Above given the the linear equations. Systems of liner equations in three variables using substitution method, the variables are (-3.2, -0.218, 0.06).
What do you mean by linear equation?The standard form for the linear equations in two variables is Ax+ By =C. For example, 2x+3y=5 is a linear equation in the standard form. When an equation is given in this form, it's pretty easy to find the both intercepts (x and y). This form is also very useful when solving systems of the two linear equations.
Solve one of the equation for one of it's variables. From the given three variables, there is no incorrect choice so choose to solve for any variable.
x= y+ z -3
Substitute the value from the first variable we solved for into the other equation and solve for the next variable.
(y+z-3) +y +3z = -2
2y+4z= 1
y= [tex]\frac{1+4z}{2}[/tex]
Substitute the value from the two variables that we solved and plug it into the remaining equation and solve for the last remaining variable.
3([tex]\frac{1+4z}{2}[/tex]+z-3) - 2 ([tex]\frac{1+4z}{2}[/tex]) + 3z= -12
3([tex]\frac{1+4z+2z-6}{2}[/tex])- 2([tex]\frac{1+4z}{2}[/tex])+ 3z= -12
3([tex]\frac{6z-5}{2}[/tex])- 2([tex]\frac{1+4z}{2}[/tex])+3z = -12
[tex]\frac{18z-15}{2}[/tex]- 1+ 4z+ 3z= -12
18z-15-2+8z +6z= -24
32z-17=-24
32z=-24+17
z=[tex]\frac{-7}{32}[/tex]= -0.218
therefore, y= 0.06
Now substitute the values:
x= 0.06+(-0.218)-3= -3.2
The three variables are (-3.2, -0.218, 0.06)
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What are the three principles of describing data?
dispersion, range and standard deviation mean, median and mode
Mean, median and mode are the three principles of describing data.
Describing data:- Describing data is also called descriptive statistics, that describes the data through several methods such as graphical representations, central tendency, variability. It summarizes the data efficiently, which helps to make any conclusion on that dataset.
The three principles of describing data are-
Mean:- The summation of all the values divided by the total number of values, is called mean. It is also called as average.Median:- The middle value is called median.Mode:- The value, which occurs most often in a set of all values, is called mode.Thus we can conclude that, mean, median and mode are the three principles of describing data.
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a farmer places beehives containing bees in her orchard to pollinate the plants. The table below shows the ratio of the number of beehives to the number of acres in the orchard if the bees pollinate the plants at a constant rate, how many acres will be pollinated by the bees in 18 beehives
I don't know helpp me with the mathhh pleaseee
Step-by-step explanation:
compare 6.51326 and square root of 39 show your work
Local time in melbourne is always 3 hours ahead of singapore time and singapore is 5 hours behind wellington, which is 12 hours ahead of london. what is the time difference between melbourne and london?
The time difference between Melbourne and London is 11.00 hours.
Here we need to find the time difference between Melbourne and London.
Here we have that the time difference between Melbourne and Singapore is 3 hours ahead.
And the Time difference between Singapore and Wellington is 5 hours behind then the difference between wellington and Melbourne is 3 hours.
Now the time difference between Wellington and London is 12 hours.
Through this we know that the time difference between Melbourne and London 11.00 hours.
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5 positive integers are arranged in
ascending order, as follows:
5, 6, 7, 7, x
The mode and the range are equal.
Find x.
x
Answer: x=12
Step-by-step explanation:
The range is: x-5
The mode is: 7
Hence,
x-5=7
x-5+5=7+5
x=12
Find the greatest common factor for each list of numbers 12,18,26,32
The midpoint of KL is (7,3). One endpoint is K (4,1), what is the coordinate for the
other endpoint L?
how to write 0.5.5555.., 0.77777.., 0.288888… and 0.711111… as a fraction
Answer:
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying the equation i2 = −1; every complex number can be expressed in the form a + bi, where a and b are real numbers. Because no real number satisfies the above equation, i was called an imaginary number by René Descartes. For the complex number a + bi, a is called the real part and b is called the imaginary part. The set of complex numbers is denoted by either of the symbols {\displaystyle \mathbb {C} }\mathbb {C} or C. Despite the historical nomenclature "imaginary", complex numbers are regarded in the mathematical sciences as just as "real" as the real numbers and are fundamental in many aspects of the scientific description of the natural world.[1][a]
Step-by-step explanation:
Answer:
iakajakakam kwokwmajsj kakajnsnsj wjjsjajsj sjsjjsjs
Step-by-step explanation:
I don't know what I'm doing wrong here, can anyone help?
if you look at the part where the first part connects with the second part:
y = 5 if x < - 2
y = -2x + 1 if -2 ≤ x < 1
we don't have a discontinuity there, so there shouldn't be a dot.
What is wrong with the graph?When we graph over intervals like (a, b) or [a, b] or something like that, we use dots to define the end of the intervals, and to denote that the function ends abruptly or we have a jump.
In this case, you can see that between the end and the second part and the beginning of the third part there is a jump, so the use of dots is correct there, but if you look at the part where the first part connects with the second part:
y = 5 if x < - 2
y = -2x + 1 if -2 ≤ x < 1
we don't have a discontinuity there, so there shouldn't be a dot.
That is the only error with the graph.
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Please help!!
Please help determine the discriminant and then state how many solutions there are and the nature of the solutions. Do not solve.
3x^(2)+5x-8=0
The discriminant is:
D = 5^2 - 4*3*(-8) = 121
Then we have two real solutions.
How to determine the discriminant?
For a quadratic equation:
a*x^2 + b*x + c = 0
The discriminant is:
D = b^2 - 4ac
If D > 0, we have two real solutions.
If D = 0 we have one real solution (it is thought as two equal solutions)
if D < 0, we have two complex solutions.
In this case, the quadratic equation is:
3x^2 + 5x - 8 = 0
Then:
a = 3
b = 5
c = -8
The discriminant is:
D = 5^2 - 4*3*(-8) = 121
Then we have two real solutions.
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how much do we pay for the mesh around the garden, which has a shape of a square measuring 25m and one ordinary meter of mesh costs 23 euros.
The cost of the mesh measuring 25 m is 2300 euros .
The perimeter of a square is that the distance lined by its four sides. Perimeter surrounds or outlines the form in a very two-dimensional plane.Since all the edges of a sq. square measure equal, therefore, the perimeter of sq. are four times its aspect, i.e. 4 × Side.The perimeter of the sq. is outlined because the total length of the boundary of a sq.. we want to feature all the edges of sq. to seek out its perimeter. By the formula of perimeter of polygonal shape, we know;
Perimeter = add of all sides
Perimeter of sq. = add of the lengths of four sides
= aspect + aspect + aspect + aspect
= 4 × side
First , we will calculate the the perimeter of the square
Perimeter of square = 25 × 4.
= 100 m
Total cost = perimeter required × cost per meter .
Cost of mesh = 100 × 23
= 2300 euros
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9. (6x +12) -2(x-7)= 19
Answer: x=-1.75
Step-by-step explanation:
(6x +12) -2(x-7)= 19
6x+12-2x-(-14)=19
6x+12-2x+14=19
6x-2x+12+14=19
4x+26=19
4x+26-26=19-26
4x=-7
x=-7/4
x=-1.75
Which of the following is equivalent to −4(2x + 3y) − 6(3q + 7p)?
−8x + 12y − 18q + 42p
−8x − 12y − 18q − 42p
−8x + 3y − 18q + 7p
−24(2x + 3y − 3q + 7p)
Answer:
−8x − 12y − 18q − 42p
Step-by-step explanation:
-4 x 3y = -12y and only number 2 is correct
The solution is Option B.
The value of the equation is A = -8x - 12y - 18q - 42p
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 given by
A = -4 ( 2x + 3y ) - 6 ( 3q + 7p )
Now , on simplifying the equation , we get
A = -4 ( 2x ) - 4 ( 3y ) - 6 ( 3q ) - 6 ( 7p )
The value of A = -8x - 12y - 18q - 42p
Therefore , the value of A is -8x - 12y - 18q - 42p
Hence , The value of the equation is A = -8x - 12y - 18q - 42p
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Mark is purchasing new tiles for his bathrooms. The home improvement store charges $48 for each box of tiles when three or fewer boxes are purchased, $45 for each box when 4 to 8 boxes are purchased, $42 for each box when 9 to 19 boxes are purchased, and $38 for each box when more than nineteen boxes are purchased.
a. Write a piecewise function describing the cost of the boxes of tile.
Answer:
f(x)=
1. 48x when x < or = 3,
2. 45x when 4 < or = x < or = 8
3. 42x when 9 < or = x < or = 19
4. 38x when x > 19
Step-by-step explanation:
3 boxes or less = Cost of tiles = $48
4 - 8 boxes ; cost = $45
9 - 19 boxes ; cost = $42
> 19 boxes ; cost = $38
what is 3000 divided by 40 with long division??
3000 ÷ 40 =
75 ⇐ Quotient
――――
40)3000 ⇐ Dividend
280
---
200
200
3000 divided by 40 is equal to quotient of 75 with no remainder.
To perform long division for 3000 divided by 40, Set up the long division format.
Determine how many times 40 can go into the leftmost digit of 3000 (which is 3).
The answer is 75. Write 75 on top of the division bar.
Now, subtract 3000 - 3000 to get the remainder.
The remainder is 0.
Hence, 3000 divided by 40 is equal to 75.
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Heidi was riding her bike on a loop that is 7/8 mile long. she rode for 1/2 mile and then stopped to rest. she rode another 1/4 mile and then had a flat tire. how far does heidi have to wak her bike to complete the loop?
Heidi has to walk her bike for (1/8) mile to complete the loop.
Given that:-
Total distance of the loop = 7/8 mile
Distance Heidi rode on her bike before she stopped for rest = 1/2 mile
Distance Heidi rode on her bike after taking the rest = 1/4 mile.
We have to find the distance Heidi has to to walk to complete the loop because she had a flat tire.
Let the distance Heidi has to to walk to complete the loop because she had a flat tire is x miles.
We know that,
Total distance of the loop = Distance Heidi rode on her bike before she stopped for rest + Distance Heidi rode on her bike after taking the rest + distance Heidi has to to walk to complete the loop because she had a flat tire.
Hence, by adding the fractions, we get
7/8 = 1/2 + 1/4 + x
7/8 = (2+1)/4 + x
7/8 = 3/4 + x
7/8 - 3/4 = x
7/8 - 6/8 = x
1/8 mile = x
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Write 26/9 as a decimal. If necessary, use a bar to indicate which digit or group of digits repeats.
Answer:
The decimal is 2.8 The 8 is the repeating decimal I just couldn't add the line to the top. So it would be 2.88888...
Step-by-step explanation:
A student and teacher are racing to finish a book. It takes the teacher 14.4 hours to complete the book. It takes the student 1.75 times as long to finish. Based on this information, which statement is true?
Answer:
I don't know about that and I don't understand
Tank A initially contained 124 liters of water. It is then filled with more water, at a constant rate of 9 liters per minute. How many liters of water are in Tank A after the following amounts of time have passed?
4 minutes
80 seconds
minutes
How many minutes have passed, , when Tank A contains the following amounts of water?
151 liters
191.5 liters
270.25 liters
liters
Tank B, which initially contained 80 liters of water, is being drained at a rate of 2.5 liters per minute. How many liters of water remain in the tank after the following amounts of time?
30 seconds
7 minutes
minutes
For how many minutes, , has the water been draining when Tank B contains the following amounts of water?
75 liters
32.5 liters
18 liters
liters
1)
In this question, we have been given Tank A initially contained 124 liters of water. It is then filled with more water, at a constant rate of 9 liters per minute.
1 minute = 9 liters
⇒ 60 seconds = 9 liters
⇒ 20 seconds = 3 liters
We need to find the amount of water in the tank A
a) when 4 minutes
Given that, 1 minute = 9 liters
Let y1 liters of water in the tank A after 4 minutes
So, we get an equation,
y1 = 9 × 4
y1 = 36 liters
36 + 124 (initial water level) = 160 liters
Hence, 160 liters of water in the tank A after 4 minutes been passed.
b) when 80 seconds
From given information, 20 seconds = 3 liters
Let y2 liters of water in the tank A after 80 seconds
So, we get an equation,
20 (y2) = 3 × 80
y2 = 12 liters
12 + 124 (initial water level) = 136 liters
Hence, 136 liters of water in the tank A after 80 seconds been passed.
Now we need to find the amount of time passed when Tank A contains the following amounts of water.
i) 151 liters
151 - 124 = 27 liters of more water filled.
As we know, 1 minute = 9 liters ..............................(Given)
Let t1 be the required time.
so, we get an equation,
9 × t1 = 1 × 27
t1 = 27 / 9
t1 = 3 minutes
This means, 3 minutes have passed when Tank A contains 151 liters of water.
ii) 191.5 liters
191.5 - 124 = 67.5 liters of more water filled.
As we know, 1 minute = 9 liters ..............................(Given)
Let t2 be the required time.
so, we get an equation,
9 × t2 = 1 × 67.5
t2 = 67.5 / 9
t2 = 7.5 minutes
t2 = 7 minutes 30 seconds
This means, 7 minutes 30 seconds have passed when Tank A contains 191.5 liters of water.
iii) 270.25 liters
270.25 - 124 = 146.25 liters of more water filled.
As we know, 1 minute = 9 liters ..............................(Given)
Let t1 be the required time.
so, we get an equation,
9 × t1 = 1 × 146.25
t3 = 146.25 / 9
t3 = 16.25 minutes
t3 = 16 minutes 15 seconds
This means, 16 minutes 15 seconds have passed when Tank A contains 270.25 liters of water.
----------------------------------------------------------------------------------------------------
2)
In this question, Tank B, which initially contained 80 liters of water, is being drained at a rate of 2.5 liters per minute.
⇒ 1 minute = 2.5 liters of water drained
⇒ 60 seconds = 2.5 liters
⇒ 10 seconds = 0.42 liters
We need to find the amount of water drained from tank B
a) after 30 seconds
Let x1 be the amount of water drained after 30 seconds
Given that, 1 minute = 2.5 liters
So, we get an equation.
10 (x1) = 30 × 0.42
x1 = 3 × 0.42
x1 = 1.26 liters
b) after 7 minutes
Let x2 be the amount of water drained after 30 seconds
Given that, 1 minute = 2.5 liters
So, we get an equation.
x2 = 7 × 2.5
x2 = 17.5 liters
Now, we need to find the time in which the water is draining when Tank B contains
i) 75 liters
80 - 75 = 5 liters of more water drained.
As we know, 1 minute = 2.5 liters water drained ............(Given)
Let t1 be the required time.
so, we get an equation,
2.5 × t2 = 5
t1 = 5 / 2.5
t1 = 2 minutes
This means, after 2 minutes Tank B contains 5 liters of water.
ii) 32.5 liters
80 - 32.5 = 47.5 liters of more water drained.
As we know, 1 minute = 2.5 liters water drained ............(Given)
Let t2 be the required time.
so, we get an equation,
2.5 × t2 = 47.5
t2 = 47.5 / 2.5
t2 = 19 minutes
This means, after 19 minutes Tank B contains 32.5 liters of water.
iii) 18 liters
80 - 18 = 62 liters of more water filled.
As we know, 1 minute = 2.5 liters water drained ............(Given)
Let t3 be the required time.
so, we get an equation,
2.5 × t3 = 62
t3 = 5 / 2.5
t3 = 24.8 minutes
t3 = 24 minutes 48 seconds
This means, after 24 minutes 48 seconds Tank B contains 18 liters of water.
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2x - 1 = 3x + 8
i ended up getting -7 but i know it’s wrong i just don’t know what i did wrong
Answer:
2x-1=3×+8
Step-by-step explanation:
2×-3x=8+1
-x=9
x=-9
The equation for line r can be written as y= 1/2 x+8. Line s, which is perpendicular to line r, includes the point (2, – 7). What is the equation of line s?
Answer:
y = -2x - 3
Step-by-step explanation:
The slopes of two perpendicular lines are negative reciprocals of each other. So slope of s is -2
using m = -2, x = 2, y = -7
y = mx + b
-7 = (-2)(2) + b
-7 = -4 + b
b = -3
y = -2x - 3
Pls help my homework is due in 7mins
Y=9
X=6
A=4
F=5
T=7
3x+4t=
Answer:
3*x+4*7p
3x+28p ok hard
What is 2 equivalent expressions for (4^9)^3
Answer:
[tex]4^{27}[/tex] and 18014398509482000
1. Which two points lie on a line with slope 2/3? A. (2, 0) and (3,0)
B. (3, –4) and (1, 2)
C. (0, 0) and (2, 3)
D. (–3, 2) and (0, 4)
2. What is the slope of the line that passes through the given points?
(6, –1) and (–3, –1)
A. undefined
B. 0
C. – 2/3
D. – 3/2
If you know the answers to the rest of the quick check please share them!
1. The two points that lie on a line with a slope of 2/3 are: D. (–3, 2) and (0, 4)
2. The slope is: B. 0.
How to Find the Slope of a Line?The formula for finding the slope of a line is:
Slope (m) = change in y/change in x
1. To find the two points that has a slope of 2/3, calculate the slope of each of them:
Slope for A = (0 - 0)/(3 - 2) = 0
Slope for B = (-4 - 2)/(3 - 1) = -3
Slope for C = (3 - 0)/(2 - 0) = 3/2
Slope for D = (4 - 2)/(0 -(-3)) = 2/3
Therefore, the two points that lie on a line with a slope of 2/3 are: D. (–3, 2) and (0, 4)
2. Slope of the line = change in y / change in x = (-1 -(-1))/(-3 - 6)
Slope (m) = 0/-9
Slope (m) = 0
The slope is: B. 0.
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Without making any calculations, which data set has the smallest standard deviation? 1, 1, 2, 2, 3, 3 1, 3, 5 0, 1, 5, 6, 9, 10 1, 1, 1, 1, 2, 2, 2, 2
Answer: 0
Step-by-step explanation:
Answer:
The answer is A
Step-by-step explanation:
Suppose point j is the midpoint of segment lm where j(5, -1) and m(0, 6). what are the coordinates of end point l?
If the midpoint of segment lm where j(5, -1) and m(0, 6), then the coordinates of end point l is (10,-8)..
Midpoint:
Midpoint of a line segment is the point that is halfway between the endpoints of the line segment.
The formula for the midpoint is,
[tex](x_m,y_m)=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]
where,
[tex](x_m,y_m)[/tex] = coordinates of the midpoint
(x₁, y₁) = coordinates of the first point
(x₂, y₂) = coordinates of the second point
Given,
Midpoint = j = (5,-1)
Second point = m = (0,6)
Now, we have to find the first midpoint l.
Let (x,y) be the coordinates of l.
Then apply the values on the formula,
Then we get,
[tex](5,-1)=(\frac{x+0}{2},\frac{y+6}{2})[/tex]
Compare the values in order to find the coordinates,
=> 5 = (x + 0) / 2
=> 5 x 2 = x + 0
=> 10 = x
Similarly,
=> -1 = (y + 6) / 2
=> -1 x 2 = y + 6
=> -2 = y + 6
=> -2 - 6 = y
=> y = -8
Therefore, the coordinates of l is (10,-8).
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there are 24 baseball teams in a league. each team plays two matches against each of the other teams, work out the total number of matches played
Answer:
I need this question too... HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
The total number of matches played is 552
How to determine the total number of matches played?The given parameters are
Teams = 24
Matches against each other = 2
So, the total number of matches played is
Total = Teams * (Teams - 1)
This gives
Total = 24 * (24 - 1)
Evaluate
Total = 552
Hence, the total number of matches played is 552
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The constant ______ of _______ between points on a line.
The slope, rise over run, or change in over the change in of a line determines its rate of change. A graph's slope triangle or two points in a table can be used to compute the slope.
How far is it between the two locations?
By calculating the sum of the absolute values of the y-coordinates, you may determine the distance between two places in different quadrants with the same x-coordinates.
What does a line's slope indicate?
A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).
Describe slope using an example?
The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. B is the b in the location where the y-intercept is located (0, b). For instance, the slope and y-intercept of the equation y = 3x - 7 are 3 and 0, respectively.Learn more about slope
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A 2-pound bag of carrots costs $7.68. What is the price per ounce?
The price of carrots per ounce is $0.24 .
Ounce is an unit of mass in the Imperial System. It is widely used throughout the world and is one of the oldest units of measurement to still exist. The unit ounce is derived from uncia, a unit of measurement in roman times.
The ounce(abbreviated oz) is equal to approximately 28.35 grams and 16 ounces make up a pound.
Now it is given that a 2-pound bag of carrots cost $7.68 .
Therefore price per pound of carrots=$7.68÷2
Price per pound=$ 3.84 .
Now we know that 16 ounces make up a pound.
Price of carrots per ounce= $3.84 ÷16
Price per ounce= $ 0.24
Therefore the price of carrots per ounce is $0.24
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