Solve the system.
3x + 2y + 4z = 11
2x – y + 3z = 4
5x – 3y + 5z = -1
Enter your answer as an ordered triple.
Someone help please!!
Answers
Answer: (x, y, z) = (-3, 2, 4)
In other words, x = -3, y = 2 and z = 4.
You'll enter the number only into each box.
===============================================================
Explanation:
There are a few routes we can take to solve this. I'll use substitution.
First let's isolate y in the second equation.
2x - y + 3z = 4
2x + 3z = 4+y
4+y = 2x+3z
y = 2x+3z-4
This is then plugged into the first equation
3x+2y+4z = 11
3x+2( y )+4z = 11
3x+2( 2x+3z-4)+4z = 11 .... replace y with 2x+3z-4; since y = 2x+3z-4
3x+4x+6z-8+4z =11
7x+10z-8 = 11
7x+10z = 11+8
7x+10z = 19 .... we'll call this equation (4) and come back to this later
--------------------------------------
Move onto the third equation (of the original equations given)
Plug in y = 2x+3z-4
5x - 3y + 5z = -1
5x - 3( y ) + 5z = -1
5x - 3( 2x+3z-4 ) + 5z = -1
5x - 6x - 9z + 12 + 5z = -1
-x - 4z + 12 = -1
-x - 4z = -1-12
-x - 4z = -13 ..... let's call this equation (5)
--------------------------------------
To recap, we found equation (4) and equation (5) to be
7x+10z = 19-x - 4z = -13We can then solve for x in equation (5) like so
-x - 4z = -13
-x = -13 + 4z
-x = 4z - 13
x = -(4z - 13)
x = -4z + 13
This is then plugged into equation (4)
7x+10z = 19
7(-4z+13)+10z = 19 .... note how we now have one variable
-28z+91+10z = 19
-18z+91 = 19
-18z = 19-91
-18z = -72
z = -72/(-18)
z = 4
We can use this value of z to find x
x = -4z+13
x = -4(4)+13
x = -16+13
x = -3
Use the values of x and z to find y. We'll revisit the first equation in which we isolated y
y = 2x+3z-4
y = 2(-3)+3(4)-4
y = -6+12-4
y = 6-4
y = 2
So overall, the solution to this system is (x, y, z) = (-3, 2, 4)
-------------------------------
Checking the answer:
We'll replace x,y,z with the values we found.
In the first equation, 3x+2y+4z = 11 becomes 3(-3)+2(2)+4(4) = 11 and that simplifies to 11 = 11. In other words, the expression 3(-3)+2(2)+4(4) turns into 11. This confirms the first equation.Repeat the same idea for the second equation. We have 2x-y+3z=4 turn into 2(-3)-2+3(4) = 4 and that simplifies to 4 = 4. The answer is verified here. The third equation 5x-3y+5z = -1 becomes 5(-3)-3(2)+5(4) = -1 which simplifies to -1 = -1. We get a true equation here as well.Since all three equations are true when (x, y, z) = (-3, 2, 4), this verifies the answer completely. This is the only solution to the system. The system is independent and consistent.
Related Questions
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Answers
Please help! I need it to move on to the next question I have 30 minutes
Answers
Answer:
uh either b or e
the others are slope-intercept
I hope this helps:)
- ♥
100 points ! What is the area of the following composite figure? All angles are right angles.
24 m^ 2
27 m ^2
29 m^ 2
22 m^ 2
Answers
Answer:
24m²
Step-by-step explanation:
..,.................
Area = 5*4+2*1+2*1
Area = 20+2+2
Area = 24m²
Answer:
24 m^2
Step-by-step explanation:
We need to study the structure well
We can find the magnitude of the big rectangle. We will need to find the total length and total breadth of the big rectangle
Then we remove the area of the four squared cut out from the big rectangle.
Total length of the rectangle is 5+1+1=7m
Then the length of the breath of the rectangle is 2+1+1=4m
So area of rectangle is given as length × breadth
Area= l×b
Area=7×4=28m²
Area of the big rectangle is 28m²
Then the squared is made of dimension 1m by 1m
Area of a square is s²
Then, a=1m
Area of the square= 1²=1m²
There are four squared side
Then, the total area of the four squared is 4×1=4m²
Then the required area is
Area=Total area - area of four squared side
Area=28m²-4m²
Area =24m²
Area of the figure is 24m²
The correct option is A.
James recently got a credit card. The APR on the card is 19.8%. What is the monthly interest rate?
A. 1.65%
B. 7.8%
C. 12%
D. 19.8%
Answers
The answer is A.
Step-by-step explanation:
ARP means Annual Percentage Rate. Annual means yearly and there are 12 months in a year so divide 19.8 by 12 and you get 1.65.
Find the value of sin theta, if tan theta = 4; 180 < theta <270.
a. -4 (square root)17/ 17
b. -4
c. -1/4
d. (square root)7/ 4
Please select the best answer from the choices provided
Ο Α
O B
О С
O D
Answers
Answer: You can use the identity THE PICTURE THAT I PUT THERE
The sign is negative because the angle is in the 3rd quadrant. This corresponds to ... a. -(4√17)/17
value of sin ( theta ) = -4 (square root of ) 17 / 17
What are Trigonometry Functions ?
Real functions which relate to an angle of a right angled triangle to ratios of two side length.
Given
tan (theta) = 4`
sin(theta) = tan (theta ) / (1 + tan ^ theta)^(1/2)
sin(theta) = 4/(1+(4)^2)^(1/2)
= 4/ (17)^ (1/2)
multiplying and dividing by 17 ^ (1/2), we get
= -4 (17) ^ (1/2) / 17 ( negative since angle is in third quadrant and tan is negative in that quadrant )
option a) -4 (square root of ) 17 / 17
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An arithmetic sequence has a 2nd term equal to 3 and 10th term equal to -13.
Find the term of the sequence that has value -93. please answer asap.
Answers
Answer:
50th term
Step-by-step explanation:
Second term, a + d = 3
Tenth term, a + 9d = -13
a + d = 3 (1)
a + 9d = -13 (2)
Subtract (1) from (2) to eliminate a
9d - d = -13 - 3
8d = -16
d = -16/8
d = -2
Substitute d = -2 into (1)
a + d = 3 (1)
a + (-2) = 3
a - 2 = 3
a = 3 + 2
a = 5
Find the term of the sequence that has value -93.
nth term = a + (n -1)d
-93 = 5 + (n - 1) -2
-93 = 5 + (-2n + 2)
-93 = 5 - 2n + 2
-93 = -2n + 7
-93 - 7 = -2n
-100 = -2n
n = -100/-2
n = 50
50th term = -93
Calculate the diameter of the circle with circumference of 154cm use π as 3.14
Answers
Answer:
d≈49.02cm
Step-by-step explanation:
C=2πr
d=2r
Solving ford
d=C
π=154
π≈49.01972cm
Answer:
All you have to do
Step-by-step explanation:
All you have to do is divide the number pie by 154 or if does not work try doing 154 by number pie
If a = -2 and b = -4 -3i, then find the value of a b in fully simplified form.
Answers
Answer:
I'm not so sure but I think it's 6 or 9i
Avery is preheating her oven before using it to bake. The initial temperature of the
oven is 65° and the temperature will increase at a rate of 10° per minute after being
turned on. What is the temperature of the oven 7 minutes after being turned on?
What is the temperature of the oven t minutes after being turned on?
Answers
Answer:
temp after 7 minutes is 135°
temp after 't' minutes: y = 65 + 10t
Step-by-step explanation:
Answer:
1) 135°
2) 65° + 10t°
Step-by-step explanation:
What is the temperature of the oven 7 minutes after being turned on?
65° (initial temperature) + 10° (temperature increase per minute) × 7 (amount of minutes)
10 × 7 = 70
65° + 70° = 135°
What is the temperature of the oven t minutes after being turned on?
65° (initial temperature) + 10° (temperature increase per minute) × t (amount of minutes)
10 × t = 10t
65° + 10t°
x is an integer and satisfies the following inequality. 5(x+4)<32 What is the maximum possible value for x?
a.6
b.3
c.2
d.0
Answers
Answer:
c.2
Step-by-step explanation:
5(x+4)<32
5(2+4)<32
10+20<30
If I simplify this what would I get and how would I do it?
Answers
Answer:
x^3y^3z^3
Step-by-step explanation:
when dividing exponents of the same base you subtract
mehjgsgwqididhdgascccknska
Answers
Answer:
Yo, thx for the free points man
Step-by-step explanation:
If it takes 2 cups of sugar for 24 cookies, how many cups of sugar will it take for 72 cookies?
Answers
Answer:
6
Step-by-step explanation:
72/24=3
3*2=6
if i have all a's and one d what is my gpa
Answers
Answer:
Step-by-step explanation:
umm like 2.8 i think
List one way you can multiply polynomials by polynomials.
a. Boxes
b. Vertically
c. Horizontally
d. All of the above
Answers
Answer:
a
Step-by-step explanation:
Have you ever devised a way to solve a problem? How?
Answers
Answer:
What kind of problem?
Step-by-step explanation:
What is the equation of the line that passes through the point (−7,−1) and has a slope of 11?
Answers
Answer:
y = 11x + 76Step-by-step explanation:
The equation of a line with a slope of "a" and containing a given point (x₀, y₀) is:
y - y₀ = a(x - x₀)
a = 11, x₀ = -7, y₀ = -1
So:
y - (-1) = 11(x - (-7))
y = 11x + 77 - 1
y = 11x + 76
A group of workers can plant 2/5 acres in days.3/4 What is the unit rate in acres per day?
Answers
Answer:
8/15
Step-by-step explanation:
Unit rate is 8 / 15 acres per day.
What is work?
"Work is defined as when force is applied on an object and it gets move in particular direction."
According to the question,
Group of workers plant 2/ 5 acres in 3 /4 days
3 / 4 days = 2/ 5 acres
1 day = [tex]\frac{2}{5}[/tex] × [tex]\frac{4}{3}[/tex]
⇒ 1 day = 8 / 15 acres
Hence, Unit rate is 8 / 15 acres per day.
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Is
Y=-3/4x -2
Y=3/4x+1
One solution many solution or no solution
Answers
8 cubed as a single power of 2
Answers
Answer:
[tex]2^{9}[/tex]
Step-by-step explanation:
Using the rule of exponents
[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex]
note that 8 = 2³ and so
8³ = (2³ )³ = [tex]2^{3(3)}[/tex] = [tex]2^{9}[/tex]
Which scenario is best represented by a linear function?
A
The area of a square, A, where the length of each side of the square is represented by
S (A= s?)
The perimeter of a square, P, where the length of each side of the square is
B represented by s
(P = 4s)
The surface area of a cube, A, where the length of each side of the cube is
C represented by s
(A = 6s )
The volume of a cube, V, where the length of each side of the cube is represented by
s(V = $)
Answers
Answer:
P=6sStep-by-step explanation:
to understand thisyou need to know about:linear functiontips and formulas:a linear function is function with two variables one dependent another one is independentlet's solve:since we can see what linear function is
the second condition is the best fit
The perimeter of a square, P, where the length of each side of the square is B represented by s(P = 4s)therefore
our answer is b
there are 56 customer in a shop.24 of them are men.the rest of the customers are women in the shop
Answers
Answer:
There are 32 women in the shop.
Answer:
32 are women
Step-by-step explanation:
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Complete the following proofs.
Given: Points R, S, T, Q on circle O
Prove: mRS + mST + mTQ = mRQ
Answers
Answer:
Match the number of statement with the same number of reasons.
Step-by-step explanation:
Here are the statements
1.
Points R, S, T, Q on circle O
2.
measure of RS+ST=RT
measure of RT+TQ=RQ
3.RS+ST+TQ=RQ
Here are the reasons
1.Given
2. Arc Addition
3. Subsitution
Which expression is equivalent to the expression below?
2(6k+4)−4(2+2k−1)
-------------------------------------------------------------------------
a} 18+48k
b} 14k−1
c} 4k−4
d} 4+4k
Answers
Answer:
D. 4+4k
Step-by-step explanation:
(12k +8) - (8+ 8k - 4)
12k +8 - 8 - 8k + 4
4k +4
d}4+4k
2(6k+4)-4(2+2k-1) writing down the question
12k+8-8-8k+4 multiplying the numbers by the coefficients
12k-8k+8-8+4 collecting like terms
4k+4 the answer
A clerk at a local camera shop earns a 5% commission on all sales. How much commission does the clerk earn on a $500 sale?
Answers
Answer:
she earns $25.00 commission
Step-by-step explanation:
.05×500=25
Find the domain and range for f(x)=pi cos(x)
Answers
Domain of f(x) = pi cos x is ALL REAL NUMBERS.
The range of f(x) = pi cos x is [-1, 1].
Jane and 3 friends decided to split the cost of a pizza evenly. The total cost was $25.48. How much does each friend have to pay?
Answers
Answer:
$6.37
Step-by-step explanation:
Jane and 3 friends = Jane + another 3 people
= 4 people in total
Total Cost of pizza = $25.48
If 4 people split $25.48 evenly,
Amount each friend has to pay = Total Cost of pizza/Total number of people
= $25.48/4
= $6.37 per friend
Each friend has to pay $6.37 each if $25.48 is splitted evenly amongst them
Can someone help me with all of these??Pls, and explain it in words because i have to record a video for it.
Answers
Answer:
Question 1: 9 Question 2: e=40
Step-by-step explanation:
Question 1: Divide both sides of the equation by the same term,Cancel terms that are in both the numerator and denominator,Divide the numbers.
Question 2: I just subtracted 56 by 16. 56-16
Question 3: To find the value of x we need to use inverse operation.???
THIS IS ALL I COULD HELP I AM SORRY!
can someone help me with this?
Answers
answer this plz maths question
Answers
Answer:
Step-by-step explanation:
[tex]\frac{3x + 5}{4x +2}=\frac{3x+4}{4x + 7}[/tex]
Cross multiply,
(3x+ 5 ) (4x + 7)=(3x + 4)*(4x + 2)
3x*4x + 3x *7 + 5*4x + 5*7 = 3x*4x + 3x*2 +4*4x + 4*2
12x² + 21x + 20x + 35 = 12x² + 6x + 16x + 8 {Combine like terms}
12x² + 41x + 35 = 12x² + 22x + 8
12x² + 41x +35 - 12x² - 22x = 8
12x² - 12x² + 41x - 22x + 35 = 8
0 + 19x + 35 = 8
19x = 8 - 35
19x = -27
x = -27/19