WILL MARK BRAINLIEST
Part 1:
Graph the following system of equations. What is the solution set?
2x + y = 3
x = 2y - 1
Part 2:
Solve the following system of equations by substitution. What is the solution set?
y = -2x + 3
x - 2y = - 1
Part 3:
Compare the systems of equations and their solutions in Parts 1 and 2. How are they similar? How are they different?
Complete your work in the space provided or upload a file that can display math symbols if your work requires it. Include the graph of the linear system of equations and the process followed in order to solve the system by substitution.
Answers
Answer:
Part 1:
The solution set of the system of equations is x = 1, y = 1
Part 2:
The solution set is x = 1, y = 1
Part 3:
The similarity of the system of equations in Parts 1 and 2 is that they have the same solution set
The difference of the system of equations in Parts 1 and 2 is that they are arranged differently
Step-by-step explanation:
Part 1:
The system of equation is given as follows;
2·x + y = 3...(1)
x = 2·y - 1...(2)
The above system of equations can be written in terms of the variable, y, as follows;
For equation (1), we have;
y = 3 - 2·x
For equation (2), we have;
y = (x + 1)/2
From the attached graph created with Microsoft Excel, we have;
The solution set (the point of intersection) of the system of equations is x = 1, y = 1
To accurately find the common solution, we have;
(x + 1)/2 = 3 - 2·x
x + 1 = 2·(3 - 2·x) = 6 - 4·x
x + 1 = 6 - 4·x
x + 4·x = 6 - 1
5·x = 5
x = 5/5 = 1
x = 1
Therefore, y = 3 - 2·x = 3 - 2× 1 = 1, at the common solution
Part 2:
y = -2x + 3
x - 2y = -1
∴ x = 2y -1
y = -2(2y -1) + 3
y = -4y + 2 + 3
5y = 5
y = 1
x = 2y - 1 = 2 - 1 = 1
x = 1
The solution set is x = 1, y = 1
Part 3
The system of equations are similar in terms of their solution
The system of equations are different in terms of their arrangement
Answer:
put the first answerer as brainliest, i just saw no one else has answered this.
Step-by-step explanation:
Related Questions
plz answer the question in the screenshot
Answers
please help me. my mom got mad at me cause I don't know anything in Pre Cal. (what I am in)
Answers
a. 4^2 + b^2 = 8^2
16 + b^2 = 64
b^2 = 48
Missing term for A = 6.93 m
Now try B for yourself
Lance made four phone calls from his cell phone today. The calls
lasted 4.7, 9.4, 2.3, and 10.6 minutes. Use mental math to find the
total amount of time he spent on the phone.
Answers
Answer:
27
Step-by-step explanation:
Just add all numbers together.
Evaluate each expression.
7) (-7) + (-10) – 5 +2 8) (-9) + 4 + (-8) – (-7)
8) (-6) – (2 x 4) – (-1) 10) (-8) + (-4 ÷ -4) – 8
Answers
Answer:
Please check the explanation.
Step-by-step explanation:
Solving the expressions
7)
given the expression
[tex]\left(-7\right)+\:\left(-10\right)\:-\:5\:+2[/tex]
[tex]\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}[/tex][tex]\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:\:[/tex][tex]\mathrm{Apply\:rule\:}+\left(-a\right)\:=\:-a[/tex]so
[tex]=\left(-7\right)-10-5+2[/tex]
[tex]=-17-5+2[/tex]
[tex]=-22+2[/tex]
[tex]=-20[/tex]
8)
[tex]\left(-9\right)+4+\left(-8\right)-\left(-7\right)[/tex]
[tex]\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}[/tex][tex]\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:\:[/tex][tex]\mathrm{Apply\:rule\:}+\left(-a\right)\:=\:-a[/tex]so
[tex]=-5+\left(-8\right)-\left(-7\right)[/tex]
[tex]=-5-8-\left(-7\right)[/tex]
[tex]=-13-\left(-7\right)[/tex]
[tex]=-13+7[/tex]
[tex]=-6[/tex]
9)
[tex]\left(-6\right)\:-\:\left(2\:\times \:4\right)\:-\:\left(-1\right)\:[/tex]
[tex]\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}[/tex][tex]\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:\:[/tex]so
[tex]\left(-6\right)-\left(2\times \:4\right)-\left(-1\right)[/tex]
Calculate within parentheses
[tex]=\left(-6\right)-8-\left(-1\right)[/tex]
[tex]=-14-\left(-1\right)[/tex]
[tex]=-14+1[/tex]
[tex]=-13[/tex]
10)
[tex]\left(-8\right)\:+\:\left(-4\:\div \:-4\right)\:-\:8[/tex]
solving
[tex]\left(-8\right)+\left(-\frac{4}{-4}\right)-8[/tex]
[tex]\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a[/tex]
[tex]=-8-\frac{4}{-4}-8[/tex]
[tex]=-8-\left(-1\right)-8[/tex]
[tex]\mathrm{Apply\:rule}\:-\left(-a\right)=a[/tex]
[tex]=-8+1-8[/tex]
[tex]\mathrm{Add/Subtract\:the\:numbers:}\:-8+1-8=-15[/tex]
[tex]=-15[/tex]
The value of the given expression 7) (-7) + (-10) – 5 +2 is -20, 8) (-9) + 4 + (-8) – (-7) is -6, 9) (-6) – (2 x 4) – (-1) is -11, 10) (-8) + (-4 ÷ -4) – 8 is -15.
What is BODMAS rule?BODMAS stands for B- bracket, O- order, D-division, M-multiplication, A- addition, S- subtraction. We use this rule when there is more than one operation are present in the mathematical expression.
7) (-7) + (-10) – 5 +2
here, we will use the BODMAS rule, the addition and subtraction will go from left to right.
= -7 -10 -5 + 2
= -17 -5 + 2
= -22 + 2
= -20
8) (-9) + 4 + (-8) – (-7)
= -9 +4 -8 +7
= -5 -8 +7
= -13 + 7
= -6
9) (-6) – (2 x 4) – (-1)
= -6 - 8 +1
= -12 + 1
= -11
10) (-8) + (-4 ÷ -4) – 8
= -8 -4/ (-4) - 8
= -8 +1 -8
= -7 -8
= -15
Therefore, the value of the given expression 7) (-7) + (-10) – 5 +2 is -20, 8) (-9) + 4 + (-8) – (-7) is -6, 9) (-6) – (2 x 4) – (-1) is -11, 10) (-8) + (-4 ÷ -4) – 8 is -15.
Learn more about the BODMAS rule here:
https://brainly.com/question/24383445
At Paulson Middle School, 75% of the sixth grade class is making a B or higher. If there are
24 students in the sixth grade class, then how many are making a B or higher?
25%
Are we Looking FOR THE PART OR THE WHOLE?
Answers
Answer:
18 students are making a B or higher
Step-by-step explanation:
24 * 75% = 18
Answer:
we are looking for the part
PLEASE PLEASE HELP I WILL GIVE BRAINALSIT
please answer 8 and 9
Answers
Answer:
8 is 7 and 9 is no, because charlie only saves around 1/4 but melody saves around 1/3
Step-by-step explanation:
Answer:
8: 7
9: No
Step-by-step explanation:
help
state the multiplicity for each root
[tex]3(x^{2} + 5)^ {2} ( {x}^{2} - 25)^{3} (x - 8)^{4} = 0[/tex]
state the multiplicity for each root
Answers
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Answers:
The two complex or imaginary roots [tex]x = i\sqrt{5}[/tex] and [tex]x = -i\sqrt{5}[/tex] have multiplicity 2.The two real roots x = 5 and x = -5 have multiplicity 3The root x = 8 has multiplicity 4======================================================
Explanation:
We'll use the zero product property to solve.
[tex]3(x^2+5)^2(x^2-25)^3(x-8)^4 = 0\\\\(x^2+5)^2=0 \text{ or } (x^2-25)^3=0 \text{ or } (x-8)^4 = 0\\\\x^2+5=0 \text{ or } x^2-25=0 \text{ or } x-8 = 0\\\\x^2=-5 \text{ or } x^2=25 \text{ or } x = 8\\\\x=\pm\sqrt{-5} \text{ or } x=\pm\sqrt{25} \text{ or } x = 8\\\\x=\pm i\sqrt{5} \text{ or } x=\pm 5 \text{ or } x = 8\\\\[/tex]
where [tex]i = \sqrt{-1}[/tex]
----------------------
The notation [tex]x=\pm i\sqrt{5}[/tex] breaks up into [tex]x=i\sqrt{5} \text{ or } x=-i\sqrt{5}[/tex]. The multiplicity of these two roots is 2 as it's the exponent of the factor [tex](x^2+5)^2[/tex]. Focus on the outermost exponent.
The notation [tex]x = \pm 5[/tex] becomes [tex]x = 5 \text{ or } x = -5[/tex]. The multiplicity of these two roots is 3 since it's the outermost exponent of the factor [tex](x^2-25)^3[/tex]
And finally, the multiplicity of the root x = 8 is 4 because it is the outermost exponent of the factor [tex](x-8)^4[/tex]
someone help :( 3333333
Answers
Answer:
5 feet
mark above answer BRILLIANT
Someone please help me with this
Answers
I’m not sure if this is correct but I hope this helps✨❤️
a pump fills a pool at a constant rate at the end of 9 minutes it has filled 1 gallon of water which table represents the relationship between the number of minutes and the number of gallons of water in the pool
Answers
Answer:
D
Step-by-step explanation:
The rate at which the pool is filled is 1 gallon per 9 minutes. If you divide all the numbers of minutes in the left side of the table with the number of gallons on the right you get 9 minutes per gallon for each of them so they follow the rate.
Jennifer bought some tulips, lilies, and roses to make bouquets. She bought the same number of tulips as lilies. She bought three more roses than tulips and lilies combined. She paid 18 cents for each tulip. The lilies were 27 cents per flower, and the roses cost 55 cents each. How many of each kind of flower did Jennifer buy if she paid $17.15 in all?
Answers
Answer:
z = 18.5
y = 15.5
x = 15.5
Step-by-step explanation:
Let
tulips = x
lilies = y
roses = z
x = y
z= x + 3 or y + 3
The equation is
0.18x + 0.27y + 0.55z = 17.15
Substitute x = y and z = y + 3 into the equation
0.18y + 0.27y + 0.55(y + 3) = 17.15
0.18y + 0.27y + 0.55y + 1.65 = 17.15
y = 17.15 - 1.65
= 15.5
x = y
x = 15.5
z = x + 3
= 15.5 + 3
= 18.5
Therefore,
z = 18.5
y = 15.5
x = 15.5
There are 4 consecutive odd integers that have a sum of 248. What is the greatest of these integers?
Answers
Answer:
63.5
Step-by-step explanation:
248/4=62
the numbers are
60.5, 61.5, 62.5, 63.5
I'll give brainlyiest to whoever answers right first.
There is a line that includes the point (1, 7)and has a slope of 7. What is its equation in slope-intercept form?
Answers
Answer:
y=7x
Step-by-step explanation:
When finding the slope intercept form using 2 points, we do the following.
y=mx+b (Slope intercept from)
y=7x+b (7 is slope)
Substitute the point
7=7(1)+b
7=7+b
b=0
y=7x
The slope intercept equation is y = 7x
Evaluate the expression |- 15| + | -7|
Answers
Answer:
Step-by-step explanation:
The lines in between the numbers are called absolute value bars. Whenever you see numbers that have absolute value bars, know that the numbers become positive.
Therefore,
|-15| = 15
|-7| = 7
Now we just add,
15+7=22
Final answer = 22
I need help please! If I can I will mark brainleist for the one who’s right!
Answers
Answer: A
Step-by-step explanation:
Answer:
D: 20 cans of tuna for $13Step-by-step explanation:
First:
1. Find out the price of one can
A: $2.50 is per can
B: $1.92 is per can
C: $2.22 is per can
D: $1.54 is per can
The second step is:
Eliminate the most expensive
So, what we have left is
B: $1.92 is per can
D: $1.54 is per can
The cheapest is D: $1.54 is per can.Which can also be said as the smallest price for each canSo the last choice is the answer.Hope this helped,
Kavitha Banarjee
Find three consecutive integers such
that the sum of the first and the
second integer is three more than the
third integer.
Answers
9514 1404 393
Answer:
4, 5, 6
Step-by-step explanation:
Let x represent the middle one. Then the sum of the first two is ...
(x -1) +x
And we want that to be 3 more than the third:
(x -1) +x = (x +1) +3
2x = x +5 . . . . . . . . . add 1, simplify
x = 5 . . . . . . . . . . . . . subtract x
Since 5 is the middle integer, the three integers are ...
4, 5, 6
Answer my math question I asked so many times I lost most of points
Answers
Answer:
f(x) = (x+1)^2 - 9
Answer:
A = 1
B = 2
C = -8
Y intercept is (0,8)
The line of symmetry is x = -1
Min/max is (-1, -9)
Opens up
Domain is (-infinity, infinity)
Range is (-9, infinity)
The vertex is (-1,-9)
Solve: 32 = y + 12.4 y = _____ & explain
Answers
Answer:
y=19.6
Step-by-step explanation:
Answer:
to get y you subtract 12.4 from both side and that is your answer.
Step-by-step explanation:
19.6 hope it correct mark brainliest if so thank u have an nice day
how many inches are in 16 centimeters?
Answers
Answer:
6 1/4 inches
Step-by-step explanation:
explain: Just use google!
Mr James has coffee worth $400/kg that he wishes to mix with 20kg of coffee worth $700/kg to get a mixture that can be sold for $500/kg. How many kg of the cheaper coffee beans should he use?
Answers
Answer:
11.3kg
Step-by-step explanation:
if 700=20
therefore 400=400*20÷700=11.3
18 points help me fast please
Answers
What equation best represents the following sentence?
The sum of a number and two is twice the number.
n+2=2n
n−2=2n
n+2=2+n
n+n=2n
Answers
Answer:
2n + 1 to find the first odd number.
Step-by-step explanation:
that is it
One litre of milk is poured into a cylindrical container of radius 10 cm. Calculate the depth of the milk in cm)to 2 dp. ( take pi = 3.142)
Answers
Answer:
Depth=3.18cm
Step-by-step explanation:
V=πr2h
1LITRE=1000CM3
v=1000cm³
1000cm3=3.142×10²×Depth
Depth= 1000/3.142×100
Depth=3.18cm
Can somebody please help me with this math question please
Answers
Answer:
Step-by-step explanation:
isosceles triangles are ones that have two equal sides and angles. this would mean that ab is equal to bc. then you substitute the values in for AB=BC, 3x-4=5x-10. you bring the variables to one side and you flip everything which is then 2x=6 and then divide by 2. this would be x=3. then you have to figure out the AB. 3(3)-4=5. then you can always check for BC, 5(3)-10=5. and they are equal! hope i helped!
MAY YOU PLEASE HELP ME!!
Answers
Answer:
D. (4, 0)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASEquality PropertiesAlgebra I
Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define systems
-x + 5y = -4
4x + 3y = 16
Step 2: Rewrite systems
x = 5y + 4
4x + 3y = 16
Step 3: Solve for y
Substitute in x: 4(5y + 4) + 3y = 16Distribute 4: 20y + 16 + 3y = 16Combine like terms: 23y + 16 = 16Subtract 16 on both sides: 23y = 0Divide 23 on both sides: y = 0Step 4: Solve for x
Define: 4x + 3y = 16Substitute in y: 4x + 3(0) = 16Multiply: 4x = 16Isolate x: x = 4And we have our final answer!
what is X for this 4x/3-3x+1=10
Answers
Answer:
x = 1
Step-by-step explanation:
(4x/3) - 3x + 1 = 10
(4x/3) -3x = 9
4x - x = 3
3x = 3
x = 1
A 2 1/2 pound bag of grass seed covers 1/8 of an acre.How much grass seed is needed for 1 acre
Answers
Answer: 8 times more 8*2 1/2 = 20 pounds.
Step-by-step explanation: If 2.5 pounds cover 1/8 then simply multiply the 2.5 by 8, since you'll need 8/8. 8/8=1.
I hope this helps :)
given function of f(x) = 2x - 1 and fg(x) = 10x + 3, find the function of g(x)
Answers
Answer:
The function of g(x) = 5x + 2
Step-by-step explanation:
Let us use the composite function to solve the question
∵ f(x) = 2x - 1
∵ f(g(x)) = 10x + 3
→ f(g(x)) means substitute x in f(x) by g(x)
∴ f(g(x)) = 2[g(x)] - 1
→ Equate the two right sides of f(g(x))
∴ 2[g(x)] - 1 = 10x + 3
→ Add 1 to both sides
∴ 2[g(x)] - 1 + 1 = 10x + 3 + 1
∴ 2[g(x)] = 10x + 4
→ Divide each term into both sides by 2
∵ [tex]\frac{2[g(x)]}{2}[/tex] = [tex]\frac{10x}{2}[/tex] + [tex]\frac{4}{2}[/tex]
∴ g(x) = 5x + 2
∴ The function of g(x) = 5x + 2
There were 124 people at a concert. Admission was $5 each for adults and $3 each for children. A total of $444 was collected from admissions. How many adults and how many children attended?
Answers
Answer:
The answer is 36 adults and 88 children.
Step-by-step explanation:
The two equations are:
x+y=124 and 5x+3y=444
Using substitution method:
5x+3(124+x)=444
5x+372-3x=444
2x=72
x=36
5(36)+3y=444
180+3y=444
3y=264
y=88
[tex]\frac{6\sqrt{3} }{7\sqrt{8} }[/tex]