solve the following system of linear equations using the elimination method
Answers
Answer:
x=-1, y=2, z=3
Step-by-step explanation:
First at all, you can divide these equations into two group. It is easier to you.
4x-2y+3z=1
3x+y+2z=5
x+3y-4z=-7
3x+y+2z=5
Then, you can simplify these group of equation that you divided.
So, we have to simplify these step by step.
First, we can simplify the first group of equation.
4x-2y+3z=1
3x+y+2z=5
We have to find which variable you want to eliminate. I choose y.
You can multiply the second equation of first group by 2 and eliminate them.
4x-2y+3z=1
6x+2y+4z=10
As the variable of y is same and we can eliminate y by addition.
4x-2y+3z=1
6x+2y+4z=10
become
10x+0+7z=11
10x+7z=11
10x+7z=11 as the third equation.
Next, simplify the second group of equation.
x+3y-4z=-7
3x+y+2z=5
Same way as the previous one. We need to find which variable that you want to eliminate. I choose y.
We need to balance for the first equation x+3y-4z=-7 at least one variable.
We need to multiply this equation by -3 below to get the same value of y to eliminate the above equation.
3x+y+2z=5 (multiply by -3)
-9x-3y-6z=-15
x+3y-4z= -7
-9x-3y-6z= -15
Here we go! Now these group has same value and variable to eliminate.
We can eliminate these equations by addition method.
x+3y-4z= -7
-9x-3y-6z= -15
-8x+0+10z= -22
-8x+10z= -22
Furthermore, we have to combine these equations that we have simplified from the previous groups.
10x+7z=11
-8x+10z= -22
10x+7z=11 and -8x+10z= -22 as a new group.
Finally, it is time to solve these equations!!
10x+7z=11
-8x+10z= -22
First equation of the above group, we can multiply by 10. Like this:
100x+70z=110
Second equation of the above group, we can multiply by 7. Like this:
-56x+70z=-154
So, we can see there are same value from these equation which are +70z and -70z.
Now, we can eliminate this variable by sum these equations.
100x+70z=110
-56x+70z=-154
44x= -44
x= -1
When we get x= -1 , we can use this value to any equation that you want. You can get the same answer as well.
When x= -1,
substitute into 100x+70z=110
100(-1)+70z=110
-100+70z=110
70z=110+100
70z=210
z=3
When z=3 and x= -1, we can substitute into x+3y-4z= -7
-1+3y-4(3)= -7
-1+3y-12= -7
3y=6
y=2
So, the answer is x= -1 , y=2 , z=3
I hope you will understand my solution and explanation. Bye!!
Related Questions
what is the inequality to 4-3x≥7
Answers
Answer:
Step-by-step explanation:
4-3x≥7
4-7≥3x
-3≥3x
or
3x≤-3
x≤-1
find the quotient the picture is the qestion
Answers
Answer:
A) 6/7
Step-by-step explanation:
Remember that two negatives will cancel to make a positive. Also, 6 ÷ 7 is 6/7
❗️5 points❗️
state the slope of the line.
A. -2
B. 0
C. 1
D. undefined
Answers
Answer:
B. 0
Step-by-step explanation:
The slope of a straight horizontal line is always equal to 0.
To support the above statement, we can show working out:
m = slope of the line
m = ( y1 - y2 ) / ( x1 - x2 )
Two points on line = ( 0 , - 2 ) , ( 1 , - 2 )
y1 = - 2
y2 = - 2
x1 = 0
x2 = 1
m = [ ( - 2 ) - ( - 2 ) ] / [ ( 0 ) - ( 1 ) ]
m = ( - 2 + 2 ) / ( 0 - 1 )
m = 0 / - 1
m = 0
The y values on a horizontal line will always be the same. When calculating the subtraction of y values in the numerator of the formula for the slope of a line, a number subtracted by itself will always equal to 0. 0 divided by any number will always equal to 0. Hence, the slope of a straight horizontal line will always equal to 0.
The probability that Stu buys a sandwich is 0.5.
The probability that Stu gets the bus is 0.7.
Assuming the events are independent, what is the probability that Stu buys a sandwich and gets the bus?
Answers
Answer:
probability that Stu buys a sandwich and gets the bus = 0.35
Step-by-step explanation:
Probability of success of two independent events is the product of the respective probabilities, i.e. the multiplication rule.
P(Sandwich) = P(S) = 0.5
P(Bus) = P(B) = 0.7
Assuming the events are independent,
probability that Stu buys a sandwich and gets the bus
= P(SB) = P(S)*P(B) = 0.5*0.7 = 0.35
Answer: 0.35
Step-by-step explanation:
First there is a 50% chance, or a 0.5 chance that Stu gets a sandwich. Then, ignoring the other .5, there is a .7 chance that he makes the bus. Thus, 1/2 of .7 is 0.35.
Hope it helps <3
Simplify (4n^4 - 3n^2 + n)+ (2n^4 -7n^2 + 9n). Express your answer without factoring.
Answers
Answer:
6n^4-10n^2+10n
Step-by-step explanation:
4 n^4+2n^4-3n^2-7n^2+9n+n
6n^4-10n^2+10n
Answer:
[tex]\boxed{6n^4- 10n^2 + 10n}[/tex]
Step-by-step explanation:
[tex](4n^4 - 3n^2 + n)+ (2n^4 -7n^2 + 9n)[/tex]
[tex]\sf Remove \ brackets.[/tex]
[tex]4n^4 - 3n^2 + n+2n^4 -7n^2 + 9n[/tex]
[tex]\sf Group \ like \ terms.[/tex]
[tex]4n^4 + 2n^4- 3n^2 -7n^2 + 9n+n[/tex]
[tex]\sf Combine \ like \ terms.[/tex]
[tex]6n^4- 10n^2 + 10n[/tex]
What is the solution to this system of linear equations? 2x + y = 1 and 3x - y = -6
Answers
Answer:
(- 1, 3 )
Step-by-step explanation:
Given the 2 equations
2x + y = 1 → (1)
3x - y = - 6 → (2)
Adding the 2 equations term by term eliminates the y- term, that is
5x = - 5 ( divide both sides by 5 )
x = - 1
Substitute x = - 1 into either of the 2 equations and evaluate for y
Substituting into (1)
2(- 1) + y = 1
- 2 + y = 1 ( add 2 to both sides )
y = 3
Solution is (- 1, 3 )
Answer: (-1,-3) or A on the quiz
Got it right
Have a nice day
The mean of 5,x,10,6,12 is 9. Find x
Answers
Answer:
12Solution,
Summation FX= 5+10+6+12+X
=33+x
N(total no.of items)=5
Now,
Mean= summation FX/N
or 9=33+X/5
or 9*5=33+X ( cross multiplication)
or 45=33+X
or -x=33-45
or -x=-12
X=12
Hope this helps...
Good luck on your assignment..
Answer:
x = 12
Step-by-step explanation:
The mean calculated by adding all the numbers of a set and dividing it by the total number of numbers. In this case, we have five numbers, but we do not know what the sum of all the numbers is because one of the numbers in under the pronumeral x. The find this out we need to work backwards. We know that when all the five numbers are added we should get 45 (it is 9 time 5 as there are five numbers in the set). The next step is to subtract 45 from the number that we known (i.e. 45 - 5 - 10 - 6 - 12). This comes to 12.
To double-check if you got the right answer you could add all five numbers include the 12 and divide it by 5 to see if the answer is 9.
A power line is to be constructed from a power station at point A to an island at point C, which is 1 mi directly out in the water from a point B on the shore. Point B is 4 mi down shore from the power station at A. It costs $5000 per mile to lay the power line under water and $3000 per mile to lay the line underground. At what point S down shores from A between the cities?
Answers
Answer:
Given :
length offshore = CS=√(1+X^2)
Cable charged = 5000√(1+X^2)
onshore length = 4-X
laying cost = 3000(4-X)
total cost:
C=5000√(1+X^2) +3000(4-X)
DC/DX
= [5000*(0.5)*2X/{√(1+X^2)}]-3000=0... for optimum
5000X=3000√(1+X^2)
25X^2=3+3X^2
22X^2=3
X=√(3/22)
= 0.3693 miles
So, it would be laid offshore to S in a manner that
BS=X=0.3693 miles
Onshore=4-0.3693
=3.6307 miles
Camila comprou um quilo de bolo de morango e dois quilos de bolo de chocalate por R$ 72,00 se o quilo do bolo de morango custa R$ 18,00 qual é o valor do quilo do bolo de chocolate?
Answers
Answer:
R$ 27,00
Step-by-step explanation:
R $ 72,00 = Um bolo de morango + dois quilos de bolo de chocalate
Um bolo de morango = R$ 18,00
R $ 72,00 = R$ 18,00 + Dois quilos de bolo de chocalate
Dois quilos de bolo de chocalate = R$72,00 - R$18,00
= R$54,00
Dois (2) quilos de bolo de chocalate = R$54,00
Um (1) quilo de bolo de chocalate = x
2x = R$ 54,00
x = R$ 54,00/2
x = R$ 27,00
Um quilo do bolo de chocolate = R$27,00
Urn A contains seven white balls and five black balls. Urn B contains four white balls and six black balls. A ball is drawn from Urn A and then transferred to Urn B. A ball is then drawn from Urn B. What is the probability that the transferred ball was black given that the second ball drawn was black
Answers
Answer:
P(X/Y) = 0.4545
Step-by-step explanation:
Let's call X that the transferred ball is black, X' that the transferend ball is white and Y the event that the second ball drawn is black.
The probability that the transferred ball was black given that the second ball drawn was black is equal to:
P(X/Y) = P(X∩Y)/P(Y)
Where P(Y) = P(X∩Y) + P(X'∩Y)
Then, the probability P(X∩Y) that the transferred ball is black and the second ball drawn is black is equal to:
P(X∩Y) = (5/12)*(7/11) = 0.2651
Because the urn A has 12 balls and 5 of them are black, then if the transferred ball is black, the urn B will contain 11 balls and 7 of them will be black balls.
At the same way, the probability P(X'∩Y) that the transferred ball is white and the second ball drawn is black is equal to:
P(X'∩Y) = (7/12)*(6/11) = 0.3181
Because the urn A has 12 balls and 7 of them are white, then if the transferred ball is white, the urn B will contain 11 balls and 6 of them will be black balls.
So, P(Y) and P(X/Y) are equal to:
P(Y) = 0.2651 + 0.3181
P(Y) = 0.5832
P(X/Y) = 0.2651/0.5832
P(X/Y) = 0.4545
Three years back, a father was 24 years older than his son. At present the father is 5 times as old as the son. Write an equation to represent this situation.
Answers
Answer: 5s -3 = s -3 + 24 5s -3 = s + 21
Step-by-step explanation:
Father f
Son s . present: f = 5s use this equation to substitute the equal value
3 years ago . f-3 = s-3 + 24
Substitute 5s for f in the second equation
5s -3 = s-3 + 24
works out as 5s -s = - 3 +3 + 24
4s = 24
4s/4 = 24/4
s = 6
The son's age is 6, The father is 30
Factorise x^2 + 10x + 16
Answers
Answer: [tex](x+2)(x+8)[/tex]
Step-by-step explanation:
1) First, we need to see which number multiplies to 16 and adds up to 10.
By looking at the factors of 16, we can see that only 2 and 8 will work.
2) Now, we need to arrange them in the factorized equation, which is always
(x+r)(x+q).
3) This will give us our final equation:
[tex](x+2)(x+8)[/tex]
If you want the roots, just do the negation of r and q and you will get it!
How does the slope of g(x) compare to the slope of f(x)?
The slope of g(x) is the opposite of the slope of f(x).
The slope of g(x) is less than the slope of f(x).
The slape of g(x) is greater than the slope of f(x).
The slope of g(x) is equal to the slope of f(x).
Answers
The slope of g(x) is less than the slope of f(x)
Explanation
Opposite slopes means the lines would have to cut perpendicularly at a 90° angle. This isn’t the case on the picture attacked.
You can see that line f(x) intersects and surpasses line g(x). Therefore it’s gradient/slope is greater.
Find m∠C. please help
Answers
Answer: 16.991°
Step-by-step explanation:
Used a triangle calculator hope this helped!
Help fast will mark you the brainlest
Answers
Answer:
55°
Step-by-step explanation:
x°+35° is a right angle
so x°+35°= 90°
then : x° = 90°-35° = 55°
Answer: x = 20
Step-by-step explanation:
This problem makes use of Supplementary Angles. Supplementary Angles states that all angles that makes up a straight line are equal to 180. Thus, 125+35+x=180
First add
160+x=180
Then subtract
x=20
Hope it helps <3
Toni invests money into an account which pays a fixed rate of compound interest each year. The total value, £V, of her investment after t years is given by the formula
Answers
Answer:
a. 1350
b. 4%
Step-by-step explanation:
here is the complete question :
Toni invests money into an account which pays a fixed rate of compound interest each year. The total value, £V, of her investment after t years is given by the formula:
V = 1350 x 1.04^t
Answer questions a & b
a - How much money did Toni invest in pounds
b - What rate of compound interest is paid each year
the formula for calculating compound interest is given by :
V = P (1 + r)^t
P = Present value -= amount invested = 1350
R = interest rate = 4%
N = number of years = t
i hope my answer helps you
Find the measure of each angle: Complementary angles with measures (5x)° and (4x−18)°
Answers
Answer:
60° and 30°
Step-by-step explanation:
Since they are complementary, the 2 equations add up to 90°
5x + 4x - 18 = 90
9x - 18 = 90
9x = 108
x = 12
Simply plug in x to find our angles:
5(12) = 60°
4(12) - 18 = 48 - 18 = 30°
Answer:
5x = 60°, 4x - 18 = 30°
Step-by-step explanation:
Sum of complementary angles is 90°.
5x + 4x - 18 = 90
9x = 90+18
9x = 108
x = 12
5x = 5* 12= 60°
4x - 18 = 4*12 - 18 = 30°
I WILL CHOOSE BRAINIEST AND 5 STARS AND A THANKS... A "necklace" is a circular string with several beads on it. It is allowed to rotate a necklace but not to turn it over. How many different necklaces can be made using 13 different beads?
Answers
Answer:
479,001,600 ways
Step-by-step explanation:
When looking at this problem, there are 13 beads that can be put on first, 12 that can be put on second as the first one was already used, 11 put on third, and so on. This means the amount of necklaces you can make are 13*12*11...*2*1, or 13 factorial (13!). But since you can rotate the necklace this means that there are each combination has 12 others just like it, just rotated(13 in total). This means we must divide 13! by 13, which makes it 12!. 12! is equal to 479,001,600, which is the answer.
Answer:
6,227,020,800 different necklaces.
Step-by-step explanation:
To start making the necklace, you will have to choose one of the 13 beads. For the next bead, you will have 13 - 1 = 12 beads to choose from. For the next bead, you will have 12 - 1 = 11 beads to choose from, and so on and so forth, until all 13 beads are used.
So, you will have 13! different necklaces, since you would have 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 156 * 110 * 72 * 42 * 120 = 17160 * 362880 = 6227020800.
So, you will have 6,227,020,800 different necklaces.
Hope this helps!
The distance from New York to Los Angeles is about 2820 miles. Each of Hannah steps measures about 2 feet long. Which is the best estimate of the number of steps Hannah would take if she walked from New York to Los Angeles? A) 30,000,000 B) 2,500,000 C) 15, 000,000 D) 7,500,000
Answers
Answer:
D
Step-by-step explanation:
convert miles to feet :
1 mile 5280 foot
2820*5280=14889600 ft
14889600/2=7444800 close to 7500000
D
Introduction to Linear Functions: Which table represents a linear function?
Answers
Answer:
The table in the top right
Step-by-step explanation:
That table represents the equation y=-2x-1. It is the only table that represents a linear equation.
To be a linear equation it has to consistently add the same amount up and right OR down and right (depending on if it's a positive or negative equation)
I have included a picture of the graph with the equation and all points on it (click/tap on it to see the full picture.)
If this helped please rate, thanks, and mark brainliest :)
The table which represents a linear function is one on the top-right corner.
What is linear function?A linear function is a mathematical relation which is characterized by a constant slope otherwise known as the rate of change of the function.
Upon evaluation of the slope of each table; only the top-right corner table has a constant slope.
slope, m = (-5-(-3))/(2-1)m = -2/1 = -2.Ultimately, a linear function is characterized by a constant slope as observed in the top-right corner table in discuss.
Read more on linear function;
https://brainly.com/question/15602982
How to solve the equation 4×3−15÷3×2+1
Answers
Answer:
3
Step-by-step explanation:
We use Order of Operations BPEMDAS.
Step 1: Multiply
12 - 15/3(2) + 1
Step 2: Divide
12 - 5(2) + 1
Step 3: Multiply
12 - 10 + 1
Step 4: Subtract
2 + 1
Step 5: Add
3
Answer: 3
Step-by-step explanation:
PEMDAS
P: No parenthesis
E: No exponents
M and D: 4x3 = 12(12-15÷3×2+1), 15÷3 = 5(12-5×2+1), 5*2 = 10(12-10+1)
A and S: 12-10 = 2(2+1), 2+1=3(3)
Question 1) While traveling to Europe, Phelan exchanged 250 US dollars for euros. He spent 150 euros on his trip. After returning to the United States he converts his money back to US dollars. How much of the original 250 US dollars does Phelan now have? Round to the nearest cent. 1 European euro = 1.3687 US dollars Question 2) To fit between two windows, the width of a bookshelf must be no greater than Six and one half feet. Mrs. Aguilar purchases a bookshelf that is 77 inches wide. Which statement describes the relationship between the width of the bookshelf and the distance between the windows? Question 3) Alina is able to swim at a rate of about 2.5 miles per hour. Talia is able to swim at a rate of 1.8 meters per second. Which statement comparing the two swimmers is accurate? 1 mile 1,609 meters.
Answers
The volume of a cube is 681472 cubic cm. Find the side of the cube.
Answers
Answer:
[tex]l = 88 cm[/tex]
Step-by-step explanation:
Volume of Cube = [tex]l*l*l[/tex]
Volume of Cube = [tex](Length)^3[/tex]
Where volume = 681472 cubic cm
=> [tex]l^3 = 681472[/tex]
Taking square root on both sides
=> [tex]l = \sqrt{681472}[/tex]
=> [tex]l = 88 cm[/tex]
Solve for x 8/11 = x/3
Answers
Explanation:
8/11 = x/3
(8/11) • 3 = x
24/11 = x
Find each difference.
(32mn2 + 50mn2) - (10mn2 - 16m2 + 64)
PLEASE HELP!!! ASAP!!!
Answers
Answer:
144mn + 32m - 64
:)
Step-by-step explanation:
Four buses were filled with children and 20 children rode in cars for a field trip. Write an expression for how many children went on the field trip A.4c B.20c C.4c+20 D.4b+20c
Answers
Answer:
C. 4c+20
Step-by-step explanation:
If 4 buses are filled with kids, to get how many kids there are in total you would have to multiply the number 4, to represent the buses, times the number of kids in 1 bus, represented by C in this case. Then you would add 20 kids to represent the number of kids traveling in cars.
With that you have 4c+20.
Drag each factor to the correct location on the image. If p(1) = 3, p(-4) = 8, p(5) = 0, p(7) = 9, p(-10) = 1, and p(-12) = 0, determine which expressions are factors of the polynomial p(x).
Answers
Answer:
Step-by-step explanation:
Recall that when we are factoring a polynomial, we are implicitly finding its roots. By finding a root, we are looking for a value of x (say c) such that p(c) =0. When this happens, our polynomial has the the polynomial (x-c) as a factor.
We are given the values of p at some values of x. We notice that p(5) = 0 and p(-12) =0. So, this means that our polynomial has as a factor the polynomials (x-5) and (x+12).
Answer:
Factor: x-5 & x+12
Not a Factor: x-1, x+4, x-7, x+10
Step-by-step explanation:
The remainder theorem states that for a polynomial p(x) and a number a, the remainder on division of p(x) by x − a is p(a). So, p(a) = 0 if and only if x − a is a factor of p(x).
Since, p(5) = 0 and p(-12) = 0, the expressions (x − 5) and (x + 12) are factors of the polynomial p(x).
Pleaaaaase help!!!!
Answers
Answer:
see below
Step-by-step explanation:
sqrt(20)
sqrt(4*5)
We know that sqrt(ab) = sqrt(a) sqrt(b)
sqrt(4) sqrt(5)
2 sqrt(5)
Answer:
We can factor down 20 with it's greatest prime GCF, which is 5. We get a 4. When we factor that down the same way, we get 2. If we repeat that process, we get 5, 2, and 2, which turns into [tex]2\sqrt{5}[/tex].
lena works for 34 hours from monday to friday at her normal rate of pay ,on saturdays she gets an overtime rate of pay ,the overtime rate is 1.5 times her normal rate, she works for 4 hours on a saturday ,altogether lena earns £320 for her weeks work , what is her normal rate of pay per hour ???
Answers
Answer: £ 8
Step-by-step explanation:
Total hours Lena works from Monday to Friday = 34 hours
Hours she works on Saturdays = 4
Overtime rate of Saturday = 1.5 times her normal rate
Let x be the normal rate.
Then , Her total earning = [tex]34 x + 4 \times(1.5x) =34x+6x=40x[/tex]
Since her total earnings for week = £ 320
So,
[tex]320=40x\\\\\Rightarrow\ x=\dfrac{320}{40}\\\\\Rightarrow\ x=8[/tex]
Thus, her normal rate of pay per hour = £ 8
Quadrilateral rust has a vertex (2,4). What are the coordinates of r' after a dilation of scale factor 3, centered at the origin, followed by translation (x,y) to (x+4,y)
Answers
Answer:
The coordinates of r' are x = 10 and y = 12.
Step-by-step explanation:
The vertex experiments two operations: Dilation and translation, whose definitions are presented herein:
Dilation with respect to origin
[tex](x',y') = (0,0) + 3\cdot (x,y)[/tex], [tex]\forall \,x,y \in \mathbb{R}[/tex]
Translation
[tex](x',y') =(x+4,y)[/tex], [tex]\forall\,x,y\in \mathbb{R}[/tex]
If [tex]x = 2[/tex] and [tex]y = 4[/tex], then:
1) [tex](2,4)[/tex] Given.
2) [tex](0,0) + 3\cdot (2,4)[/tex] Dilation with respect to origin.
3) [tex](6,12)[/tex] Vectorial sum and scalar multiplication.
4) [tex](6+4,12)[/tex] Translation.
5) [tex](10,12)[/tex] Vectorial sum. Result.
The coordinates of r' are x = 10 and y = 12.
Answer:
10,12 is the answer
Step-by-step explanation:
I just did it on a p e x