Q3).
0.4x + 0.3y = 1.7
0.7x - 0.2y = 0.8
Solve it by using substitution method.
Answers
Step-by-step explanation:
[tex] \green{\large\underline{\sf{Solution-}}}[/tex]
Given pair of linear equations are
[tex]\rm :\longmapsto\:0.4x + 0.3y = 1.7 \\ \\ \rm :\longmapsto\:0.7x - 0.2y = 0.8[/tex]
can be rewritten as on multiply by 10,
[tex]\rm :\longmapsto\:4x + 3y = 17 - - - - (1)\\ \\ \rm :\longmapsto\:7x - 2y = 8 - - - - - (2)[/tex]
From equation (2)[tex]\rm :\longmapsto\:2y = 7x - 8[/tex]
[tex]\rm\implies \:\boxed{\tt{ y = \frac{7x - 8}{2}}} - - - - (3) [/tex]
On substituting the value of y in equation (1), we get
[tex]\rm :\longmapsto\:4x + 3\bigg( \dfrac{7x - 8}{2} \bigg) = 17[/tex]
[tex]\rm :\longmapsto\:\dfrac{8x + 21x - 24}{2} = 17[/tex]
[tex]\rm :\longmapsto\:29x - 24 = 34[/tex]
[tex]\rm :\longmapsto\:29x = 34 + 24[/tex]
[tex]\rm :\longmapsto\:29x = 58[/tex]
[tex]\bf\implies \:x = 2 - - - - (4)[/tex]
On substituting x = 2 in equation (3), we get
[tex]\rm :\longmapsto\:y = \dfrac{7 \times 2 - 8}{2} [/tex]
[tex]\rm :\longmapsto\:y = \dfrac{14 - 8}{2} [/tex]
[tex]\rm :\longmapsto\:y = \dfrac{6}{2} [/tex]
[tex]\bf\implies \:y = 3[/tex]
So, we get
[tex]\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\bf{x = 2} \\ \\ &\bf{y = 3} \end{cases}\end{gathered}\end{gathered}[/tex]
VerificationFrom equation (1),
[tex]\rm :\longmapsto\:0.4x + 0.3y = 1.7[/tex]
On substituting the value of x and y, we get
[tex]\rm :\longmapsto\:0.4(2) + 0.3(3) = 1.7[/tex]
[tex]\rm :\longmapsto\:0.8 + 0.9 = 1.7[/tex]
[tex]\rm :\longmapsto\:1.7 = 1.7[/tex]
Hence, Verified▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
Basic Concept :-To solve systems using Method of Substitution, follow this procedure:
1. Select one equation and solve it for one of its variables.
2. In the other equation, substitute the value of one variable evaluated in step 1 to reduced the equation to one variable.
3. Solve the equation to get the value of this variable
4. Substitute the value found in to first equation involving both variables and solve for the other variable.
Related Questions
What is the value of 4C9 ?
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Answer:
the value is 126
Step-by-step explanation:
have a good day
Tony has a small fish tank that is 3 feet long, 2 feet high, and 1 foot wide. He wants to buy more fish, so he will need a fish tank with a larger volume. What would be the volume of a fish tank, in cubic feet, that has a scale factor of 3 compared with each dimension of his old fish tank?
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Solve for x: 15x²=x+2
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hope its helps u
Explanation
Ellen,Krista,and Tori decide to buy their Mrs.Hannigan a fabulous pink flamingos purse The cost of the purse is $205 (what a bargain!). Home much money will each person pay if the cost is split equally ?
Answers
A contractor needs to buy nails to build a house. The nails come in small boxes and large boxes. Each small box has 150 nails and each large box has 400 nails. The contractor bought 2 more small boxes than large boxes, which altogether had 1950 nails. Write a system of equations that could be used to determine the number of small boxes purchased and the number of large boxes purchased. Define the variables that you use to write the system.
Answers
Answer:
The number of small and large boxes purchased are:
2 small boxes.
6 large boxes.
Step-by-step explanation:
To solve the unknowns, two equations must be established with the information provided:
150X + 400Y = 2700 (the price of the boxes and the final number of nails, where X is the small boxes and Y the large boxes)
Y = 3X (Large boxes are triple the small ones)
Then equation 2 is replaced in equation one and variable X is cleared:
150X + 400 (3X) = 2700
150X + 1200X = 2700
1350X = 2700
X = 2700/1350
X = 2
Finally, the value of X is replaced in equation 2 to find the number of large boxes:
Y = 3X
Y = 3 (2)
Y = 6
PLS MARK AS BRAINLIEST :)
Each student that buys school lunch pays $2.75. The cafeteria typically brings in between $1168.75 and $1438.25. How many students does the cafeteria usually serve?A. Model this situation using an inequality.B. Describe in words the quantities that would work in this situation.C. Write your answer in both interval and set notation.Your answer:
Answers
Which type of flower received a prime number of votes. Used the graph
Answers
Answer:
Where is the graph to use
Find the sets of numbers to which
belongs.
Select all that apply.
D A. integers
B. irrational numbers
C. natural numbers
D. rational numbers
E. whole numbers
F.
real numbers
Answers
Answer:
4/7 = 0.57142857……
Step-by-step explanation:
integer NO cause it has a decimal
irrational NO cause it can be written as a fraction
Natural NO cause it has decimals
Rational YES because it’s a fraction
whole NO cause decimals
Real YES cause it’s a number
Help help me pleaseee and thanks
Answers
Answer:
10
Step-by-step explanation:
sqrt. 100 = 10
because base x height = area
base and height must be same length in a square
Clara got 11 books at the book fair. That's 5% of all the books at the Book-fair. How many books are at the Book-fair in total?
Answers
there are 220 total books at the book fair
Answer:
220
Step-by-step explanation:
1) 11 (books) - 5%
x (total of books) - 100%
2) Cross multiplicate (100% is one and 5% is 0.05)
3) 11 - 0.05x
4) Switch x - [0.05x - 11]
5) Divide - [x = 220]
mary filled a water cooler with 6 1/2 gallons of water. She forgot to close the plug and 3 5/6 gallons leaked out?
help
Answers
Now, subtract 3 5/6 from 6 3/6.
The answer is 2 4/6
Answer: 2 2/3 gallons left
explanation:
6 1/2 = 6 3/6
6 3/6 - 3 5/6 = 2 2/3
proof: 2 2/3 + 3 5/6 = 6 3/6
Help meh, i need help
Answers
Answer: #1: 4[tex]\\\sqrt{2}[/tex]
#2: -6x^7
Step-by-step explanation:
#1 simplify the radical expression
10[tex]\sqrt{2}[/tex] - [tex]\sqrt{72}[/tex]
10[tex]\sqrt{2}[/tex] - 6[tex]\sqrt{2\\}[/tex]
collect like terms
Solution: 4[tex]\sqrt{2}[/tex]
#2 combine like terms
-3*2 = -6 then add the 5 and 2
A 145-inch board is cut into two pieces. One piece is four times the length of the other. Find the length of the shorter piece.
i need to figure this out in the next 20 mins cause i have to turn this in to get a good grade please...
Answers
Answer:
4x + x = 145, x=29 (shorter piece)
5x=145
x=145/5 = 29
Step-by-step explanation:
Find the number of sides of a regular polygon if one interior angle is 120 degrees.
03
04
05
06
Answers
Answer:
06
Step-by-step explanation:
because the formula says so
Who prosecuted Ernesto Miranda
Answers
Answer:
Twila Hoffman
Step-by-step explanation:
Which of the following is NOT a function?
Answers
Answer:
a x=-3
Step-by-step explanation:
The equation x = 3 represents a vertical line and not a mapping from values of x to values of y. For one thing, it fails the vertical line test for functions at the value x = 3.
Rewrite 5/12 and 3/4 so they have a common denominator
Answers
Answer:
5/12 = 5/12
3/4 = 9/12
Step-by-step explanation:
The common denominator is 12.
5/12 is already in the common form.
3/4= 3*3 / (4 * 3) = 9/12
please help me please
Answers
Here's the solution in attachment :
IF U HELP I PROMISE I WILL MARK U
Answers
-4y = -16 - 9x
y = 4 + 9/4x
y = 9/4x + 4
m = 9/4
perpendicular m = -4/9x
y = -4/9x + 4 is the answer to problem 3.
3x - 2y = -2
-2y = -2 - 3x
y = 1 + 3/2x
y = 3/2x + 1
m = 3/2x
perpendicular m = -2/3x
y = -2/3x + 1 is the answer to V problem 4.
Answer:
Step-by-step explanation:
How do I solve -5x+7>22 algebraically?
Answers
The attached image is the picture. Hope it helps!!!
Which of the following best describes the slope of the line below?
O A. Zero
B. Negative
C. Positive
D Undefined
Answers
Answer:
B
Step-by-step explanation:
going down on the right
Answer:
B
Step-by-step explanation:
Aline with zero slope is a horizontal line parallel to the x- axis
A line with undefined slope is a vertical line parallel to the y- axis
A line sloping upwards from left to right has a positive slope
A line sloping downwards from left to right has a negative slope.
The line shown slopes downwards from left to right and has a negative slope
Simplify 11 square root 1215
Answers
Answer:
9 • sqrt(15)
Step-by-step explanation:
hello everyone ,
i am having some problems solving this question in maths
Arrange 13.25 kg, 14560 g, 13.6 kg, 12000 g in descending order ,
Write the following decimals as fractions. Reduce the fractions to lowest
form.
a) 3.6 b) 12.5
i hope u also consider explaining
thank you all .
Answers
Answer:
Descending order:
14560g
13.6kg
13.25kg
12000g
a.) [tex]\frac{18}{5}[/tex]
b.) [tex]\frac{25}{2}[/tex]
Step-by-step explanation:
To find the difference between kg or g, either divide kg by 100 to convert to g, or multiply g by 1000 to convert to kg.
If we were to put everything into g:
14560g
13600g
13250g
12000g
See how they are still in the correct order?
If we were to put everything into kg:
14.56kg
13.6kg
13.25kg
12kg
Still in descending order!
___________________
Now to find out how to put the decimals into fractions:
Multiply by 10 (since there is only 1 digit behind the decimal, for every digit behind the decimal you multiply by another factor of 10, so if you have 2.55 you multiply by 100)
Following this we get:
36
125
Now divide by the same factor (10), we can't change the value of the number, just the way they look!
[tex]\frac{36}{100}[/tex]
[tex]\frac{125}{10}[/tex]
All that's left is it reduce!
[tex]\frac{18}{5}[/tex]
[tex]\frac{25}{2}[/tex]
And as you can see, we are back to the number I had put in the solution!
What is the missing value
Answers
Answer:
I am not entirely sure but I think it is 1.
Step-by-step explanation:
Don't quote me on this though. Please tell me if I am wrong.
y = x - 5 and y = -x + 3
Answers
Answer:
Point form:
(4,-1)
x=4,y=-1
Step-by-step explanation:
Graph:
Answer:
x = 4 , y = -1
Step-by-step explanation:
Note that both equations equal y. Set the two equations equal to each other.
x - 5 = y = -x + 3
x - 5 = -x + 3
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other.
First, add x and 5 to both sides of the equations:
x (+x) - 5 (+5) = -x (+x) + 3 (+5)
x + x = 3 + 5
2x = 8
Next, divide 2 from both sides of the equation:
(2x)/2 = (8)/2
x = 8/2
x = 4
Plug in 4 for x in the given equations and solve:
y = x - 5
y = (4) - 5
y = -1
y = -x + 3
y = -(4) + 3
y = -1
x = 4 , y = -1 are your answers.
~
~
please help me!! Will give Brainly if correct
Answers
Answer:
-1
Step-by-step explanation:
Let's take two points on the line- (0,2) and (2,0).
To find the slope:
[tex]m = \frac{y_2 - y_1}{x_2-x_1}\\m = \frac{0 - 2}{2-0}\\m = \frac{-2}{2}\\m = -1[/tex]
The slope is -1.
If Olivia has 68,79, and 74 for his 3 tests, what must he get on his 4th test in order to have an 80 average?
Answers
(68+79+74)= 221/3 =73.7
80 x 4 = 320
320-221 = 99
He must get 99 on his 4th test.
Thanks
PLEASE HELP! I’m almost finished with this assignment if someone could answer these questions correctly I’ll give you Brainliest for saving me haha!
c. When a rational and an irrational number are added, is the sum rational or irrational?
Explain.
Type your response here:
d. When a nonzero rational and an irrational number are multiplied, is the product rational or
irrational? Explain.
Type your response here:
e. Which system of numbers is most similar to the system of polynomials?
Type your response here:
f. For each of the operations—addition, subtraction, multiplication, and division—determine
whether the set of polynomials of order 0 or 1 is closed or not closed. Consider any two
polynomials of degree 0 or 1.
Type your response here:
Answers
C. The sum of any rational number and any irrational number will always be an irrational number.
Explanation: Each time they assume the sum is rational; however, upon rearranging the terms if their equation, they get a contradiction (that an irrational number is equal to a rational number). Since the assumption that the sum of a rational and irrational number is rational leads to a contradiction, the sum must be irrational.
Answer:
D. Any nonzero rational number times an irrational number is irrational.
Explanation: Assume r is nonzero and rational, and x is irrational. If rx = q, and q is rational, then x = q/r, which is rational. This is a contradiction.
Answer:
E. The system of polynomials is almost the same with the system of whole numbers.
Explanation: We count with and use a base 10 (decimal) system. Polynomials such as the function above are a “base x” system.
Answer:
F. Addition, subtraction, and multiplication would all be closed because every answer would be a polynomial. Division is not closed because when we divide numbers, sometimes they don’t divide evenly, leaving us with a remainder, which we can write as a fraction.
Explanation: (in answer)
I hope this at least semi helps!
Devon records 4 hours of reality shows on her DVR. She records comedy shows for 3/8 of that amount of time. Devon watches all the reality and comedy shows in half-hour sittings.
Part A: Find the number of hours of comedy shows that devon records.
Part B: Find the total number of hours of reality and comedy shows that devon records.
Part C: Find the number of half-hour sitting needed to watch all the shows.
PLZ HELP DUE TODAY 100 POINTS!!
Answers
#1
We need 3/8 of 4hours[tex]\\ \rm\rightarrowtail 3/8(4)=3/2=1.5h[/tex]
#2
Rest after comedy is Reality shows.
4-1.5=2.5hhow many gallons are equivalent to 20 points
Answers
Answer:
2.31964e-7
Step-by-step explanation:
Answer:
3 gallons
Step-by-step explanation: