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
need help pls answer it
Answers
Answer:
1 5/6 or answer C
Step-by-step explanation:
First: Parenthesis 4/5-1/4 or 11/20x 1/2 is 11/40
Bottom: 1/2*4/5 is 2/5 - 1/4 which is 3/20
11/40 *20/3
11/6 or 1 5/6 which would be answer C.
Hope this helps!
Happy Holidays!
Answer:
C
Step-by-step explanation:
top 4/5-1/4 or 11/20x 1/2 = 11/40
bottom 1/2*4/5 is 2/5 - 1/4 = 3/20
PLEASE ANSWER THIS I BEG FOR YOUR MERCY!!!!!!!!!!!! if you dont know....dont answer
Answers
Answer:
the answer is the second choice
Step-by-step explanation:
hopefully this helps :)
Tim is a first grader and reads 43 words per minute. Assuming he maintains the same rate, use the double number line to find how many words he can read in 5 minutes. Words 0 43 Minutes 0 1 Tim can read words in 5 minutes.
as a timeline
Answers
Answer:
all you have to do is Just divided the numbers
Step-by-step explanation:
÷
The solution of a system of equations with no solution describes what kind of lines?
options:
parallel
coincidental
perpendicular
intersecting
Answers
Answer:
parallel
Step-by-step explanation:
The answer is parallel because Since parallel lines never cross, then there can be no intersection; that is, for a system of equations that graphs as parallel lines
Plz help fast and correct!!!! (I will report if answer is stupid!!!)
Answers
Slope: 4/3
Y-int: 2
Equation: y = 4/3x + 2
B.
Slope: -1/3
Y-int: -1
Equation: y= -1/3x - 1
Triangles XYZ and RST are similar. XY
is 24 inches, YZ is 16 inches, XZ is
12 inches, RS is 18 inches, and RT is
9 inches. Find the length of ST.
Answers
Answer:
g
Step-by-step explanation:
please answer this. thank you
Answers
You bought a can of black beans last week that cost $1.34. This week, the store advertised a sale where 5 cans of beans cost $6.00. You bought one can of beans this week as well. Find the cost per can, and determine how much less the can of beans cost this week compared to last week.
Answers
Answer:
1. $1.2
2. $0.14
Step-by-step explanation:
Step one:
given data
Black beans last week that cost $1.34
Step two:
This week's price
5 cans of beans cost $6.00
The cost per can is
= 6/5
=$1.2
The difference in price
=1.34-1.2
= $0.14
For a soccer practice, the coach set up four cones, labeled W, X, Y, and Z, to mark the edges of the rectangular field. Suppose the field is drawn on a coordinate plane, where the x- and y-values represent the position, in yards, from the center of the field, which is located at (0, 0). The location of the cones are as follows. Cone W is located at (-38, -53). Cone X is located at (-38, 53). Cone Y is located at (38, 53). Cone Z is located at (38, -53). What is the perimeter of the field? A. 364 yards B. 8,056 yards C. 182 yards D. 38 yards
Answers
Answer:
A. 364 yards
Step-by-step explanation:
The distance between two points [tex]A(x_1,y_1)\ and\ B(x_2,y_2)[/tex] on the coordinate plane is given as:
[tex]|AB|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The cone W, X, Y and Z form a rectangle.
The perimeter for the rectangle = 2(length + breadth)
[tex]Length=|WX|=\sqrt{(-38-(-38))^2+(53-(-53))^2}=106 \\\\Breadth=|XY|=\sqrt{(38-(-38))^2+(53-53)^2}=76[/tex]
Perimeter = 2(length + breadth) = 2(106 + 76) = 364 yards
16 pearls/20opals = 8pearls/ blank opals complete each equivalent ratio
Answers
Answer:
10
Step-by-step explanation:
16/20=8/10
16/2=8
20/2=10
16 pearls/20opals=8perals/10opals
Samantha and her friends are going on a road trip that is 245 7/50 miles long. They have already driven 128 53/100. How much farther do they have to go?
Answers
Answer:
They have to drive 182, 2820 miles more.
Step-by-step explanation:
... ;)
Answer:
no :)
Step-by-step explanation:
Find the common difference of the arithmetic sequence –9, -7, -5, ...
Answers
if I’m wrong I’m so sorry and please tell me I’m wrong for other that have to use this.
If I’m right ya!! XD
Hope this helps you!
-Pam Pam
Select all of the equations that are equivalent to 3.2 + 6 = 27
3x=21
3.x=33
X+ 6 = 24
x + 2 = 9
Answers
please help I will mark brainliest
Answers
Answer: look up alaskan pipeline
Step-by-step explanation:
Charlie bought 2 3/4 pounds of pears for $0.76 per pound and 2 3/4 pounds of grapes for $1.40 per pound. How much money in dollars and cents did charlie pay for the pears and grapes.
Answers
Answer
Charlie paid $5.94
Step-by-step explanation:
0.76x2 3/4=2.09
1.40x2.75=3.85
3.85+2.09=$5.94
if x^3+ax^2-18x+b = (x+5)(x-4)(x+2) what is a and b
Answers
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
[tex] (x + 5)(x - 4)(x + 2) = [/tex]
[tex](x + 5) ({x}^{2} - 2x - 8) = [/tex]
[tex] {x}^{3} - 2 {x}^{2} - 8x + 5 {x}^{2} - 10x - 40 = \\ [/tex]
[tex] {x}^{3} + 3 {x}^{2} - 18x - 40[/tex]
_________________________________
Compare :
[tex] {x}^{3} + 3 {x}^{2} - 18x - 40[/tex]
[tex] {x}^{3} + a {x}^{2} - 18x + b[/tex]
Thus :
[tex]a = 3[/tex]
and
[tex]b = - 40[/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
A person can pay $26 for a membership to the science museum and then go to the
museum for just $1 per visit. What is the maximum number of visits a member of the
science museum can make for a total cost of $34?
Answers
Answer:
8 visits
Step-by-step explanation:
26+8 visits (1 dollar a visit)= 34
Answer:
8
Step-by-step explanation:
Task: Nonpermissible Values for Rational Expressions [30 points] Write a rational expression that has the nonpermissible values x=0 and x=17. Explain your reasoning using complete sentences.
Answers
Answer:
A rational expression that has the nonpermissible values [tex]x = 0[/tex] and [tex]x = 17[/tex] is [tex]f(x) = \frac{4}{x\cdot (x-17)}[/tex].
Step-by-step explanation:
A rational expression has a nonpermissible value when for a given value of [tex]x[/tex], the denominator is equal to zero. In addition, we assume that both numerator and denominator are represented by polynomials, such that:
[tex]f(x) = \frac{p(x)}{q(x)}[/tex] (1)
Then, the factorized form of [tex]q(x)[/tex] must be:
[tex]q(x) = x\cdot (x-17)[/tex] (2)
If we know that [tex]p(x) = 4[/tex], then the rational expression is:
[tex]f(x) = \frac{4}{x\cdot (x-17)}[/tex] (3)
A rational expression that has the nonpermissible values [tex]x = 0[/tex] and [tex]x = 17[/tex] is [tex]f(x) = \frac{4}{x\cdot (x-17)}[/tex].
can someone help me
Answers
Answer:
A is a function
Step-by-step explanation:
Hope the image helps.
Karen owns a seafood restaurant orders trout from an online retailer each pound trout cost $28 and the company charges a four dollar fee for shipping the order however if Karen orders 10 or more pounds the trout cost only $22 per pound but the shipping fee is eight dollars which Price
Answers
Answer:
228
Step-by-step explanation:
22*10-220
220+8=228
plzzzzzzzz help
The regular price of a coat is $35.25. During a sale, the coat rang up for $19.99. What was the percent off of the coat during the sale? (5 points)
a
The sale was for a 43% decrease.
b
The sale was for a 76% increase.
c
The sale was for a 76% decrease.
d
The sale was for a 43% increase.
Answers
Answer:
a
The sale was for a 43% decrease.
Step-by-step explanation:
The computation of the percent off of the coat during the sale is shown below:
Regular price is $35.25
And, in the sale the price is $19.99
So, the percent off would be
= ($35.25 - $19.99) ÷ ($19.99)
= 43% decrease
hence, the percent off of the coat during the sale is 43% decrease
Therefore the correct option is a.
And, all the other options are incorrect
please help i dont want to fail
Answers
Answer: -2.2
Step-by-step explanation:
Answer:
-3/5 which is the third line between 0 and -1 if you're going back from 0.
What the slope (6,-4) and (4,-4)
Answers
Answer:
0
Step-by-step explanation:
-4 - -4 = 0
6-4 = 2
0/2 = 0
Answer:
change in y change in x
The change in x
is equal to the difference in x-coordinates (also called run), and the change in y
is equal to the difference in y-coordinates
m=y2−y1x2−x1
Substitute in the values of x
and y
into the equation to find the slope.
m=−4−(4)−3−(6)
m=8/9
NEED HEPP FAST MARKING PEOPLE AS BRAINLIST
Answers
Answer:
yes becasue their sides have the same length and angles
Step-by-step explanation:
What is the common differenec in 7, 6, 5, 4,...
Answers
Answer:
d = - 1
Step-by-step explanation:
The common difference d between consecutive terms is
6 - 7 = 5 - 6 = 4 - 5 = - 1
Answer:
Step-by-step explanation:
Help plzzzzzzzzzzzzzz
Answers
Answer:
∠E
Step-by-step explanation:
∠E is between PE and EN
Please give the explanation for all three parts. Will provide brainly. No fakes or will get reported. Thanks
Answers
Why is ADEC a trapezoid?
A trapezoid is a quadrilateral with one pair of parallel sides. Since D and E are midpoints, it would be parallel to AC. AD and EC are not parallel since they cross each other at point B.
(I couldn't read the last part of the second question :( )
The radius of a cone is increasing at a constant rate of 7 meters per minute, and the volume is decreasing at a rate of 236 cubic meters per minute. At the instant when the radius of the cone is 99 meters and the volume is 180 cubic meters, what is the rate of change of the height? The volume of a cone can be found with the equation V=\frac{1}{3}\pi r^2 h.V= 3 1 πr 2 h. Round your answer to three decimal places.
Answers
Answer:
The rate of change of the height is 0.021 meters per minute
Step-by-step explanation:
From the formula
[tex]V = \frac{1}{3}\pi r^{2}h[/tex]
Differentiate the equation with respect to time t, such that
[tex]\frac{d}{dt} (V) = \frac{d}{dt} (\frac{1}{3}\pi r^{2}h)[/tex]
[tex]\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (r^{2}h)[/tex]
To differentiate the product,
Let r² = u, so that
[tex]\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (uh)[/tex]
Then, using product rule
[tex]\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h\frac{du}{dt}][/tex]
Since [tex]u = r^{2}[/tex]
Then, [tex]\frac{du}{dr} = 2r[/tex]
Using the Chain's rule
[tex]\frac{du}{dt} = \frac{du}{dr} \times \frac{dr}{dt}[/tex]
∴ [tex]\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h(\frac{du}{dr} \times \frac{dr}{dt})][/tex]
Then,
[tex]\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}][/tex]
Now,
From the question
[tex]\frac{dr}{dt} = 7 m/min[/tex]
[tex]\frac{dV}{dt} = 236 m^{3}/min[/tex]
At the instant when [tex]r = 99 m[/tex]
and [tex]V = 180 m^{3}[/tex]
We will determine the value of h, using
[tex]V = \frac{1}{3}\pi r^{2}h[/tex]
[tex]180 = \frac{1}{3}\pi (99)^{2}h[/tex]
[tex]180 \times 3 = 9801\pi h[/tex]
[tex]h =\frac{540}{9801\pi }[/tex]
[tex]h =\frac{20}{363\pi }[/tex]
Now, Putting the parameters into the equation
[tex]\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}][/tex]
[tex]236 = \frac{1}{3}\pi [(99)^{2} \frac{dh}{dt} + (\frac{20}{363\pi }) (2(99)) (7)][/tex]
[tex]236 \times 3 = \pi [9801 \frac{dh}{dt} + (\frac{20}{363\pi }) 1386][/tex]
[tex]708 = 9801\pi \frac{dh}{dt} + \frac{27720}{363}[/tex]
[tex]708 = 30790.75 \frac{dh}{dt} + 76.36[/tex]
[tex]708 - 76.36 = 30790.75\frac{dh}{dt}[/tex]
[tex]631.64 = 30790.75\frac{dh}{dt}[/tex]
[tex]\frac{dh}{dt}= \frac{631.64}{30790.75}[/tex]
[tex]\frac{dh}{dt} = 0.021 m/min[/tex]
Hence, the rate of change of the height is 0.021 meters per minute.
Sarah has 13 gallons of gas in her car at the beginning of a trip. Every hour Sarah drives, she uses 2.5 gallons of gas. Answer the questions below regarding the relationship between the gallons of gas remaining in the tank and the total hours driven. I need A function relating these variables is C(x)=?
(need help kinda quick, pls and thank you!)
Answers
Explanation: Since she is using gas, the function will be negative and decreasing. Also the initial amount was 13 gallons, this would be the y-intercept.
help me if u r a brainlist
Answers
Answer: ight bet
i/yes
ii/no
iii/no
iv/no
v/no
vi/no
Step-by-step explanation: