please help me with this system of equations problem before I go insane the preferable solving methods would be through substitution or elimination
Answers
Answer:
x=8, y=0, z=-3
Step-by-step explanation:
Preferable is substitution because there is less room for mistakes but its long so here goes bare with me on this one :D
Name your equations
4x+2y-5z=47 (first eq)
x-2y+6z=-10 (second eq)
9x-7y-z=75 (third eq)
Lets take the easiest eq to isolate one variable lets take 2nd eq
[tex]x-2y+6z=-10\\x=2y-6z-10[/tex]
now this becomes our fourth eq
now again take the easiest eq to isolate another variable lets take the 3rd eq
[tex]9x-7y-z=75\\9x-7y-75=z[/tex]
now this becomes our fifth eq
and now plug in our fifth eq in the fourth eq because we now have z in terms of x and y
[tex]x=2y-6z-10\\x=2y-6(9x-7y-75)-10\\x=2y-54x+42y+450-10\\x+54x=2y+42y+450-10\\55x=44y+440\\\\x=\frac{44y+440}{55}[/tex]
and now we got our sixth equation which is x only in terms of y.
now we plug in our sixth equation in our fifth eq to get z in terms of y only
[tex]z=9x-7y-75\\\\z=9(\frac{44y+440}{55}) -7y-75\\z=\frac{396y+3960}{55} -7y-75\\z=\frac{396y+3960-385y-4125}{55} \\z=\frac{11y-165}{55}[/tex]
now we have our seventh eq and x &z in terms of just one variable y , now we put equation of z and x which is our sixth eq and seventh eq in our first eq.
[tex]4x+2y-5z=47\\\\4(\frac{44y+440}{55})+2y-5(\frac{11y-165}{55}) =47\\\\\frac{176y+1760}{55} +2y-47=\frac{11y-165}{11} \\\\\frac{176y+1760}{55} -\frac{11y-165}{11} -47=-2y\\\\\frac{176y+1760}{55}-(y-15) -47=-2y\\\\\frac{176y+1760}{55} -y-32=-2y\\\\\\frac{176y+1760}{55}=-2y+y+32 \\\\176y+1760=55(-y+32)\\176y+1760=-55y+1760\\176y-55y=1760-1760\\121y=0\\y=0[/tex]
and now finally we got y=0 now we need the value of x and z, put the value of y=0 in our seventh eq (z equation)
[tex]z=\frac{11y-165}{55} \\\\z=\frac{11(0)-165}{55} \\\\z=\frac{-165}{55}\\\\z=-3[/tex]
and now we put the value of y=0 in our sixth eq (x equation)
[tex]x=\frac{44y+440}{55} \\\\x=\frac{44(0)+440}{55} \\\\x=\frac{440}{55} \\\\x=8[/tex]
and now we got all the three values and hence the solution of the system of equation is
x=8, y=0, z=-3
Related Questions
b) Simplify 2-(3-a) = -4
Answers
Answer:
-1+a
Step-by-step explanation:
2-(3-a) = (2-3-(-a)) = -1+a
Answer:
a=-3
Step-by-step explanation:
First off subtract 2 from both sides:
-(3-a)=-6
Then distribute the negative:
-3+a=-6
Finally add 3 to both sides:
a=-3
tadah!!
Hope that helps.
Triangle ABC has vertices A (1,1) B (7,1) C (4,9) (A)Find the perimeter of triangle ABC. (B) Find the area of triangle ABC
Answers
9514 1404 393
Answer:
perimeter = 6+2√73 ≈ 23.09 unitsarea = 24 units²Step-by-step explanation:
It can help to draw a figure.
The altitude of this isosceles triangle is 8 units, and it splits the base into equal lengths of 3 units. Using the Pythagorean theorem, we find the length of a side to be ...
BC = AC = √(3² +8²) = √73
The perimeter is the sum of the lengths of those two sides and the base:
P = 2(√73) +6 ≈ 23.088 . . . units
The area is given by the formula ...
A = 1/2bh
A = (1/2)(6 units)(8 untis) = 24 units²
__
The perimeter is 6+2√73 ≈ 23.09 units.
The area is 24 units².
There is a proportional relationship between the number of months a person has had a streaming movie subscription and the total amount of money they have paid for the subscription. The cost for 6 months is $47.94. What is the constant of proportionality in this relationship? What does the constant of proportionality tell us about the situation?
Answers
Answer: proportionality constant = 7.99
It means for every 1 month, the amount need to pay = $7.99 .
Step-by-step explanation:
When y is directly proportional to y , then the equation for this relationship is given by :-
[tex]y=mx[/tex], (i)
where m is the proportionality constant.
here, it is given that number of months a person has had a streaming movie subscription is proportional to the total amount of money they have paid for the subscription.
If cost for 6 months is $47.94.
Put x= 6 and y= 47.94 in (i), we get
47.94 =6m
Divide both sides by 6 , we get
7.99 =m
So proportionality constant = 7.99
It means for every 1 month, the amount need to pay = $7.99 .
The constant of proportionality (k) is 7.99. This tells us that the subscription per month is $7.99.
Recall:
A proportional relationship is modelled with the equation, y = kx.
k is the constant of proportionality between y and x.
k = y/x
Given:
x = number of months (6)
y = total amount paid for subscription (47.94)
If 6 months subscription costs $47.94, therefore,
k = 47.94/6
k = 7.99
Constant of proportionality is therefore 7.99. This tells us that the subscription for per month is $7.99.
Learn more here:
https://brainly.com/question/11703625
The area of the triangle below is 2/5 square foot.
What is the length, in feet, of the base of the
triangle?
Answers
Answer:
B. 2/3
Step-by-step explanation:
The equation for area of a triangle is A=1/2bh
so we can plug in what were given
2/5 =1/2(6/5)b now we solve for b
2/5=6/10 b
2/5 divided by 6/10 =b
2/5 x 10/6 =b
4/6=b
2/3=b
You drop a seashell into the ocean from a height of 40 feet. Write an equation that models the height h in feet) of the seashell above the water after seconds. How long is the seashell in the air? Round your answer to the nearest tenth.
Answers
Answer:
t=1.58 seconds
Explanation:
The equation which models the height h of the seashell above water after t seconds
Height of seashell above water after t seconds; h = 40 - 8t²
Time that seashell is in air; t = 1.58 s
The sea shell is dropped under gravity and thus, from Newton's equations of motion, we know that height/distance is;
S = ut + ½gt²
Since it was dropped from a height and not the ground, then;
h = height of shell from ground
h_o = height from which the shell was dropped.
Thus, we have;
h - h_o = ut + ½gt²
We are told that the seashell was dropped into the ocean from a height of 40 ft. Thus;
h_o = 40 ft
It was dropped from rest and so; u = 0 ft/s
Acceleration due to gravity is; g = -32ft/s² (since it is free fall)
Thus;
h - 40 = 0(t) + ½(-32t²)
h = 40 - 8t²
The time that the seashell in the air will be after it has hit the surface which will be when h = 0.
Thus;
0 = 40 - 16t²
16t² = 40
t² = 40/16
t² = 2.5
t = √2.5
t = 1.58 s
Read more at; brainly.com/question/17576926
HELPPP me pleaseeeeeeeeeee
Answers
Answer: Y=104
Step-by-step explanation: Angle 1 is 2x which means it is 76, 180-76 gives you 104
help show work
42,44,46,48,50
assig 9
Answers
Answer: see below
Step-by-step explanation:
42) 11 < 3y + 2 < 20
-2 -2 -2
9 < 3y < 18
÷3 ÷3 ÷3
3 < y < 6
Graph: o----------o
3 6
44) 36 ≥ 1 - 5z > -21
-1 -1 -1
35 ≥ -5z > -22
÷ -5 ↓ ÷ -5 ↓ ÷ -5
7 ≤ z < 4.4
Graph: o------------ ·
4.4 7
46) 6b + 3 < 15 or 4b - 2 > 18
-3 -3 +2 +2
6b < 12 4b > 20
÷6 ÷6 ÷4 ÷4
b < 2 or b > 5
Graph: ←--------o o---------→
2 5
48) 8d < -64 and 5d > 25
÷8 ÷8 ÷5 ÷5
d < -8 and d > 5
there is no number that is both less than - 8 and greater than 5
No Solution
Graph: (empty)
50) 15x > 30 and 18x < -36
÷15 ÷15 ÷18 ÷18
x > 2 and x < -2
there is no number that is both less than - 2 and greater than 2
No Solution
Graph: (empty)
What is the volume of the cylinder below
Answers
Answer:
I think d or b
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
A label printer prints 7 labels in 3.4 seconds. How long will it take to print 56 pages of labels?
Answers
Answer:
27.20seconds
Step-by-step explanation:
hope this helped,brainliest?
Find the perimeter of the given figure.
Answers
Select True or False for each statement.
A.16.302 rounded to the nearest whole number is 16 feet per second.
Select True or False for each statement.
16.302 rounded to the nearest whole number is 16 feet per second.
16.302 rounded to the nearest tenth is 16.3.
16.302 rounded to the nearest hundredth is 16.31.
16.302 rounded to the nearest tenth is 16.3.
C.16.302 rounded to the nearest hundredth is 16.31.
Answers
Answer:
True
True
False
Look at the table. Bob ran 3 miles in 18 minutes. Complete the table:
Answers
Answer:
First one, Third one, Fifth one, and the last one too.
Step-by-step explanation:
Answer:
Step-by-step explanation:
First, make a ratio:
18 min/ 3mile = 6 min/mile
now multiply to finish the table:
1: 6
3: 18
5: 30
10: 60
25: 150
What’s the surface area to these 2 pls help me
Answers
Answer:
the answer is 40
Step-by-step explanation:
its simple try and do the link that I put you'll understand how to do this better
please help asap, the question is
Do you see a pattern? If so, explain your reasoning. and What predictions can you make about future rectangles in the set if your pattern continues?
Answers
Answer: the pattern is that the rectangles width and length get timed 2.
Step-by-step explanation: that pattern will continue until the rectangle will get bigger than the unobservant universe...
A recipe calls for 4 cups of flour to 6 tablespoons of shortening. How many tablespoons of shortening are needed for 6 cups of flour?
Answers
Answer:
8 tablespoons of shortening
Step-by-step explanation:
mathhhh
I'm soooo freakin' bad at math bruh....someone please help :/
28. Which of the following pairs of integers will give you a sum of −12 and a product of 35?
a. −6, −6
b. −4, −8
c. −5, −7
d. 5, 7
29. If Jess has 3 more nickels than dimes for a total of $1.50, how many of each does he have?
a. 7 nickels, 4 dimes
b. 12 nickels, 9 dimes
c. 13 nickels, 10 dimes
d. 6 nickels, 12 dimes
30. The length of a rectangle is 9 inches greater than the width. The area is 36 in.2. Find the dimensions.
a. 2 in. by 11 in.
b. 4 in. by 9 in.
c. 3 in. by 12 in.
d. 2 in. by 18 in.
Answers
29. B (12 nickels, 9 dimes) 60+90
30. C (width=3 in) (length=12 in) (3)(12)=36in^2
kala needs to make a total of 80 deliveries this week. So far she has completed 28 of them. What percentage of her total deliveries has kala completed?
Answers
Answer:
35 %
Step-by-step explanation:
50 % of 80 is 40 so 28% of 80 is 35%
if you just divide 80 by 28 you will get 35.
1/9 of 54 bottles of water = ? bottles
Answers
Answer:
6
Step-by-step explanation:
If you divide 54 in 9 parts it will come out to 6, to check this work divide 54 by 6.
6
Step-by-step explanation:
First you would turn it into a decimal to get .111 repeating then you would multiple it by 54 to get 5.99 repeating do you would round up to get 6
pls help ill give brainliest
Answers
There were 5 boys for every 7 girls at Rayville High School last year. If there were 420 students at the school, how many were girls?
Answers
Answer:
240
Step-by-step explanation:
The temperature at 6:00 am in New York was -7 °C. At 2:00 pm the
temperature in New York was 7 °C. What was the change in the temperature
temperature?
Answers
Answer
10 degrees c
Step-by-step explanation:
Which one of the following words is a pronoun A) Two B) Him C) Boys D) Go
Answers
Answer:
I believe it is Him.
Step-by-step explanation:
Answer:
B) Him
Step-by-step explanation:
Him refers to someone else, and that is exactly what a pronoun does!
4c = d for c
Solve for indicated variable.
Answers
Answer:
c=1/4d
Step-by-step explanation:
Answer:
c = d/4
Step-by-step explanation:
solve this literal equation using inverse operations:
4c = d
/4 /4
c = d/4
Write 45 as a product of primes.
Use index notation where appropriate.
Answers
3*3*5=45
Therefore:
3^2 *5 = 45
can u guys help with my one question i have left
Answers
Answer:
Weeks in a Year. A normal year has 365 days, which is 52 Weeks and 1 Day. A leap year has 366 days, which is 52 .
Step-by-step explanation:
hope this helps :)
Answer:
I think 6
Step-by-step explanation:
365/12=30.42
30.42/5= 6.08
A patient is placed in an elliptical tank that is 178 centimeters long and 102 centimeters wide to undergo sound wave lithotripsy treatment for kidney stones. Determine where the sound emitter and the stone should be positioned relative to the center of the tank
Answers
Complete Question
The diagram for this question is shown on the first uploaded image
Answer:
The position of the emitter is [tex]E = + 72.9 \ cm\ from\ the\ center [/tex]
The position of the stone is [tex]S = - 72.9 \ cm\ from\ the\ center [/tex]
Step-by-step explanation:
From the question we are told that
The length is l = 178 cm
The width is w = 102 cm
Generally the position of the stone along the horizontal axis is mathematically evaluated as
[tex]h = \frac{178}{2}[/tex]
=> [tex]h = 89 \ cm [/tex]
Generally the position of the emitter along the vertical axis is mathematically evaluated as
[tex]k = \frac{102}{2}[/tex]
=> [tex]k = 51 \ cm [/tex]
Generally the resultant position of both stone and the emitter is
[tex]R = \pm \sqrt{h^ 2 - k^2}[/tex]
=> [tex]R = \pm \sqrt{89^ 2 - 51^2}[/tex]
=> [tex]R = \pm 72.9 \ cm [/tex]
Hence the position of the emitter is [tex]E = + 72.9 \ cm[/tex]
the position of the stone is [tex]S = - 72.9 \ cm[/tex]
PLEASE HELP I AM BEING TIMED.
A frame designer is making a triangular frame. she has two sides of length 20 inches and 28 inches. What are the possible lengths for the third side?
Answers
54/x = 9/7
What does X=
Answers
Answer:
the answer is 42.
Step-by-step explanation:
9 times 6 is 54.
7 times 6 is 42.
Answer:
It'd be 486/7 or 69 and 3/7
Step-by-step explanation:
A store sells new video games for $45 each. Used video games sell for $18 each. Alex is buying 2 new video games and x used video games. Which equation can be used to find y, the total price Alex must pay in dollars?
Answers
Answer:
u = t/18 - 5
Step-by-step explanation:
45n + 18u = t where t is the total price, n is the number of new video games, and u is the number of used video games
plug in two:
90 + 18u = t
solve in terms of u:
18u = t - 90
u = t/18 - 5
can i get a thanks and brainliest please?
what is the average rate of change for the line graphed in the figure above
Answers
Answer:
5/8
Step-by-step explanation:
I used the slope formula of y2-y1/x2-x1