Answers
We consider 2 pairs or equations, for example (1, 2) and (2, 3), and eliminate one of the variables in each pair, creating a system of 2 linear equations with 2 unknowns.
Note that the third equation contains -2y which can be used to eliminate easily -6y in the second equation, and -4y in the fourth.
i) consider equations 1 and 3:
-3x-4y-3z=-7
5x-2y+5z=9
multiply the second equation by -2:
-3x-4y-3z=-7
-10x+4y-10z=-18
adding the 2 equations we have -13x-13z=-25
ii) consider equations 2 and 3. Multiply the third equation by -3:
2x-6y+2z=3
-15x+6y-15z=-27
adding the 2 equations we have -13x-13z=-24
So we got -13x-13z is -25, but also -24. this means the system is inconsistent, so it has no solution.
Answer: the system has no solutions
Related Questions
Find the parabola whose minimum is at (−12,−2)(−12,−2) rather than the point given in the book. the parabola's equation is y=x2+ax+by=x2+ax+b, where
Answers
[tex]y-k=a(x-h)^2[/tex]
where (h, k) is the vertex of the parabola.
Given that the vertex of the parabola is (-12, -2), the equation of the parabola is given by
[tex]y-(-2)=a(x-(-12))^2 \\ \\ y+2=a(x+12)^2=a(x^2+24x+144)=ax^2+24ax+144a \\ \\ y=ax^2+24ax+114a-2 \\ \\ y=x^2+24x+ \frac{114a-2}{a} [/tex]
For a = 1,
[tex]y=x^2+24x+112[/tex]
The parabola whose minimum is at (−12,−2) is given by the equation [tex]y=x^2+ax+b[/tex], where a = 24 and b = 112.
If you randomly choose a letter in the word "mathematics", find the probability that you choose an "a".
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(number of desired outcomes)/(total number of outcomes)
Here, the total number of ways you can pick a single letter from the word "mathematics" is 11 (m, a, t, h, e, m, a, t, i, c, s), and the number of a's available to choose from is 2, therefore you have a 2/11 chance of choosing an "a" at random from the word "mathematics."
The larger of two numbers is 3 more than twice the smaller. if the twice the larger is decreased by 5 times the smaller the result is 0. find the two numbers
Answers
JIMMMM! :)
Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 2^x and y = 4^x−2 intersect are the solutions of the equation 2^x = 4^x−2. (4 points)
Part B: Make tables to find the solution to 2^x = 4^x−2. Take the integer values of x between −4 and 4. (4 points)
Part C: How can you solve the equation 2^x = 4^x−2 graphically? (2 points)
Answers
The x coordinates are the inputs of the functions f(x) = 2^x and g(x) = 4^(x-2)
If we have some input x that leads to f(x) = g(x), then this x value is a solution. It makes the equation f(x) = g(x) true. This is why the x coordinate of the intersection point of y = 2^x and y = 4^(x-2) is the solution.
-------------------------------------------------------------------------
Part B
See attached for the table. See figure 1.
This is how you get the results you see in the table
Plug x = -4 into f(x) to get:
f(x) = 2^x
f(-4) = 2^(-4)
f(-4) = 0.0625
Do the same for g(x):
g(x) = 4^(x-2)
g(-4) = 4^(-4-2)
g(-4) = 4^(-6)
g(-4) = 0.000244140625
-------------------
Plug x = -3 into f(x) to get:
f(x) = 2^x
f(-3) = 2^(-3)
f(-3) = 0.125
Do the same for g(x):
g(x) = 4^(x-2)
g(-3) = 4^(-3-2)
g(-3) = 4^(-5)
g(-3) = 0.0009765625
-------------------
Plug x = -2 into f(x) to get:
f(x) = 2^x
f(-2) = 2^(-2)
f(-2) = 0.25
Do the same for g(x):
g(x) = 4^(x-2)
g(-2) = 4^(-2-2)
g(-2) = 4^(-4)
g(-2) = 0.00390625
-------------------
Plug x = -1 into f(x) to get:
f(x) = 2^x
f(-1) = 2^(-1)
f(-1) = 0.5
Do the same for g(x):
g(x) = 4^(x-2)
g(-1) = 4^(-1-2)
g(-1) = 4^(-3)
g(-1) = 0.015625
-------------------
Plug x = 0 into f(x) to get:
f(x) = 2^x
f(0) = 2^(0)
f(0) = 1
Do the same for g(x):
g(x) = 4^(x-2)
g(0) = 4^(0-2)
g(0) = 4^(-2)
g(0) = 0.0625
-------------------
Plug x = 1 into f(x) to get:
f(x) = 2^x
f(1) = 2^(1)
f(1) = 2
Do the same for g(x):
g(x) = 4^(x-2)
g(1) = 4^(1-2)
g(1) = 4^(-1)
g(1) = 0.25
-------------------
Plug x = 2 into f(x) to get:
f(x) = 2^x
f(2) = 2^(2)
f(2) = 4
Do the same for g(x):
g(x) = 4^(x-2)
g(2) = 4^(2-2)
g(2) = 4^(0)
g(2) = 1
-------------------
Plug x = 3 into f(x) to get:
f(x) = 2^x
f(3) = 2^(3)
f(3) = 8
Do the same for g(x):
g(x) = 4^(x-2)
g(3) = 4^(3-2)
g(3) = 4^(1)
g(3) = 4
-------------------
Plug x = 4 into f(x) to get:
f(x) = 2^x
f(4) = 2^(4)
f(4) = 16
Do the same for g(x):
g(x) = 4^(x-2)
g(4) = 4^(4-2)
g(4) = 4^(2)
g(4) = 16
Note that since the input x = 4 leads to the same output (16) this makes x = 4 a solution.
-------------------------------------------------------------------------
Part C
To solve graphically, you need to use the table in part B to draw a curve through the set of points. Then determine where the curves cross (if they cross at all). You may need to adjust the graph window if the intersection point is off the screen.
See figure 2 for the graph (attached as well). Point A in green is the intersection point.
A = (4,16)
so x = 4 is the solution to f(x) = g(x).
Part A: The point or points of intersection are the values of the variables which satisfy both equations at a particular point.
If [tex]y=2^x and y=4 ^{x-2} [/tex] and the solution of which will satisfy both equations. This idea of equating the two equations is something that you would have come across before, maybe without realizing it.
Consider this:
[tex]x^2 + 6x + 9=0 This can also be looked at as being the two equations: y=x^2 +6x+9 and y=0 [/tex]
So the points of intersection are the roots in this case and satisfy the equation:
[tex]x^2 + 6x +9=0 This explains why it will be the solution to: 2^x = 4 ^{x-2} , because this is the equation formed at the intersection.[/tex]
Part B:
You just put integer values between -4 and 4 in each equation and when the output is the same for both that is the solution.
[tex]2^ ^{-4} = 0.0625 , [/tex] and [tex]4 ^{-6} = 0.000244[/tex]
[tex]2 ^{-3} = 0.125, [/tex] [tex]4 ^{-5} =0.000977[/tex]
[tex]2 ^{-2} =0.25[/tex] and [tex]4 ^{-4} =0.003906[/tex]
[tex]2 ^{-1}= -0.5,[/tex] and [tex]4 ^{-3} =0.01563[/tex]
[tex]2^0 =1[/tex] , and [tex]4 ^{-2} =0.0625[/tex]
[tex]2^1 = 2 [/tex] and [tex]4 ^{-1} =0.25[/tex]
[tex]2^2 =4 [/tex] and [tex]4^0 =1[/tex]
[tex]2^3 =8[/tex] and [tex]4^1=4[/tex]
[tex]2^4 =16, [/tex] and [tex]4^2 = 16 [/tex] (This is the solution when x=4)
Part C:
To solve graphically you just plot the two equations [tex]=2^x[/tex] and [tex]y=4 ^{x-2} [/tex]
Together graph of [tex]y=2^x [/tex] and [tex]y=4 ^{x-2} [/tex]
The picture below is how the graph looks like.
Full Credit to my online calculator 'cause we don't have a graphing calculator here.
I hope I helped!
find four consecutive even integers such that 2 times the sum of the first and second is 14 more than 3 times the fourth.
Answers
2 (x + x+ 2) = 3(x + 6) + 14
4x + 4 = 3x + 18 + 14
x = 18 + 14 - 4 = 28
the four integers are 28,30,32 and 34.
The required four consecutive even integers are given as 28, 30, 32, and 34.
Given that,
Four consecutive even integers such that 2 times the sum of the first and second is 14 more than 3 times the fourth.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
Let, the first term be a, and the common difference be d,
And series 2n, 2n + 2, 2n +4, 2n + 6
According to the question,
2[2n + 2n + 2] = 14 + 3[2n + 6]
8n + 4 = 14 + 6n + 18
2n = 28
n = 14
Series can be given as,
28, 30, 32, 34
Thus, the required four consecutive even integers are given as 28, 30, 32, and 34.
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Please help me! And can you explain how you got that answer please?
Answers
8 = 2^(3)
so
(8)^(-1) = (2^3)^(-1) = 2^(3*-1) = 2^(-3)
What is the area of a rectangle with vertices at (−3, −1) , (1, 3) , (3, 1) , and (−1, −3) ? Enter your answer in the box. Do not round any side lengths.
Answers
[tex]d = \sqrt{{(y2 - y1)}^{2} + {(x2 - x1)}^{2} }[/tex]
[tex]w = \sqrt{{(1 - 3)}^{2} + {(3 - 1)}^{2} } \\ = \sqrt{( {( - 2)}^{2} + {(2)}^{2})} = \sqrt{4 + 4} \\ = \sqrt{8} \: = [/tex]
[tex]l = \sqrt{({(3 - - 1)}^{2} + {(1 - - 3)}^{2})} \\ = \sqrt{({(3 + 1)}^{2} + {(1 + 3)}^{2})} \\ = \sqrt{({(4)}^{2} + {(4)}^{2})} \\ = \sqrt{({16} + {16})} \: = \sqrt{32} [/tex]
[tex]a \: = l \times w = \sqrt{32} \times \sqrt{8} \\ = \sqrt{256} = 16 \: {units}^{2} [/tex]
Can somebody please help me?
Answers
Eleven less than seven times a number is five more than six times the number.
Answers
The problem is a simple algebraic equation in the form 7x - 11 = 6x + 5. By rearranging and simplifying, we find the solution is x = 16.
Explanation:The question presents a mathematical statement that needs to be solved for the variable. Translating the words into an equation, we get: 7x - 11 = 6x + 5. This equation is saying seven times a number (we'll call it 'x') reduced by eleven is equal to six times that number increased by five.
To solve for 'x', first, rearrange the equation to get all 'x' terms on one side and constants on the other. By subtracting 6x from both sides, we get x - 11 = 5. Then, add 11 to both sides to isolate 'x': x = 16.
So, the number or 'x' that satisfies this equation is 16.
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x = 16.
To solve this, let the unknown number be represented by x.
We can set up the equation based on the given information:
7x - 11 = 6x + 5
Subtract 6x from both sides of the equation:
7x - 6x - 11 = 6x - 6x + 5
Simplify the equation:
x - 11 = 5
Add 11 to both sides:
x - 11 + 11 = 5 + 11
Simplify the equation:
x = 16
Thus, the number is 16.
1. What is the product of -2.5 and 8.77 ?
2. Alexander purchased a computer on sale. The original price was $1,200. The sale price was 5/6 of the original price. How much did Alexander pay for the computer?
3. Mara finished 1/5 of her assignment on Saturday and 3/8 of her assignment on Sunday. What Fraction of her assignment did she complete on Saturday and Sunday?
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2. 5/6 of 1,200 is 1000. 1,200÷6=200 200•5=1000.
3. 1/5+3/8. Find like denominators. (40) 8/40+15/40=23/40 or as a decimal, 0.575.
Hoped I helped!
2. $200
3. 23/40
Sarah is 50 years old. she is twice as old as her friend bill and bill is 5 times as old as his sister jane. jane's mom is 12 times older than jane. what is the age difference between jane's mom and sarah?
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Sarah is twice as old as Bill so 2X=50 and X=25 so Bill is 25. Bill is 25 and bill is 5 times older than his sister Jane so 5n=25 N=5 so Jane is 5 years old. Jane's mom is 12 time older than Jane so 12x5=60 and so
60-50=10 so the answer is 10
Max spent $53 and now has no money left. How much did he have before his purchase
Answers
An equation is formed when two equal expressions. The amount Max had before his purchase is $53.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given that Max spent $53 and now has no money left. Therefore, we can write the details as,
The amount spent on the purchase = $53
The amount left after purchase = $0
Let the amount before purchase be represented by M. Therefore, we can write the amount remaining after purchase as,
Amount before purchase - Amount spent on purchase = Amount remaining after purchase
M - $53 = $0
Adding 53 on both sides.
M - 53 + 53 = 53
M = 53
M = $53
Thus, the amount Max had before his purchase is $53.
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hard question ! Jessica is selling books during the summer to earn money for college. She earns a commission on each sale but has to pay for her own expenses. After a month of driving from neighborhood to neighborhood and walking door-to-door, she figures out that her weekly earnings are approximately a linear function of the number of doors she knocks on. She writes the equation of the function like this: E(x) = 20x - 50, where x is the number of doors she knocks on during the week and E(x) is her earnings for the week in dollars. Which of the following are reasonable interpretations of the y-intercept of Jessica's function? Check all that apply.
A. Her expenses are $50 per week.
B. She can earn $20 per week even if she does not knock on any doors.
C. If she does not knock on any doors at all during the week, she will lose $50.
D. She will lose $20 per week if she does not knock on any doors.
Answers
Answer:
A and C
Step-by-step explanation:
Just answered on apex
Nick’s house is 4.28 miles from school. if nick’s average stride length is 3.1 feet, how many strides will it take him to walk to school?
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You make a large bowl of salad to share with your friends. Your brother eats 1/3 of it before they come over
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Now, your brother ate 1/3 of the original amount.
This means that:
The amount left to be divided among your friends = m - (1/3) m = (2/3) m
Now, we need to divide this amount among the six friends of yours, therefore:
the amount that each friend gets can be calculated by dividing the (2/3) m which is the left portion of the salad by the number of friends as follows:
each friend receives = [(2/3) m] / 6 = (1/9) m
How to do this ?? How
Answers
The two bars | | is used to indicate the function absolute value.
Remember this definition:
| x | = - x if x < 0 and x if x > 0
So, | x | > c =>
x > c or x > - c
Therefore:
|ax - b| > c => ax - b > c or ax - b > - c
That is the third option of the answer list.
Answer:
|ax - b| > c
The two bars | | is used to indicate the function absolute value.
Remember this definition:
| x | = - x if x < 0 and x if x > 0
So, | x | > c =>
x > c or x > - c
Therefore:
|ax - b| > c => ax - b > c or ax - b > - c
Step-by-step explanation:
For items 14 and 15 use the following functions
f(x)=5x+1
g(x)=3x-4
14. Evaluate f(2), g(2), (f o g) (2), and (g o f)(2).
15. Write the composite functions h(x)=g(f (x)) and k(x)=f(g(x)).
Answers
PLEASE HELP!
Solve for t: A=P (1+rt)
Answers
A = P + Prt
A - P = Prt
(A - P)/Pr = t
Step 1) A = P*(1+rt)
Step 2) A = P*(1)+P*(rt)
Step 3) A = P+P*(rt)
Step 4) A-P = P+P*(rt)-P
Step 5) A-P = P*(rt)
Step 6) A-P = t*(Pr)
Step 7) (A-P)/(Pr) = (t*(Pr))/(Pr)
Step 8) (A-P)/(Pr) = t
Step 9) t = (A-P)/(Pr)
----------------------------------------------
and here are the explanations for each step
Step 1) Nothing to do here. This is the original equation
Step 2) Distribute the outer P term into each inner term (1 and rt)
Step 3) Multiply P and 1 to get P*(1) = P
Step 4) Subtract P from both sides
Step 5) Simplify. Note how the P-P on the right side becomes 0P = 0 which goes away on the right side
Step 6) Rearrange the terms on the right side to go from P*(rt) to t*(Pr).
Step 7) Divide both sides by Pr.
Step 8) Simplify. The Pr term on the right side divides with itself to get 1. Because 1 times anything is itself, we effectively have Pr cancel out and go away.
Step 9) Flip the equation so that the t is on the left side
----------------------------------------------
The answer is t = (A-P)/(Pr) which can be written as [tex]t = \frac{A-P}{Pr}[/tex]
The parenthesis in the equation t = (A-P)/(Pr) are important because we are specifying that we are dividing all of "A-P" all over all of "Pr"
How long is the minute hand on a clock whose tip travels 15 cm from 1:15 to 1:30 to the nearest tenth?
Answers
Answer:
The length of minute hand is 9.5 cm
Step-by-step explanation:
We are given the minute hand move from 1:15 to 1:30
Time for 1:30 to 1:30 = 15 minutes
Tip of minute hand move 15 cm in 15 minutes.
In 60 minutes = 360°
In 1 minute = 6°
In 15 minutes = 90°
Formula: [tex]\theta=\dfrac{L}{r}[/tex]
[tex]\theta=90^\circ[/tex]
Now we change [tex]\theta=90^\circ[/tex] into radian
[tex]Radian=\dfrac{\pi}{180^\circ}\times 90^\circ=\dfrac{\pi}{2}[/tex]
L=15 cm
R = Length of minute hand.
[tex]\dfrac{\pi}{2}=\dfrac{15}{R}[/tex]
[tex]R=\dfrac{30}{\pi}\approx 9.5[/tex]
Hence, The length of minute hand is 9.5 cm
The height of the closet is 96 inches, and aisha would like to have 4 rows of cube organizers. what is the most the height of each cube organizer can be
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so the greatest height of each cube can be : 96/4 = 24 inches
Answer: the most the height of each cube organizer can be 24 inches
Step-by-step explanation:
Since we have given that
Height of the closet = 96 inches
Number of rows of cube organizers = 4
Greatest height of each cube organizer can be is given by
[tex]\frac{96}{4}=24[/tex]
Hence, the most the height of each cube organizer can be 24 inches.
Multiplication property: if angle j equals 30 then 2m angle j equals
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Which algebraic expression is a polynomial with a degree of 2?
a)4x3 − 2x
b10x2 −
c)8x3+ + 3
d)6x2 − 6x + 5
Answers
the one u have marked is not a polynomial because it has a variable in the square root...a polynomial cannot have that
Answer:
D) 6x² − 6x + 5 has degree 2.
Step-by-step explanation:
Given : Polynomial .
To find : Which algebraic expression is a polynomial with a degree of 2.
Solution: We have given polynomial
Degree : The highest power of the polynomial is called degree.
We can see from the given polynomials two polynomial have 2 power
first is [tex]10x^{2} -\sqrt{x}[/tex].
Second is 6x² − 6x + 5.
But the first term have root so, it is not a polynomial.
So 6x² − 6x + 5 has degree 2
Therefore, D) 6x² − 6x + 5 has degree 2.
Bill ate 1/4 pound of trail mix on his first break during a hiking trip. On his second break, he ate 1/6 pound. How many pounds of trail mix did he eat during both breaks? Explain.
Answers
1/4+1/6
LCM of 4 and 6 = 12
3/12 + 2/12
Add the numerators:
5/12
So, he ate 5/12 of a pound of bars in both breaks.
Hope this helps!
What are the slope and the y-intercept of the line shown in the graph?
(A) y-intercept = 2 and slope = -3
(B) y-intercept = 2 and slope = 3
(C) y-intercept = 3 and slope = 2
(D) y-intercept = -3 and slope = 2
Answers
the slope is rise over run. Try to choose two points on the line that you can make out the location of like (0,2) and (1,-1) is close enough. Count rise down -3 over run right +1 = -3 slope
y-intercept = 2
slope = -3
let's take the 2 coordinates from the line.
(0, 2)(1, -1)
The y-intercept is when x = 0, When x = 0, y = 2 . This means the y-intercept is 2.
m = slope = -1 - 2 / 1 - 0 = -3 / 1 = -3
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Help me please don’t know how to do this and I have psat in a week.
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x = 3/2
x = -5
Since 3/2 = 1.5 is larger than -5, this means r = 3/2 = 1.5 and s = -5
Subtract r and s:
r - s = (3/2) - (-5)
r - s = (3/2) + (5)
r - s = (3/2) + (5/1)
r - s = (3/2) + (10/2)
r - s = (3+10)/2
r - s = 13/2
Therefore the final answer is B) 13/2
HELLLLLPPP PLLEASEEE
Answers
The answer is B
Which type of triangle has one angle with a measurement greater than 90°? A. Obtuse B. Acute C. Isosceles D. Right
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ABCD is a rectangle. The length of BD is 8 units and m
What is the length of AC and m
Answers
The new shanghai restaurant offers a choice of five appetizers, two choices of soups, and eleven choices of entrees for its lunch special. how many different complete lunches can be ordered from the restaurant's lunch special menu?
Answers
5*2*11 = 110
Final answer:
Using the Multiplication Principle, a customer can choose from 110 different complete lunch combinations by selecting one of each option (appetizer, soup, and entrée) from the menu at the New Shanghai restaurant.
Explanation:
To determine the total number of different complete lunches that can be ordered from the restaurant's lunch special menu, we apply The Multiplication Principle of counting. The principle states that if one event can occur in m ways and another independent event can occur in n ways, then the total number of ways both events can occur together is the product of m and n. In the context of ordering a lunch, each choice (appetizer, soup, and entrée) represents an independent event.
For appetizers, there are 5 choices.
For soups, there are 2 choices.
For entrées, there are 11 choices.
Following the Multiplication Principle, the total number of different complete lunches is calculated as follows:
5 appetizers × 2 soups × 11 entrées = 110 different complete lunches.
Therefore, customers have the opportunity to choose from 110 unique complete lunch combinations at the New Shanghai restaurant.
A quadrilateral whose opposite sides are parallel and congruent and whose opposite angles are congruent is a ____. a. trapezoid c. kite b. heptagon d. parallelogram.
PLZ ANSWER ASAP!!