points (0, 2) and (5, 4).
Which statement is entirely correct?
Equation A has a steeper slope, because 4/5 is greater than 2/5.Equation A has a steeper slope, because 4 fifths is greater thanEquation B has a steeper slope, because 4/5 is greater than 2/5.Equation B has a steeper slope, because 4 fifths is greater thanEquation A has a steeper slope, because 5/2 is greater than 4/5.Equation A has a steeper slope, because 5 halves is greater thanEquation B has a steeper slope, because 5/2 is greater than 4/5.a simple random sample of 64 concert tickets was drawn from a normal population. the mean and standard deviation of the sample were $120 and $25, respectively. we want to determine whether the mean of tickets is not equal to $125. find the p-value for this hypothesis testing.
Answers
By using the hypothesis test, to determine whether the mean of tickets is not equal to $125 is calculated as 58%.
We must compute the sample's z-score using the sample mean and standard deviation in order to determine the p-value for this hypothesis test. The z-score calculates how far the sample mean deviates from the population mean by standard deviations.
The difference between the two means is $5 if the population mean is $125 and the sample mean is $120. Given that the sample's standard deviation is $25,
z-score = [tex]\frac{5}{25}[/tex] = 0.2.
We must utilize the z-score to hunt for the equivalent value in a typical normal table in order to determine the p-value. The chance of selecting a sample with a mean of $120 from a population with a mean of $125 is known as the p-value.
The probability that a sample with a z-score of 0.2 would be taken from a population with a mean of $125 is the p-value in this instance. When we look for 0.2 in a typical normal table, we discover that the p-value is roughly 0.58. As a result, 0.58 is the p-value for this hypothesis test. The probability that a sample with a mean of $120 would be taken from a population with a mean of $125 is therefore 58%.
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Phillip has 18 video games. Emily has r video games. Together, Phillip and Emily have a combined total of less than 30 video games. What is an inequality that could be used to represent this situation
Answers
The inequality that represents relationship the number of video games of Phillip and Emily is 18 + r < 30.
What are types of symbols to connect two expressions?
There are two types symbols that connect two expressions. One is known as equal sign and another one is inequality. There are various symbol under inequality and they are less than, greater than, less than or equal, greater than or equal.
Given that Phillip has 18 video games. Emily has r video games.
The number of video games that Phillip and Emily have is 18 + r.
Also given that together, Phillip and Emily have a combined total of less than 30 video games.
Thus 18 + r < 30
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Which of tha following describes the graph of a quadratic function? O a. It opens to the right O b. It opens to the left O c. Its axis of symmetry is a vertical line O d. Its axis of symmetry is a horizontal line
Answers
A parabola is a curved form that represents the graph of a quadratic function. The vertex of a parabola is one of its focal points. The highest or lowest point on the graph corresponds to it. Consider it similar to the parabola's endpoint.
What does the term "quadratic function" mean?
A quadratic function has the formula f(x) = ax2 + bx + c, with a, b, and c being integers and a not equal to zero. A parabola is the shape of a quadratic function's graph.
The basic "U" shape of a parabola is the same whether it opens upward or downward, or with a different "width" or "steepness."
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Draw a line with the given slope through the given point. What other point
lies on that line?
Answers
Answer:
a. Point B
b. Point D
c. Point E
d. Point B
Step-by-step explanation:
See the attached image for a graphed solution with color-coded lines drawn.
How do you write 0.0045 in scientific notation?
Answers
Answer:
[tex]4.5 x 10^{-3} \\[/tex]Step-by-step explanation:
What is the first step made in copying the length of a line segment AB onto another line from the lesson? O Without changing the setting of the compass, place the compass point on one endpoint of the new line segment and swing it so that it intersects the second segment. O Using your straightedge, construct a segment that is longer than the given segment. O Use the compass to measure the length of the segment. O Find a line segment or create a line segment by using your straightedge.
Answers
The first step is to draw a line longer than the given AB line.
What is line segment?An area or portion of a line with two endpoints is referred to as a line segment. A line segment, in contrast to a line, has a known length. A line segment's length can be calculated using either metric measurements like millimeters or centimeters, or conventional measurements like feet or inches.
What is the difference between line and line segment?A line can be extended on both ends forever while a line segment has endpoints.
Step 1: You are instructed to copy line segment AB.
Step 2: A line segment that is longer than line segment AB is drawn in step two. Identify C as one of its endpoints.
Step 3: Position the anchor on one endpoint of line segment AB and the pencil point on the other endpoint of the segment by opening your compass.
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Which of the following are quadratic equations?
(v) 2x^2 −3x +9=0
Answers
2x^2 −3x +9=0 is the given equation that is quadratic.
What is quadratic?The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the general form ax^2 + bx + c = 0. where a, b, and c are numerical coefficients and x is an unknown variable.
Is a quadratic 2 or 4?Quadratic expressions are those involving powers of x up to the second power, not the fourth power, hence the prefix quad signifies "four" rather than "two."
As highest power of variable is 2 so the expression 2x^2 −3x +9=0 is quadratic.
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How do you simplify i^100?
Answers
The solution of i^100 = 1 is [tex]i^{100} = 1[/tex] .
Simplify
Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
Power
In mathematical relationships, power is referred to the number of times a number is multiplied by itself meaning the number you get raising a number to an exponent whereas an exponent can be defined as the number of times the number is used in a multiplication. Exponents are often known as powers or indices.
Exponents
Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner. For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as 34, where 4 is the exponent and 3 is the base. The whole expression 34 is said to be power.
Rewrite [tex]i^{100}[/tex] as [tex](i^{4} )^{25}[/tex]
One to any power is one.
1
From the fact that [tex]i^{2}[/tex] = −1,
Then
([tex]-1^{50}[/tex]) = 1 as −1 raised to any even power is 1.
[tex]i^{100} = 1[/tex]
i^100 = 1
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suppose you have a 3-year lease on a truck that allows 10,000 miles per year, with a 32 cents per mile penalty for overages. in the first year you drive 9,295 miles, in the second year 11,040 miles, and in the third year 12,093 miles. how much of a mileage penalty, if any, do you owe?
Answers
Therefore , the total mileage penalty you owe is $1,002.56
What is equation ?In algebra, an equation is a well-formed formula that connects two expressions with the equals sign to express the equality of the two terms. For example, in French, an équation is described as comprising one or more variables, whereas in English, an equation is any well-formed formula that consists of two expressions connected with the equals sign.
Here,
Given:
a truck with a three-year lease and a 10,000-mile annual mileage cap
32 cents per mile penalty for overages
a) first year you drive 9,295 miles
therefore,
Projected Total Miles= Actual Average Miles per day * Length of Lease
9,125 miles = 25 * 365 days
Allowed Total Miles =Annual Miles Allowed / 12 months * Length of Lease
10,000 miles = 10,000 / 12 months * 12 months
Projected Excess Miles = 0
Projected Lease-end Mileage Charge =Projected Excess Miles * Excess Miles Charge
$0.00 = 0 * $0.32
Therefore first year no excess milage penalty
b)second year you drive 11,040 miles
Projected Total Miles Actual Average Miles per day * Length of Lease
10,950 miles = 30 * 365 days
Allowed Total Miles =Annual Miles Allowed / 12 months * Length of Lease
10,000 miles = 10,000 / 12 months * 12 months
Projected Excess Miles =Projected Total Miles - Allowed Total Miles
1040 miles = 11,040 - 10,000
Projected Lease-end Mileage Charge = Projected Excess Miles * Excess Miles Charge
$332.8 = 1040 * $0.32
Therefore second year $332.8 excess milage penalty
C)third year you drive 12,093 miles
Projected Total Miles Actual Average Miles per day * Length of Lease
10,950 miles = 30 * 365 days
Allowed Total Miles =Annual Miles Allowed / 12 months * Length of Lease
10,000 miles = 10,000 / 12 months * 12 months
Projected Excess Miles =Projected Total Miles - Allowed Total Miles
2093 miles =12,093 - 10,000
Projected Lease-end Mileage Charge = Projected Excess Miles * Excess Miles Charge
$669.76= 2093 * $0.32
Therefore second year $669.76 excess milage penalty
Therefore , the total mileage penalty you owe is $669.76 + $332.8=$1,002.56
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Does the picture represent a function?
Yes or No
Answers
Answer: Yes
Step-by-step explanation: To determine if this graph represents a function, we use what is called the vertical line test.
In other words, if we can draw a vertical or straight up and down line that passes through more than one point on the graph, the relation is not classified as a function.
In this case, it's impossible to draw such a line that hits more than one point on the graph so the relation is a function.
Tristan has $1.40 worth of nickels and dimes. He has twice as many nickels as dimes. Write a system of equations that could be used to determine the number of nickels and the number of dimes that Tristan has. Define the variables that you use to write the system.
Answers
The equation will be d(x+2y) = $1.40,where x = cost of dimes , y = cost of nickels, t = number of dimes.
What is an equation?
In mathematics, equation represent two expressions are equal.
e.g. x + 2y = 3,
Here , x + 2y is one expression and 3 is another, which are equated using equal to symbol.
Let's us consider ,
Number of dimes = t
Then number of nickels = 2t
Cost of one dime = x
Cost of one nickel = y
Then the total cost = xt +2yt
And total cost given = $1.40
So, the final equation = t(x+2y) = 1.40
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The soccer team voted on what they wanted to eat. There are 20 members on the team. Six members voted for pizza, 10 voted for chicken, and the rest voted for hot dogs.
Which ratio represents the number of votes for hot dogs to chicken?
Responses
1/5
2/5
3/5
5/2
Answers
The ratio represents the number of votes for hot dogs to chicken is 2/5 ,
What is ratio?
Comparing two numbers by dividing them is how ratios work. Your formula would be A/B if you were contrasting one data point (A) with another data point (B). By doing so, you are multiplying information A by information B.Given,
Number of members voted for pizza = 6
Number of members voted for chicken = 10
Number of members voted for hot dogs = 20 - (10 +6) = 4
Now we have to determine the ratio represents the number of votes for hot dogs to chicken.
Number of members voted for hot dogs / Number of members voted for chicken = 4/10
= 2/5
Thus, the ratio represents the number of votes for hot dogs to chicken is 2/5.
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as more independent variables are added to a regression model, the coefficient of determination tends to increase. how is this bad?
Answers
This bad is because It can lead to adding variables with little or no predicative power.
Given,
In the question:
As more independent variables are added to a regression model, the coefficient of determination tends to increase.
How is this bad?
Now, According to the question:
Let's know:
What is meant by a regression model?
A regression model is a statistical model that estimates the relationship between one dependent variable and one or more independent variables using a line (or a plane in the case of two or more independent variables).
Hence, This bad is because It can lead to adding variables with little or no predicative power.
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Solve the following equation for x. 10 = 2 - 4 (ax - 3) a. -5/a b. 5/a c. 1/a d. -1/a
Answers
Answer: c. [tex]\frac{1}{a}[/tex].
Step-by-step explanation:
10 = 2 - 4(ax - 3)
10 = 2 - 4ax + 12
10 = 14 - 4ax
Minus 14 on both sides.
-4 = -4ax
Divided -4 on both sides.
1 = ax
Divided a by both sides to solve x.
[tex]\frac{1}{a}[/tex] = x
Therefore, the answer is c.
question content area top part 1 compare the slopes of the lines for y=f(x) and y=g(x) to determine if they are parallel.
Answers
A line's steepness can be determined by looking at its slope.Slope of the line is 15.
How do you find slope of a line?Determine the coordinates of two points along the line that you choose.Find the difference between these two points' y-coordinates (rise). Find the difference between these two points' x-coordinates (run).
Slope of a line passing through two points (x1 ,y1)and will be given by,
Slope 'm' =y2 - y2/ x2- x1
Function 'f' passes through two points (0, 20) and (1, 35).
Slope of the line = 35 -20/1-0= 15
In a similar manner, function 'g' passes through (0, 22) and (1, 37).
Slope of the line = 37 - 22/ 1-0 = 15
Therefore, m1 = m2
Since, slopes of both the lines are equal, lines will be parallel.
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Find the 14th term of the arithmetic sequence -x-5, 6x - 7, 13x - 9,...
Answers
Answer: a₁₄=90x-31
Step-by-step explanation:
-x-5, 6x-7, 13x-9 ...
Hence,
a₁=-x-5
a₂=6x-7
a₃=13x-9
d=a₂-a₁
d=6x-7-(-x-5)
d=6x-7+x+5
d=7x-2
aₙ=a₁+d(n-1)
a₁₄=-x-5+(7x-2)(14-1)
a₁₄=-x-5+13(7x-2)
a₁₄=-x-5+91x-26
a₁₄=90x-31
8x - 3 /AX 4x + 3 When angles form a linear pair, their sum is 180°. 8x - 3+ 4x + 3 = 180 [?]x + [] = 180
Answers
Answer:
12x + 0 = 180x = 15Step-by-step explanation:
You are given the equation 8x -3 +4x +3 = 180 and asked to simplify it and solve for x.
SimplifiedCollecting terms, we have ...
(8 +4)x +(-3 +3) = 180
12x + 0 = 180
Dividing by the coefficient of x gives ...
x = 180/12 = 15
The value of x is 15.
define the level of significance. multiple choice it is the probability of a type ii error. it is the probability of a type i error. it is a z-value of 1.96. it is the beta error.
Answers
By information provided in the question, we can say that It is the probability of a Type I error.
what is probability?The proportion of favorable outcomes to all possible outcomes for an event is known as the probability. The quantity of positive outcomes in an experiment with 'n' outcomes is represented by x. The following equation can be used to determine the likelihood of an event:
Probability (event) = positive outcome / overall outcome = x/n
It refers to the likelihood of a Type I mistake.
The likelihood that a Type I error will occur, or the likelihood that a null hypothesis will be rejected when it is true, determines the degree of significance.
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Graph the functions to find the x values that satisfy the inequality.
f(x)=-2(x+3)^2+5
g(x)=x+7
For what values of x is f(x)≤g(x)?
Options:
(-∞,∞)
No values of x
[-5, -2]
(-∞, -5]∪[-2, ∞)
Answers
no value of x for f(x) ≤ g(x)
What do you mean by function?
Function, in mathematics, a formula, rule, or law that defines the relationship between one variable (the independent variable) and another (the dependent variable).
The types of functions can be roughly classified into four types. Based on item:
One-to-one functions, many-to-one functions, on functions, one-to-one, and within functions.
Given functions:
f(x)=-2(x+3)^2+5
g(x)=x+7
According to the graph given for the functions there is no value of x for which f(x) ≤ g(x) .
Therefore, no value of x for f(x) ≤ g(x)
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The lid of a rectangular box of side
[tex]40cm \: by \: 10m[/tex]
is to be sealed all round with tape.
[tex]what \: is \: the \: length \: of \: the \: tape \: required[/tex]
Answers
total length = 2(40) + 2(1000) = 80 + 2000 = 2080cm
the following percentages of chloride were found: 42.62%, 43.10%, 42.90%, and 42.75%. what is the average deviation from the mean
Answers
The average deviation from the mean is 0.19 that can be calculated from the mean.
An average is calculated for a set of numbers that are of the same value range.
Mean = (32.52+32.14+32.61+32.75)/4 = %32.50
Standard deviation =
|32.50-32.52| = 0.02
|32.50-32.14| = 0.36
|32.50-32.61| = 0.11
|32.50-32.75| = 0.25
(.02+.36+.11+.25)/4= 0.19
So the standard deviation is 0.19
Relative deviation = .19/32.50=0.0058 or %0.58
Yes, %32.14, because it deviates too far from the average.
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at a gas station, lora took 1/6 minute to fill 3/5 gallon of gas. at this rate, how many gallons of gas could lora fill in 1 minute?
Answers
The number of gallons of gas that Lora can fill in 1 minute will be 18/5 or 3.6 gallons.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.
At a gas station, Lora took 1/6 minute to fill 3/5 gallons of gas. And we know that the ratio will remain constant.
Let 'x' be the number of gallons. Then the amount of gallons in each minute is calculated as,
(3/5) / (1/6) = x / 1
Simplify the equation, then we have
(3/5) / (1/6) = x / 1
(3/5) × 6 = x
x = 18 / 5
x = 3.6 gallons
The number of gallons of gas that Lora can fill in 1 minute will be 18/5 or 3.6 gallons.
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Jayden and his children went into a grocery store and he bought $8 worth of apples and bananas. Each apple costs $1 and each banana costs $0.50. He bought twice as many bananas as apples. By following the steps below, determine the number of apples, x,x, and the number of bananas, y,y, that Jayden bought.
Determine three ways to have twice as many bananas as apples:
Answers
The number of apples that Jayden bought is 4 and the number of bananas he wants to buy is 8.
The number of ways we can have twice as many bananas as apples is:
8 bananas 4 apples
10 bananas 5 apples
12 bananas 6 apples
How many apples and bananas did Jayden buy?The first step is to form of system of equations that represent the question:
x + 0.50y = 8 equation 1
y = 2x equation 2
The substitution method would be used to determine the required values.
x + (0.50 x 2x) = 8
x + x = 8
2x = 8
x = 8 / 2
x = 4
Substitute for x in equation 2:
y = (2 x 4)
y = 8
The total number of fruits bought is 12 (4 + 8):
The number of ways we can have twice as many bananas as apples :
8 bananas 4 apples
10 bananas 5 apples
12 bananas 6 apples
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Question 11
Erica recorded the number of sales she made during each of the first 4 months when she began her new career. Erica plotted the data on a coordinate grid, and she noted that the data correlate to an exponential equation, as shown What is the domain of the function shown in the graph?
Answers
The domain of the graph is {1, 2, 3, 4}
What is Domain?"All the values" that are input into a function are referred to as the domain of a function. The set of all potential inputs for a function is its domain.
Given:
As, we know domain of a function is the set of all possible inputs for the function.
from the Graph, we can find the coordinates ( 1, 10), (2, 20), (3, 40) and ( 4, 80)
So, the domain of the graph is {1, 2, 3, 4}
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The graph of a linear function passes through (-8,4) and (4,5).What is the equation of the function?
Answers
The linear function that passes through (-8,4) and (4,5) will be y = (1/12)x + 14/3.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
A linear equation or function is given as ;
y = mx + b
The slope (m) associated with two points (x₁, y₁) and (x₂, y₂) is given by
Slope = (y₂ - y₁)/(x₂ - x₁)
The slope associated with (-8,4) and (4,5) will be as,
m = (5 - 4)/(4 + 8) = 1/12
Thus, y = (1/12)x + b
Put (4,5)
5 = (1/12)4 + b
b = 5 - 1/3
b = 14/3
Thus, y = (1/12)x + 14/3
Hence "The linear function that passes through (-8,4) and (4,5) will be y = (1/12)x + 14/3".
For more about the linear function,
brainly.com/question/21107621
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