Learning task 2
A. Solve the systems of equations by a) graphing b) elimination c) substitution
Eq. 1: 2x - 3y = -1; Eq. 2: y = x - 1
B. Solve the problem using any method.
The sum of two numbers is 32 and the difference is 2. Find the numbers
Answers
The given equations are
[tex]2x-3y=-1\cdots(i) \\\\y=x-1\cdots(ii)[/tex]
(a) Solution by graphing both the equations:
Graph for both the equations (i) and (ii) are in the figure. The point of intersection of both the graph is the solution of the equations.
From the graph, the point of intersection is (4,3)).
Hence, the required solution is (4,3).
(b) Solution by elimination method:
Equations (ii) can be written as -x+y=-1, now multiply it by 2, we have
[tex]-2x+2y=-2\cdots(iii)[/tex]
Add equations (i) and (iii), we have
2x-3y=-1
-2x+2y=-2
__________
[tex]\Rightarrow -3y+2y=-1-2\\\\ \Rightarrow -y=-3\\\\ \Rightarrow y=3.[/tex]
Putting the value of y=3 in equation (i), we have
[tex]2x-3\times 3=-1 \\\\\Rightarrow 2x=-1+9=8 \\\\\Rightarrow x=8/2=4[/tex]
Hence, the required solution is (4,4).
(c) Solution by substitution method:
Substituting the value of y from equation (ii) to equation (i), we have
[tex]2x-3(x-1)=-1 \\\\\Rightarrow 2x-3x+3=-1 \\\\\Rightarrow -x=-1-4=-4 \\\\\Rightarrow x=4[/tex]
Putting the value of x=4 in equation (i), we have
[tex]y=4-1=3[/tex].
Hence, the required solution is (4,3).
Related Questions
5h + 10 = 4h + h + 15
Answers
Answer:
h = no solution
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define
5h + 10 = 5h + 15
Step 2: Solve for h
Subtract 5h on both sides: 10 ≠ 15Here we see that 10 does not equal 15.
∴ h has no solution.
Final Answer: No Solution
Steps/Reasons:
Step 1: Simplify [tex]4h + h + 15[/tex] to [tex]5h + 15[/tex].
[tex]5h + 10 = 5h + 15[/tex]
Step 2: Cancel [tex]5h[/tex] from both sides.
[tex]10 = 15[/tex]
Step 3: Because [tex]10 = 15[/tex] is false, there is no solution.
No Solution
~I hope I helped :)~
what is this answer? :)
Answers
Answer:
the answer is b
Step-by-step explanation:
will mark brainliest for the correct answer! just read the english, okay? the other language is the translation for the english.
Answers
Answer:
Step-by-step explanation:
Given equation is,
y = 3x² - 6x + 11
a). y = 3x² - 6x + 11
= 3(x² - 2x) + 11
= 3(x² -2x + 1 - 1) + 11
= 3(x² - 2x + 1) - 3 + 11
= 3(x - 1)² + 8
Comparing this equation with y = a(x - b)² + c
a = 3, b = 1 and c = 8
b). For minimum value of x,
Since, vertex of the graph is given by (b, c),
Minimum value of x will be,
x = b
x = 1
c). Vertex of the parabola → (b, c)
→ (1, 8)
For y-intercept,
By substituting x = 0 in the equation,
y = 3(0 - 1)² + 8
y = 11
Now we can sketch the graph by using the table of input - output values.
x -2 -1 0 1 2 3
y 35 20 11 8 11 20
Which expression is the simplest form of
(x4/7)^7
Answers
Answer:
7
Step-by-step explanation:
Please help!!!! With 8 and 9
Answers
Answer:
8. slope: = 1/2
9. equation: y=1/2x
Plzz what the answer I’m stuck
Answers
Answer:
the answer to your question is 576 square feet
Step-by-step explanation:
Step 1: 96 ÷ 4 = 24
Step 2: 24×24 =576
The equation 125 + 37.52x = y models the amount of money in your wallet Y is the total amount of dollars and x is the number of weeks from today. Is the equation in slope intercept form? Explain
If you graphed this situation what would the slope represent? Explain
If you graphed this situation what would the y intercept be and what would it represent?
What units make sense for the slope?
Answers
Answer:
Please check solution for answer
Step-by-step explanation:
The general equation of for the slope of a line is
y = mx + c
where m is slope and c is the y-intercept
a). Yes it is in the slope-intercept form
b) The slope would represent the amount of money in dollars per week that is in the wallet
c) The y-intercept would be 125 and it is the amount of money present in the wallet before today
d) The slope would have a unit of dollars per week
PLEASE HELP. SOON. I really need help i’m struggling a lot lol
Answers
Answer: A
Step-by-step explanation: trust me bro
How long will it be from December 18 from 8:25 am to December 24 to 4.30 pm
Answers
Please show steps on how you simplified it
Answers
Answer:
4(3^2)
3^2=9
4(9)= 36
Answer:
4(3•3)
4(9)
36
Step-by-step explanation:
3 to the second power is equal to 3•3, which is equal to 9
Then you do 4 times 9, equals to 36
Write the first ten terms of a sequence whose first term is -10 and whose common difference is -2. PLS ANSWER CORRECT ANSWER WILL GET BRAINLIEST 100 POINTSSS
Answers
Answer:
T
n
+
1
=
T
n
+
d
T
1
=
a
Where the first term is equal to
a
and the common difference is
d
.
Option a can be expressed as follows:
T
n
+
1
=
T
n
+
4
T
1
=
1
Option c can be expressed as follows:
T
n
+
1
=
T
n
−
4
T
1
=
1
Hence both are arithmetic sequences (the other two options are geometric sequences with common ratios of 4 and 0.25 respectively)
Hope that helps :)
Step-by-step explanation:
g(x)=−x−2, find g(1)
Answers
Answer:
g(1) = -3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Function NotationStep-by-step explanation:
Step 1: Define
g(x) = -x - 2
g(1) is x = 1
Step 2: Evaluate
Substitute in x: g(1) = -1 - 2Subtract: g(1) = -3What Is the solution of the system? HELPPPPPP
Answers
Answer:
2,2
Step-by-step explanation:
the lines intercept at 2,2
Learning Task 2 without graphing tell whether the graphs of the system of equations are parallel, perpendicular,intersecting or coinciding
1.y = x + 7 and y = - x + 2
2.Y = 5x and y = 5x - 1
3. 2x + y = 1 and 2y + 4x = 2
4. Y = 2x + 3 and y = -x - 4
Answers
Answer:
1.Perpendicular
2. Parallel
3. Parallel
4.
Step-by-step explanation:
If two lines are parallel, slope is equal
If perpendicular, product of slopes is -1
y = mx + c is the general equation of a line form
m represents slope
1. slope is -1 and 1, they are perpendicular
2. Slope is 5 in both cases, they are parallel
3. slope is equal; equation ii is same as i if rewritten
They are parallel
4.
2. Bob bought 24 hockey tickets for $83. Adult tickets cost $5.50 and child tickets cost $2.00. How many child tickets did he buy?
Answers
Answer:
worked it out is correct your answers are there
Step-by-step explanation:
there are your answers
Which statement is true about a shape and its dilation? A.The corresponding angles of a shape and its dilation are congruent. B.The corresponding angles of a shape and its dilation are not congruent. C.The side lengths of a dilation are always smaller than the corresponding side lengths of the original shape. D.The corresponding side lengths of a shape and its dilation are congruent.
Answers
Answer:
A.The corresponding angles of a shape and its dilation are congruent.
Step-by-step explanation:
Dilation is a type of rigid transformation in which the dimension of a shape is either increased or decreased to produce its image. It involves a change in the dimensions of the shape by a required factor. In the process, the side lengths of the image are different to the original lengths. But the angles are not affected.
Thus, the respective angles of the given shape and its image are the same.
The appropriate answer to the given question is A.
THIRTY POINTS Will mark branliest if right.
Which expression is equal to the expression below?
(2 x 6)^4
A. 2^4 x 6^4
B. 8^4
C. 4 x (2 x 6)
D. 2 x (6)^4
Answers
Answer:A
Step-by-step explanation:A
What is the absolute value of -0.58?
Answers
Answer:
0.58 I think because absolute value is positive
Stacy starts a savings account with $15. Each month she deposits 6$ more into her
account. Stacy now has $81 in her account. Write an equation, then solve, to find how
many months Stacy has deposited money into her savings account.
Answers
Answer:
After 11 months, Stacy will have $81 in her savings account.
Step-by-step explanation:
15 + 6m = 81
6m = 66
m = 11
Write an expression and solve. Cole wants to buy a shirt for $25. The sales tax
is 8%. How much will the shirt cost?
Show your work:
A. $27
B. $33
C. $45
D. $227
Answers
Answer:
A
Step-by-step explanation:
8% of 25 is 2 so 25 + 2 =27
What is five times 5
Answers
Answer:
It is 25
Step-by-step explanation: 5 10 15 20 25
5*5 =25
Hope this help:)
Three friends pay 1025 to rent a vacation home. Beth contributed $80 more than danny. Katie contributed $20 less than Beth. How much did Danny contribute?
Answers
Answer:
Danny contributed $295
Step-by-step explanation:
Assume that Danny contributed $x
∵ Danny contributed x
∵ Beth contributed $80 more than Danny
→ Add The amount of Danny by $80 to get the amount od Beth
∴ Beth contributed x + 80
∵ Katie contributed $20 less than Beth
→ Subtract the amount of Beth by 20 to get the amount of Katie
∴ Katie contributed x + 80 - 20
∴ Katie contributed x + 60
∵ The three friends pay $1025
→ Add their amounts and equate the sum by 1025
∴ x + x + 80 + x + 60 = 1025
→ Add the like terms in the left side
∵ (x + x + x) + (80 + 60) = 1025
∴ 3x + 140 = 1025
→ Subtract 140 from both sides
∴ 3x + 140 - 140 = 1025 - 140
∴ 3x = 885
→ Divide both sides by 3
∴ x = 295
∵ x represents the amount of Danny contributed
∴ Danny contributed $295
A sphere is inscribed inside a cube with edges of 6 cm. In cubic centimeters, what is the volume of the sphere in terms of ?
Answers
Substituting,
V = (4/3)π(3 cm)³
V = 36π cm³
What is the graph of the given function?
f(x) = -2(x – 3)2 + 4
Graph
Answers
Answer:
the graph attached is the answer
88 x 88/22 x 11 x 11
Answers
Answer:
42592
Step-by-step explanation:
Answer:42592
Step-by-step explanation: So what you do is do 88 times 88/22 and so on :)
A point on the ocean floor is 5,962 m below sea level. Express this elevation as an integer.
the elevation as an integer is ___ m.
Answers
Answer:
-5,962 m
Step-by-step explanation:
Since the point is below sea level, it will be a negative number as an integer.
it is 5,962 m below sea level, so as an integer, it will be -5,962 m.
So, the elevation as an integer is -5,962 m
50.2 x 1 10² tenths equal?
Answers
Answer:
607,420
Step-by-step explanation:
hope it is correct and helps
ASAP
Solve the following equation by graphing each line below.
a) 2x+3=-x+9
b) Where do the two lines intersect? Write your answere in the form (x,y)
Answers
Answer:
x=2
Step-by-step explanation:
2x+x+3=9
2x+x=9-3
3x=9-3
3x=6
x=2
Answer:
a) 2x + 3 = -x + 9
or, 3x = 6
# x = 2 since there is no y in the equation the value of y could be 0.
b) it intersects at ( 2, 0 )
Step-by-step explanation:
Find the distance between the pair of points (2,-5) and (3,-7).
Answers
Answer:
2.24Step-by-step explanation:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\(2,-5)\quad\implies\quad x_1=2\,,\ \ y_1=-5\\\\(3,-7)\quad\implies\quad x_2=3\,,\ \ y_2=-7\\\\d=\sqrt{(3-2)^2+(-7+5)^2}= \sqrt{1^2+(-2)^2}=\sqrt{1+4}=\sqrt5=2.236....\approx2.24[/tex]
Derek needs 2 gallons water to mix a sport drink , but he only has a 1 cup measuring cup.
Answers
Answer:
He can fill up his fill up his measuring cup 8 times that is pretty simple
Step-by-step example
4 cups is in one gallon