Exploring Systems of Linear Equations 2x +3y =8 and 3x+y= -2
Answers
The solution of the linear equations will be ( -2, 4).
What is an equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
Given equations are:-
2x +3y = 8 and 3x+y= -2Solving the equations by elimination method:-
2x +3y = 8
3x+y= -2
Multiply the second equation by 3 and subtract from the first equation.
2x +3y = 8
-9x -3y = 6
----------------
-7x = 14
x = -2
Out of the value of x in any one equation, we will get the value of y.
3x+y= -2
3 ( -2) + y = -2
-6 + y = -2
y = 4
The graph of the equations is also attached with the answer below.
Therefore the solution of the linear equations will be ( -2, 4).
The complete question is given below:-
Exploring Systems of Linear Equations 2x +3y =8 and 3x+y= -2. Find the value of x and y and draw a graph for the system of linear equations.
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Related Questions
Vernon Taber deposits $600 into an ordinary annuity after each quarter for 4 years. The account pays 4% interest compounded quarterly. Find the a) future value, and b) total interest earned.
Answers
The future value is $10,354.72.
The total interest earned is $754.72.
What is the future value and the interest earned?When an amount is compounded quarterly, it means that both the amount deposited and interest already earned increases in value every quarter.
The future value = quarterly deposit x annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = interest rate = 4% / 4 = 1%n = number of years = 4 x 4 = 16Annuity factor = [1.01^16) - 1 ] / 0.01 = 17.26
17.26 x 600 = $10,354.72
Total interest earned = future value - total amount deposited
Total amount deposited = $600 X 4 X 4 = 9600
$10,354.72 - 9600 = $754.72
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how do i factor f(x)= x^4 - 4x^3 +3x^2 + 4x -4 into linear terms?
Answers
The factor of the polynomial f(x) = x⁴ - 4x³ + 3x² + 4x -4 are x = -1, x = 1 and x = 2.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the function f(x) = x⁴ - 4x³ + 3x² + 4x -4. The factor of the polynomial f(x) = x⁴ - 4x³ + 3x² + 4x -4 are x = -1, x = 1 and x = 2.
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If three times a number added to 2 is divided by the number plus 4 the result is eight thirds. Find the number
Answers
Answer:
26
Step-by-step explanation:
(3a+2)/(a+4) = 8/3
(3a+2) = (8/3)(a+4)
(3a+2) = a*8/3 + 4*8/3
(3a+2) = 8a/3 + 32/3
3a - 8a/3 = 32/3 - 2
9a/3 - 8a/3 = 32/3 - 6/3
9a - 8a = 32 - 6
a = 26
Check:
(3*26 + 2) / (26+4) = 8/3
(78+2) / 30 = 8/3
80 / 30 = 8/3
4. The parents made pies for the school bake sale to pay for the next field trip.
They made 55 apple pies and 45 blueberry pies. How many pies did they make
altogether? Estimate first, then solve.
Answers
The total number of pies they made altogether is 100.
How many pies did they make altogether?
In order to determine this value, add the number of blueberry pies with the number of apple pies. Addition is the mathematical operation that is used to determine the sum of two or more numbers.
The total number of pies = 55 + 45 = 100 pies
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Pls Help! Geometry
Find the area of the shaded region.
Answers
Answer: 112.5 square cm
Step-by-step explanation:
The area of the rectangle is [tex](20)(9)=180[/tex] square cm.
The area of the white triangle is [tex]\frac{1}{2}(9)(20-3-2)=67.5[/tex] square cm.
So, the area of the shaded region is [tex]180-67.5=112.5[/tex] square cm.
Which of the following examples illustrates ordinal numbers?
A. Marie counted the number of chips on her plate and said, " I have eight".
B. Gracie told Bradly she would be the first one to go down the slide.
C. Bennett said he had more blocks than anyone.
Answers
Answer:
30-5×2 of 3+(19-3) ÷8
Step-by-step explanation:
30-5×6+(19-3)÷8
30-5×6+16÷8
30-30+8
38-30
8
Answer:
Step-by-step explanation:
b
For a certain company, the cost for producing x items is 60x+300 and the revenue for selling x items is 100x−0.5x2 .
The profit that the company makes is how much it takes in (revenue) minus how much it spends (cost). In economic models, one typically assumes that a company wants to maximize its profit, or at least wants to make a profit!
Part a: Set up an expression for the profit from producing and selling x items. We assume that the company sells all of the items that it produces. (Hint: it is a quadratic polynomial.)
Part b: Find two values of x that will create a profit of $50 .
The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2;4;6 or x+1;x−1 ). The order of the list does not matter. To enter a−−√ , type sqrt(a).
x=
Preview
Part c: Is it possible for the company to make a profit of $2,500 ?
Answers
The answers are
A. The equation for the profit from selling the items is P = 40x-0.5x²-300. b. The values of x are 10 and 70.c. It is not possible to have the profit of 2500How to solve for the expressionWe have the cost function in this question to be
C(x) = 60x+300
We have the function of the revenue to be
Revenue = 100x−0.5x²
A. The formula for revenue function is given
revenue - cost
This is expressed as
= (100x−0.5x²)-60x+300
We have to collect like terms and open the equation above.
This given us:
40x-0.5x²-300B. when profit = 50$
We have p = 40x-0.5x²-300
50 = 40x-0.5x²-300
Multiply the two sides by 10
This gives
500 = 400x - 5x² - 3000
This gives a quadratic equation
5x² - 400x - 3500 = 0
To solve the equation you have to make use of a quadratic calculator.
This gives us the values
x = 10x = 70c. We have P = 40x-0.5x²-300.
at P = 2500
2500 = 40x-0.5x²-300.
Multiply the equation by 10
25000 = 400x - 5x² - 3000
collect like terms
400x - 5x2 - 3000 +28000
400x -5x2 +28000
We have to take the discriminant
-400² - 4*5*28000
= -400000
The discriminant is negative hence it is not possible.
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what to write it here
Answers
Answer:
84 degrees
Step-by-step explanation:
Angle A = 83 degrees
Angle B = x degrees
Angle C = 135 degrees
Angle CDE = 122 degrees
We know that the four inner corners of a quadrilateral should add up to 360 degrees. Two supplementary angles will add up to 180 degrees. Adjacent angles on a straight line will always be supplementary. Knowing this, just solve for <ADC and add that amount to <A and <C. Then, subtract that sum from 360 degrees.
<ADC = 180-122 = 58
58+83+135 = 276
360-276 = 84 degrees
TIME REMAINING
59:23
Jessie graphed one of the lines in a system of equations: y = 3 x minus 2. If the system has an infinite number of solutions, which statements are true? Check all that apply.
On a coordinate plane, a line goes through (0, negative 2) and (1, 1).
Any point in the coordinate plane is a solution because it has an infinite number of solutions.
Point (1, 1) is a solution because it is one of the points on the line already graphed.
It is impossible to tell if (–1,–5) is a solution without seeing the other line graphed.
Point (20, 58) is a solution because it results in a true statement when the point values are substituted into the equation of the line.
When the other line in the system is graphed, it will share all points with the line already graphed.
Answers
Answer:
a & c
Step-by-step explanation:
Answer:
B) Point (1, 1) is a solution because it is one of the points on the line already graphed.
D) Point (20, 58) is a solution because it results in a true statement when the point values are substituted into the equation of the line.
E) When the other line in the system is graphed, it will share all points with the line already graphed.
Step-by-step explanation:
Choose the letter of the equation for
the graph.
Answers
Answer:
a
Step-by-step explanation:
The midline is at y=2.
Eliminate c, d, eAlso, since there is no horizontal shift amongst the remaining options, we know that since y=2 when x=0, this means it must be a sine curve.
This means the answer is a.
Solve the system using substitution.
y - 3x = 1
2y - X = 12
([?], [ ?])
Answers
Answer:
x = 2 , y = 7
Step-by-step explanation:
Since
y-3x = 1
y = 3x+1 - equation 1
2y-x = 12 - equation 2
Since we are using substitution method,
we will substitute equation 1 into equation 2.
[tex]2(3x + 1) - x = 12 \\ 6x + 2 - x = 12 \\ 5x + 2 = 12 \\ 5x = 12 - 2 \\ 5x = 10 \\ x = \frac{10}{5} \\ = 2[/tex]
Now we substitute x into equation 1 to find y.
[tex]y = 3(2) + 1 \\ = 6 + 1 \\ = 7[/tex]
Therefore x = 2, y = 7.
In stats would a test looking at gender & holiday preference would I do a Chi-squared test? Which is the explanatory & which is the response variable?
Any help provided is appreciated. Thanks!
Answers
In statistics, a Chi-squared test may be used to determine holiday choice and gender and α (alpha) is the response variable.
What is the Chi-squared test?A statistical technique called the chi-square test is used to compare actual outcomes with predictions.
The goal of this test is to establish if a discrepancy between actual and predicted data is the result of chance or a correlation between the variables you are researching.
Whether there is a statistically significant association between categorical variables is determined by the Chi-square test of independence.
This issue is addressed by a hypothesis test. The chi-square test of association is another name for this assessment.
Hence,in stats would a test looking at gender & holiday preference yes you can do a Chi-squared test and α(alpha) is the response variable.
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Find the Equation of the Perpendicular Line
Instructions: Find the equation of the line through point (-1, 2) and perpendicular to x + 3y = 3.
y =
Answers
Answer:
y = 3x +5
Step-by-step explanation:
The equation of a perpendicular line can be formed by swapping the x- and y-coefficients, and negating one of them. The constant in the equation will be chosen to make the equation true at the given point.
Coefficients swappedThe desired equation in the given standard form will be ...
3x -y = c . . . . . . for some new constant c
Note that we have kept the x-coefficient positive, and have negated the y-coefficient.
Constant valueThe new constant will make the equation true at the point (-1, 2):
3(-1) -(2) = c = -5
So, the standard-form equation is ...
3x -y = -5
Slope-intercept formThe answer form suggests you want to solve this for y. Adding y+5 to both sides will give the form you want:
3x -y +(y+5) = -5 +(y+5)
3x +5 = y
y = 3x +5
7/8 divided by 9/10[tex]7/8 divided by 9/10[/tex]
Answers
Step-by-step explanation:
a ) Solution,
[tex] = \frac{7}{8} \div \frac{9}{10} \\ [/tex]
[tex] = \frac{7}{8} \times \frac{10}{9} \\ [/tex]
[tex] = \frac{70}{72} \\ [/tex]
Change into lowest term....
[tex] = \frac{35}{36} \\ [/tex]
please find the inverse of this
y=log base 4 x^4
Answers
Step-by-step explanation:
[tex]y = log_{4}( {x}^{4} ) [/tex]
Swap x and y.
[tex]x = log_{4}( {y}^{4} ) [/tex]
Solve for y.
[tex]x= 4 log_{4}(y) [/tex]
[tex] \frac{1}{4} x = log_{4}(y) [/tex]
[tex]4 {}^{ \frac{1}{4}x } = y[/tex]
So the inverse is
[tex]4 {}^{ \frac{x}{4} } = f {}^{ - 1} (x)[/tex]
We have found that:
(X,₁)=(3,-1)
• m = 3
●
Substituting these values in (y - y₁) = m(x-x1), we'll get the equation of the line as:
Answers
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
Find the equation of the line, with the info given.
[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]
The formula used in this problem is,
[tex]\bf{y-y_1=m(x-x_1)}[/tex]□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□
[tex]\bf{y-(-1)=3(x-3)[/tex] | simplify
[tex]\bf{y+1=3(x-3)}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=y+1=3(x-3)}[/tex]
[tex]\boxed{\bf{aesthetic \not101}}[/tex]
A convenience store recently started to carry a new brand of soft drink. Management is interested in estimating future sales volume to determine whether it should
continue to carry the new brand or replace it with another brand. The following table provides the number of cans sold per week. Use both the trend projection with
regression and the exponential smoothing (let a=0.4 with an initial forecast for week 1 of 574) methods to forecast demand for week 13. Compare these methods by
using the mean absolute deviation and mean absolute percent error performance criteria. Does your analysis suggest that sales are trending and if so, by how much?
2
5
Period 1
3 4
574 635 652 739 679
Sales
with regression forecast.
(Enter your response rounded to the nearest whole number.)
(1) Obtain the trend projection
The forecast for week 13 is
6
637
7
723
8
691
9
773
10
718
11
656
12
729
Answers
The forecast for week 13 is 9.7%
a) MAD without the forecast = 43.71
MAD with the forecast = 45.59
b) MAPE = 0.097
MAPE= 9.7%
642 602 656 747 663 618 731 726 679 737 664 740
Mean Absolute deviation is given as
MAD = [Σ|x - μ|]/N
We first calculate the mean
Mean = Σx/N
Mean = (642+602+656+747+663+618+731+726+679+737+664+740)/12
Mean = (8205/12)
Mean= 683.75
absolute deviations from the mean
|642-683.75| + |602-683.75| + |656-683.75| + |747-683.75| + |663-683.75| + |618-683.75| + |731-683.75| + |726-683.75| + |679-683.75| + |737-683.75| + |664-683.75| + |740-683.75|
Absolute deviations from the mean
41.75+81.75+27.75+63.25+20.75+65.75+47.25+42.25+4.75+53.25+19.75+56.25= 524.5.
What is the formula for absolute mean deviation?MAD = [Σ|x - μ|]/N
MAD = (524.5/12)
MAD = 43.71
If we include the forecast for the 13th week
642 602 656 747 663 618 731 726 679 737 664 740 747
Mean = (8205+747)/13
Mean = 688.62
absolute deviations from the mean
|642-688.62| + |602-688.62| + |656-688.62| + |747-688.62| + |663-688.62| + |618-688.62| + |731-688.62| + |726-688.62| + |679-688.62| + |737-688.62| + |664-688.62| + |740-688.62| + |747-688.62|
Absolute deviations from the mean
=46.62+86.62+32.62+58.38+25.62+70.62+42.38+37.38+9.62+48.38+24.62+51.38+58.38
= 592.62
MAD = (592.62/13)
MAD = 45.59.
b) MAPE is used to check forecast errors
MAPE = (1/N) Σ [|x-f|/x]
where N = Sample size = 12
x = each variable
f = the forecasted value = 747
x = 642, 602, 656, 747, 663, 618, 731, 726, 679, 737, 664, 740
Σ[|xf|/x]=0.164+0.241+0.139+0+0.112+0.209+0.022+0.029+0.100+0.014+0.125+0.009
Σ [|x-f|/x] = 1.164
MAPE = (1.164/12)
MAPE = 0.097
MAPE=9.7%
The forecast for week 13 is 9.7%.
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Each side of a hexagon is 10 inches longer than the previous side. What is the length of the shortest side of this hexagon if its perimeter is 401 inches?
Answers
Answer:
41.83 inches
Step-by-Step Explanation:
You have to trust me. I helped my brother with this.
The length of the shortest side of the hexagon is approximately 41.83 inches
Let's denote the length of the shortest side of the hexagon as "x" inches. According to the given information, each side of the hexagon is 10 inches longer than the previous side.
So, the lengths of the sides of the hexagon can be expressed as follows:
First side: x inches
Second side: (x + 10) inches
Third side: (x + 20) inches
Fourth side: (x + 30) inches
Fifth side: (x + 40) inches
Sixth side: (x + 50) inches
To find the perimeter of the hexagon, we sum up the lengths of all the sides:
Perimeter = x + (x + 10) + (x + 20) + (x + 30) + (x + 40) + (x + 50)
We know that the perimeter is given as 401 inches, so we can set up the equation:
401 = x + (x + 10) + (x + 20) + (x + 30) + (x + 40) + (x + 50)
Simplifying the equation:
401 = 6x + 150
Subtracting 150 from both sides:
251 = 6x
Dividing both sides by 6:
x = 251/6
Therefore, the length of the shortest side of the hexagon is approximately 41.83 inches (rounded to two decimal places).
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14. If m is a positive integer, then which of the
following is equivalent to 4m + 4m + 4m + 4m?
(A) 4m+1
(B) 4^4m
(C) 4^4m + 1
(D) 4m +4
Answers
Hello!
Simplifying :
⇒ 4m + 4m + 4m + 4m
⇒ 4(4m)
None of the above
What is the range of the function shown on the graph above HELP
Answers
Answer:
C. 0 ≤ y ≤ 7
Step-by-step explanation:
Range is the interval of the numbers on the y-axis. The numbers go from y-value 1 to y-value 7. Since the circles at the ends are closed, this means 0 and 7 are included in the range, so ≤ is included instead of <.
Write the statement as an equation." Three is subtracted from the reciprocal of a number. Let x be equal to the number .
Answers
Answer:
1/x - 3
Step-by-step explanation:
The number is x.
The reciprocal of the number is 1/x.
3 is subtracted from the reciprocal of a number.
1/x - 3
FOR 50 POINTS!
In great detail, describe how to solve the advanced function below.
4^(8 - 2x) = 256
I understand the solution to the problem is (2). I would like a detailed description of how exactly to solve this problem.
Answers
The value of x in the equation is 2.
What is indices?Indices singular index is a branch of algebra that deals with the power or exponent of variables.
Laws of indices help us to evaluate indicial expressions and equations.
Analysis:
[tex]4^{8-2x}[/tex] = 256
Here 4 is the base number while 8-2x is the exponent or index.
So for us to evaluate this, we need to write 256 in its index form having its base as 4 also.
so 256 in base 4 index form is [tex]4^{4}[/tex]
[tex]4^{8-2x}[/tex] = [tex]4^{4}[/tex]
since both sides have the same base number, we equate only their exponent
8-2x = 4
-2x = 4 - 8
-2x = -4
x = -4/-2 = 2
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What is the range of the averages in this class? histogram group of answer choices 65 points 80 points 30 points none of the above
Answers
The range of the averages in a class with a maximum point of 100 point and a minimum point of 20 point is 80 points
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Range is the difference between the maximum value and minimum value of a data set. Hence:
Range = Maximum - Minimum
Let us assume that the maximum point is 100 point and the minimum point is 20 point, hence:
Range = 100 - 20 = 80 points
The range of the averages in a class with a maximum point of 100 point and a minimum point of 20 point is 80 points
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What is the greatest common factor of 6, 42, and 18?
Answers
Answer:
Step-by-step explanation:
1) List the factors of each number.
Factors of 6 : 1, 2, 3, 6
Factors of 42 : 1, 2, 3, 6, 7, 14, 21, 42
Factors of 18 : 1, 2, 3, 6, 9, 18
2) Find the largest number that is shared by all rows above. This is the GCF.
GCF = 6
what is the percentage of change from 12 to 19
Answers
Answer:
(19-12):12*100 =
(19:12-1)*100 =
158.33333333333-100 = 58.33
Instructions: Solve the quadratic equation and simplify your answer(s).
7x2=−12−5x
x=
-5
+
√
,
-5
−
√
14
14
Answers
[tex]7x^2 = -12-5x\\\\7x^2 + 5x+12=0\\\\x=\frac{-5 \pm \sqrt{5^{2}-4(7)(12)}}{2(7)}\\\\\boxed{x=\frac{-5 \pm i \sqrt{311}}{14}}[/tex]
A bus travels from Boston to New York 220 miles. The bus departs at 2pm and arrives at new York at 7pm. what's the average speed?
Answers
2
Drag each number or expression to the correct location on the table. Each number or expression can be used more than once, but not all
numbers or expressions will be used.
Complete the empty cells in the table by determining all terms, constants, and coefficients for both algebraic expressions.
-5 7 5
Expressions
Terms
Constants
Coefficients
-5a
11
Reset
4a2
4a2. -5a-3
Next
7(-3x + 5) + 1ly
7(-3x + 5)
11y
5
Answers
The empty cells in the table by determining all terms, constants, and coefficients for both algebraic expressions will be:
Constant = -3Coefficient = -4, -5How to illustrate the information?In the first expression, the equation is given as 4a² - 5a - 3 while in the second expression, the equation is given as 7(-3x + 5) + 11y.
In this second expression, the term is 7(3x + 5), 11y. The constants are -7 and 5. Lastly, the coefficients are -3, and 11.
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Help
Note that: The solution must be non zero
Spam/Irrelevant answers will
be reported
Answers
Answer:
Step-by-step explanation:
[tex]y'' + \omega^2 y = 0[/tex]
has characteristic equation
[tex]r^2 + \omega^2 = 0[/tex]
with roots at [tex]r = \pm\sqrt{-\omega^2} = \pm|\omega|i[/tex], hence the characteristic solution is
[tex]y = C_1 e^{i|\omega|x} + C_2 e^{-i|\omega|x}[/tex]
or equivalently,
[tex]y = C_1 \cos(|\omega|x) + C_2 \sin(|\omega|x)[/tex]
With the given boundary conditions, we require
[tex]y(0) = 0 \implies C_1 = 0[/tex]
and
[tex]y'(\pi) = 0 \implies -|\omega| C_1 \sin(|\omega|\pi) + |\omega| C_2 \cos(|\omega|\pi) = 0[/tex]
With [tex]C_1=0[/tex], the second condition reduces to
[tex]|\omega| C_2 \cos(|\omega|\pi) = 0[/tex]
Assuming [tex]C_2\neq0[/tex] (because we don't want the trivial solution [tex]y=0[/tex]), it follows that
[tex]\cos(|\omega|\pi) = 0 \implies |\omega|\pi = \pm\dfrac\pi2 + 2n\pi \implies |\omega| = 2n\pm\dfrac12[/tex]
where [tex]n[/tex] is an integer. In order to ensure [tex]|\omega|\ge0[/tex], we must have [tex]n\ge1[/tex] if [tex]|\omega|=2n-\frac12[/tex], or [tex]n\ge0[/tex] if [tex]|\omega|=2n+\frac12[/tex].
Someone please help!
Answers
Answer: horizontal
Step-by-step explanation: there going across sideways and not up and down