The system of equation is inconsistent as these three equations does not give any solution.
How to solve three variable equations?
In comparison to equations with two variables, a three-variable linear equation requires a little more work to solve. The extra variable is the cause of this complexity.
Even if there are various ways to solve this kind of equation, the elimination technique is still the simplest.
To solve three variable linear equations using the elimination approach, follow these steps:
1. Avoid using fractions and decimals and write all the equations in standard form.
2. Pick an appropriate variable to remove.
3. Remove the chosen variable from any two of the three equations.
4. Choose another set of the two equations, and then take the same chosen variable out.
5. For the two variables they each include, solve the two equations from stages three and four.
6. Replace the answer in fifth step.
7. Reverify by putting them again in the equation.
So according to these given Equations we have to find the value of x, y and z respectively,
-2x + 15y + z = 44
4x + 3y + 3z = 18
-3x+6y-z = 8
After solving these three equations we do not get any solutions.
Hence the system of equations is inconsistent.
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In the problem on the previou page uppoe alex wanted to know how many week it would take him to work 51 hour alex work 3 hour a day and 4 day a week
Since you cannot have a partial week, it would take Alex at least 5 weeks to work 51 hours at this rate.
What is time and work?Time and work is a mathematical concept that includes determining the amount of time necessary to do a specific quantity of labor. This idea is frequently applied in daily life and a number of industries, including manufacturing, construction, and project management.
Problems with time and work include two factors: the quantity of employees and the amount of time needed to finish a task. The quantity of effort is fixed and unchanging. The formula Work = Time * Number of Workers must be applied in order to overcome these issues.
For instance, if a task requires three people to finish it in six hours, the total quantity of work completed is six hours multiplied by three, or 18 hours.
How to solve?
If Alex works 3 hours a day and 4 days a week, he works a total of 3 hours * 4 days = 12 hours per week.
To work 51 hours, it would take Alex 51 hours / 12 hours/week = 4.25 weeks.
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An item is regularly priced at $30 . it is on sale for 70% off the regular price. how much (in dollars) is discounted from the regular price?
The amount in dollars discounted from the regular price is $21
Calculating discounted amountFrom the question, we are to determine the amount that is discounted from the regular price
From the given information,
The regular price is $30
and
The item is on sale for 70% off the regular price.
Thus,
The amount discounted from the regular price = 70% of $30
The amount discounted from the regular price = 70% × $30
The amount discounted from the regular price = 0.7 × $30
The amount discounted from the regular price = $21
Hence, the amount is $21
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100 Points + Brainliest if correct and well explained:
A recent survey at a local recreation center reported that 79% of the participants played pickleball. Of those who play pickleball, 6% are female. Of those who do not play pickleball, 21% are male. Based on this information, construct a two-way relative frequency table. Round all values to the nearest whole percentage.
Male Female Total
Plays pickleball 77% 2% 79%
Does not play pickleball 6% 15% 21%
Column Totals 83% 17% 100%
Male Female Total
Plays pickleball 74% 5% 79%
Does not play pickleball 4% 17% 21%
Column Totals 78% 22% 100%
Male Female Total
Plays pickleball 75% 4% 79%
Does not play pickleball 4% 17% 21%
Column Totals 79% 21% 100%
Male Female Total
Plays pickleball 76% 3% 79%
Does not play pickleball 4% 17% 21%
Column Totals 80% 20% 100%
Answer:
[tex]\begin{array}{|l|c|c|c|}\cline{1-4} \vphantom{\dfrac12}& \sf Male & \sf Female & \sf Total\\\cline{1-4} \vphantom{\dfrac12}\sf Plays \; pickleball & 74\%& 5\% & 79\%\\\cline{1-4} \vphantom{\dfrac12}\sf Does\;not\;play\; pickleball &4\% & 17\%& 21\%\\\cline{1-4} \vphantom{\dfrac12}\sf Column\;Totals&78\%&22\%& 100\%\\\cline{1-4}\end{array}[/tex]
Step-by-step explanation:
Create a blank frequency table:
[tex]\begin{array}{|l|c|c|c|}\cline{1-4} \vphantom{\dfrac12}& \sf Male & \sf Female & \sf Total\\\cline{1-4} \vphantom{\dfrac12}\sf Plays \; pickleball & & &\\\cline{1-4} \vphantom{\dfrac12}\sf Does\;not\;play\; pickleball & & &\\\cline{1-4} \vphantom{\dfrac12}\sf Column\;Totals&&& 100\%\\\cline{1-4}\end{array}[/tex]
If 79% of the participants played pickleball, then 21% of the participants do not play pickleball.
Input these percentages into the table:
[tex]\begin{array}{|l|c|c|c|}\cline{1-4} \vphantom{\dfrac12}& \sf Male & \sf Female & \sf Total\\\cline{1-4} \vphantom{\dfrac12}\sf Plays \; pickleball & & & 79\%\\\cline{1-4} \vphantom{\dfrac12}\sf Does\;not\;play\; pickleball & & & 21\%\\\cline{1-4} \vphantom{\dfrac12}\sf Column\;Totals&&& 100\%\\\cline{1-4}\end{array}[/tex]
Of those who play pickleball, 6% are female.
Therefore, of those who play pickleball, 94% must be male.
The total percentage of those who play pickleball is 79%, so find 6% and 94% of 79%:
[tex]\begin{aligned}\textsf{Plays pickleball (female)}&=6\% \; \sf of \; 79\%\\&=0.06 \times 0.79\\&=0.0474\\&=5\%\; \sf (nearest\;percent)\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Plays pickleball (male)}&=94\% \; \sf of \; 79\%\\&=0.94 \times 0.79\\&=0.7426\\&=74\%\; \sf (nearest\;percent)\end{aligned}[/tex]
Input the found percentages into the table:
[tex]\begin{array}{|l|c|c|c|}\cline{1-4} \vphantom{\dfrac12}& \sf Male & \sf Female & \sf Total\\\cline{1-4} \vphantom{\dfrac12}\sf Plays \; pickleball & 74\%& 5\% & 79\%\\\cline{1-4} \vphantom{\dfrac12}\sf Does\;not\;play\; pickleball & & & 21\%\\\cline{1-4} \vphantom{\dfrac12}\sf Column\;Totals&&& 100\%\\\cline{1-4}\end{array}[/tex]
Of those who do not play pickleball, 21% are male.
Therefore, of those who do not play pickleball, 79% must be female.
The total percentage of those who do not play pickleball is 21%, so find 21% and 79% of 21%:
[tex]\begin{aligned}\textsf{Does not play pickleball (male)}&=21\% \; \sf of \; 21\%\\&=0.21 \times 0.21 \\&=0.0441\\&=4\%\; \sf (nearest\;percent)\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Does not play pickleball (female)}&=79\% \; \sf of \; 21\%\\&=0.79 \times 0.21\\&=0.1659\\&=17\%\; \sf (nearest\;percent)\end{aligned}[/tex]
Input the found percentages into the table and calculate the column totals:
[tex]\begin{array}{|l|c|c|c|}\cline{1-4} \vphantom{\dfrac12}& \sf Male & \sf Female & \sf Total\\\cline{1-4} \vphantom{\dfrac12}\sf Plays \; pickleball & 74\%& 5\% & 79\%\\\cline{1-4} \vphantom{\dfrac12}\sf Does\;not\;play\; pickleball &4\% & 17\%& 21\%\\\cline{1-4} \vphantom{\dfrac12}\sf Column\;Totals&78\%&22\%& 100\%\\\cline{1-4}\end{array}[/tex]
Answer:
c
Step-by-step explanation:
i took the test :)
Use the graph of f(x) to find the following values.
a)f(-4)
b)f(-5)
c)f(3)
d)f(4)
a) [tex]f(-4)[/tex] is equal to the output when [tex]x=-4[/tex]. Therefore, [tex]f(-4)=-7[/tex].
b) [tex]f(-3)=-11[/tex]
c) [tex]f(3)=-3[/tex]
d) [tex]f(4)=-1[/tex]
Sophia scored 92% on a math test. If the test had 50 questions, how many did she get correct?
Answer:46 answers :)
Step-by-step explanation:
explain why a 2 x 2 matrix can have at most two distinct eigenvalues. explain why an n x 11 matrix can have at most n distinct eigenvalues.
An n x 11 matrix can have a maximum of n different eigenvalues, whereas a 2 x 2 matrix can only have a maximum of two. Below, there is a detailed explanation of this.
What is a matrix simple definition?a collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the integers. In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics.
What's the matrix theory?The study of matrices is the main focus of the mathematical field known as matrix theory. It started out as a branch of linear algebra but quickly expanded to cover topics in graph theory, algebra, combinatorics, and statistics.
solution of a 2 x 2 matrix is in given form:
|A - λI| = 0
here,
A = eigenvalue
I = identity matrix
now
|A - λI| = (a11 - λ)
(a22 - λ) - a12a21 = 0
the solutions of above equation are 2 x 2 matrix's eigenvalues.
just like this, a matrix of size n by n may have up to n different eigenvalues as its characteristic equation is a polynomial of nth degree with up to n roots (i.e. n eigenvalues). all due to the equation form: |A - I| = 0, where A is an eigen and I is an identity matrix.
by expanding the determinant:
|A - I| = (-1)
having coefficients c1, c2,..., cn, having sum = zero.
which is nth degree polynomial equation consisting of n possible solutions, that are basically n x n matrix's eigenvalues .
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The seating capacity of the gym at Union Hill is 550. So far, there are 210 fans already at the basketball game. How many more fans can attend the game?
Answer:
340
Step-by-step explanation:
550 - 210 = 340
The drama club sold 800 tickets to their spring play. Floor seats cost 110 each and balcony seats cost 8$ each. Tickets sales were 7740. How many floor seat tickets were sold
There were 14-floor seat tickets sold to their spring play.
What is the Linear equation?A linear equation is defined as an equation in which the highest power of the variable is always one.
Let's assume x be floor seat tickets and y be balcony seats
As per the given formation, the equation would be as:
x + y = 800 ....(i)
110x + 8y = 7740 ...(ii)
Multiply by 8 into equation (i), and subtract into equation (ii),
110x + 8y - 8x - 8y = 7740 - 6400
102x = 1340
x = 1340/102
x = 13.7 ≈ 14
Therefore, there were 14-floor seat tickets sold.
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Please answer fast loads of points!!!!!!!
Answer:
wednesday: 4
thursday: 32
Step-by-step explanation:
Suppose a sale price is $18 and the discount is 25%. Explain how to find the regular price.
Answer:
Step-by-step explanation:
x - 0.25x = 18
3/4x = 18
x = 24
A school sold 461 tickets for the school play. Student tickets cost $3 and adult tickets cost $4. Ticket sales totaled $1624.
Part A. Write and solve a system of equations to model this situation.
Part B. Then explain the meaning of your solution.
The system of equations to model this situation is given by;
x + y = 461
3x + 4y = 1624
The school sold 220 students tickets and 241 adult tickets.
How to write and solve equation?let
Number of students tickets = x
Number of adults tickets = y
x + y = 461
3x + 4y = 1624
From (1)
x = 461 - y
Substitute into (2)
3x + 4y = 1624
3(461 - y) + 4y = 1624
1383 - 3y + 4y = 1624
- 3y + 4y = 1624 - 1383
y = 241
Substitute into (1)
x + y = 461
x + 241 = 461
x = 461 - 241
x = 220
In conclusion 220 students tickets and 241 adults tickets were sold.
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The enrollment for a school in 2010 was 1510 students. In 2020, the enrollment was 860 students. Find and interpret the rate of change in enrollment from 2010 to 2020.
Then the enrollment change rate from 2010 to 2020 is -52.2%.
What is rate of change?A rate of change is the rate at which one quantity changes in relation to another. For example, Change in y = change in x = change in distance = change in time.Here ,
Formulate 860 - 1510 / 1510 based on the given condition.
We have calculate the difference or sum = -650/1245
By converting a fraction to a decimal we get, = -0.52208
we have to multiply a number by its numerator and denominator by 100,
We get,
= -0.52208*100/100
-52.208/100 is the product or quotient.
Hence ,
In 2010, a school had 1510 students enrolled. In 2020, there will be 860 students enrolled. Then the enrollment change rate from 2010 to 2020 is -52.2%.
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The chart shows Maria's workout schedule. Today she worked out with weights and then had a long run. When is the next time Maria will do both workouts on the same day?
The next time Maria will do both workouts on the same day is 15 days
When next Maria will do both workouts on the same day?Weights = every 3 days Long run = every 5 daysFind the lowest common multiple (LCM) for both weight days and long-run days
3 = 3 , 6, 9, 12, 15, 18, 21
5 = 5, 10, 15, 20, 25, 30
The lowest common multiple (LCM) for both weight days and long-run days is 15
Therefore, Maria will do both workout again in 15 days time.
Complete question:
The chart shows Maria's workout schedule. Today she worked out with weights and then had a long run. When is the next time Maria will do both workouts on the same day? Weights every 3 days and long run every 5 days
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On the blueprint of a house, 44 millimeters represents 8 meters. The length of the living room is 33 millimeters on the blueprint. What is
the actual length of the living room?
Answer:
Step-by-step explanation:
The actual length of the explanation is 6 meters.
The diagram shows a sector of a circle radius 10 cm.
Find the perimeter of the sector, giving your answer correct to 1 decimal place.
Answer:
P ≈ 43.6 cm
Step-by-step explanation:
the perimeter (P) is the sum of the 2 radii and the arc
arc length = circumference of circle × fraction of circle
= 2πr × [tex]\frac{135}{360}[/tex]
= 2π × 10 × 0.375
= 20π × 0.375
≈ 23.6 cm ( to 1 decimal place )
Then
P = 23.6 + 10 + 10 = 43.6 cm
Choose the graph of the linear equation.
y = −2x − 8
The equation of line is y = -2x - 8 and the slope is -2
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
y = -2x - 8 be equation (1)
The equation is of the form y = mx + b where m is the slope and b is the y-intercept
Substituting the values in the equation , we get
The slope of the line m = -2
The y intercept of the line b = -8
Now , the graph of the linear equation is given below
Hence , the equation of line is y = -2x - 8
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Solve:
3x/2-5= 7
Please give full explanation
Answer:x=8
Step-by-step explanation:
3x/2-5=7
Move all terms not containing x to the right side of the equation by adding 5 to both sides
3x/2-5+5=7+5
3x/2=12
Multiply both sides of the equation by 2/3 to isolate x.
3x/2*2/3=12*2/3
x=24/3
x=8
Answer: x= 8
Step-by-step explanation:
3x/2-5=7
3x/2 = 12
3x = 24
x= 8
If you can, please give me a Brainliest, thank you!
Given the function: y = 3x + 12 identify the independent and dependent variables.
In the given equation y = 3x + 12, x is the independent variable and y is the dependent variable.
What is an equation?A mathematical connection in which the values of one or more independent variables uniquely determine the values of a dependent variable.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the equation is y = 3x + 12. Here in the equation, the value of the y variable is dependent on the value of x. Then the x variable is independent and the y variable is dependent and depends upon the x variable.
Therefore, in the given equation y = 3x + 12, x is the independent variable and y is the dependent variable.
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24. The following fractions compare the number of free throws made to the number taken by
basketball players:
Smith:
13
19
Haller:
12/20
Dennis:
14/17
Ballard:
17/22
Rank the free throw accuracy of these players from lowest to highest. Justify.
The free throw accuracy of these players can be ranked from lowest to highest as Haller, Smith, Ballard, and Dennis.
What is a fraction?
A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, or three-quarters.
To rank the free throw accuracy of these players from lowest to highest, we need to compare the fraction of free throws made to the total number of free throws taken by each player.
The fraction of free throws made to the total number of free throws taken is called the free throw percentage.
The free throw percentage for each player can be calculated by dividing the number of free throws made by the number of free throws taken and expressing the result as a decimal.
For example, the free throw percentage for Smith can be calculated as follows:
Free throw percentage = 13/19 = 0.68
We can use this same method to calculate the free throw percentage for the other players:
Haller: Free throw percentage = 12/20 = 0.6
Dennis: Free throw percentage = 14/17 = 0.82
Ballard: Free throw percentage = 17/22 = 0.77
Based on these calculations, the free throw accuracy of these players can be ranked from lowest to highest as follows:
Haller: Free throw percentage = 0.6
Smith: Free throw percentage = 0.68
Ballard: Free throw percentage = 0.77
Dennis: Free throw percentage = 0.82
Hence, the free throw accuracy of these players can be ranked from lowest to highest as Haller, Smith, Ballard, and Dennis.
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Ellie and Mary went to the Stef bakery. Ellie bought 3 cakes and 6 filled donuts for $10.14. Mary bought 4 of each for $8.32. What is the price of each type of pastry?
On solving the provided question, by substitution method we got that y=1.43 and x=o.65
What is substitution method?To solve systems of linear equations, use the algebraic technique of substitution. The name of the technique implies that it involves substituting the values of variables from one equation into another.
x=cakes , y=donuts
3x+6y=$10.14 ------ eqt.1
4x+4y=$8.32 ------ eqt.2
solve eqt.1 for "y"
y=1.43
x=o.65
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The correct question is
Ellie and Mary went to the Stef bakery. Ellie bought 3 cakes and 6 filled donuts for $10.14. Mary bought 4 of each for $8.32. What is the price of each type The price of a is The price
A groundskeeper needs
grass seed to cover a circular field, 290 feet in diameter.
A store sells 50-pound bags of grass seed.
One pound of grass seed covers about 400 square feet
of field
What is the smallest number of bags the groundskeeper must buy to cover the circular field?
Explain or show your reasoning
The smallest number of bags the groundskeeper must buy to cover the field is 165 bags.
What is Area of a circle?Area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula, A = πr²
A groundskeeper needs grass seed to cover a circular field, 290 feet in diameter. A store sells 50 pound bags of grass seed. One pound of grass seed covers about 400 square feet of field.
The smallest number of bags the groundskeeper must buy to cover the field.
Diameter of the field = 290 feet
Radius = 145 feet
Area of the circular field = πr²
= 3.14 ×145²
= 66018.5ft²
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Find the sum of 2x2 + 5x + 7 and - 1022 - 7x + 1.
[tex](2x^2 + 5x + 7) + ( - 1,022 - 7x + 1)\\\\2x^2 + 5x + 7 - 1,022 - 7x + 1\\\\2x^2 + 5x + 7 - 1,022 - 7x + 1\\\\2x^2-2x-1,014[/tex]
Tamar's house is greater than 472 and less than 500 which number can be on Tamar's house?
490
472 <490<500
it fits the criteria
i need this asap pleaseee
The correct option using linear equations is [tex]y\leq 2.85x[/tex].
What are linear equations?
A linear equation is one with variables of power 1, such as ax+b = 0, where x is the variable and a and b are fundamental values. Equations are claims that two mathematical expressions comprising one or more variables are equal. The term "linear equation" refers to an equation where the greatest power of the variable is one.
Since the budget is y, the total amount spent on fuel must be less than or equal to the budget. Since it is $2.85 per gallon, the correct equation would be [tex]y\leq 2.85x[/tex].
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the gold prospector panned for gold 1000 times and actually found some 53 of those times. what is the probability that he will find the gold the next time he pans for gold?
Probability is the possibility of happening an event.
Given that, the gold prospector panned for gold 1000 times and actually found 53 times of those times.
The probability that he will find the gold next time is:
53/1000
= 0.053
Hence, the probability that he will find the gold the next time he pans for gold is 0.053.
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A food truck vendor averages 150 tacos sold when the price per taco is $1. A study shows that the average number of tacos sold will increase by 25 tacos for every $1 that the price per taco is
lowered
Which equation models the food truck's average sales in dollars, S, in terms of the price for taco, x?
A S = 25x + 250
B
S=-25x + 250
C S = x(25x + 250)
D
S = x(-25x + 250)
S = 25x + 250 is the equation models the food truck's average sales in dollars, S, in terms of the price for taco, x.
Define equation.Equation is a declaration that two expressions with variables or integers are equal. In essence, equations are questions, and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics. Simple algebraic equations with merely addition or multiplication to differential equations, exponential equations with exponential expressions, and integral equations are examples of different types of equations. They are employed to represent a number of physics laws. also see equation system.
Given
A food truck vendor averages 150 tacos sold when the price per taco is $1.
A study shows that the average number of tacos sold will increase by 25
tacos for every $1 that the price per taco is lowered.
The calculation needed to determine which equation best represents the food truck's average sales in dollars, s, in terms of the price per taco, x, is as follows:
S = 25x + 250
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Rewrite 1/14x^3y + 8/14 xy^2 using a common factor
Answer:
1/14 xy (x² + 8y)
Step-by-step explanation:
common factor of the number = 1/14
common factor of letter part = xy
x³ : x = x²
y : y = 1
1/14 xy (x²
x : x = 1
y² : y = y
1/14 xy (x² + 8y)
The table represents some points on the graph of linear
function f.
Answer: None of these
Step-by-step explanation:
The slope of the graph of [tex]f[/tex] is [tex]\frac{-224-64}{-2-1}=96[/tex].
Using point-slope form,
[tex]f(x)-64=96(x-1)\\\\f(x)-64=96x-96\\\\f(x)=96x-32[/tex]
Therefore, none of the options are correct. This can be confirmed by an online calculator.
ayúdenme por favor...
Answer:
konsi bhasha h bhai ye?
Step-by-step explanation:
i dont understand
A store has apples on sale for $21.00 for 6 pounds.if an apple approximately 5 ounces,how many apples can you buy for $168.00?
Part 1 The cost per pound of the apples on sale is ——-
Part 2 you can buy————pounds of apples for $168.00
Part 3 since 1 pound =16 ounces,so there are about ____apples in each pound
Part 4 you can buy approximately——— apples for $168.00
Help pls
Answer:
A store has apples on sale for $21.00 for 6 pounds.if an apple approximately 5 ounces,how many apples can you buy for $168.00?
you can buy approximately 256 apples
Step-by-step explanation:
Part 1 The cost per pound of the apples on sale is —3.50—-
Part 2 you can buy——48——pounds of apples for $168.00
Part 3 since 1 pound =16 ounces,so there are about __3__apples in each pound
Part 4 you can buy approximately—256— apples for $168.00