solve each system of equations by showing the process of substitution.
a) y=-1/4 x and x+2y=4
b) y=-x-2 and 3x+3y=6
c) -8x+2y=4 and y=4x+2
pLS help
Answers
Answer:
A. {x,y}={-2,-3}
// Solve equation [2] for the variable x
[2] x = 2y + 4
// Plug this in for variable x in equation [1]
[1] (2y+4) - y = 1
[1] y = -3
// Solve equation [1] for the variable y
[1] y = - 3
// By now we know this much :
x = 2y+4
y = -3
// Use the y value to solve for x
x = 2(-3)+4 = -2
B. [1] 3x=3y-6
[2] y=x+2
Equations Simplified or Rearranged :
[1] 3x - 3y = -6
[2] -x + y = 2
Solve by Substitution :
// Solve equation [2] for the variable y
[2] y = x + 2
// Plug this in for variable y in equation [1]
[1] 3x - 3•(x +2) = -6
[1] 0 = 0 => Infinitely many solutions
C.Step by Step Solution
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System of Linear Equations entered :
[1] 4x - y = 2
[2] 8x - 2y = 4
Solve by Substitution :
// Solve equation [1] for the variable y
[1] y = 4x - 2
// Plug this in for variable y in equation [2]
[2] 8x - 2•(4x-2) = 4
[2] 0 = 0 => Infinitely many solutions
Answer:
Step-by-step explanation:
a) y = -1/4x --------------(I)
x + 2y = 4 -----------------(II)
Substitute y = (-1/4)x in equation (I)
[tex]x + 2*\dfrac{-1}{4}x=4\\\\\\x -\dfrac{1}{2}x=4\\\\Multiply \ the \ entire \ equation \ by \ 2 \\\\2x -x = 8\\\\x=8[/tex]
[tex]Substitute \ x = 8 \ in \ equation \ (I)\\\\y=\dfrac{-1}{4}*8\\\\\\y = -2[/tex]
Answer: x = 8 ; y = -2
b) y = -x - 2 --------------(i)
3x + 3y = 6 -----------(ii)
Divide equation (ii) by m
x + y = 2
y = -x + 2 ----(iii)
From (i) and (iii), it shows that these lines have same slope. So, they are parallel lines
Answer: No solution
3) -8x + 2y =4
2y = 8x + 4
Divide the entire equation by 2
y = 4x + 2 -------------(i)
y = 4x + 2 ----------------(ii)
From (i) and (ii), we come to know that these lines coincide.So, they have infinite solutions.
Related Questions
The answer need help fast please
Answers
Answer:
D.) Equation (4)
Step-by-step explanation:
1. y= (2)+6 =8
2. y=2(2)+4 =8
3. y= 3(2)+2 =8
4. y=5(2)-4 =6
In-n-Out sells their cheeseburger for 4.50 but they charge .50 for extra patties. Carls Jr. sells a cheeseburger for 4.25 and will charge .75 cents for an extra patty. When will the burgers cost the same amount? How many extra patties do they have to order? Solve using tables.
Answers
Answer:
just add 0.75 on the bottom
Step-by-step explanation:
im stumped on this question. someone help me plss
Answers
Answer:
One of the answers could be linear
Step-by-step explanation:A linear graph is always a straight line, and this looks to demonstrate that. Sorry if this is incorrect, just my understanding.
a pet company makes a small bag that holds 2 pounds of dog food. They want a large bag of 40 pounds. What factor will the surface area of the bag increase ?
Answers
Answer: 20
Step-by-step explanation:
You do 40➗2 which you would get 20.
Then you would round 20 to the nearest tenth, then you get 20.
Because if the number on the left/right is between 0 and 4, the whole number stays the same.
Note: 0-4 stays the same 5-9 higher number.
For example: Rounding 164 to the nearest tenth will become 160.
Six cantaloupes are cut up and served into thirty-two equal portions for a catering event. Which of the following shows the amount of cantaloupe in each portion?
Answers
Answer:
Step-by-step explanation:
Take the six cantaloupes divide it by 32 pieces 6 divided by 32 is 0.1875
The amount of the cantaloupe in each portion will be;
⇒ 5.33
What is mean by Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
Six cantaloupes are cut into 32 equal portions for a catering event.
Now,
Since, Six cantaloupes are cut into 32 equal portions.
Hence,
In each portion, the amount of cantaloupe = 32 ÷ 6
= 32 / 6
= 5.33
Therefore,
The amount of the cantaloupe in each portion will be;
⇒ 5.33
Learn more about the division method visit:
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A Uber charges $3.50 for pick up and $0.40 per mile. The ride costs $7.50. How far did they travel?
Answers
Find the value of x.
Step by Step
Answers
Answer:
sorryi dont know
Step-by-step explanation:
Which decimal is less than 2.87? 2.859 C. 2.971 b. 2.8711 d. 2.88 Please select the best answer from the choices provided
Answers
Answer:
Step-by-step explanation:
2.859 is less than the rest
Answer:
2.859 is ur answer.
..............
If 3a+5=12, what is the value of 6a+14?
Answers
Answer:For example, choice A is incorrect because if the value of 10x + 3 were 4, then it would follow that x = 0.1, and the value of 5x + 6 would be 6.5, not 10.
Step-by-step explanation:
The answer is
283a + 5 = 12
subtract 5 from both sides
3a = 7
divide by 3 on both sides to isolate "a"
a = 7/3
Substitute 7/3 for "a" in the second equation
6(7/3) + 14
6 multiplied by 7/3 = 42/3 = 14
14 + 14 = 28
Complete the function operation.
For the function [tex]\frac{32}{x+3}[/tex], find [tex](g^{-1} * g)(5)[/tex]
Answers
Answer:
5
Step-by-step explanation:
[tex]g(x)=\frac{32}{x+3}\\\\\implies g^{-1}(x)=\frac{32}{x}-3\\\\g^{-1}o \ g=[g(g^{-1}(x))]=\frac{32}{\frac{32}{x}-3+3}=x\\\\\implies (g^{-1}o \ g)(5)=5[/tex]
Emily has some marbles. After Mrs. Kim gave her another 21 marbles, the number of marbles became four times the number of marbles at first. How many marbles does Emily have now?
Answers
Answer:
Emily has 84 marbles now
Step-by-step explanation:
21×4
=84
Which logarithmic equation is equivalent to 25 = 32? log232 = 5 log532 = 2 log325 = 2 log25 = 32.
Answers
Logarithmic function is the inverse of the exponential function. The logarithmic function that is equivalent to 2⁵ = 32 is log₂32=5.
What is the Logarithm function?A log function is a way to find how much a number must be raised in order to get the desired number.
[tex]a^c =b[/tex]
can be written as
[tex]\rm{log_ab=c[/tex]
where a is the base to which the power is to be raised,
b is the desired number that we want when power is to be raised,
c is the power that must be raised to a to get b.
Given to us
2⁵ = 32
As we know that we can convert a number powered to another number therefore exponential function into a log function, thus,
[tex]2^5 = 32\\\\\rm log_2 32 = 5[/tex]
Hence, the logarithmic function that is equivalent to 2⁵ = 32 is log₂32=5.
Learn more about Logarithmic function:
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x y
−1 −10
3 14
y= ?x + (?)
Answers
Answer:
12. 5
11.
10
10
15. 7
14. 11
2
=
16
16
18. 3
+
11
17
3
4
co
loo
8
Step-by-step explanation:
12. 5
11.
10
10
15. 7
14. 11
2
=
16
16
ANSWER PLS FREE BRAINLIEST
Answers
Answer:
[tex]x = \frac{-1}{4}[/tex]
Step-by-step explanation:
[tex]\frac{2}{x} = -8[/tex]
[tex]2 = -8x[/tex]
[tex]x = \frac{-2}{8}[/tex]
[tex]x = \frac{-1}{4}[/tex]
Answer:
[tex]\sf x=-\cfrac{1}{4}[/tex]
Step-by-step explanation:
[tex]\sf \cfrac{2}{x}=-8[/tex]
[tex]\sf \cfrac{2}{x}x=-8x[/tex]
[tex]\sf 2=-8x[/tex]
[tex]\sf \cfrac{-8x}{-8}=\cfrac{2}{-8}[/tex]
[tex]\sf x=-\cfrac{1}{4}[/tex]
Bella needs 15 quarters of paint for one wall in her cellar she has 2 1/4 gallons left over from painting the other walls she has another 5 quarts that her neighbor gave her is that enough paint
Answers
0.0455 quarters of paints is not enough to paint the wall. she needs 15 quarters.
She needs 15 quarters of paint for one wall .
She has 2 1 / 4 gallons left over from painting the other walls and she also has another 5 quarts that her neighbour gave her.
Therefore,
Conversion of measurement units4 quarts = 1 gallon
5 quarts = 5 / 4 gallons
Then,
total gallon = 9 / 4 + 5 / 4 = 14 / 4 = 7 / 2 gallons
Therefore,
1 gallons = 0.01301053418982 quarters
7 / 2 gallons = ?
cross multiply
number of quarters = 3.5 × 0.01301053418982
number of quarters = 0.0455 quarters
Therefore, 0.0455 quarters of paints is not enough to paint the wall. she needs 15 quarters.
learn more on algebra here; https://brainly.com/question/821377
Find the volume of a sphere, whose diameter is 8 mm.(Take n = 3.14) (Round your answer to the nearest tenth).
Answers
[tex] \\ [/tex]
Diameter sphere = 8mm[tex]\small \pi = 3.14[/tex][tex] \\ [/tex]
To find:-Volume of sphere[tex] \\ [/tex]
Solution:To find volume of sphere first we have to convert Diameter into radius .
Diameter = 2 radius
So:-
⇢Diameter = 2 radius
[tex]\\[/tex]
⇢Radius = Diameter/2
[tex]\\[/tex]
⇢Radius = 8/2
[tex]\\[/tex]
⇢Radius = 2 × 2 × 2/2
[tex]\\[/tex]
⇢Radius = 2 × 2/1
[tex]\\[/tex]
⇢Radius = 4/1
[tex]\\[/tex]
⇢Radius = 4 mm.
[tex]\\[/tex]
Now Finally Let's find volume of sphere.
We know:-
[tex]\\[/tex]
[tex]\star\boxed{\rm Volume~of~sphere=\frac{4}{3}\pi r^3}[/tex]
so:-
[tex]\\\\[/tex]
[tex]\dashrightarrow \sf Volume~of~sphere=\frac{4}{3}\times 3.14 \times 4^3\\[/tex]
[tex]\\\\[/tex]
[tex]\dashrightarrow \sf Volume~of~sphere=\dfrac{4}{3}\times \dfrac{314}{100} \times 4^3\\[/tex]
[tex]\\\\[/tex]
[tex]\dashrightarrow \sf Volume~of~sphere=\dfrac{4}{3}\times \dfrac{314}{100} \times 4\times 4\times 4\\[/tex]
[tex]\\\\[/tex]
[tex]\dashrightarrow \sf Volume~of~sphere=\dfrac{4}{3}\times \dfrac{314}{100} \times 64\\[/tex]
[tex]\\\\[/tex]
[tex]\dashrightarrow \sf Volume~of~sphere=1.33\times \dfrac{314}{100} \times 64\\[/tex]
[tex]\\\\[/tex]
[tex]\dashrightarrow \sf Volume~of~sphere= \dfrac{1.33\times314 \times 64}{100}\\[/tex]
[tex]\\\\[/tex]
[tex]\dashrightarrow \sf Volume~of~sphere= \dfrac{26,727.68}{100}\\[/tex]
[tex]\\\\[/tex]
[tex]\dashrightarrow \sf Volume~of~sphere=26,7.28 (approx)\\[/tex]
[tex]\\\\[/tex]
[tex] \therefore \underline{ \textbf{ \textsf{Volume~of~sphere = \red{26,7.28(approx)}}}}[/tex]
Find the measure of x
Answers
Answer:
x=3.24
Step-by-step explanation:
cos(29)=x/3.7
x=3.7 cos(29)
x=3.24
Hope it helps!
(6,5) and (3, 7.5)
slope:
Answers
Step-by-step explanation:
Slope formula:
[tex] \frac{y2}{x2} - \frac{y1}{x1} = m[/tex]
m = slope
Substitute the points into the formula format:
[tex] \frac{7.5}{3} - \frac{5}{6} = m[/tex]
Solve:
[tex] \frac{ 7.5}{3} - \frac{5}{6} = \frac{2.5}{ - 3} [/tex]
[tex] \frac{ 2.5}{ - 3} = - \frac{5}{6} [/tex]
The slope equals -5/6.
PLEASE ANDWER ASAP WILL GIVE BRAINLIEST
choose all fractions equivalent to each given fraction
Answers
Answer:
(a) Yes Yes No No
(b) Yes No No Yes
Step-by-step explanation:
(a) [tex]\frac{-9}{10}=-\frac{9}{10}[/tex]
[tex]\frac{9}{-10}=-\frac{9}{10}[/tex]
[tex]\frac{-9}{-10}=\frac{9}{10}[/tex]
[tex]\frac{9}{10}=\frac{9}{10}[/tex]
(b) [tex]\frac{-3}{8}=\frac{3}{-8}[/tex]
[tex]\frac{3}{8}=\frac{3}{8}[/tex]
[tex]\frac{-3}{-8}=\frac{3}{8}[/tex]
[tex]-\frac{3}{8}=\frac{3}{-8}[/tex]
The quotient of 10 and a
Answers
Answer:
The answer I believe is 10? Sorry if i am wrong
Step-by-step explanation:
in algebra, if there is a variable without a coefficient, then it just means 1. So a = 1, and 10 ÷ 1 = 10
How do you do this problem and show work
Answers
Answer
the answer is 16 but i cant tell if there is anything after that is there?
Step-by-step explanation:
Answer:
1/x^8
Step-by-step explanation:
x^3*x^2 = x^5
x*x*x*x*x*x*x = x^7
x^5 / x^7 = 1/x^2
(1 / x^2)^4 = 1^4 / x^2*4 = 1/x^8
How many kilograms is a rice packet that weighs 750 g?
(Please answer quick!)
Answers
Answer:
0.750 kg
Step-by-step explanation:
Hi there ,
As you know 1 kg = 1000g
So when we convert g to kg then we divide the given value of grams by 1000.
So in this case we have 750 grams, changing it we have :
[tex]\frac{750}{1000}[/tex]
Since there are 3 zeroes in 1000 we move the decimal point by 3 places to the left leaving the answer as : 0.750 kg or [tex]\frac{750}{1000}[/tex] kg
Please mark me as brainliest if you found the above answer helpful
A plane has traveled 26 miles on a course heading 48º east of north. How far north (x) has the plane traveled at this point, to the nearest tenth of a mile?
Answers
Answer:
17.39
Step-by-step explanation:
48+a = 90
x= 42
sin 42 = x / 26
x = 17.39
Which of these is a service industry?
A. a textile plant
B. an oil refinery
C. an aircraft manufacturer
D. a dry-cleaning store
I think its either c or b but more but not so sure.... help......
Answers
Its D i hope that helped
help plssssssssssssssssss
Answers
Answer:
28.26 units³
Step-by-step explanation:
gi solved kopo yan
The soccer team is selling bags of popcorn for $3 each and cups of lemonade for $2 each. To make a profit, they must collect a total of more than $120. Solutions can be represented by coordinates (p,c), where p represents the number of bags of popcorn sold and c represents the number of cups of lemonade sold. Is the coordinate (10,45) a solution to the inequality? Explain your reasoning or show your work.
Answers
3x + 2y ≥ 120
you are asking me to confirm whether the below statement is true
10 * 3 + 45 *2 ≥ 120 ?
30 + 90 = 120
120 ≥ 120
its not greater but its equal which means it is a possible solution
Of the following transformations, which of the following is not one that maintains congruence?
a. A dilation with a scale factor of 0.5
b. A reflection over the x-axis
c. A translation 1 unit left
d. A dilation with a scale factor of 1
Answers
Answer:
A because its not the one that maintains congruence
Step-by-step explanation:
^^^^^
Joel borrowed 518,000 for 6 years at simple interest to purchase a vehicle. If Joel repaid a
total of $20,953.80, at what rate did he borrow the money?
Answers
Answer:
2.735%
Step-by-step explanation:
The amount due on principal P after t years at rate r is ...
A = P(1 +rt)
Filling in the given values, we can solve for r:
20,953.80 = 18000(1 +6r)
20953.80/18000 -1 = 6r = 0.1641
r = 0.1641/6 = 0.02735 = 2.735%
Joel's interest rate was 2.735%.
In the table to the right, the P(0) is blank so we can assume P(O) = 0 What does a probability equal to zero mean?
Answers
Answer:
It means there is no chance this will happen or in other words a 0% chance
Step-by-step explanation:
HELPPPP I need the answer for this math equation
Answers
Answer:
4x-8u+10
Step-by-step explanation:
You take the -2 inside the brackets to remove the brackets. (parenthesis=brackets)
-2×-2x=4x
-2×+4u=-8u
-2×-5=10
4x-8u+10