Answers
Looking at the first system of equations,
16x - 10y = 10
-8x - 6y = 6
If we multiply both sides of the second equation by 2, the coefficient of x is exactly the negative of the coefficient of x in the first equation.
-8x - 6y = 6
⇒ 2 (-8x - 6y) = 2 (6)
⇒ -16x - 12y = 12
By combining this new equation with the first one, we can eliminate x and solve for y :
(16x - 10y) + (-16x - 12y) = 10 + 12
⇒ -22y = 22
⇒ y = -1
Then we just solve for x by replacing y in either equation.
16x - 10y = 10
⇒ 16x - 10 (-1) = 10
⇒ 16x + 10 = 10
⇒ 16x = 0
⇒ x = 0
The main idea behind elimination is combining the given equations in just the right amount so that one of the variables disappears. The "right amount" involves using the LCM of the coefficients of a given variable. In this example, the x-coefficients had LCM(8, 16) = 16, so we only had to scale one of the equations (the one with -8x) to cancel all the x terms.
If we wanted to eliminate y first instead, we first note that LCM(6, 10) = 30. To get 30 as a coefficient on y, in the first equation we would have multiplied by 3:
16x - 10y = 10
⇒ 3 (16x - 10y) = 3 (10)
⇒ 48x - 30y = 30
And in the second equation, we would have multiplied by -5 (negative so that upon combining the equations, we end up with -30y + 30y = 0):
-8x - 6y = 6
⇒ -5 (-8x - 6y) = -5 (6)
⇒ 40x + 30y = -30
Now combining the two scaled equations gives
(48x - 30y) + (40x + 30y) = 30 + (-30)
⇒ 88x = 0
⇒ x = 0
We then solve for y :
16x - 10y = 10
⇒ -10y = 10
⇒ y = -1
so we end up with the same solution as before.
Related Questions
Question 28
What is the speed in m/s of a car that travels 30km in 20 minutes?
A: 1500 m/s B: 150 m/s
C: 90 m/s
D: 540 m/s
E: None of these
Answers
Answer:
E none of these
Step-by-step explanation:
first convert the 30 km into m
it will be 30000m
speed = distance /time taken
convert the time into seconds too it will be 1200
so 30000/1200 = 25m/s
none of the above
The path of a ball thrown can be modeled by the equation f(x)=−16x^2+45x+6, where x is the horizontal distance. Use a transformation to create a new model in which the ball is thrown twice as far. What is the new equation, what is the transformation, and how did you pick this?
Answers
Answer:
g(x) = -4x^2 +(45/2)x +6
Step-by-step explanation:
A function is scaled horizontally by replacing x with x/k, where k is the expansion factor. Here, we want to expand the graph horizontally by a factor of 2, so the new function will be f(x/2).
g(x) = f(x/2) = -16(x/2)^2 +45(x/2) +6
g(x) = -4x^2 +(45/2)x +6
Guided Practice
Give a reason to justify the equation.
3y+ (-5y) = [3+ (-5)]y
A. Commutative Property of Addition
B. Associative Property of Addition
C. Distributive Property
Answers
the sum of 2 integers is 61 and their difference is 29.
Answers
Answer:
16 and 45
Step-by-step explanation:
Just use guess and check, start with a number too low like 10+39=49. Then go up until you find the number or until you go over.
Please help please please
Answers
Answer:
39
Step-by-step explanation:
284-5(7)²
284-(5×49)
284-245
39
Answer:
The Answer Is 70
Step-by-step explanation:
So first you have do the parentheses, (2+5) = 7
Then do the exponents [tex]7^{2}[/tex] 7.7 = 49
Next do the Multiplying 49.5= 214
Finally Subtract 284-214=70
I Hope This Helps You :)
Columbus would have taken some live animals aboard for food sources. If there were one hundred forty one animals, of which seventy two were rabbits and the rest were chickens,what percentage of animals were chickens? Round your answer to the nearest percent.
Answers
Answer:
49
Step-by-step explanation:
hope it will help I think 49 is the answer
HELP ME PLEASE 20 POINTS
In a certain chemical the ratio of zinc to copper is 4 to 17 a jar of the chemical contains 595 grams of copper. How many grams of zinc does it contain
Answers
Answer:93 grams Zinc
Step-by-step explanation:3 Zinc : 13 Copper
x 31 x 31
93 Zinc, 403 Copper
or
set up a proportion, cross multiply, and solve for the variable:
3(403) = 13(x)
3(31) = x
93 = x
Which option is an example of a survey?
A. Asking students in a school how much time they spend exercising
B. Flipping a coin 50 times and counting the number of heads
C. Measuring the heights of the players on the basketball team
D. Testing the effectiveness of a new reading program by allowing a
classroom to use it and comparing the results with another
classroom that doesn't use it
Answers
Answer:
I think the answer is A
Step-by-step explanation:
The example of a survey are; A. Testing the effectiveness of a new reading program by allowing a classroom to use it and comparing the results with another classroom that doesn't use it
What is an survey?An survey is a technique used to confirm or deny a hypothesis, as well as assess the likelihood or effectiveness of something that has never been tried before.
Since Experiments show what happens when a specific factor is modified, which sheds light on cause-and-effect relationships.
The survey asks participants to quantify their trust in politicians while a numerical scale, with 1 being the least amount of trust.
Example of a survey;
Testing the effectiveness of a new reading program by allowing a classroom to use it and comparing the results with another classroom that doesn't use it
To learn more about experiments refer to:
brainly.com/question/25303029
#SPJ2
Given that f(x)=x-5 g(x)=5x and h(x)=-f(x+1)-3g(x-1), then what is the value of h(3)?
please show step by step answer.
Answers
Answer:
Step-by-step explanation:
f(x) = x - 5 and g(x) = 5x
- f(x + 1) = - ( x + 1 - 5 ) = 4 - x
- 3g(x - 1 ) = - 3 [ 5 (x - 1)] = 15 - 15x
h(x) = 4 - x + 15 - 15x = 19 - 16x
h(3) = 19 - 16(3) = - 29
A patio measures 120 cm long and 70 cm wide. If a tile measures25 cm. How many tiles will be needed to cover the patio?
Answers
Answer:
So, multiply 120 by 70 cm for the area which is 8,400. Divide that by 25 cm which would be 336. That would be your final answer. (A tip for these problems is to draw it because it makes it easier sometimes.)
Thanks Mark As Brainlist
pleaseee help lol also show work if you can please
Answers
Answer:
Answer is x = 31.5
Step-by-step explanation:
Explanation is in the picture. Pls give brainliest. :D
Please answer circle theorem question.
Many thx.
Answers
Answer:
x = 125
Step-by-step explanation:
Tangents from an external point to a circle are congruent , that is
CA = CB
Then Δ ABC is isosceles with base angles being congruent
∠ BAC = ∠ ABC = [tex]\frac{180-70}{2}[/tex] = [tex]\frac{110}{2}[/tex] = 55°
∠ ABC and x are adjacent angles on a straight line and sum to 180° , so
x = 180° - 55° = 125°
Then x = 125
Which sequence shows the numbers in order from least to
greatest?
1
2
-3
4
3
-3
OA) 2 3
} }
OB) Ź. *.
oc) * * Ź
OD) * *
4
Answers
Answer:
-3 1 2 3 4
Step-by-step explanation:
Answer:
-3 1 2 3 4
Step-by-step explanation:
Solve the system of equations using substitution?
Y=3x+1
Y+2=4x
Answers
nasa pick po yong answers
#CARRYONLEARNING
love y'all
If correct Brainlyest
Answers
Answer:
c is the answer
Step-by-step explanation:
simplified on left-hand side is 2<5 and it is the same as -2<5
hope this helped :)
A plot of land doubles in size by adding x meters to the length and x meters to the width of the land?if the original plot had an area of 200 by 300 meters ,what is the value x?
Answers
Answer:
x = 100
Step-by-step explanation:
The larger area is ...
A = LW
A = (300+x)(200+x) = x^2 +500x +60,000
The smaller area is ...
A = (200)(300) = 60,000
We want the larger area to be double the smaller area, so ...
x^2 +500x +60,000 = 2(60,000)
x^2 +500x = 60,000 . . . . . . . . . . . . subtract 60,000
x^2 +500x + 62500 = 122500 . . . add 250^2 to complete the square
(x +250)^2 = 350^2
We're interested in the positive solution, so we can take the positive square root to find it:
x +250 = 350
x = 100 . . . . . . . . . subtract 250
_____
The graph shows the quadratic in the form x^2 +500x -60,000. That is, we're looking for zeros (x-intercepts) of the function.
I need help with this
Answers
If I understand the problem correctly
The blank on the left would be 14
and the blank on the top would be 350
Which graph represents the function?
Answers
Answer:
First one ( top left)
This has an open circle at y = 3 which means the 3 is not included.
Then the y value of the second line equals the x value.
The two on the right are not correct because they use a closed dot for a strict inequality (the one without the line under it has the empty dot)
The bottom left one can’t be correct in my eyes because the second equation says that y (f(x)) equals x if x is greater than or equal to one. But the range of the numbers don’t go beyond (0,1).
The top left is inclusive of numbers that are greater than 1.
Let me know how it goes I am not the best at math
Can someone plz help Me?
Answers
Answer:
C.
Step-by-step explanation:
Dont quote me but im pretty sure it's C here's why:
2/3 is .667 which means the trash compactor crushes the trash .01 kilo per 1 second 3/8 minutes being closest .25 means that it can crush it roughly in 22 second or 3/8 minutes.
in the united states 16 out of every 20 cans are recycled what percent of cans are recycled
Answers
Answer:
80%
Step-by-step explanation:
First, you multiply 20 by 5, which gives you 100. Then multiply 16 by 5, which is 80. 80 out of 100 is 80%
Answer:80%
Step-by-step explanation:16/20=0.8 Knowing this the answer will be 80% of cans are recycled in this equation
A cylinder has a height of 18 feet.
Its volume is 16,334.28 cubic feet.
What is the radius of the cylinder?
Answers
The answer is 17, Volume = h × π×r^2
Divide by known height from both sides
Divide by pi
square root
Please don’t answer just for points! Help is really needed~
Answers
i dont understand
what do we need to do?
2 is 65
3 is 148
4 is 32
I am not sure at all.
-5x-/(3x-7)+4(3x-5)-(6x-9)
Answers
Answer:
-5x / 9x - 18
Step-by-step explanation:
= - 5x- / ( 3x - 7 ) + 4 ( 3x - 5 ) - ( 6x - 9 )
= applying rule : ( a ) = a
then, ( 3x - 7 ) = 3x - 7
= - 5x- / 3x - 7 + 4 ( 3x - 5 ) - ( 6x - 9 )
= applying the fraction rule : -a/b = a/b
= 5x / 3x - 7 + 4 ( 3x - 5 ) - ( 6x - 9 )
= -5x / 9x - 8. Answer!
h(x) = 2x2 + x + -3
Find h(2)
Answers
algebra 1
F(x) passes through 0, -1 and 5 , 14
G(x) passes through -6 , -1 and -1, 14
Describe two types of transformations that can be used to transform f(x) to g(x)
Solve for k in each type of transformation.
Write an equation for each type of transformation that can be used to transform f(x) to g(x).
Answers
g(x)= -6, -1, -1, 14
g(x)=f(x)+k
-6= 0+k
K=-6
A)
B) g(x)=f(x)+k
-1=-1+ k
k=-1+1=0
> 5.0
q(x)=f(x)+k
-1=5+k
k=-1-5=-6
g×=f×+k
14= 14+k
k= 0
K=-6,0,-6,0
Find the total surface area of this triangular prism
25 cm
24 cm
10 cm
14 cm
Answers
Answer:
Area = (Length * (a + a * (sin(Angle γ) / sin(Angle γ + Angle β)) + a * (sin(Angle β) / sin(Angle γ+Angle β)))) + a * ((a * sin(Angle γ)) / sin(Angle γ + Angle β)) * sin(Angle β)
please keep it simple
Answers
Answer:
A B C D E F G H I J K L M N O P Q R S T U V W X Y ZDefine the domain: {(2,3),(0,3),(4,2),(5,6)}
A. 2, 0, 4, 5
B. 0
C. 6
D. 3, 2, 6
Answers
D=A. 2,0,4,5
how many possible number of facemask and face shield can an online seller could sell to get an amount of the least php2 000 based on the data above
Answers
PLS HELP using only the marking in the diagram, what theorem can be used to show that the two triangles are congruent
a.) AAS
b.)ASA
c.)HL
d.)SSS
Answers
We can see that angles BAC and EDF are equal
We can also see that lines AC and DF are equal
And we can see that angles ACB and DFE are equal